加拿大国际袋鼠数学竞赛试题及答案-2016年 Parents Questions

合集下载

加拿大国际袋鼠数学竞赛试题及答案-2018年

I N T E R N A T I O N A L C O N T E S T-G A M EM A T H K A N G A R O OC A N AD A,2018I N S T R U C T I O N SG R A D E1-21.You have 45 minutes to solve 18 multiple choice problems. For eachproblem, circle only one of the proposed five choices. If you circle more than one choice, your response will be marked as wrong.2.Record your answers in the response form. Remember that this is the onlysheet that is marked, so make sure you have all your answers transferred to the response form before giving it back to the contest supervisor.3.The problems are arranged in three groups. A correct answer of the first 6problems is worth 3 points. A correct answer of the problems 7-12 is worth4 points. A correct answer of the problems 13-18 is worth5 points. Foreach incorrect answer, one point is deducted from your score. Each unanswered question is worth 0 points. To avoid negative scores, you start from 18 points. The maximum score possible is 90.4.The use of external material or aid of any kind is not permitted.5.The figures are not drawn to scale. They should be used only for illustrationpurposes.6.Remember, you have about 2 to 3 minutes for each problem; hence, if aproblem appears to be too difficult, save it for later and move on to another problem.7.At the end of the allotted time, please give the response form to thecontest supervisor.8.Do not forget to pick up your Certificate of Participation on your way out!Good luck!Canadian Math Kangaroo Contest teamCanadian Math Kangaroo ContestPart A: Each correct answer is worth 3 points1.Which shape cannot be formed using and ?(A) (B) (C) (D) (E)2.At least how many 4-ray stars like this are glued together tomake this shape ?(A) 5 (B) 6 (C) 7 (D) 8 (E) 93.This pizza was divided into equal slices.How many slices are missing?(A) 1 (B) 2 (C) 3 (D) 4 (E) 54.How many kangaroos must be moved from one park to the other in order toget the same number of kangaroos in each park?(A) 4 (B) 5 (C) 6 (D) 8 (E) 95.Which of these ladybugs has to fly away so that the rest of them have 20dots in total?(A) (B) (C) (D) (E)6.Emilie builds towers in the following patternWhich one will be the tower number 6?(A) (B) (C) (D) (E)Part B: Each correct answer is worth 4 points7.If ◊+ ◊ = 4 and ∆ + ∆ + ∆ = 9, what is the value of ◊ + ∆ = ?(A) 2 (B) 3 (C) 4 (D) 5 (E) 68.Lisa has 4 pieces , but she only needs 3 forcompleting her puzzle frame . Which piece will be left over?(A)(B)(C)(D) (E)or9.How many right hands are in this picture?(A) 3 (B) 4 (C) 5 (D) 6 (E) 710.The dog went to its food following a path. In total it made 3 right turns and2 left turns. Which path did the dog follow?(A) (B) (C)(D) (E)11.What number is in the box marked "?" ?(A) 6 (B) 13 (C) 24 (D) 29 (E) Some other number12.Charles cut a rope in three equal pieces and then made some equal knotswith them. Which figure correctly shows the three pieces with the knots?(A) (B)(C) (D)(E)Part C: Each correct answer is worth 5 points13.How many circles and how many squares are covered by the blot in thepicture?(A) 1 circle and 3 squares(B) 2 circles and 1 square(C) 3 circles and 1 square(D) 1 circles and 2 squares(E) 2 circles and 2 squares14.Diana shoots three arrows at a target.On her first try, she gets 6 points and the arrows land like this: 6 pointsOn her second try, she gets 8 points and the arrows land like this: 8 pointsOn her third try, the arrows land like this:? points How many points will she get the third time?(A) 8 (B) 10 (C) 12 (D) 14 (E) 1615.How many different numbers greater than 10 and smaller than 25 with distinct digits can we make by using any two of the digits 2, 0, 1, and 8?(A) 4 (B) 5 (C) 6 (D) 7 (E) 816.Mark had some sticks of length 5 cm and width 1 cm.With the sticks he constructed the fence below.What is the length of the fence?(A) 20 cm(B) 21 cm(C) 22 cm (D) 23 cm (E) 25 cmlength17.The road from Anna's house to Mary's house is 16 km long.The road from Mary's house to John's house is 20 km long.The road from the crossroad to Mary's house is 9 km long.How long is the road from Anna’s house to John's house?(A) 7 km (B) 9 km (C) 11 km (D) 16 km (E) 18 km18.There are four ladybugs on a 4×4 board. Two are asleep and do not move.The other two ladybugs move one square every minute (up, down, left, or right). Here are pictures of the board for the first four minutes:Minute 1 Minute 2 Minute 3 Minute 4Which of these is a picture of the fifth minute (Minute 5)?(A) (B) (C) (D) (E)International Contest-GameMath Kangaroo Canada, 2018Answer KeyGrade 1-21 A B C D E 7 A B C D E 13 A B C D E2 A B C D E 8 A B C D E 14 A B C D E3 A B C D E 9 A B C D E 15 A B C D E4 A B C D E 10 A B C D E 16 A B C D E5 A B C D E 11 A B C D E 17 A B C D E6 A B C D E 12 A B C D E 18 A B C D EI N T E R N A T I O N A L C O N T E S T-G A M EM A T H K A N G A R O OC A N AD A,2018I N S T R U C T I O N SG R A D E3-41.You have 60 minutes to solve 24 multiple choice problems. For each problem,circle only one of the proposed five choices. If you circle more than one choice, your response will be marked as wrong.2.Record your answers in the response form. Remember that this is the only sheetthat is marked, so make sure you have all your answers transferred to the response form before giving it back to the contest supervisor.3.The problems are arranged in three groups. A correct answer of the first 8problems is worth 3 points. A correct answer of the problems 9-16 is worth 4 points. A correct answer of the problems 17-24 is worth 5 points. For each incorrect answer, one point is deducted from your score. Each unanswered question is worth 0 points. To avoid negative scores, you start from 24 points. The maximum score possible is 120.4.The use of external material or aid of any kind is not permitted.5.The figures are not drawn to scale. They should be used only for illustrationpurposes.6.Remember, you have about 2 to 3 minutes for each problem; hence, if a problemappears to be too difficult, save it for later and move on to another problem.7.At the end of the allotted time, please give the response form to the contestsupervisor.8.Do not forget to pick up your Certificate of Participation on your way out!Good luck!Canadian Math Kangaroo Contest teamGrade 3-42018 Canadian Math Kangaroo ContestPart A: Each correct answer is worth 3 points1.Lea has 10 rubber stamps. Each stamp has one of the digits:0, 1, 2, 3, 4, 5, 6, 7, 8, 9.She prints the date of St. Patrick’s Day 2018:How many different stamps does she use?(A) 5(B) 6 (C) 7 (D) 9 (E) 102.The picture shows three flying arrows and nine fixedballoons. When an arrow hits a balloon, it bursts,and the arrow flies further in the same direction.How many balloons will be hit by the arrows?(A) 2 (B) 3 (C) 4(D) 5 (E) 63.Susan is six years old. Her sister is one year younger, and her brother is one yearolder. What is the sum of the ages of the three siblings?(A) 10 (B) 15 (C) 18 (D) 21 (E) 304.Here is a picture of Sophie the ladybug. She turns around. Which picture ofthe ladybugs below is not Sophie?(A)(B)(C)(D)(E)5.Lucy folds a sheet of paper in half. Then she cuts a piece out of it. What willshe see when she unfolds the paper?(A)(B)(C) (D)(E)1 70320186. A table is set for 8 people.How many settings have the fork to the left of the plate and the knife to the right of the plate?(A) 5(B) 4 (C) 6 (D) 2 (E) 3 7.Emily added two 2-digit numbers correctly on paper. Then she painted out two cells,as shown below.What is the sum of two digits in the painted cells?(A) 5(B) 7 (C) 8 (D) 9 (E) 13 8.First, Diana scores 12 points in total with three arrows. On her second turn shescores 15 points.How many points does she score on her third turn?(A) 18 (B) 19 (C) 20 (D) 21 (E) 22 Part B: Each correct answer is worth 4 points9.How many different numbers greater than 12 and smaller than 58 with distinct digitscan we make by using any two of the digits 0, 1, 2, 5, and 8?(A) 3(B) 5 (C) 7(D) 8 (E) 912 points15 points ? points10.Roberto makes designs using tiles like this .How many of the following five designs can he make?(A) 1 (B) 2 (C) 3 (D) 4 (E) 511.Each of these five figures ,, , , , appears exactly once in everycolumn and every row of the given table.Which figure must we put in the cell with the question mark?(A) (B) (C) (D) (E)12.Toby glues 10 cubes together to make the structure shown.He paints the whole structure, even the bottom.How many cubes are painted on exactly four of their faces?(A) 6 (B) 7 (C) 8 (D) 9 (E) 1013.The opposite faces of a cube are identical, being dark, bright or patterned.Which picture below is the unfolded net of this cube?(A)14.Tom cuts two types of pieces out of grid paper.What is the smallest number of pieces identical to the ones shown that Tom needs to build the boat in the picture?(A) 5 (B) 6 (C) 7 (D) 8 (E) 915.The rooms in Kanga's house are numbered. Baby Roo entersthe main door, passes through some rooms and leaves thehouse. The numbers of the rooms that he visits are alwaysincreasing. Through which door does he leave the house?(A) A (B) B (C) C (D) D (E) E16.Peta rabbit had 20 carrots. She ate two carrots every day. She ate the twelfth carroton Wednesday. On which day did she start eating the carrots?(A) Monday (B) Tuesday (C) Wednesday (D) Thursday (E) FridayPart C: Each correct answer is worth 5 points17.The belt shown in the drawing can be fastened in five ways.How much longer is the belt fastened in one hole than the belt fastened in all five holes?(A) 4 cm (B) 8 cm (C) 10 cm (D) 16 cm (E) 20 cm18.In an ancient writing the symbols represent thenumbers 1, 2, 3, 4, and 5. Nobody knows which symbol represents which number.We know thatWhich symbol represents the number 3?(A)(B) (C) (D) (E)19. A stained-glass tile is flipped along the black line. The figure shows the tile after thefirst flip.What will the stained-glass tile look like after the third flip (at the far right)?(A)(B)(C)(D)(E)20.The large rectangle is made up of squares of varied sizes. The three smallest squareseach have an area of 1, as shown.What is the area of the largest square?(A) 81 (B) 100 (C) 110 (D) 121 (E) 14421.Five ducklings walk behind the mother duck in a row from the oldest to the youngestlike this: Dina and Becca walk right one after the other, Mingo walks behind Lisa but in front of Becca, Becca walks directly in front of Pip. What is the name of theyoungest duckling?(A) Dina (B) Pip (C) Becca (D) Lisa (E) Mingo22.Four balls each weigh 10, 20, 30 and 40 grams. Which ball weighs 30 grams?(A) A (B) B (C) C (D) D (E) it could be A or B23.Lois wants to write the numbers from 1 to 7 in the grid shown.Two consecutive numbers cannot be written in two neighbouringcells. Neighbouring cells meet at the edge or at a corner. Whatnumbers can she write in the cell marked with a question mark?(A) all seven numbers (B) only odd numbers(C) only even numbers (D) only number 4(E) only the numbers 1 or 7 24.The distance from Anna's to Mary's house is 16 kilometers along the shown road.The distance from Mary's to Nick's house is 20 kilometers.The distance from Nick's to John's house is 19 kilometers.How far is Anna's house from John's?(A) 15 (B) 16(C) 18(D) 19 (E) 20 ?International Contest-GameMath Kangaroo Canada, 2018Answer KeyGrade 3-41 A B C D E 9 A B C D E17 A B C D E2 A B C D E10 A B C D E 18 A B C D E3 A B C D E 11 A B C D E 19 A B C D E4 A B C D E 12 A B C D E 20 A B C D E5 A B C D E 13 A B C D E21 A B C D E6 A B C D E 14 A B C D E 22 A B C D E7 A B C D E 15 A B C D E 23 A B C D E8 A B C D E 16 A B C D E24 A B C D EI N T E R N A T I O N A L C O N T E S T-G A M EM A T H K A N G A R O OC A N AD A,2018I N S T R U C T I O N SG R A D E5-121.You have 75 minutes to solve 30 multiple choice problems. For eachproblem, circle only one of the proposed five choices. If you circle more than one choice, your response will be marked as wrong.2.Record your answers in the response form. Remember that this is theonly sheet that is marked, so make sure you have all your answers transferred to that form before giving it back to the contest supervisor. 3.The problems are arranged in three groups. A correct answer of the first10 problems is worth 3 points. A correct answer of problems 11 -20 isworth 4 points. A correct answer of problems 21-30 is worth 5 points. For each incorrect answer, one point is deducted from your score. Each unanswered question is worth 0 points. To avoid negative scores, you start from 30 points. The maximum score possible is 150.4.The use of external material or aid of any kind is not permitted.5.The figures are not drawn to scale. They should be used only forillustration purposes.6.Remember, you have about 2 to 3 minutes for each problem; hence, if aproblem appears to be too difficult, save it for later and move on to another problem.7.At the end of the allotted time, please give the response form to thecontest supervisor.8.Do not forget to pick up your Certificate of Participation on your way out!Good luck!Canadian Math Kangaroo Contest teamCanadian Math Kangaroo ContestPart A: Each correct answer is worth 3 points1.The drawing shows 3flying arrows and 9fixed balloons. Whenan arrow hits a balloon, it bursts, and the arrow flies further inthe same direction. How many balloons will not be hit byarrows?(A) 3 (B) 2(C) 6(D) 5(E) 42.The image shows a structure made of three objects.What does Peter see if he looks at the structure from above?(A)(B)(C) (D) (E)3.Diana played darts throwing arrows toward a target with three sections. First she got 14 points with twoarrows on the target. The second time she got 16 points. How many points did she get the third time?(A) 17(B) 18(C) 19 (D) 20 (E) 22 4. A garden is divided into identical squares. A fast snail and a slow snail move along the perimeter of thegarden starting simultaneously from the corner S but in different directions. The slow snail moves at the speed of 1 metre per hour (1 m/h) and the fast one at 2 metres per hour (2 m/h).At what point will the two snails meet?(A) A (B) B (C) C (D) D(E) E 14 points16 points ? A B CDE S 1 m/h2 m/h5.In which of the four squares is the fraction of the black area the largest?(A) A (B) B (C) C (D) D (E) they are all the same6. A star is made out of four equilateral triangles and a square. The perimeter of thesquare is 36 cm. What is the perimeter of the star?(A) 144 cm (B) 120 cm (C) 104 cm (D) 90 cm (E) 72 cm7.From the list 3, 5, 2, 6, 1, 4, 7 Masha chose 3 different numbers whose sum is 8. From the same list Dashachose 3 different numbers whose sum is 7. How many common numbers have been chosen by both girls?(A) none (B) 1 (C) 2 (D) 3 (E) impossible to determine8.We move a bead along a piece of wire. What shall we see when the beadcomes to the end of the wire?(A) (B) (C)(D) (E)9.There are 3squares in the figure. The side length of the smallest square is 6 cm.What is the side length of the biggest square?(A) 8(B) 10(C) 12(D) 14(E) 1610.In the following figure, the circles are light bulbs connected to some other lightbulbs. Initially, all light bulbs are off. When you touch a light bulb, this light bulband all its neighbours (e.g., the light bulbs connected to it) are lit.At least how many light bulbs do you have to touch to turn on all the light bulbs?(A) 2 (B) 3 (C) 4 (D) 5 (E) 6Part B: Each correct answer is worth 4 points11.Each square contains one of the numbers 1, 2, 3, 4, or 5, so that both of thecalculations following the arrows are correct. A number may be used morethan once. What number goes into the box with the question mark?(A) 1 (B) 2 (C) 3 (D) 4 (E) 5 12. Nine cars arrive at a crossroads and drive off as indicated by the arrows. Which figure shows these cars after leaving the crossroads?(A)(B) (C) (D) (E) 13. The faces of a cube are painted black, white or grey so that opposite faces are of different colour. Which of the following is not a possible net of this cube?(A)(B) (C) (D) (E)14.In a box there are many one-euro, two-euro and five-euro coins. A dispenser draws coins out of the box – one at a time, and stops when three identical coins are taken out. What is the largest possible amount that can be withdrawn? (A) 24 (B) 23 (C) 22 (D) 21 (E) 1515.Two girls, Eva and Olga and three boys, Adam, Isaac and Urban play with a ball. When a girl has the ball, she throws it to the other girl or to a boy. When a boy has the ball, he throws it to another boy but never to the boy from whom he just received it. Eva starts by throwing the ball to Adam. Who will do the fifth throw?(A) Adam (B) Eva (C) Isaac (D) Olga (E) Urban16.Emily wants to enter a number into each cell of the triangular table. The sum of thenumbers in any two cells with a common edge must be the same. She has alreadyentered two numbers. What is the sum of all the numbers in the table?(A) 18 (B) 20 (C) 21 (D) 22 (E) impossible to determine17.John coded a correct addition calculation naming the digits AA , BB , CC and DD .Which digit is represented by BB ?(A) 0 (B) 2 (C) 4 (D) 5(E) 6 + A B C C B A D D DD18.On Monday Alexandra shares a picture with 5 friends. For several days, everybody who receives thepicture, sends it once on the next day to two friends. On which day does the number of people who have seen the picture (including Alexandra) become greater than 75, if it is known that no one receives the picture more than once?(A) Wednesday (B) Thursday (C) Friday (D) Saturday (E) Sunday 19.The sum of the ages of Kate and her mother is 36, and the sum of the ages of her mother and her grandmother is 81. How old was the grandmother when Kate was born? (A) 28 (B) 38 (C) 45 (D) 53 (E) 56 20.Annie replaced the letters with numbers in the word KANGAROO (identical letters with the same digits, different letters with different digits) so that she got the largest possible 8-digit number, which is not a multiple of 4. What is the sum of the last three digits replacing the word ROO? (A) 13 (B) 14 (C) 12 (D) 15 (E) 11Part C: Each correct answer is worth 5 points21.Captain Hook has plundered a safe that contains 2520 gold coins. During the night, each of his pirates secretly took out some coins just for themselves. The first one took out �12�of the coins, the second one�13�of the remaining coins, the third one �14�of the remaining coins and so on. When Captain Hook opened the safe in the morning, he found only 252 coins inside. How many pirates are commanded by Captain Hook?(A) 8 (B) 9 (C) 10 (D) 11 (E) 12 22.In the figure on the right, the five balls A, B, C, D and E weigh 30, 50, 50, 50 and 80 grams, but not necessarily in this order. Which ball weighs 30 grams? (A) A (B) B (C) C (D) D (E) E23.If A, B, C are distinct digits, which of the following numbers cannot be the largest possible 6-digit number written using three digits A, two digits B, and one digit C? (A) AAABBC (B) CAAABB (C) BBAAAC (D) AAABCB (E) AAACBB 24.In the World of Numbers, there are many number-machines, which work in the following way: the machine adds the two beginning digits of the number and replaces them by their sum. For example, beginning with the number 87312 and using six such machines we obtain:How many such machines should be used in order to get the number times509...9 from the numbertimes1009...9? (A) 50(B) 60(C) 100(D) 80(E) Not possible to obtain this number8731215312 6312 91210212 3Page 525.Nick wants to arrange the numbers 2, 3, 4, ..., 10 into several groups such that the sum of the numbers in each group is the same. What is the largest number of groups he can get?(A) 2 (B) 3 (C) 4 (D) 6 (E) other answer 26.Peter cut an 8-cm wide wooden plank with a saw into 9 parts across the width of the plank.One piece was a square, the other were rectangles. Then he arranged all the pieces together as shown in the picture. What was the length of the plank?(A) 150 cm (B) 168 cm (C) 196 cm (D) 200 cm (E) 232 cm 27.Write 0 or 1 in each cell of the 5×5 table so that each 2×2 square of the 5×5 table contains exactly 3 equal numbers. What is the largest possible sum of all the numbers in the table?(A) 22 (B) 21 (C) 19 (D) 17 (E) 1528.14 people are seated at a round table.Each person is either a liar or tells the truth. Everybody says: "Both my neighbours are liars". What is themaximum number of liars at the table?(A) 7 (B) 8 (C) 9(D) 10(E) 1429.There are eight domino tiles on the table (pic 1). One half of one tile is covered. The 8 tiles can be arranged into a 4×4 square (pic 2), so that the number of dots in each row and column is the same.How many dots are on the covered part? (A) 1 (B) 2 (C) 3 (D) 4(E) 530.Four ladybugs sit on different cells of a 4×4 grid.One of them is sleeping and does not move. Each time you whistle, the other three ladybugs move toa free neighbouring cell. They can move up, down,right or left but they are not allowed to go back tothe cell they just came from. Which of the following images might show the result after the fourth whistle?(A)(B)(C)(D)(E)pic 1pic 2initial position after firstwhistleafter second whistle after third whistle Both my neighboursare liars.International Contest-GameMath Kangaroo Canada, 2018Answer KeyGrade 5-61 A B C D E 11 A B C D E21 A B C D E2 A B C D E 12 A B C D E 22 A B C D E3 A B C D E 13 A B C D E23 A B C D E4 A B C D E 14 A B C D E 24 A B C D E5 A B C D E15 A B C D E 25 A B C D E6 A B C D E16 A B C D E 26 A B C D E7 A B C D E 17 A B C D E 27 A B C D E8 A B C D E 18 A B C D E 28 A B C D E9 A B C D E 19 A B C D E 29 A B C D E10 A B C D E 20 A B C D E30 A B C D EI N T E R N A T I O N A L C O N T E S T-G A M EM A T H K A N G A R O OC A N AD A,2018I N S T R U C T I O N SG R A D E5-121.You have 75 minutes to solve 30 multiple choice problems. For eachproblem, circle only one of the proposed five choices. If you circle more than one choice, your response will be marked as wrong.2.Record your answers in the response form. Remember that this is theonly sheet that is marked, so make sure you have all your answers transferred to that form before giving it back to the contest supervisor. 3.The problems are arranged in three groups. A correct answer of the first10 problems is worth 3 points. A correct answer of problems 11 -20 isworth 4 points. A correct answer of problems 21-30 is worth 5 points. For each incorrect answer, one point is deducted from your score. Each unanswered question is worth 0 points. To avoid negative scores, you start from 30 points. The maximum score possible is 150.4.The use of external material or aid of any kind is not permitted.5.The figures are not drawn to scale. They should be used only forillustration purposes.6.Remember, you have about 2 to 3 minutes for each problem; hence, if aproblem appears to be too difficult, save it for later and move on to another problem.7.At the end of the allotted time, please give the response form to thecontest supervisor.8.Do not forget to pick up your Certificate of Participation on your way out!Good luck!Canadian Math Kangaroo Contest teamPage 1Canadian Math Kangaroo ContestPart A: Each correct answer is worth 3 points1.When the letters of the word MAMA are written vertically above one another, the word has a vertical line of symmetry. Which of these words also has a vertical line of symmetry when written in the same way?(A) ROOT (B) BOOM (C) BOOT (D) LOOT (E) TOOT2.A triangle has sides of length 6, 10 and 11. An equilateral triangle has the same perimeter. What is the length of each side of the equilateral triangle?(A) 6 (B) 9 (C) 10 (D) 11 (E) 273.Which number should replace ∗in the equation 2 ∙ 18 ∙ 14 = 6 ∙ ∗ ∙ 7to make it correct?(A) 8 (B) 9 (C) 10 (D) 12 (E) 154.The panels of Fergus' fence are full of holes. One morning, one of the panels fell flat on the floor.Which of the following could Fergus see as he approaches his fence?(A) (B) (C) (D) (E)5.How many possible routes are there to go from A to B in the direction indicated by the arrows?(A) 2 (B) 3 (C) 4 (D) 5 (E) 66.Martha multiplied two 2-digit numbers correctly on a piece of paper.Then she scribbled out three digits as shown.What is the sum of the three digits she scribbled out? (A) 5 (B) 6 (C) 9 (D) 12 (E) 14 7.A large rectangle is made up of nine identical rectangles whose longest sides are 10 cm long. What is the perimeter of the large rectangle?(A) 40 cm(B) 48 cm(C) 76 cm(D) 81 cm(E) 90 cm8. A hotel on an island in the Caribbean advertises using the slogan "350 days of sun every year!''. According tothe advert, what is the smallest number of days Willi Burn has to stay at the hotel in 2018 to be certain of having two consecutive days of sun?(A) 17 (B) 21 (C) 31 (D) 32 (E) 359.The diagram shows a rectangle of dimensions 7 × 11 containing two circles eachtouching three of the sides of the rectangle. What is the distance between the centres of the two circles?(A) 1 (B) 2(C) 3(D) 4 (E) 510.Only one of the digits in the year 2018 is a prime number. How many years will pass till the next year whenall of the digits in the year number are prime numbers?(A) 201 (B) 202 (C) 203 (D) 204 (E) 205Part B: Each correct answer is worth 4 points11.Square AAAAAAAA has sides of length 3 cm. The points MM and NN lie on AAAA and AAAA so that AAMMand AANN split the square into three pieces of the same area. What is the length of AAMM?(A) 0.5 cm (B) 1 cm (C) 1.5 cm (D) 2 cm (E) 2.5 cm12.A rectangle is divided into 40 identical squares. The rectangle contains more than one row of squares. Avacoloured the middle row. What is the largest possible number of squares that remain uncoloured?(A) 20 (B) 30 (C) 32 (D) 35 (E) 3913.A lion is hidden in one of three rooms. A note on the door of room 1 reads "The lion is here". A note on thedoor of room 2 reads "The lion is not here". A note on the door of room 3 reads "2+3=2×3". Only one of these statements is true. In which room is the lion hidden?(A) In room 1 (B) In room 2 (C) In room 3 (D) It may be in any room(E) It may be in either room 1 or room 214.Valeriu draws a zig-zag line inside a rectangle, creating angles of 10°,14°,33°, and 26°as shown.What is the size of angle θθ?(A) 11°(B) 12°(C) 16°(D) 17°(E)33°。

加拿大国家中小学数学竞赛( kangaroo math 袋鼠竞赛)2017年五六年级(含答案)

I N T ER N A T I ON A L CO N T E S T-GA M EM A TH KA N GA RO OC A N A DA, 2017INSTRUCTIONSGRADE 5-61.You have 75 minutes to solve 30 multiple choice problems. For each problem, circle onlyone of the proposed five choices. If you circle more than one choice, your response will be marked as wrong.2.Record your answers in the response form. Remember that this is the only sheet that ismarked, so make sure you have all your answers transferred here by the end of the contest.3.The problems are arranged in three groups. A correct answer of the first 10 problems isworth 3 points. A correct answer of problems 11-20 is worth 4 points. A correct answer of problems 21-30 is worth 5 points. For each incorrect answer, one point is deducted from your score. Each unanswered question is worth 0 points. To avoid negative scores, you start from 30 points. The maximum score possible is 150.4.Calculators and graph paper are not permitted. You are allowed to use rough paper for draftwork.5.The figures are not drawn to scale. They should be used only for illustration.6.Remember, you have about 2-3 minutes for each problem; hence, if a problem appears tobe too difficult, save it for later and move on to the other problems.7.At the end of the allotted time, please submit the response form to the contest supervisor.Please do not forget to pick up your Certificate of Participation!Good luck! Canadian Math Kangaroo Contest team2017 CMKC locations: Algoma University; Bishop's University; Brandon University; Brock University; Carlton University; Concordia University; Concordia University of Edmonton; Coquitlam City Library; Dalhousie University; Evergreen Park School; F.H. Sherman Recreation & Learning Centre; GAD Elementary School; Grande Prairie Regional College; Humber College; Lakehead University (Orillia and Thunder Bay); Laurentian University; MacEwan University; Memorial University of Newfoundland; Mount Allison University; Mount Royal University; Nipissing University; St. Mary’s University (Calgary); St. Peter’s College; The Renert School at Royal Vista; Trent University; University of Alberta-Augustana Campus; University of British Columbia (Okanagan); University of Guelph; University of Lethbridge; University of New Brunswick; University of Prince Edward Island; University of Quebec at Chicoutimi; University of Quebec at Rimouski; University of Regina; University of Toronto Mississauga; University of Toronto Scarborough; University of Toronto St. George; University of Windsor; The University of Western Ontario; University of Winnipeg; Vancouver Island University; Walter Murray Collegiate, Wilfrid Laurier University; YES Education Centre; York University; Yukon College.2017 CMKC supporters: Laurentian University; Canadian Mathematical Society; IEEE; PIMS.Canadian Math Kangaroo ContestPart A: Each correct answer is worth 3 points1.A fly has 6 legs, a spider has 8 legs. Together, 3 flies and 2 spiders have as many legs as 9 chickens andseveral cats. How many cats are there?(A) 2 cats (B) 3 cats (C) 4 cats (D) 5 cats (E) 6 cats2.Alice has 4 pieces of this shape: . Which picture can she not make from these four pieces?(A) (B) (C)(D) (E)3.Kalle knows that 1111 × 1111 = 1234321. What is the answer of 1111 × 2222?(A) 3456543 (B) 2346642 (C)2457642 (D) 2468642 (E) 43212344.There are 10 islands and 12 bridges, as depicted in the figure. All bridgesare open for traffic right now. What is the smallest number of bridges thatmust be closed in order to stop the traffic between A and B?(A) 1 (B) 2 (C) 3 (D) 4 (E) 55.Martin wants to colour the squares of the rectangle so that 1/3 of allsquares are blue and half of all squares are yellow. The rest of the squaresare to be coloured red.How many squares will he colour red?(A) 1 (B) 2 (C) 3 (D) 4 (E) 56.When the car wheels make one full rotation the car moves forward by about 1.8 meters. Approximatelyhow many kilometres will the car move forward after 10,000 full rotations of the wheels?(A) 1.8 (B) 18 (C) 180 (D) 1 800 (E) 18 0007.There are 32 students in Mrs. Vicky’s class. Part of the students took one pencil each from the box withpencils on the teacher’s desk. Then a third of the remaining students took 3 pencils each, and there were no more pencils left in the box. How many pencils were there in the box at first?(A) 16 (B) 24 (C) 32 (D) 43 (E) 648.Three rhinoceroses Jane, Kate and Lynn go for a walk: Jane first, Kate in the middle, and Lynn – last. Janeweighs 500 kg more than Kate. Kate weighs 1000 kg less than Lynn. Which of the following pictures may show Jane, Kate and Lynn in the order they walked?(A) (B)(C) (D)(E)9.Peter and Nick are both working on "Kangaroo" contest problems. For every two problems that Petersolves, Nick manages to solve three problems. In total, the boys solved 30 problems. How many problems did Nick solve more than Peter?(A) 5 (B) 6 (C) 7 (D) 8 (E) 910.Bob folded a piece of paper, used a hole puncher and punched exactly one hole in the folded paper.Then, he unfolded the piece of paper, which looked as shown below.Which of the following pictures shows the lines along which Bob folded the piece of paper?(A) (B) (C) (D) (E)Part B: Each correct answer is worth 4 points11.A special die has a number on each of its six faces. The sums of the numbers on opposite faces are all equal. Five of the numbers are 5, 6, 9, 11 and 14. What number is on the sixth face? (A) 4 (B) 7 (C) 8 (D) 13 (E) 15 12.Tom wrote all the numbers from 1 to 20 in a row and obtained the 31‐digit number1234567891011121314151617181920.Then he deleted 24 of the 31 digits, so that the remaining number was as large as possible. Which number was it? (A) 9671819 (B) 9567892 (C) 9781920 (D) 9912345 (E) 981819213.Peter went hiking in the mountains for 5 days. He started on Monday and his last trip was on Friday. Each day he walked 2km more than the day before. The total distance he walked during the five days was 70km. What distance did Peter walk on Thursday? (A) 12 km (B) 13 km (C) 14 km (D) 15 km (E) 16 km14.In a chocolate store, one chocolate costs $3. One day the store had a deal: “Buy two and get a third one free” and Adam decided to take 49 chocolates. How much did he pay for the chocolates? (A) $75 (B) $98 (C) $99 (D) $102 (E) $14715.Eight kangaroos stood in a line as shown in the diagram.At some point, two kangaroos standing side by side and facing each other exchanged places by jumping past each other. This was repeated until no further jumps were possible. How many exchanges were made? (A) 2 (B) 10 (C) 12 (D) 13 (E) 1616.The Modern Furniture store is selling sofas, loveseats, and chairs made from identical modular pieces as shown in the picture. Including the armrests, the width of the sofa is 220 cm and the width of the loveseat is 160 cm.What is the width of the chair? (A) 60 cm (B) 80 cm (C) 90 cm(D) 100 cm(E) 120 cmsofa loveseatchair220 cm160cm17.There are five padlocks and 5 keys – one for each of them (see the figure). The number code on each key has been modified into a letter code on the corresponding padlock. Equal digits have been replaced by the same letter, and different digits – by different letters. What is the number code on the fifth key?(A) 382(B) 282 (C) 284 (D) 823 (E) 82418.Boris has an amount of money and three magic wands that he can use only once. Wand A adds $1. Wand S subtracts $1. Wand D doubles the amount. In which order must he use these wands to obtain the largest amount of money? (A) DAS (B) ASD (C) DSA (D) ADS (E) SAD19.A vase weighs 600 g when one third of it is filled with water. The same vase weighs 800 g when two thirds of it are filled with water. What is the weight of the vase when it is empty? (A) 100 g (B) 200 g (C) 300 g (D) 400 g (E) 500 g20.Rafael has three squares. The first one has side length 2 cm. The second one has side length 4 cm and a vertex is placed in the centre of the first square. The last one has side length 6 cm and a vertex is placed in the centre of the second square, as shown in the picture. What is the area of the figure? (A) 32 cm 2 (B) 51 cm 2 (C) 27 cm 2 (D) 16 cm 2 (E) 6 cm 2Part C: Each correct answer is worth 5 points21.The natural numbers are arranged in the form of a triangle: 1 is in the first row, 2 and 3 are in the second row, 4, 5 and 6 are in the third row, and so on. What is the sum of the numbers written in the 10‐th row?(A) 490(B) 495 (C) 500(D) 505 (E) 5101 2 3 456.. .22.There are eight balls numbered with the numbers 40, 80, 100, 101, 190, 200, 260 and 292 in a bag.Martina takes four balls out of the bag and calculates the sum of the numbers on these balls. It appears that this sum is half of the sum of the numbers on the balls that remain in the bag. What is the greatest number written on the balls taken out?(A) 101 (B) 200 (C) 260 (D) 190 (E) 29223.The structure on the figure is made of unit cubes glued together. Morten wants toput it into a rectangular box. What are the dimensions (length, width and height)of the smallest box he can use?(A) 3 × 3 × 4 (B) 3 × 5 × 5 (C) 3 × 4 × 5 (D) 4 × 4 × 4 (E) 4 × 4 × 524.Four players scored goals in a handball game. All of them scored a different number of goals. One of theplayers, Mike, scored the least number of goals. The other three players scored 20 goals in total. What is the largest number of goals Mike could have scored?(A) 2 (B) 3 (C) 4 (D) 5 (E) 625.Ala likes even numbers, Beata likes numbers divisible by 3, Celina likes numbers divisible by 5. Each ofthese three girls went separately to a basket containing 8 balls with numbers written on them, and took all the balls with numbers she liked. It turned out that Ala collected balls with numbers 32 and 52, Beata ‐ 24,33 and 45, Celina ‐ 20, 25 and 35. In what order did the girls approach the basket?(A) Ala, Celina, Beata (B) Celina, Beata, Ala (C) Beata, Ala, Celina(D) Beata, Celina, Ala (E) Celina, Ala, Beata26.The picture of a kangaroo in the first (leftmost) triangle was reflected across the dotted lines, as in mirrors.The first two reflections are shown.What does the reflection look like in the shaded triangle?(A) (B) (C) (D) (E)27.The numbers 1, 2, 3, 4, and 5 must be written in the five cells in the figure, respecting the following rules:-If a number is just below another number, it must be greater.-If a number is just to the right of another number, it must be greater.In how many ways can this be done?(A) 3 (B) 4 (C) 5 (D) 6 (E) 828.John wrote a natural number in each of the four boxes in the bottom row of the diagram. Then he wrote ineach of the other boxes the sum of the two numbers in the boxes immediately underneath. What is the largest number of odd numbers that could appear in the completed diagram?(A) 4 (B) 5 (C) 6 (D) 7 (E) 829.Julia has four pencils of different colours and wants to use some or all of them to paint the map of anisland divided into four countries, as in the picture. Any two countries with a common border must be coloured differently on the map. How many different colourings of this map are possible? (Twocolourings are considered different if at least one of the countries is coloured differently).(A) 12 (B) 18 (C) 24 (D) 36 (E) 4830.A bar consists of two grey cubes and one white cube glued together as shown in the figure.Which cube can be built from nine such bars?(A) (B) (C) (D) (E)International Contest-GameMath Kangaroo Canada, 2017Answer KeyGrade 5-61 A B C D E 11 A B C D E21 A B C D E2 A B C D E12 A B C D E 22 A B C D E3 A B C D E 13 A B C D E23 A B C D E4 A B C D E 14 A B C D E 24 A B C D E5 A B C D E 15 A B C D E 25 A B C D E6 A B C D E 16 A B C D E 26 A B C D E7 A B C D E 17 A B C D E 27 A B C D E8 A B C D E 18 A B C D E 28 A B C D E9 A B C D E 19 A B C D E 29 A B C D E10 A B C D E 20 A B C D E 30 A B C D E。

2016年袋鼠数学竞赛-初二

Singapore Math Kangaroo Contest 2017Secondary 2 Contest PaperName:School:INSTRUCTIONS:1.Please DO NOT OPEN the contest booklet until the Proctor has given permission to start.2.TIME : 1 hour and 30 minutes3.There are 30 questions in this paper. 3 points, 4 points and 5 points will be awarded for eachcorrect question in Section A, Section B and Section C respectively. No points are deducted for Unanswered question. 1 point is deducted for Wrong answer.4.Shade your answers neatly in the answer entry sheet.5.PROCTORING : No one may help any student in any way during the contest.6.No calculators are allowed.7.All students must fill and shade in your Name, Index number, Level and School in theAnswer sheet provided.8.MINIMUM TIME: Students must stay in the exam hall for at least 1 hour and 15 minutes.9.Students must show detailed working and transfer answers to the answer entry sheet.10.No spare papers can be used in writing this contest. Enough space is provided for yourworking of each question.11. Y ou must return this contest paper to the proctor.Rough WorkingSection A (Correct –3points |Unanswered –0points |Wrong –deduct 1point)Question 1What is the time 17hours after 17:00?(A )8:00(B )10:00(C )11:00(D )12:00(E )13:00Question 2A group of girls stand in a circle.Xena is the fourth on the left from Yana.She is also the seventh on the right from Yana.How many girls are in the group?(A )9(B )10(C )11(D )12(E )13Question 3What number must be subtracted from −17to obtain −33?(A )−50(B )−16(C )16(D )40(E )50Question 4The diagram shows a stripy isosceles triangle and its height.Each stripe has the same height.What fraction of the area in the triangle is white?(A )1/2(B )1/3(C )2/3(D )3/4(E )2/5Question 5Which of the following equation is correct?(A )41=1.4(B )52=2.5(C )63=3.6(D )74=4.7(E )85=5.8The diagram shows two rectangles whose sides are parallel.What is the diﬀerence in the perimeters of the two rectangles?(A)12m(B)16m(C)20m(D)21m(E)24m Question7Bob folded a piece of paper twice and then cut one hole through the folded piece of paper.When he unfolded the paper,he saw the arrangement shown in the diagram below.How did Bob fold his piece of paper?(A)(B)(C)(D)(E)Question8The sum of three diﬀerent positive integers is7.What is the product of these three integers?(A)12(B)10(C)9(D)8(E)5Question9The diagram shows four overlapping hearts.The areas of the hearts are1cm2,4cm2,9cm2and16 cm2.What is the shaded area?(A)9cm2(B)10cm2(C)11cm2(D)12cm2(E)13cm2Yvonne has20dollars.Each of her four sisters has10dollars.How much does Yvonne have to give to each of her sisters,such that each of theﬁve girls has the same amount of money?(A)2(B)4(C)5(D)8(E)10Section B(Correct–4points|Unanswered–0points|Wrong–deduct1point)Question11Annie the Ant started at the left end of a pole and crawled 23of its length.Bob the Beetle startedat the right end of the same pole and crawled 34of its length.What fraction is the length of the polebetween Annie and Bob?(A)38(B)112(C)57(D)12(E)512Question12One sixth of the audience in a theatre were adults.Twoﬁfths of children were boys.What fraction of the audience were girls?(A)1/2(B)1/3(C)1/4(D)1/5(E)2/5Question13In the diagram,the dashed line and the black path form seven equilateral triangles.The length of the dashed line is20.What is the length of the black path?(A)25(B)30(C)35(D)40(E)45Four cousins Ema,Iva,Rita and Zina are3,8,12and14years old,although not necessarily in that order.Ema is younger than Rita.The sum of the ages of Zina and Ema is divisible by5.The sum of the ages of Zina and Rita is also divisible by5.How old is Iva?(A)14(B)12(C)8(D)5(E)3Question15This year there were more than800runners participating in the Kangaroo Hop.Exactly35%of the runners were women and there were252more men than women.How many runners were there in total?(A)802(B)810(C)822(D)824(E)840Question16Rachel wants to write a number in each box of the diagram shown.She has already written two of the numbers.She wants the sum of all the numbers to be equal to35,the sum of the numbers in the ﬁrst three boxes to equal22,and the sum of the numbers in the last three boxes to equal25.What is the product of the numbers she writes in the shaded boxes?(A)63(B)108(C)0(D)48(E)39Question17Simon wants to cut a piece of thread into nine pieces of the same length and marks his cutting points. Barbara wants to cut the same piece of thread into only eight pieces of the same length and also marks her cutting points.Carl then cuts the thread at all the cutting points that are marked.How many pieces of thread does Carl obtain?(A)15(B)16(C)17(D)18(E)19Two segments,each1cm long,are marked on opposite sides of a square of side8cm.The ends of the segments are joined as shown in the diagram.What is the shaded area,in cm2?(A)2(B)4(C)6.4(D)8(E)10Question19Tycho wants to prepare a schedule for his jogging.He wants to jog exactly twice a week,and on the same days every week.He never wants to jog on two consecutive days.How many such schedules are there?(A)16(B)14(C)12(D)10(E)8Question20Emily wants to write a number into each cell of a3×3table so that the sum of the numbers in any two cells with common sides that share an edge which is always the same.She has already written two numbers,as shown in the diagram.What is the sum of all the numbers in the table?(A)18(B)20(C)21(D)22(E)23Section C(Correct–5points|Unanswered–0points|Wrong–deduct1point)Question21The numbers of degrees in the angles in a triangle are three diﬀerent integers.What is the minimum possible sum of its smallest and largest angles?(A)61◦(B)90◦(C)91◦(D)120◦(E)121◦Ten kangaroos stood in a line as shown in the picture below.At some point,two kangaroos standing side by side and facing each other exchanged places by jumping past each other.This was repeated until no further jumps were possible.How many exchanges were made?(A)15(B)16(C)18(D)20(E)21Question23Diana has nine numbers:1,2,3,4,5,6,7,8and9.She adds2to some of them,and5to all the others.What is the smallest number of diﬀerent results she can obtain?(A)5(B)6(C)7(D)8(E)9Question24Buses leave the airport every3minutes to drive to the city centre.A car leaves the airport at the same time as one bus and drives to the city centre by the same route.It takes takes60minutes and 35minutes for each bus and the car respectively to drive from the airport to the city centre.How many buses does the car pass on its way to the centre,excluding the bus it left with?(A)8(B)9(C)10(D)11(E)13Question25Olesia’s tablecloth has a regular pattern,as shown in the diagram.What percentage of the tablecloth is black?(A)16(B)24(C)25(D)32(E)36Each digit in the sequence starting with2,3,6,8,8is obtained in the following way:theﬁrst two digits are2and3and afterwards each digit is the last digit of the product of the two preceding digits in the sequence.What is the2017th digit in the sequence?(A)2(B)3(C)4(D)6(E)8Question27Mike had125small cubes.He glued some of them together to form a big cube with nine tunnels leading through the whole cube as shown in the diagram.How many of the small cubes are there which he did not use?(A)52(B)45(C)42(D)39(E)36Question28Two runners are training on a720metre circular track.They run in opposite directions,each at constant speed.Theﬁrst runner takes four minutes to complete the full loop and the second runner takesﬁve minutes.How many metres does the second one run between two consecutive meetings of the two runners?(A)355(B)350(C)340(D)330(E)320Sarah wants to write a positive integer in each box in the diagram so that each number above the bottom row is the sum of the two numbers in the boxes immediately underneath.What is the largest number of odd numbers that Sarah can write?(A)5(B)7(C)8(D)10(E)11Question30The diagram shows parallelogram ABCD with area S.The intersection point of the diagonals of the parallelogram is O.The point M is marked on DC.The intersection point of AM and BD is E and the intersection point of BM and AC is F.The sum of the areas of the triangles AED and BF C is 13S.What is the area of the quadrilateral EOF M,in terms of S?(A)16S(B)18S(C)110S(D)112S(E)114S。

2016年5-6年级袋鼠数学竞赛

(A) 1
√ (B) 2
(C) 3
(D) 5
(E) 6
6.Tom和John各使用了相同数量的立方体建了一个长方体的盒子
(每个立方体的大小相同)。上图是Tom的盒子，下图是John的盒子的
第一层。John的盒子共有多少层？
(A) 2
(B) 3
√ (C) 4
(D) 5
(E) 6
6 ×2×2 = 24（块）
(i)第一个数字是1,
(ii)接下来的每个数字都和之前一个数字一样或更大，
(iii)所有数字的和是5。请问他共写了多少个数目？
(A) 4
√ (B) 5
(C) 6
(D) 7 (E) 8
11111
1112
1 22
113
14
20. Luigi开了一间小餐馆。他的朋友Giacomo给了他一些正方形的桌子
和一些椅子。如果他把全部桌子当单桌用，每张桌子有4把椅子，
只野猫。如果她每天给她的每一只猫吃相同数量的猫粮，祖母所买的
猫粮能维持多少夭？
√ (A) 8 (B) 7
(C) 6
(D) 5 (E) 4
4只猫
12天的猫粮
1只猫
48天的猫粮 6只猫
8天
15. BENJAMIN里的每个字母各代表数字1, 2, 3, 4, 5, 6或7其中一个。
不同的字母代表不同的数字。BENJAMIN的数目是单数并且可以
10.有五只松鼠A, B, C, D和E坐在线上。它们将会把6个有交叉标记的坚果
拾取。在同一时刻，每只松鼠会以相同的速度向最靠近的坚果奔跑。
每当一只松鼠拾取一颗坚果后就会马上向另一颗最靠近的坚果奔跑。
请问哪只松鼠会拾取两个坚果？

美国袋鼠数学竞赛试题及答案

美国袋鼠数学竞赛试题及答案一、选择题（每题2分，共10分）1. 如果一个数的平方等于81，那么这个数是：A. 9B. -9C. 3D. -32. 下列哪个分数是最接近0.5的？A. 0.49B. 0.51C. 0.48D. 0.523. 如果一个圆的半径是5厘米，那么它的周长是多少厘米？A. 15πB. 10πC. 20πD. 25π4. 一个班级有30名学生，其中1/3是男生，其余是女生。

这个班级有多少名女生？A. 20B. 10C. 15D. 55. 一个数的立方是-27，这个数是：A. -3B. 3C. -27D. 27二、填空题（每题3分，共15分）6. 如果一个数的平方根是4，那么这个数是______。

7. 一个直角三角形的两条直角边分别是3和4，那么它的斜边长度是______。

8. 一个数的1/4加上5等于10，这个数是______。

9. 如果一个数的1/5是2，那么这个数是______。

10. 一个数的2倍加上3等于11，这个数是______。

三、解答题（每题5分，共20分）11. 一个长方形的长是20厘米，宽是10厘米，求它的面积。

12. 如果一个数的平方加上这个数等于10，求这个数。

13. 一个圆的直径是14厘米，求它的面积。

14. 一个数的立方加上这个数的平方再加上这个数等于64，求这个数。

答案1. B（-9的平方是81）2. B（0.51最接近0.5）3. C（周长=2πr，r=5，所以周长=2*π*5=10π）4. A（女生人数=30*(2/3)=20）5. A（-3的立方是-27）6. 16（4的平方是16）7. 5（根据勾股定理，斜边=√(3^2+4^2)=5）8. 36（设这个数为x，x/4+5=10，解得x=36）9. 10（设这个数为x，x/5=2，解得x=10）10. 4（设这个数为x，2x+3=11，解得x=4）11. 面积=长*宽=20*10=200平方厘米12. 设这个数为x，x^2+x=10，解得x=(-1+√41)/2 或 x=(-1-√41)/2（舍去负根）13. 面积=πr^2，r=直径/2=7，所以面积=π*7^2=49π平方厘米14. 设这个数为x，x^3+x^2+x=64，解得x=4结束语希望这份试题能够帮助同学们更好地准备美国袋鼠数学竞赛，同时也能够激发大家学习数学的热情。

2016年袋鼠数学竞赛-四年级

Singapore Math Kangaroo Contest 2017Primary 4 Contest PaperName:School:INSTRUCTIONS:1.Please DO NOT OPEN the contest booklet until the Proctor has given permission to start. 2.TIME : 1 hour and 30 minutes3.There are 30 questions in this paper. 3 points, 4 points and 5 points will be awarded for each correct question in Section A, Section B and Section C respectively. No points are deducted for Unanswered question. 1 point is deducted for Wrong answer. 4.Shade your answers neatly in the answer entry sheet. 5.PROCTORING : No one may help any student in any way during the contest. 6.No calculators are allowed. Name, Index number, Level and School in the 7.All students must fill and shade in your Answer sheet provided. 8.MINIMUM TIME: Students must stay in the exam hall for at least 1 hour and 15 minutes. 9.Students must show detailed working and transfer answers to the answer entry sheet. 10.No spare papers can be used in writing this contest. Enough space is provided for your working of each question. 11. Y ou must return this contest paper to the proctor. Rough WorkingSection A(Correct–3points |Unanswered –0points |Wrong –deduct 1point)Question 1Which of the pieces(A,B,C,D,E)willﬁt in between the two pieces below,such that the two equations formed will be true?8–3=2(A)=55–1(B)=34–2(C)=51+2(D)=45–3(E)=51+1Question2John looks through the window as shown in the picture below.He only sees half the number of kangaroos in the park.How many kangaroos are there in the park in total?(A)12(B)14(C)16(D)18(E)20Two gridded transparent sheets are darkened in some squares,as shown in the picture below.They are both placed on top of the board shown in the middle.The the pictures behind the darkenedsquares cannot be seen.Only one of the pictures can still be seen,which pictureisit?(A)(B)(C)(D)(E)Question 4A original picture of footprints(left)was rotated in a particular way.The result is shown on the rightofthe original picture.Which pair of footprints are missing?(A)(B)(C)(D)1(E)Question5What number is hidden behind the panda? – 10 = 10+ 6 = – 6 = +8 + 8 = A(A)16(B)18(C)20(D)24(E)28In the table below,the correct sums are shown.What number is in the box with the question mark?(A)10(B)12(C)13(D)15(E)16Question7Dolly accidentally broke the mirror into pieces.How many pieces have exactly four sides?(A)2(B)3(C)4(D)5(E)6Question8Which option shows the necklace below when it is untangled?(A)(B)(C)(D)(E)Section B(Correct–4points|Unanswered–0points|Wrong–deduct1point)Question9The picture below shows the front of Ann’s house.The back of her house has three windows and no door.What does Ann see when she is standing from the back of her house?(A)(B)(C)(D)(E)Question10Which option is correct?(A)(B)(C)(D)(E)Balloons are sold in packets of 5,10and 25.Marius buys exactly 70balloons.What is the smallest number of packets he could buy?(A )3(B )4(C )5(D )6(E )7Question 12Bob folded a piece of paper.He cut exactly one hole through the folded paper.Then he unfolded the piece of paper and saw the result as shown in the picture below.How did Bob fold his piece of paper?(A )(B )(C )(D )(E )Question 13There is a tournament at a pool.At ﬁrst,13children signed up,and then another 19signed up.Six teams with an equal number of members are needed for the tournament.At least how many more children need to sign up so that the six teams can be form?(A )1(B )2(C )3(D )4(E )5Question 14Numbers are placed in the cells of the 4×4square shown in the picture below.Mary selects any 2×2square in 4×4square and adds up all the numbers in the four cells.What is the largest possible sum she can get?(A )11(B )12(C )13(D )14(E )15David wants to cook5dishes on a stove with only2burners.The time he needed to cook the5dishes are40mins,15mins,35mins,10mins and45mins.What is the shortest possible time in which he can cook all5dishes?(He can only remove a dish from the stove when it is fully cooked.)(A)60min(B)70min(C)75min(D)80min(E)85minQuestion16be written in the circle containing the question mark?Which number shouldSection C(Correct–5points|Unanswered–0points|Wrong–deduct1point)Question17The picture shows a group of building blocks and a plan of these blocks.Some ink has dripped onto the plan.What is the sum of the numbers covered by the ink?3411131(A)3(B)4(C)5(D)6(E)7How long is the train?340 m110 m(A)55m(B)115m(C)170m(D)220m(E)230mQuestion19George trains at his schoolﬁeld atﬁve o’clock every afternoon.The journey from his house to the bus stop takes5minutes.The bus journey takes15minutes.It takes him5minutes to go from the bus stop to theﬁeld.The bus runs every10minutes from six in the morning.What is the latest time he has to leave his house in order to arrive at theﬁeld exactly on time?(A)(B)(C)(D)(E)Question20A small zoo has a giraﬀe,an elephant,a lion and a turtle.Susan wants to plan a tour where she sees 2diﬀerent animals.She does not want to start with the lion.How many diﬀerent tours can she plan?(A)3(B)7(C)8(D)9(E)12Four brothers have eaten11cookies in total.Each of them has eaten at least one cookie and no two of them have eaten the same number of cookies.Three of them have eaten9cookies in total and one of them has eaten exactly3cookies.What is the largest number of cookies one of the brothers has eaten?(A)3(B)4(C)5(D)6(E)7Question22Zosia has hidden some smileys in some of the squares in the table.In some of the other squares she writes the number of smileys in the neighbouring squares as shown in the picture.Two squares are said to be neighbouring if they share a common side or a common corner.How many smileys has she hidden?(A)4(B)5(C)7(D)8(E)11Question23Ten bags contain diﬀerent numbers of candies from1to10in each of the bag.Five boys took two bags of candies each.Alex got5candies,Bob got7candies,Charles got9candies and Dennis got15 candies.How many candies did Eric get?(A)9(B)11(C)13(D)17(E)19Question24Kate has4ﬂowers,one with6petals,one with7petals,one with8petals and one with11petals. Kate tears oﬀone petal from threeﬂowers.She does this several times,choosing any threeﬂowers each time.She stops when she can no longer tear one petal from threeﬂowers.What is the smallest number of petals which can remain?(A)1(B)2(C)3(D)4(E)5Rough Working。

2016年袋鼠数学竞赛-三年级

Singapore Math Kangaroo Contest 2017Primary 3 Contest PaperName:School:INSTRUCTIONS:1.Please DO NOT OPEN the contest booklet until the Proctor has given permission to start.2.TIME : 1 hour and 30 minutes3.There are 30 questions in this paper. 3 points, 4 points and 5 points will be awarded for eachcorrect question in Section A, Section B and Section C respectively. No points are deducted for Unanswered question. 1 point is deducted for Wrong answer.4.Shade your answers neatly in the answer entry sheet.5.PROCTORING : No one may help any student in any way during the contest.6.No calculators are allowed.7.All students must fill and shade in your Name, Index number, Level and School in theAnswer sheet provided.8.MINIMUM TIME: Students must stay in the exam hall for at least 1 hour and 15 minutes.9.Students must show detailed working and transfer answers to the answer entry sheet.10.No spare papers can be used in writing this contest. Enough space is provided for yourworking of each question.11. Y ou must return this contest paper to the proctor.Rough WorkingSection A(Correct–3points|Unanswered–0points|Wrong–deduct1point)Question1Which of the pieces(A,B,C,D,E)willﬁt in between the two pieces below,such that the two equations formed will be true?8–3=2(A )=55–1(B )=34–2(C)=51+2(D)=45–3(E)=51+1Question2John looks through the window as shown in the picture below.He only sees half the number of kangaroos in the park.How many kangaroos are there in the park intotal?(A)12(B)14(C)16(D)18(E)20Two gridded transparent sheets are darkened in some squares,as shown in the picture below.They are both placed on top of the board shown in the middle.The the pictures behind the darkened squares cannot be seen.Only one of the pictures can still be seen,which picture isit?Question 4original picture rotated in a particularway.The resultfootprints are missing?(A )(B )(C )(D )1(E )Question 5What number is hidden behind the panda?– 10 = 10+ 6 =– 6 = +8+ 8= A(A )16(B )18(C )20(D )24(E )28In the table below,the correct sums are shown.What number is in the box with the question mark?(A)10(B)12(C)13(D)15(E)16Question7Dolly accidentally broke the mirror into pieces.How many pieces have exactly four sides?(A)2(B)3(C)4(D)5(E)6Question8Which option shows the necklace below when it is untangled?(A)(B)(C)(D)(E)Section B(Correct–4points|Unanswered–0points|Wrong–deduct1point)Question9The picture below shows the front of Ann’s house.The back of her house has three windows and no door.What does Ann see when she is standing from the back of her house?(A)(B)(C)(D)(E)Question10Which option is correct?(A)(B)(C)(D)(E)Balloons are sold in packets of5,10and25.Marius buys exactly70balloons.What is the smallest number of packets he could buy?(A)3(B)4(C)5(D)6(E)7Question12Bob folded a piece of paper.He cut exactly one hole through the folded paper.Then he unfolded the piece of paper and saw the result as shown in the picture below.How did Bob fold his piece of paper?(A)(B)(C)(D)(E)Question13There is a tournament at a pool.Atﬁrst,13children signed up,and then another19signed up.Six teams with an equal number of members are needed for the tournament.At least how many more children need to sign up so that the six teams can be form?(A)1(B)2(C)3(D)4(E)5Question14Numbers are placed in the cells of the4×4square shown in the picture below.Mary selects any2×2 square in4×4square and adds up all the numbers in the four cells.What is the largest possible sum she can get?(A)11(B)12(C)13(D)14(E)15David wants to cook5dishes on a stove with only2burners.The time he needed to cook the5dishes are40mins,15mins,35mins,10mins and45mins.What is the shortest possible time in which he can cook all5dishes?(He can only remove a dish from the stove when it is fully cooked.)(A)60min(B)70min(C)75min(D)80min(E)85minQuestion16Which number should be(A)10(B)11(C)12(D)13(E)14Section C(Correct–5points|Unanswered–0points|Wrong–deduct1point)Question17The picture shows a group of building blocks and a plan of these blocks.Some ink has dripped onto(A)3(B)4(C)5(D)6(E)7How long is the train?(A)55m(B)115m(C)170m(D)220m(E)230mQuestion19George trains at his schoolﬁeld atﬁve o’clock every afternoon.The journey from his house to the bus stop takes5minutes.The bus journey takes15minutes.It takes him5minutes to go from the bus stop to theﬁeld.The bus runs every10minutes from six in the morning.What is the latest time he has to leave his house in order to arrive at theﬁeld exactly on time?(A)(B)(C)(D)(E)Question20A small zoo has a giraﬀe,an elephant,a lion and a turtle.Susan wants to plan a tour where she sees 2diﬀerent animals.She does not want to start with the lion.How many diﬀerent tours can she plan?(A)3(B)7(C)8(D)9(E)12Four brothers have eaten11cookies in total.Each of them has eaten at least one cookie and no two of them have eaten the same number of cookies.Three of them have eaten9cookies in total and one of them has eaten exactly3cookies.What is the largest number of cookies one of the brothers has eaten?(A)3(B)4(C)5(D)6(E)7Question22Zosia has hidden some smileys in some of the squares in the table.In some of the other squares she writes the number of smileys in the neighbouring squares as shown in the picture.Two squares are said to be neighbouring if they share a common side or a common corner.How many smileys has she hidden?(A)4(B)5(C)7(D)8(E)11Question23Ten bags contain diﬀerent numbers of candies from1to10in each of the bag.Five boys took two bags of candies each.Alex got5candies,Bob got7candies,Charles got9candies and Dennis got15 candies.How many candies did Eric get?(A)9(B)11(C)13(D)17(E)19Question24Kate has4ﬂowers,one with6petals,one with7petals,one with8petals and one with11petals. Kate tears oﬀone petal from threeﬂowers.She does this several times,choosing any threeﬂowers each time.She stops when she can no longer tear one petal from threeﬂowers.What is the smallest number of petals which(A)1(B)2(C)3(D)4(E)5。

袋鼠数学历年试题

袋鼠数学历年试题今天咱们来聊聊袋鼠数学的历年试题呀。

袋鼠数学竞赛可有趣啦。

它的试题就像一个个小挑战，等着我们去攻克。

我做过一些历年的试题，那里面的题目可真是五花八门。

比如说有一道关于小动物分果子的题目。

就像在一个大森林里，小兔子有一堆果子，它要分给小松鼠和小猴子一些。

题目里告诉我们小兔子有多少个果子，小松鼠想要几个，小猴子又想要几个。

然后问我们小兔子还剩下几个果子呢。

这就像我们平时和小伙伴分小零食一样呀。

我当时就想着我和我的好朋友分糖果的情景，就很容易算出答案啦。

还有那种关于图形的题目。

就像我们在玩拼图游戏。

有一个大的图形，然后又给了我们几个小的图形，问我们怎么把小图形拼到大图形里面去呢。

我记得有一次是一个像房子形状的大图形，小图形有三角形、正方形。

我就想象着我在搭积木盖房子，把那些小图形一块一块地放在合适的位置。

这让我觉得做试题就像在玩游戏一样。

在历年试题里，也有关于数字排队的题目。

就好比小动物们排队领东西，数字们也要排队。

它会告诉我们一些数字的位置，然后问另一个数字应该在什么地方。

我想到了我们在学校排队做早操，我站在某个同学后面，那另一个同学又该站哪里呢？这样想的话，题目就变得很简单了。

这些试题不仅仅是为了考试，还让我们学会用有趣的方式思考数学问题。

我每次做完一些试题，就感觉自己像一个聪明的小探险家，又发现了数学世界里的一个小秘密。

而且当我做对一道题的时候，那种开心就像我在学校跑步比赛得了第一名一样。

虽然有时候也会遇到很难的题目，就像爬山遇到很陡的坡。

但是只要我们不放弃，再仔细看看题目，就像在山上找另外的小路一样，总会找到解决的办法的。

我特别喜欢做袋鼠数学的历年试题，因为它让数学变得不再那么枯燥。

你们要是有机会做这些试题，一定会像我一样，发现数学原来是这么好玩的东西呢。

它就像一个充满惊喜的大盒子，每一道试题都是一个小惊喜在等着我们去打开。

加拿大国际袋鼠数学竞赛试题-2013年

(A) 12
(B) 8
(C) 4
(D) 2
(E) 0
3. Which of the dresses has less than seven dots, but more than five dots?
(A)
(B)
(C)
(D)
(E)
Grade 1-2
Year 2013
4. A lot of babies were born in the zoo last year: two baby lions, three baby dolphins and four baby eagles.
tulips. They started at 9:00 in the morning. At what time will they finish planting all 20 tulips?
(A) At 9:10
(B) At 9:20 (C) At 9:40
(D) At 9:50
(E) At 10:00
(C) 2 and 0
(D) 6 and 9
(E) 7 and 1
2. There are twelve books on a shelf and four children in a room. How
many books will be left on the shelf if each child takes one book?
(A) 16
(B) 30
(C) 50
(D) 52
(E) 70
18. In a park there are babies in four-wheel strollers and children on two-wheel bikes. Paula counted wheels and the total was 12. When she added the number of strollers to the number of bikes, the total was 4. How many two-wheel bikes are there in the park?

新加坡袋鼠数学竞赛5年级考卷中文版(2016)

注意事项：
1.在监考老师宣布开始考试之前，请不要打开考卷
2.时间：1小时30分钟
3.本考卷有30个题。

第一部分每题3分，第二部分每题4分，第三部分每题5分。

不答没有分，
答错均扣一分。

4.在答题纸上清晰地涂黑选项
5.监考：在竞赛过程中，任何人不准以任何形式帮助学生。

6.不允许带计算器。

7.所有的学生必须在考卷上填写和涂黑你的名字，考号，年级和学校
8.最少时间：学生必须在考场待够1小时15分钟
9.学生必须提供详细演算过程并把答案写在答题纸上
10.不提供多余的演算纸。

每个题目已经提供足够的演算空间。

11.必须把考卷还给监考老师。

（完）。

2016年袋鼠数学竞赛-三年级

2016年袋⿏数学竞赛-三年级Singapore Math Kangaroo Contest 2017Primary 3 Contest PaperName:School:INSTRUCTIONS:1.Please DO NOT OPEN the contest booklet until the Proctor has given permission to start.2.TIME : 1 hour and 30 minutes3.There are 30 questions in this paper. 3 points, 4 points and 5 points will be awarded for eachcorrect question in Section A, Section B and Section C respectively. No points are deducted for Unanswered question. 1 point is deducted for Wrong answer.4.Shade your answers neatly in the answer entry sheet.5.PROCTORING : No one may help any student in any way during the contest.6.No calculators are allowed.7.All students must fill and shade in your Name, Index number, Level and School in theAnswer sheet provided.8.MINIMUM TIME: Students must stay in the exam hall for at least 1 hour and 15 minutes.9.Students must show detailed working and transfer answers to the answer entry sheet.10.No spare papers can be used in writing this contest. Enough space is provided for yourworking of each question.11. Y ou must return this contest paper to the proctor.Rough WorkingSection A(Correct–3points|Unanswered–0points|Wrong–deduct1point)Question1Which of the pieces(A,B,C,D,E)will?t in between the two pieces below,such that the two equations formed will be true?8–3=2(A )=55–1(B )=34–2(C )=51+2(D)=45–3(E)=51+1Question2John looks through the window as shown in the picture below.He only sees half the number of kangaroos in the park.How many kangaroos are there in the park intotal?(A)12(B)14(C)16(D)18(E)201Two gridded transparent sheets are darkened in some squares,as shown in the picture below.They are both placed on top of the board shown in the middle.The the pictures behind the darkened squares cannot be seen.Only one of the pictures can still be seen,which picture isit?Question 4original picture rotated in a particular way.The resultfootprints are missing?(A )(B )(C )1(D )1(E )Question 5What number is hidden behind the panda?– 10 = 10+ 6 =– 6 = +8 + 8 = A (A )16(B )18(C )20(D )24(E )282In the table below,the correct sums are shown.What number is in the box with the question mark?(A)10(B)12(C)13(D)15(E)16Question7Dolly accidentally broke the mirror into pieces.How many pieces have exactly four sides?(A)2(B)3(C)4(D)5(E)6Question8Which option shows the necklace below when it is untangled?(A)(B)(C)(D)(E)3Section B(Correct–4points|Unanswered–0points|Wrong–deduct1point)Question9The picture below shows the front of Ann’s house.The back of her house has three windows and no door.What does Ann see when she is standing from the back of her house?(A)(B)(C)(D)(E)Question10Which option is correct?(A)(B)(C)(D)(E)Balloons are sold in packets of5,10and25.Marius buys exactly70balloons.What is the smallest number of packets he could buy?(A)3(B)4(C)5(D)6(E)7Question12Bob folded a piece of paper.He cut exactly one hole through the folded paper.Then he unfolded the piece of paper and saw the result as shown in the picture below.How did Bob fold his piece of paper?(A)(B)(C)(D)(E)Question13There is a tournament at a pool.At?rst,13children signed up,and then another19signed up.Six teams with an equal number of members are needed for the tournament. At least how many more children need to sign up so that the six teams can be form?(A)1(B)2(C)3(D)4(E)5Question14Numbers are placed in the cells of the4×4square shown in the picture below.Mary selects any2×2 square in4×4square and adds up all the numbers in the four cells.What is the largest possible sum she can get?(A)11(B)12(C)13(D)14(E)15David wants to cook5dishes on a stove with only2burners.The time he needed to cook the5dishes are40mins,15mins,35mins,10mins and45mins.What is the shortest possible time in which he can cook all5dishes?(He can only remove a dish from the stove when it is fully cooked.)(A)60min(B)70min(C)75min(D)80min(E)85minQuestion16Which number should be(A)10(B)11(C)12(D)13(E)14Section C(Correct–5points|Unanswered–0points|Wrong–deduct1point)Question17The picture shows a group of building blocks and a plan of these blocks.Some ink has dripped onto(A)3(B)4(C)5(D)6(E)7How long is the train?(A)55m(B)115m(C)170m(D)220m(E)230mQuestion19George trains at his school?eld at?ve o’clock every afternoon.The journey from his house to the bus stop takes5minutes.The bus journey takes15minutes.It takes him5minutes to go from the bus stop to the?eld.The bus runs every10minutes from six in the morning.What is the latest time he has to leave his house in order to arrive at the?eld exactly on time?(A)(B)(C)(D)(E)Question20A small zoo has a gira?e,an elephant,a lion and a turtle.Susan wants to plan a tour where she sees 2di?erent animals.She does not want to start with the lion.How many di?erent tours can she plan? (A)3(B)7(C)8(D)9(E)12Four brothers have eaten11cookies in total.Each of them has eaten at least one cookie and no two of them have eaten the same number of cookies.Three of them have eaten9cookies in total and one of them has eaten exactly3cookies.What is the largest number of cookies one of the brothers has eaten?(A)3(B)4(C)5(D)6(E)7Question22Zosia has hidden some smileys in some of the squares in the table.In some of the other squares she writes the number of smileys in the neighbouring squares as shown in the picture.Two squares are said to be neighbouring if they share a common side or a common corner.How many smileys has she hidden?(A)4(B)5(C)7(D)8(E)11Question23Ten bags contain di?erent numbers of candies from1to10in each of the bag.Five boys took two bags of candies each.Alex got5candies,Bob got7candies,Charles got9candies and Dennis got15 candies.How many candies did Eric get?(A)9(B)11(C)13(D)17(E)19Question24Kate has4?owers,one with6petals,one with7petals,one with8petals and one with11petals. Kate tears o?one petal from three?owers.She does this several times,choosing any three?owers each time.She stops when she can no longer tear one petal from three?owers.What is the smallest number of petals which(A)1(B)2(C)3(D)4(E)5。

2016年袋鼠数学竞赛-高一

Singapore Math Kangaroo Contest 2017Secondary 4 Contest PaperName:School:INSTRUCTIONS:1.Please DO NOT OPEN the contest booklet until the Proctor has given permission to start.2.TIME : 1 hour and 30 minutes3.There are 30 questions in this paper. 3 points, 4 points and 5 points will be awarded for eachcorrect question in Section A, Section B and Section C respectively. No points are deducted for Unanswered question. 1 point is deducted for Wrong answer.4.Shade your answers neatly in the answer entry sheet.5.PROCTORING : No one may help any student in any way during the contest.6.No calculators are allowed.7.All students must fill and shade in your Name, Index number, Level and School in theAnswer sheet provided.8.MINIMUM TIME: Students must stay in the exam hall for at least 1 hour and 15 minutes.9.Students must show detailed working and transfer answers to the answer entry sheet.10.No spare papers can be used in writing this contest. Enough space is provided for yourworking of each question.11. Y ou must return this contest paper to the proctor.Rough WorkingSection A(Correct–3points|Unanswered–0points|Wrong–deduct1point)Question1In this diagram,each number is the sum of the two numbers immediately below it.What number is in the most bottom left box?(A)15(B)16(C)17(D)18(E)19Question2Peter wrote the word KANGAROO on a piece of transparent glass as shown in the picture below. What will he see if heﬂips the paper over to its right and then rotates it one half-turn?(A)(B)(C)(D)(E)Question3Angela made a decoration with grey and white asteroids by overlaping them from biggest at the bottom,to the smallest at the top.The areas of the asteroids are1cm2,4cm2,9cm2and16cm2. What is the total area of the visible grey regions?(A)9cm2(B)10cm2(C)11cm2(D)12cm2(E)13cm2 Question4Maria has24dollars.Every one of her3siblings has12dollars.How much does she have to give each of her siblings,such that everyone has the same amount?(A)1dollar(B)2dollars(C)3dollars(D)4dollarsj(E)6dollarsWhich option shows the path of the midpoint of the wheel when the wheel rolls along the zig-zag-curve shown?(A)(B)(C)(D)(E)Question6Some girls were dancing in a circle.Antonia was theﬁfth to the left from Bianca and the eighth to the right from Bianca.How many girls were in the group?(A)11(B)12(C)13(D)14(E)15Question7Circle of radius1rolls along a straight line from the point K to the point L,where KL=11π.What does the circle look like at L?LK(A(B)(C)(D(E)Question8Martin is taking part in a chess competition.He won9out of15matches.If he wins the next5 matches,what will his success rate be in the competition?(A)60%(B)65%(C)70%(D)75%(E)80%Question9One eighth of the guests at a wedding were children.Three sevenths of the adult guests were men. What fraction of the wedding guests were women?(A)12(B)13(C)15(D)17(E)37My maths teacher has a box with coloured buttons.There are203red buttons,117white buttons and28blue buttons.What is the least number of buttons he must take from the box without looking, to ensure he has at least3buttons of the same colour?(A)3(B)6(C)7(D)28(E)203Section B(Correct–4points|Unanswered–0points|Wrong–deduct1point)Question11ABCD is a trapezoid with sides AB parallel to CD,where AB=50,CD=20.E is a point on the side AB such that the segment DE divides the given trapezoid into two parts of equal area.Calculate the length AE.(A)25(B)30(C)35(D)40(E)45Question12How many positive integers A,which satisfy the property that exactly one of the numbers A or A+20 is a4-digit number?(A)19(B)20(C)38(D)39(E)40Question13Six perpendiculars lines are drawn from the midpoints on each sides of the triangle to each of the other two sides.What fraction of the area of the initial triangle does the resulting hexagon cover?(A)13(B)25(C)49(D)12(E)23The squares of three consecutive positive integers adds up to770.What is the largest of these3 integers?(A)15(B)16(C)17(D)18(E)19Question15A belt drive system consists of the wheels A,B and C,which rotate without a slippage.B turns4 full rounds when A turns5full rounds,and B turns6full rounds whenC turns7full rounds.Find the perimeter of A if the perimeter of C is30cm.(A)27cm(B)28cm(C)29cm(D)30cm(E)31cm Question16Mr Tan wants to prepare a schedule for his jogging over the next few months.Every week,he wants to jog on the same days of the week and he never wants to jog on two consecutive days.In addition, he wants to jog three times per week.How many schedules can he choose from?(A)6(B)7(C)9(D)10(E)35Question17Four brothers have diﬀerent heights.Tom is shorter than Victor by x cm.Tom is taller than Peter by x cm.Oscar is shorter than Peter by by x cm.Tom is184cm tall and the average height of all the four brothers is178cm.How tall is Oscar?(A)160cm(B)166cm(C)172cm(D)184cm(E)190cm Question18It rained7times during the holiday.When it rained in the morning,it was sunny in the afternoon. When it rained in the afternoon,it was sunny in the morning.There were5sunny mornings and6 sunny afternoons.How many days did the holiday last at least?(A)7(B)8(C)9(D)10(E)11Jenny decided to write numbers in the cells of the3×3table below.The sums of the numbers in any 2×2squares are the same.The three numbers in the corner cells have already been written as shown in theﬁgure.Which number should she write in the bottom right corner cell?(A)5(B)4(C)1(D)0(E)Impossible to determineQuestion20Seven positive integers a,b,c,d,e,f,g are written in a row.The sum of all the seven positive integers is equals to2017;any two neighbouring numbers diﬀer by±1.Which of the numbers can be equal to 286?(A)only a or g(B)only b or f(C)only c or e(D)only d(E)any of themSection C(Correct–5points|Unanswered–0points|Wrong–deduct1point)Question21There are4children of diﬀerent ages under18.The product of their ages is882.Assuming that their ages are integers,ﬁnd the sum of their ages.(A)23(B)25(C)27(D)31(E)33Question22On the faces of a given dice these numbers appear:−3,−2,−1,0,1,2.If you throw it twice and multiply the two results,what is the probability that the product is negative?(A)12(B)14(C)1136(D)1336(E)13Question23Given a two digit number ab.The six digit number ababab is divisible by?(A)2(B)5(C)7(D)9(E)11My friend wants to use a special seven digit password.The digits of the password occur exactly as many times as its digit value.The same digits of this number are always written consecutively.For example4444333or1666666.How many possible passwords can he choose from?(A)6(B)7(C)10(D)12(E)13Question25Paul wants to write a natural number in each box in the diagram such that each number is the sum of the two numbers in the boxes immediately underneath.At most how many odd numbers can Paul write?(A)13(B)14(C)15(D)16(E)17Question26Liza calculated the sum of angles of a convex polygon.She missed one of the angles and so her result was2017◦.What angle did she miss?(A)37◦(B)53◦(C)97◦(D)127◦(E)143◦Question27There are30dancers standing in a circle and facing the centre.After the”Left”command some dancers turned to the left and all the others-to the right.Those dancers who were facing each other, said”Hello”.It turned out to be10such dancers.Then after the command”Around”all the dancers made a180◦turn.Again,those dancers who were facing each other,said”Hello”.How many dancers said”Hello”?(A)10(B)20(C)8(D)15(E)impossible to determineOn a balance scale,3diﬀerent masses are put at random on each pan and the result is shown in the picture.The masses are of101,102,103,104,105and106grams.What is the probability that the 106gram mass stands on the heavier(right)pan?(A)75%(B)80%(C)90%(D)95%(E)100% Question29A andB are on the circle with centre M.P B is tangent to the circle at B.The distances P A and MB are integers,P B=P A+6.How many possible values are there for MB?(A)0(B)2(C)4(D)6(E)8Question30Point D is chosen on the side AC of triangle ABC so that DC=AB.Points M and N are the midpoints of the segments AD and BC,respectively.If∠NMC=αthen∠BAC always equals to(E)60◦(A)2α(B)90◦−α(C)45◦+α(D)90◦−α2Rough Working。

加拿大国际袋鼠数学竞赛试题-2013年

加拿⼤国际袋⿏数学竞赛试题-2013年Grade 1-2International Contest-Game MATH KANGAROOPart A: Each correct answer is worth 3 points. 1. Which digits are missing?Year 2013(A) 3 and 5 (B) 4 and 8(C) 2 and 0(D) 6 and 9(E) 7 and 12. There are twelve books on a shelf and four children in a room. Howmany books will be left on the shelf if each child takes one book?(A) 12(B) 8(C) 4(D) 2(E) 03. Which of the dresses has less than seven dots, but more than five dots?(A)(B)(C)(D)(E)Grade 1-2Year 20134. A lot of babies were born in the zoo last year: two baby lions, three baby dolphins and four baby eagles. How many legs do all these babies have altogether?(A) 20(B) 18(C) 16(D) 14(E) 125. Several students want to plant 20 tulips in the school garden. It takes ten minutes for them to plant five tulips. They started at 9:00 in the morning. At what time will they finish planting all 20 tulips?(A) At 9:10(B) At 9:20 (C) At 9:40(D) At 9:50(E) At 10:006. How many more bricks are there in the larger stack?(A) 4(B) 5(C) 6(D) 7Part B: Each correct answer is worth 4 points.(E) 107. Ann has. Barb gave Eve. Jim has. Bob has. Who is Barb?(A)(B)(C)8. There is a path with square tiles.(D)(E)How many tiles fit in the area inside?(A) 5(B) 6(E) 9Grade 1-2Year 20139. Cat and Mouse are moving to the right. When Mouse jumps 1 tile, Cat jumps 2 tiles at the same time.On which tile does Cat catch Mouse?(A) 1(B) 2(C) 3(D) 4(E) 510. I am a number. If you count by tens you will say my name. I am not ten. If you add me to 30, you will get anumber less than 60. Who am I?(A) 20(B) 30(C) 40(D) 50(E) 6011. There is a house on each corner of the streets. The housesare shown on the map. Two new houses will be built oneach street between the corner houses. How many houseswill there be in all?(A) 8(B) 12(C) 16(D) 20(E) Other answer12. Kasia has 3 brothers and 3 sisters. How many brothers and how many sisters does her brother Mike have?(A) 3 brothers and 3 sisters(B) 3 brothers and 4 sisters(C) 2 brothers and 3 sisters(D) 3 brothers and 2 sisters(E) 2 brothers and 4 sistersPart C: Each correct answer is worth 5 points.13. Ania makes a large cube from 27 small white cubes. She paints all the faces of the large cube. Then Ania removes four small cubes from four of the corners, as shown. While the paint is still wet, she stamps each of the new faces onto a piece of paper. How many of the following stamps can Ania make?(A) 1(B) 2(C) 3(D) 4(E) 514. Ann has a lot of these pieces:She tries to put them in the square, as many as possible. How many cells shall be left empty?(A) 0(B) 1(C) 2(D) 3(E) 4Grade 1-215. In a game it is possible to make the following exchanges:Year 2013Adam has 6 pears. How many strawberries will Adam have, when he trades all his pears for juststrawberries?(A) 12(B) 36(C) 1816. Sophie makes a row of 10 houses with matchsticks. In the picture you can see the beginning of the row. How many matchsticks does Sophie need altogether?(A) 50(B) 51(C) 55(D) 60(E) 6217. A square box is filled with two layers of identical square pieces of chocolate. Kirill has eaten all 20 pieces in the upper layer, which are along the walls of the box. How many pieces of chocolate are left in the box?(A) 16(B) 30(C) 50(D) 52(E) 7018. In a park there are babies in four-wheel strollers and children on two-wheel bikes. Paula counted wheels and the total was 12. When she added the number of strollers to the number of bikes, the total was 4. How many two-wheel bikes are there in the park?(A) 1(B) 2(C) 3(D) 4(E) Other numberGrade 3-4Year 2013International Contest-Game MATH KANGAROOPart A: Each correct answer is worth 3 points. 1. In which figure is the number of black kangaroos bigger than the number of white kangaroos?(A)(B)(C)(D)(E)2. Aline writes a correct calculation. Then she covers two digits which are the same with a sticker:Which digit is under the stickers?(A)(B)(C)(D)(E)3. Monica arrived in the Kangaroo Camp on July 25th in the morning and left the camp on August 3rd inthe afternoon. How many nights did she sleep in the camp?(A) 7(B) 9(C) 10(D) 30(E) 84. How many triangles of all sizes can be seen in the picture below?(A) 9(B) 10(C) 11(D) 13(E) 125. In London 2012, the USA won the most medals: 46 gold, 29 silver and 29 bronze. China was secondwith 38 gold, 27 silver and 23 bronze. How many more medals did the USA win compared to China?(A) 6(B) 14(C) 16(D) 24Grade 3-4Year 20136. There are three families in my neighbourhood with three children each; two of the families havetwins. All twins are boys. At most how many girls are in these families?(A) 2(B) 3(C) 4(D) 5(E) 67. Vero's mother prepares sandwiches with two slices of bread each. A package of bread has 24 slices.How many sandwiches can she prepare from two and a half packages of bread?(A) 24(B) 30(C) 48(D) 34(E) 268. About the number 325, five boys said:Andrei: "This is a 3-digit number"Boris: "All digits are distinct"Vick: "The sum of the digits is 10"Greg: "The units digit is 5"Danny: "All digits are odd"Which of the boys was wrong?(A) Andrei(B) Boris(C) Vick(D) Greg(E) DannyPart B: Each correct answer is worth 4 points. 9. The rectangular mirror was broken.Which of the following pieces is the missing part of the broken mirror?(A)(B)(C)(D)(E)10. When Pinocchio lies, his nose gets 6 cm longer. When he tells the truth, his nose gets 2 cm shorter. When his nose was 9 cm long, he told three lies and made two true statements. How long was Pinocchio's nose afterwards?(A) 14 cm(B) 15 cm(C) 19 cm(D) 23 cm(E) 31 cmGrade 3-4Year 201311. John is 33 years old. His three sons are 5, 6 and 10 years old. In how many years will the three sons together be as old as their father?(A) 4(B) 6(C) 8(D) 10(E) 1212. On the map, white lines represent streets. There are pictograms on some intersections (for example, trafic light, basket, tram). Ann started walking at the beginning of the middle vertical street in the direction of the arrow. At every intersection of streets she turned either to the right or to the left. First she turned right, then left, then again left, then right, then left, and finally again left. Which of the landmarks did Ann approach in the end?(A)(B)(E)13. Schoolmates Andy, Betty, Cathie and Dannie were born in the same year. Their birthdays were on February 20th, April 12th, May 12th and May 25th, not necessarily in this order. Betty and Andy were born in the same month. Andy and Cathie were born in the same day of different months. Who of these schoolmates is the oldest?(A) Andy(B) Betty(C) Cathie (D) Dannie (E) impossible to determine14. In the Adventure Park, 30 children took part in two of the adventures. 15 of them participated in the "moving bridge" contest, and 20 of them went down the zip-wire. How many of the children took part in both adventures?(A) 25(B) 15(C) 30(D) 10(E) 515. Which of the five pieces in the answers fits with the piece in the separate picture, so that together they form a rectangle?(A)(B)(C)(D)(E)16. Children in the school club had to arrange fitness balls according to their size from the biggest to the smallest one. Rebecca was comparing them and said: the red ball is smaller than the blue one, the yellow one is bigger than the green one, and the green one is bigger than the blue one. What is the correct order of the fitness balls?(A) green, yellow, blue, red (D) yellow, green, blue, red(B) red, blue, yellow, green (E) blue, yellow, green, red(C) yellow, green, red, blueGrade 3-4Year 2013Part C: Each correct answer is worth 5 points.17. In the shown triangle, first we join the midpoints of all the three sides. This way, we form a smaller triangle. We repeat this one more time with the smaller triangle, forming a new even smaller triangle, which we colour in red. How many triangles of the size of the red triangle are needed to cover completely the original triangle, without overlapping?Note: Midpoint of a side is the point that divides the side in two parts of the same length.(A) 5(B) 8(C) 10(D) 16(E) 3218. There are oranges, apricots and peaches in a big basket. How many fruits are there in the basket if the peaches and the apricots together are 18, the oranges and the apricots together are 28 and 30 fruits are not apricots?(A) 46(B) 20(C) 40(D) 38(E) 2919. In December Tom-the-cat slept for exactly 3 weeks. Which calculations should we do in order to find how many minutes he stayed awake during this month?(A) (31 – 7) × 3 × 24 × 60(B) (31 – 7 × 3) × 24 × 60(C) (30 – 7 × 3) × 24 × 60(D) (31 – 7 ) × 24 × 60(E) (31 – 7 × 3) × 24 × 60 × 6020. Basil has several domino tiles, as shown in the figure. He wants to arrange them in a line according to the well-known "domino rule": in any two tiles that are next to each other, the squares that touch must have the same number of points. What is the largest number of tiles he can arrange in this way?(A) 3(B) 4(C) 521. Cristi has to sell 10 glass bells that vary in price: 1 euro, 2 euro, 3 euro, 4 euro, 5 euro, 6 euro, 7 euro, 8 euro, 9 euro, 10 euro. In how many ways can Cristi divide all the glass bells in three packages so that all the packages have the same price?(A) 1(B) 2(C) 3(D) 4(E) Such a division is not possible.Grade 3-4Year 201322. Nancy bought 17 cones of ice-cream for her three children. Misha ate twice as many cones as Ana. Dan ate more ice-cream than Ana but less than Misha. How many cones of ice-cream did Dan eat?(A) 4(B) 5(C) 6(D) 7(E) 823. Peter bought a carpet 36 dm wide and 60 dm long. The figure shows part of this carpet. As seen, the carpet has a pattern of small squares containing either a sun or a moon. You can count that along the width there are nine squares. When the carpet is fully unrolled, how many moons will be seen?(A) 68(B) 67(C) 65(D) 63(E) 6024. Beatrice has a lot of pieces like the grey one in the picture. At least how many of these grey pieces will she need to makea grey square?(A) 3(B) 4(C) 6(D) 8(E) 16Grade 11-12International Contest-Game MATH KANGAROOPart A: Each correct answer is worth 3 points.Year 20131. Which of the following numbers is the largest?(A) 2013(B) 20+13(C) 2013(D) 2013(E) 20 × 132. Four circles of radius 1 are touching each other and a smaller circle as seen in the picture. What is the radius of the smaller circle?(A) 2 ?11 (B)23 (C)43 (D)47 (E)163. A three-dimensional object bounded only by polygons is called a polyhedron. What is the smallestnumber of polygons that can bind a polyhedron, if we know that one of the polygons has 12 sides?(A) 12(B) 13(E) 244. The cube root of 333 is equal to(A) 33(B) 333 ?1(C) 323(D) 332(E) ( 3)35. The year 2013 has the property that its number is made up of the consecutive digits 0, 1, 2 and 3.How many years have passed since the last time a year was made up of four consecutive digits?(A) 467(B) 527(C) 581(D) 693(E) 9906. Let f be a linear function for which f(2013) – f(2001) = 100. What is f(2031) – f(2013)?(A) 75(B) 100(C) 120(D) 150(E) 1807. Given that 2 < x < 3, how many of the following statements are true?4 < x2 < 94 < 2x < 96 < 3x < 9 0 < x2 ? 2x < 3(A) 0(B) 1(C) 2(D) 3(E) 48. Six superheroes capture 20 villains. The first superhero captures one villain, the second capturestwo villains and the third captures three villains. The fourth superhero captures more villains thanany of the other five. What is the smallest number of villains the fourth superhero must havecaptured?(A) 7(B) 6(C) 5(D) 4(E) 3Grade 11-12Year 20139. In the cube to the right you see a solid, non-transparent pyramid ABCDS with base ABCD, whose vertex S lies exactly in the middle of an edge of the cube. You look at this pyramid from above, from below, from behind, from ahead, from the right and from the left. Which view does not arise?(A)(B)(C)(D)(E)10.Whena certainsolid substancemelts,itsvolume increasesby1 12.By how much doesitsvolumedecrease when it solidifies again?(A)1 10(B)1 11(C)1 12(D)1 13(E)1 14Part B: Each correct answer is worth 4 points.11. The diagram shows two squares of equal side length placed so thatthey overlap. The squares have a common vertex and the sides make anangle of 45 degrees with each other, as shown. What is the area of theoverlap as a fraction of the area of one square?1 (A)21 (B)2(C) 1? 1 2(D) 2 ?12 ?1 (E)212.How many positive integers n exist such that bothn 3and 3nare three-digit integers?(A) 12(B) 33(C) 34(D) 100(E) 30013. A circular carpet is placed on a floor of square tiles. All the tiles which have more than one point in common with the carpet are marked grey. Which of the following is an impossible outcome?(A)(B)(C)(D)(E)14. Consider the following statement about a function f on the set of integers: "For any even x, f(x) is even." What would be the negation of this proposition?(A) For any even x, f(x) is odd(B) For any odd x, f(x) is even(C) For any odd x, f(x) is odd(D) There exists an even number x such that f(x) is odd(E) There exists an odd number x such that f(x) is oddGrade 11-12Year 201315. How many pairs (x,y) of positive integers satisfy the equation x2 y3 = 612 ?(A) 6(B) 8(C) 10(D) 12(E) Another number.16. Given a function W (x) = (a ? x)(b ? x)2 , where a < b. Its graph is in one of the following figures. In which one?(A)(B)(C)(D)(E)17. Consider a rectangle, one of whose sides has a length of 5. The rectangle can be cut into a squareand a rectangle, one of which has the area 4. How many such rectangles exist?(A) 1(B) 2(C) 3(D) 4(E) 518. Assume that x2 ? y2 = 84 , where x and y are positive integers. How many values may theexpression x2 + y2 have?(A) 1(B) 2(C) 3(D) 5(E) 619. In the triangle ABC the points M and N on the side AB are such that AN = ACand BM = BC. Find ∠ACB if ∠MCN = 43°.(A) 86°(B) 89°(C) 90°(D) 92°(E) 94°20. A box contains 900 cards numbered from 100 to 999. Any two cards have different numbers.Fran?ois picks some cards and determines the sum of the digits on each of them. At least how manycards must he pick in order to be certain to have three cards with the same sum?(A) 51(B) 52(C) 53(D) 54(E) 55Part C: Each correct answer is worth 5 points.21. How many pairs (x,y) of integers with x ≤ y exist such that their product equals 5 times their sum?(A) 4(B) 5(C) 6(D) 7(E) 822. Let f (x), x ∈ R be the function defined by the following properties: f is periodic with period 5 andf (x) = x2 when x ∈[?2,3) . What is f(2013) ?(A) 0(B) 1(C) 2(D) 4(E) 923. We have many white cubes and many black cubes, all of the same size. We want to build a rectangular prism composed by exactly 2013 of these cubes so that they are placed alternating a white cube and a black cube in all directions. If we start putting a black cube in one of the eight corners of the prism, how many black squares will we see on the exterior surface of the solid?(A) 887(B) 888(C) 890(E) It depends on the dimensions of the prism(D) 892Grade 11-12Year 201324. How many solutions (x,y), where x and y are real numbers, does the equation x2 + y2 = x + yhave? (A) 1(B) 5(C) 8(D) 9(E) Infinitely many.25. There are 2013 points marked inside a square. Some of them are connected to the vertices of thesquare and with each other so that the square is divided into non-overlapping triangles. All markedpoints are vertices of these triangles. How many triangles are formed this way?(A) 2013(B) 2015(C) 4026(D) 4028(E) impossible to determine26. There are some straight lines drawn on the plane. Line a intersects exactly three other lines and lineb intersects exactly four other lines. Linec intersects exactly n other lines, with n ≠ 3, 4 .Determine the number of lines drawn on the plane.(A) 4(B) 5(C) 6(D) 7(E) Another number.27. The sum of the first n positive integers is a three-digit number in which all of the digits are thesame. What is the sum of the digits of n?(A) 6(B) 9(C) 12(D) 15(E) 1828. On the island of Knights and Knaves there live only two types of people: Knights (who always speak the truth) and Knaves (who always lie). I met two men who lived there and asked the taller man if they were both Knights. He replied, but I could not figure out what they were, so I asked the shorter man if the taller was a Knight. He replied, and after that I knew which type they were. Were the men Knights or Knaves?(A) They were both Knights.(B) They were both Knaves.(C) The taller was a Knight and the shorter was a Knave.(D) The taller was a Knave and the shorter was a Knight.(E) Not enough information is given.29. Julian has written an algorithm in order to create a sequence of numbers as a1 = 1,am+n = am + an + mn , where m and n are natural numbers. Find the value of a100.(A) 100(B) 1000(C) 2012(D) 4950(E) 505030. The roundabout shown in the picture is entered by 5 cars at the same time, eachone from a different direction. Each of the cars drives less than one round and notwo cars leave the roundabout in the same direction. How many differentcombinations are there for the cars leaving the roundabout?(A) 24(B) 44(C) 60(D) 81(E) 120Year 2013Grade 1 and 2 DBACCB DEDABE DACBDBGrade 3 and 4 DDBBCDBE BDBADEBD DDBCEBBBGrade 5 and 6 ECCBEBBECD CCDBADDACD ADBABDBBDBGrade 7 and 8 DBACEECEAC DEBCBAABBC AEDCCABDBCGrade 9 and 10 DBCCBAECBC DBDADDBCEB DCCEEDCCBBGrade 11 and 12 CABDCDEBED DAEDEADBEC ADCED*CBDEB*Answer E was also accepted as correct for Q25 Answers。

加拿大国际袋鼠数学竞赛试题 -2008年

International Kangaroo Mathematics Contest 2008Ecolier Level: Class (3 & 4)Max Time: 2 Hours3-point problems1)We eat 3 meals a day. How many meals do we eat in a week?A) 7 B) 212)An adult ticket to the ZOO costs 4 rupees, the ticket for a child is 1 rupee cheaper. How many rupees must a father pay to enter the ZOO with his two children?A) 6 B) 10 3)We make a sequence of figures with tiles. The first four figures have 1, 4, 7 and 10 tiles, respectively.How many tiles will the fifth figure have? A) 13 B) 144)Ayesha has 37 CDs. Her friend Aniqa said: “If you give me 10 of your CDs, we will both have the same number of CDs.” How many CDs does Aniqa have?A) 17 B) 27 5)How many stars are inside the figure?A) 95 B) 100Rabia has drawn a point on a piece of paper. She now draws four straight lines that pass through this point. Into how many sections do these lines divide the paper?A) 4 B) 87)In six and one half hours it will be four hours after midnight. What time is it now?A) 21:30 B) 10:308)The storm made a hole in the front side of the roof. There were 10 roof tiles in each of 7 rows. How many tiles are left on the front side of the roof?A) 57 B) 599)Ejaz is making figures with two triangular cards shown. Which figure he cannot get?A) B)Ahmad multiplies by 3, Nasir adds 2, and Tahir subtracts 1. In what order can they do this to convert 3 into 14?A) Ahmad, Nasir, Tahir B) Nasir, Ahmad, Tahir11)Usman is taller than Noman and shorter than Salman. Who is the tallest?A) Usman B) Salman12)Abida made the figure on the right out of five cubes. Which ofthe following figures (when seen from any direction) can shenot get from the figure on the right side if she is allowed tomove exactly one cube?A) B)13)Which of the following figures is shown most often in the above sequence?B) All of them are shown equally often14)In a hotel, how many two-bed rooms should be added to 5 three-bed rooms to host 21 guests?A) 3 B) 615)There are three songs on a CD. The first song is 6 minutes and 25 seconds long, the second song is 12 minutes and 25 seconds long, and the third song is 10 minutes and 13 seconds long. How long are all the three songs together?A) 29 minutes 3 seconds B) 31 minutes 13 seconds16)We have a large number of blocks of 1 x 2 x 4 cm. We will try to put as many of these blocks as possible in a box of 4 x 4 x 4 cm so that we can close the box with a lid. How many blocks fit in?A) 8 B) 1017)Shaheen shoots two arrows at the target. In the drawing we see that her score is 5. If both arrows hit the target, how many different scores can she obtain?A) 6 B) 318)A garden in the shape of a square is divided into a pool (P) a flowerbed (F) a lawn (L) and a sandpit (S) (see the picture). The lawn and the flowerbed are in the shape of a square. The perimeter of the lawn is 20 m, the perimeter of the flowerbed is 12 m. What is the perimeter of the pool?A) 12 m B) 16 m19)Zahid has as many brothers as sisters. His sister Zahida has twice as many brothers as she has sisters. How many children are there in this family?A) 3 B) 7 20)How many two-digit numbers are there in which the digit on the right is larger than the digit on the left?A) 26 B) 36_______________________________GOOD LUCK !。

加拿大国家中小学数学竞赛( kangaroo math 袋鼠竞赛)2018年三四年级(含答案)

I N T E R N A T I O N A L C O N T E S T-G A M EM A T H K A N G A R O OC A N AD A,2018I N S T R U C T I O N SG R A D E3-41.You have 60 minutes to solve 24 multiple choice problems. For each problem,circle only one of the proposed five choices. If you circle more than one choice, your response will be marked as wrong.2.Record your answers in the response form. Remember that this is the only sheetthat is marked, so make sure you have all your answers transferred to the response form before giving it back to the contest supervisor.3.The problems are arranged in three groups. A correct answer of the first 8problems is worth 3 points. A correct answer of the problems 9-16 is worth 4 points. A correct answer of the problems 17-24 is worth 5 points. For each incorrect answer, one point is deducted from your score. Each unanswered question is worth 0 points. To avoid negative scores, you start from 24 points. The maximum score possible is 120.4.The use of external material or aid of any kind is not permitted.5.The figures are not drawn to scale. They should be used only for illustrationpurposes.6.Remember, you have about 2 to 3 minutes for each problem; hence, if a problemappears to be too difficult, save it for later and move on to another problem.7.At the end of the allotted time, please give the response form to the contestsupervisor.8.Do not forget to pick up your Certificate of Participation on your way out!Good luck!Canadian Math Kangaroo Contest teamCanadian Math Kangaroo Contest Part A: Each correct answer is worth 3 points1.Lea has 10 rubber stamps. Each stamp has one of the digits:0, 1, 2, 3, 4, 5, 6, 7, 8, 9.She prints the date of St. Patrick’s Day 2018:How many different stamps does she use?(A) 5(B) 6 (C) 7 (D) 9 (E) 102.The picture shows three flying arrows and nine fixedballoons. When an arrow hits a balloon, it bursts,and the arrow flies further in the same direction.How many balloons will be hit by the arrows?(A) 2 (B) 3 (C) 4(D) 5 (E) 63.Susan is six years old. Her sister is one year younger, and her brother is one yearolder. What is the sum of the ages of the three siblings?(A) 10 (B) 15 (C) 18 (D) 21 (E) 304.Here is a picture of Sophie the ladybug. She turns around. Which picture ofthe ladybugs below is not Sophie?(A)(B)(C)(D)(E)5.Lucy folds a sheet of paper in half. Then she cuts a piece out of it. What willshe see when she unfolds the paper?(A) (B) (C) (D)(E)1 70320186. A table is set for 8 people.How many settings have the fork to the left of the plate and the knife to the right of the plate?(A) 5(B) 4 (C) 6 (D) 2 (E) 3 7.Emily added two 2-digit numbers correctly on paper. Then she painted out two cells,as shown below.What is the sum of two digits in the painted cells?(A) 5(B) 7 (C) 8 (D) 9 (E) 13 8.First, Diana scores 12 points in total with three arrows. On her second turn shescores 15 points.How many points does she score on her third turn?(A) 18 (B) 19 (C) 20 (D) 21 (E) 22 Part B: Each correct answer is worth 4 points9.How many different numbers greater than 12 and smaller than 58 with distinct digitscan we make by using any two of the digits 0, 1, 2, 5, and 8?(A) 3(B) 5(C) 7 (D) 8 (E) 912 points15 points ? points10.Roberto makes designs using tiles like this .How many of the following five designs can he make?(A) 1 (B) 2 (C) 3 (D) 4 (E) 511.Each of these five figures ,, , , , appears exactly once in everycolumn and every row of the given table.Which figure must we put in the cell with the question mark?(A) (B) (C) (D) (E)12.Toby glues 10 cubes together to make the structure shown.He paints the whole structure, even the bottom.How many cubes are painted on exactly four of their faces?(A) 6 (B) 7 (C) 8 (D) 9 (E) 1013.The opposite faces of a cube are identical, being dark, bright or patterned.Which picture below is the unfolded net of this cube?(A)14.Tom cuts two types of pieces out of grid paper.What is the smallest number of pieces identical to the ones shown that Tom needs to build the boat in the picture?(A) 5 (B) 6 (C) 7 (D) 8 (E) 915.The rooms in Kanga's house are numbered. Baby Roo entersthe main door, passes through some rooms and leaves thehouse. The numbers of the rooms that he visits are alwaysincreasing. Through which door does he leave the house?(A) A (B) B (C) C (D) D (E) E16.Peta rabbit had 20 carrots. She ate two carrots every day. She ate the twelfth carroton Wednesday. On which day did she start eating the carrots?(A) Monday (B) Tuesday (C) Wednesday (D) Thursday (E) FridayPart C: Each correct answer is worth 5 points17.The belt shown in the drawing can be fastened in five ways.How much longer is the belt fastened in one hole than the belt fastened in all five holes?(A) 4 cm (B) 8 cm (C) 10 cm (D) 16 cm (E) 20 cm18.In an ancient writing the symbols represent thenumbers 1, 2, 3, 4, and 5. Nobody knows which symbol represents which number.We know thatWhich symbol represents the number 3?(A)(B) (C) (D) (E)19. A stained-glass tile is flipped along the black line. The figure shows the tile after thefirst flip.What will the stained-glass tile look like after the third flip (at the far right)?(A)(B)(C)(D)(E)20.The large rectangle is made up of squares of varied sizes. The three smallest squareseach have an area of 1, as shown.What is the area of the largest square?(A) 81 (B) 100 (C) 110 (D) 121 (E) 14421.Five ducklings walk behind the mother duck in a row from the oldest to the youngestlike this: Dina and Becca walk right one after the other, Mingo walks behind Lisa butin front of Becca, Becca walks directly in front of Pip. What is the name of theyoungest duckling?(A) Dina (B) Pip (C) Becca (D) Lisa (E) Mingo22.Four balls each weigh 10, 20, 30 and 40 grams. Which ball weighs 30 grams?(A) A (B) B (C) C (D) D (E) it could be A or B23.Lois wants to write the numbers from 1 to 7 in the grid shown.Two consecutive numbers cannot be written in two neighbouringcells. Neighbouring cells meet at the edge or at a corner. Whatnumbers can she write in the cell marked with a question mark?(A) all seven numbers (B) only odd numbers(C) only even numbers (D) only number 4(E) only the numbers 1 or 7 24.The distance from Anna's to Mary's house is 16 kilometers along the shown road.The distance from Mary's to Nick's house is 20 kilometers.The distance from Nick's to John's house is 19 kilometers.How far is Anna's house from John's?(A) 15 (B) 16(C) 18(D) 19 (E) 20 ?International Contest-GameMath Kangaroo Canada, 2018Answer KeyGrade 3-41 A B C D E 9 A B C D E17 A B C D E2 A B C D E10 A B C D E 18 A B C D E3 A B C D E 11 A B C D E 19 A B C D E4 A B C D E 12 A B C D E 20 A B C D E5 A B C D E 13 A B C D E21 A B C D E6 A B C D E 14 A B C D E 22 A B C D E7 A B C D E 15 A B C D E 23 A B C D E8 A B C D E 16 A B C D E24 A B C D E。

袋鼠数学试题

袋鼠数学试题袋鼠数学试题第一部分：选择题1. 已知等差数列的首项为14，公差为6，求第十项的值。

A) 54 B) 42 C) 68 D) 902. 某家庭每月固定收入为3000元，每月固定支出为2000元。

若家庭每月剩余收入为200元，家庭每月可用剩余收入购买书籍数量为：A) 10本 B) 20本 C) 30本 D) 40本3. 已知长方形的长为5cm，宽为3cm，求其面积。

A) 5cm² B) 8cm² C) 15cm² D) 18cm²4. 下列哪个图形是正方形？A) 长方形 B) 梯形 C) 圆形 D) 正方形5. 若甲数为8，乙数为-4，丙数为12，则甲数与乙数的和与丙数之和的差为：A) 0 B) 4 C) 8 D) 126. 若某数的1/6等于4，求这个数。

A) 24 B) 18 C) 22 D) 287. A、B 和 C 三人一起去买礼物，共花费500元。

C用自己的1/4的份额和A说，他受到了严重的财务困境，无法支付自己的份额，于是A和 B各多支付了25元。

现在 C只给了A和B各100元，请问礼物的总价格为多少元？A) 750 B) 600 C) 400 D) 3508. 若一周7天中，星期日这天是第几天？A) 第2天 B) 第6天 C) 第7天 D) 第1天9. 若一个圆的半径为4cm，求其周长。

A) 16cm B) 8πcm C) 4πcm D) 8cm10. 30除以一个数得到3，求这个数。

A) 1 B) 2 C) 3 D) 10第二部分：填空题1. 一年有____个星期。

2. 平行线上的对应角度相等，这是____定理。

3. 同底数相乘，底数不变，指数____.4. 值为负数的根不存在，是因为____.5. 一个正方形的面积是4cm²，其边长是____cm.6. 一个数减去它的5倍等于____.7. 余角是____角与给定角度的差.8. 若两个角的和为90°，则这两个角互为____角.9. 圆心角等于____角.10. √2是一个____数.第三部分：解答题1. 一个分数的分母是6，如果分子减去2是分母的2倍，求这个分数是多少？2. 某数减去2的四次方等于20，求这个数。

2016年袋鼠数学竞赛-一年级

(A)
(B)
(C)
(D)
(E)
Question 14 Brian and William stand in a queue. Brian knows that there are 7 people in front of him. William knows that there are in total 11 people in the queue. If Brian is right in front of William, how many people are in the queue behind William?
Singapore Math Kangaroo Contest 2017
Primary 1 Contest Paper
Name: School:
INSTRUCTIONS: 1. Please DO NOT OPEN the contest booklet until the Proctor has given permission to start. 2. TIME : 1 hour and 30 minutes 3. There are 30 questions in this paper. 3 points, 4 points and 5 points will be awarded for each
(A) Adam
(B) Basil
(C) Charlie
(D) David
(E) Edgar
Question 2 In the picture below, there are 5-pointed, 6-pointed and 7-pointed stars. How many 5-pointed stars are there?

加拿大国际袋鼠数学竞赛试题 -2011年

3point problemsPROBLEM 01Basil wants to paint the word KANGAROO. He paints one letter each day. He starts on Wednesday.On what day will he paint the last letter?(A) Monday(B) Tuesday(C) Wednesday(D) Thursday(E) FridayPROBLEM 02A caveman wants to balance the two set of stones shown in the picture. Which extra stone should he put on the right-hand side to make both sides equally heavy?(B)(D) (E)PROBLEM 03A toy kangaroo is on one square of a board, as shown in the picture.A child moves the toy from one square to a neighbouring square. He uses the following order: first to the right, then upwards, then to the left, then downwards, and then to the right. Which of the following pictures shows where the toy will be at the end?(C)(D)PROBLEM 04Simon got up one hour and a half ago. In three hours and a half, he will take the train to grandmother's. How long before the train departure did he get up?(A) 2 hours (B) 3 and a halfhours(C) 4 hours (D) 4 and a halfhours(E) 5 hoursMaria described one of the five figures below in the following way. ``It is not a square. It is grey. It is(A) A(B) B(C) C(D) D(E) E PROBLEM 06Lenka paid 1 euro and 50 cents for three scoops of ice-cream. Miso paid 2 euros and 40 cents for two cakes. How much did Igor pay for one scoop of ice-cream and one cake?(A) 1 euro 70cents(B) 1 euro 90cents(C) 2 euro 20cents(D) 2 euro 70cents(E) 3 euro 90cents PROBLEM 07A tower clock strikes on the hour (that is, at 8:00, 9:00, 10:00 and so on) as many times as the hour. The clock also strikes once when the time is half past an hour (that is, at 8:30, 9:30, 10:30 and so on). How many times did the clock strike from 7:55 to 10:45?(A) 6(B) 18(C) 27(D) 30(E) 33 PROBLEM 08Which figure has the largest area?(A) (B) (C) (D) (E)4point problemsPROBLEM 09The poulterer has boxes of 6 eggs and boxes of 12 eggs. What is the smallest number of boxes he needs in order to store 66 eggs?(A) 5(B) 6(C) 9(D) 11(E) 13In a school class all pupils have at least one pet and at most two pets. The pupils have recorded howmany pupils are there in this class?(A) 11(B) 12(C) 13(D) 14(E) 17 PROBLEM 11There are 13 coins in John's pocket. Each coin is either 5 or 10 cents. Which of the following cannot be the total value of John's coins?(A) 80 cents(B) 60 cents(C) 70 cents(D) 115 cents(E) 125 cents PROBLEM 12The sheet shown in the picture is folded along the thick line.(A) A(B) B(C) C(D) D(E) E PROBLEM 13Ann, Bob, Cleo, Dido, Eef, and Fer each roll a die. They all get different numbers.The number Ann rolled is twice Bob's number.The number Ann rolled is three times Cleo's.The number Dido rolled is four times Eef's.What number did Fer roll?(A) 2(B) 3(C) 4(D) 5(E) 6 PROBLEM 14A quiz show has the following rules. Every participant has 10 points at the beginning and has to answer 10 questions. For a correct answer 1 point is added and for an incorrect answer 1 point is taken away. Mrs Smith had 14 points at the end of the quiz show. How many incorrect answers did she give?(A) 3(B) 4(C) 5(D) 6(E) 7The picture shows a magic maze.At each square of the maze there is a piece of cheese. Mouse Ron enters the maze and wants to leave with as many pieces of cheese as he can. He cannot step on any square twice. What is the largest number of pieces of cheese he can get?(A) 17(B) 33(C) 37(D) 41(E) 49 PROBLEM 16During a party each of two identical cakes was divided into four equal parts. Then each of these parts was divided into three equal slices. Each person at the party got a slice of cake and three slices were left over. How many people were at the party?(A) 24(B) 21(C) 18(D) 27(E) 135point problemsPROBLEM 17Four girlfriends Masha, Sasha, Dasha and Pasha sit on a bench as seen.First Masha exchanged places with Dasha.Then Dasha exchanged places with Pasha.At the end the girls sat on the bench in the following order from left to right, as shown in the picture: Masha, Sasha, Dasha, Pasha.(A) Masha, Sasha, Dasha, Pasha (B) Masha, Dasha,Pasha, Sasha(C) Dasha, Sasha,Pasha, Masha(D)Sasha, Masha,Dasha, Pasha(E) Pasha, Masha,Sasha, DashaThe digital watch in the picture shows two different digits.How many times a day does this watch show the same digit in all four positions?(A) 1 (B) 24 (C) 3 (D) 5(E) 12PROBLEM 19The picture shows an arrangement of four identical dice.On each die, the total number of pips on each pair of opposite faces is 7. What does the arrangement look like from behind? (A) (B) (C) (D) (E)PROBLEM 20You have the three cards shown in the picture.You can form different numbers with them, for example 989 or 986.Altogether, how many different 3-digit numbers can you form with these three cards? (A) 4(B) 6(C) 8(D) 9(E) 12The pieces cannot cover each other. Which of the following pieces cannot be used by Andra to make the pattern?PROBLEM 22How many cubes were used to build the castle?(A) 56(B) 60(C) 64(D) 68(E) 72 PROBLEM 23He now writes each of the numbers 1, remaining circles so that the sum of the numbers along each side of the square is equal to 13. What will be the sum of the numbers in the shaded circles?(A) 12(B) 13(C) 14(D) 15(E) 16PROBLEM 24Sylvia drew three shapes made from hexagons, as shown in the picture.She continues with this pattern. How many hexagons will the fifth figure contain?(A) 37(B) 49(C) 57(D) 61(E) 64Math Kangaroo2011March17,2011Levels1and2Kangourou Sans Fronti`e resMathematics Promotion Society Math Kangaroo in USAMath Kangaroo2011in USAInternational Competition in MathematicsThursday,March17,2011Levels1and2This test consists of24questions on4pages.You have75minutes to complete it.Calculators are not allowed!Please enter your answers on the answer form provided.Please put your name and ID number on the line below.3Point Problems1.Consecutive positive numbers were placed in the cells of the table below.What number is missing from the middle cell?12?45A)0B)1C)3D)62.6+2=A)5B)6C)7D)83.Sharon had10dolls.She gave Betty one of her dolls.How many dolls does Sharon have now?A)6B)7C)8D)94.There are2boys and2dogs and nobody else on the playground.How many legsare there on this playground?A)12B)10C)8D)45.Which month sometimes has only29days?A)January B)February C)March D)April6.7students and a teacher are ready for a snack.There are7glasses ofmilk,8candy bars and1cup of coﬀee ready for them.Each student willhave the same snack.How many candy bars will the teacher get with hiscoﬀee?A)0B)1C)2D)3c Math Kangaroo in USA,NFP Math Kangaroo2011March17,2011Levels1and27.What is the sum of the digits in the number2011?A)202B)31C)4D)138.Katie’s doll is wearing a dress,has two braids and is holding oneﬂower in her hand.Which picture shows Katie’s doll?4Point Problems9.At the end of the skiing season,there were12pairs of ski boots left at the store.How many ski boots counted one-by-one were left at the store?A)6B)12C)24D)410.The picture below shows a puzzle with one piece miss-ing.Which of the pieces below needs to be added to thepuzzle in order for it to make a picture of a cat?A)B)C)D)11.Today is3/12/2011.No item can be sold after the date shown below it.Which of the items cannot be sold?A)9/15/2011B)3/4/2012C)7/11/2011D)2/25/201112.In36years,Mark’s grandmother will celebrate her100th birthday.How old is Mark’s grand-mother now?A)74B)64C)66D)3613.Anne has several dogs and4cats.The number of her cats’ears is equal to the number of her dogs’paws.How many dogs does Anne have?A)8B)2C)4D)6 c Math Kangaroo in USA,NFP Math Kangaroo2011March17,2011Levels1and2 14.Toﬁnd her toy,Marie needs to follow the path which is marked by the following signs in this order:,,,,,,,,.Which toy belongs to Marie?5Point Problems15.The picture below shows part of a train schedule.Right now,it’s8:45.Mr.Smith will go from Chicago to Indianapolis on the next train.The trip will take2hours and45minutes.What time will Mr.Smith arrive in Indianapolis?CHICAGO–DeparturesINDIANAPOLIS6:558:309:1511:1512:50A)11:30B)12:00C)11:15D)12:1516.Katie bought three identical pencils,two identical pens and two identical erasers,and paid $11.60.Hannah bought one pencil,two pens and two erasers,and she paid$8.40.How much does one pencil cost?A)$1.20B)$1.50C)$1.60D)$3.2017.Natalie folded a piece of paper in half and cut out a shape,as shown in thepicture to the right.Which of the pictures below shows the piece of paper after itwas unfolded?A)B)C)D)18.Mr.and Mrs.Taylor have three daughters.The youngest is5years old.The middle daughter is4years younger than the oldest daughter and6years older than the youngest daughter.How old is the Taylors’oldest daughter?A)10B)11C)9D)15 c Math Kangaroo in USA,NFP Math Kangaroo 2011March 17,2011Levels 1and 219.The ﬂowers in the ﬂower shop were kept in three vases.There were 16ﬂowers in the ﬁrst vase,11ﬂowers in the second vase,and 17ﬂowers in the third vase.The owner decided to sell only bouquets of 5ﬂowers each.After selling some bouquets,she noticed that she did not have enough ﬂowers to make another bouquet.How many ﬂowers did she have left?A)1B)2C)3D)420.Simon has two identical aquariums.There are 26quarts of water in one,and 42quarts of water in the other.How many quarts of water does Simon need to pour from the second aquarium into the ﬁrst in order to have the same amount of water in both?A)6B)16C)10D)821.Fido the Dog,Philemon the Cat and 4monkeys together weigh 24lbs.Fido and one monkey together weigh 11lbs.Philemon and 2monkeys together weigh 1lb less than Fido and one monkey weigh together.Each of the monkeys weighs the same.How much does Philemon weigh?A)3lbs B)4lbs C)5lbs D)6lbs22.Anita,Clara,Michael and Daniel had an apple eating contest.The person who ate the most apples won.Daniel ate more apples than Clara,and Michael ate fewer apples than Anita.We also know that Daniel did not win.Who ate the most apples?A)Anita B)Clara C)Michael D)We cannot know.23.What number do we need to put in the ﬁrst square in order to get 100as the result after doing all the operations shownbelow?A)11B)9C)14D)1224.Paul and Jon were building using identical cube blocks.Paul made the building shown in Picture 1.Picture 2shows Paul’s building as seen from above.Picture 3shows Jon’s building as seen from above.(Note:The numbers in each square indicate how many blocks are placed one on top of another in that place.)Which of the answers shows Jon’sbuilding?Picture 1.1111123Picture 2.1112223Picture 3.A)B)C)D)c Math Kangaroo in USA,NFP Page 。

2016年袋鼠数学竞赛-Secondary-2

Singapore Math Kangaroo Contest 2016Rough WorkingSection A(Correct–3points|Unanswered–0points|Wrong–deduct1point)1.How many whole numbers are there between20.16and3.17?(A)15(B)16(C)17(D)18(E)192.Which of the following traﬃc signs has the largest number of lines of symmetry?(A)(B)(C)(D)(E)3.What is the sum of the two marked angles?(A)150◦(B)180◦(C)270◦(D)320◦(E)360◦4.Jenny had to add26to a certain number.Instead she subtracted26and obtained-14. What number should she have obtained?(A)28(B)32(C)36(D)38(E)425.Joanna turns a card over about its lower edge and then about its right-hand edge,as shown in theﬁgure.What does she see?(A)(B)(C)(D)(E)6.Kanga combines555groups of9stones into a single pile.She then splits the resulting pile into groups of5stones.How many groups does she get?(A)999(B)900(C)555(D)111(E)457.In my school,60%of the teachers get to school by bike,which is45teachers.Only12%of the teachers use their car to get to school.How many teachers use their car to get to school?(A)4(B)6(C)9(D)10(E)128.What is the shaded area?(A)50(B)80(C)100(D)120(E)1509.Two pieces of rope have lengths1m and2m.Alex cuts the pieces into several parts.All the parts have equal lengths.Which of the following could not be the total number of parts he obtains?(A)6(B)8(C)9(D)12(E)1510.Four towns P,Q,R and S are connected by roads,as shown.A race uses each road exactly once.The race starts at S andﬁnishes at Q.How many possible routes are there for the race?(A)10(B)8(C)6(D)4(E)2Section B(Correct–4points|Unanswered–0points|Wrong–deduct1point)11.The diagram shows four identical rectangles placed inside a square.The perimeter of each rectangle is16cm.What is the perimeter of the larger square?(A)16cm(B)20cm(C)24cm(D)28cm(E)32cm12.Petra has49blue beads and one red bead.How many beads must Petra remove so that 90%of her beads are blue?(A)4(B)10(C)29(D)39(E)4013.Which of the following fractions has a value closest to12?(A)2579(B)2759(C)2957(D)5279(E)579214.Ivor writes down the results of the quarter-ﬁnals,the semi-ﬁnals and theﬁnal of a knock-out tournament.The results are(not necessarily in this order):Bart beat Antony,Carl beat Damien,Glen beat Henry,Glen beat Carl,Carl beat Bart,Ed beat Fred and Glen beat Ed. Which pair played in theﬁnal?(A)Glen and Henry(B)Glen and Carl(C)Carl and Bart(D)Glen and Ed(E)Carl and Damien15.Anne has glued some cubes together,as shown.She rotates the solid to look at it from diﬀerent angles.Which of the following can she not see?(A)(B)(C)(D)(E)16.Tim,Tom and Jim are triplets(three brothers born on the same day).Their twin brothers John and James are3years younger.Which of the following numbers could be the sum of the ages of theﬁve brothers?(A)36(B)53(C)76(D)89(E)9217.A3cm wide rectangular strip of paper is grey on one side and white on the other.Maria folds the strip,as shown.The grey trapeziums are identical.What is the length of the original strip?(A)36cm(B)48cm(C)54cm(D)57cm(E)81cm18.Two kangaroos Jum and Per start to jump at the same time,from the same point,in the same direction.They make one jump per second.Each of Jum’s jumps is6m in length.Per’s ﬁrst jump is1m in length,the second is2m,the third is3m,and so on.After how many jumps does Per catch Jum?(A)10(B)11(C)12(D)13(E)1419.Seven standard dice are glued together to make the solid shown.The faces of the dice that are glued together have the same number of dots on them.How many dots are on the surface ofthe solid?(A)24(B)90(C)95(D)105(E)12620.There are20students in a class.They sit in pairs:exactly one third of the boys sit witha girl and exactly one half of the girls sit with a boy.How many boys are there in the class?(A)9(B)12(C)15(D)16(E)18Section C(Correct–5points|Unanswered–0points|Wrong–deduct1point)21.Inside a square of area36,there are shaded regions as shown in theﬁgure.The total shaded area is27.What is p+q+r+s?(A)4(B)6(C)8(D)9(E)1022.Theo’s watch is10minutes slow,but he believes that it is5minutes fast.Leo’s watch is 5minutes fast,but he believes that it is10minutes slow.At the same moment,each of them looks at his own watch.Theo thinks it is12:00.What time does Leo think it is?(A)11:30(B)11:45(C)12:00(D)12:30(E)12:4523.Twelve girls met in a coﬀee shop.On average,they ate1.5cupcakes.None of them ate more than two cupcakes and two of them had only mineral water.How many girls ate two cupcakes?(A)2(B)5(C)6(D)7(E)824.Little Red Riding Hood is delivering waﬄes to three grannies.She starts with a basket full of waﬄes.Just before she enters each of the grannies’houses,the Big Bad Wolf eats half of the waﬄes in her basket.When she leaves the third granny’s house,she has no waﬄes left.She delivers the same number of waﬄes to each granny.Which of the following numbers deﬁnitely divides the number of waﬄes she started with?(A)4(B)5(C)6(D)7(E)925.The cube below is divided into64small cubes.Exactly one of the cubes is grey.On the ﬁrst day,the grey cube changes all its neighbouring cubes to grey(two cubes are neighbours if they have a common face).On the second day,all the grey cubes do the same thing.How many grey cubes are there at the end of the second day?(A)11(B)13(C)15(D)16(E)1726.Several diﬀerent positive integers are written on a blackboard.The product of the smallest two of them is16.The product of the largest two is225.What is the sum of all the integers?(A)38(B)42(C)44(D)58(E)24327.The diagram shows a pentagon.Sepideh drawsﬁve circles with centres A,B,C,D,E such that the two circles on each side of the pentagon touch.The lengths of the sides of the pentagon are given.Which point is the centre of the largest circle that she draws?(A)A(B)B(C)C(D)D(E)E28.Katie writes a diﬀerent positive integer on each of the fourteen cubes in the pyramid. The sum of the nine integers written on the bottom cubes is equal to50.The integer written on each other cube is equal to the sum of the integers written on the four cubes underneath it. What is the greatest possible integer that can be written on the top cube?(A)80(B)98(C)104(D)110(E)11829.A train hasﬁve carriages,each containing at least one passenger.Two passengers are said to be”neighbours”if either they are in the same carriage or they are in two adjacent carriages. Each passenger has either exactlyﬁve or exactly ten”neighbours”.How many passengers are there in the train?(A)13(B)15(C)17(D)20(E)There is more than one possibility.30.A3×3×3cube is built from15black cubes and12white cubes.Five faces of the larger cube are shown.Which of the following is the sixth face of the large cube?(A)(B)(C)(D)(E)END OF PAPER。

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

Canadian Math Kangaroo ContestPart A: Each correct answer is worth 3 points1.Which letter on the board is not in the word "KOALA"?(A) R (B) L (C) K (D) N (E) O2.In a cave, there were only two seahorses, one starfish and three turtles. Later, five seahorses, three starfishand four turtles joined them. How many sea animals gathered in the cave?(A) 6 (B) 9 (C) 12 (D) 15 (E) 183.Matt had to deliver flyers about recycling to all houses numbered from 25 to 57. How many houses got theflyers?(A) 31 (B) 32 (C) 33 (D) 34 (E) 354.Kanga is 1 year and 3 months old now. In how many months will Kanga be 2 years old?(A) 3 (B) 5 (C) 7 (D) 8 (E) 95.(A) 24 (B) 28 (C) 36 (D) 56 (E) 806. A thread of length 10 cm is folded into equal parts as shown in the figure.The thread is cut at the two marked places. What are the lengths of the three parts?(A) 2 cm, 3 cm, 5 cm (B) 2 cm, 2 cm, 6 cm (C) 1 cm, 4 cm, 5 cm(D) 1 cm, 3 cm, 6 cm (E) 3 cm, 3 cm, 4 cm7.Which of the following traffic signs has the largest number of lines of symmetry?(A) (B) (C) (D) (E)8.Kanga combines 555 groups of 9 stones into a single pile. She then splits the resulting pile into groups of 5stones. How many groups does she get?(A) 999 (B) 900 (C) 555 (D) 111 (E) 459.What is the shaded area?(A) 50 (B) 80 (C) 100 (D) 120 (E) 15010.In a coordinate system four of the following points are the vertices of a square. Which point is not a vertexof this square?(A) (−1;3)(B) (0;−4)(C) (−2;−1)(D) (1;1)(E) (3;−2)Part B: Each correct answer is worth 4 points11.There are twelve rooms in a building and each room has two windows and one light. Last evening, eighteenwindows were lighted. In how many rooms was the light off?(A) 2 (B) 3 (C) 4 (D) 5 (E) 612.Which three of the five jigsaw pieces shown can be joined together to form a square?(A) 1, 3 and 5 (B) 1, 2 and 5 (C) 1, 4 and 5 (D) 3, 4 and 5 (E) 2, 3 and 513.John has a board with 11 squares. He puts a coin in each of eight neighbouring squareswithout leaving any empty squares between the coins. What is the maximum numberof squares in which one can be sure that there is a coin?(A) 1 (B) 3 (C) 4 (D) 5 (E) 614.Which of the following figures cannot be formed by gluing these two identical squares of paper together?(A) (B) (C) (D) (E)15.Each letter in BENJAMIN represents one of the digits 1, 2, 3, 4, 5, 6 or 7. Different letters represent differentdigits. The number BENJAMIN is odd and divisible by 3. Which digit corresponds to N?(A) 1 (B) 2 (C) 3 (D) 5 (E) 716.Seven standard dice are glued together to make the solid shown. The faces of the dice thatare glued together have the same number of dots on them. How many dots are on the surfaceof the solid?(A) 24 (B) 90 (C) 95 (D) 105 (E) 12617.Jill is making a magic multiplication square using the numbers 1, 2, 4, 5, 10, 20, 25, 50 and 100. The productsof the numbers in each row, in each column and in the two diagonals should all be the same. In the figure you can see how she has started. Which number should Jill place in the cell with the question mark?(A) 2 (B) 4 (C) 5 (D) 10 (E) 2518.What is the smallest number of planes that are needed to enclose a bounded part in three-dimensional space?(A) 3 (B) 4 (C) 5 (D) 6 (E) 719.Each of ten points in the figure is marked with either 0 or 1 or 2. It is known thatthe sum of numbers in the vertices of any white triangle is divisible by 3, while thesum of numbers in the vertices of any black triangle is not divisible by 3. Three ofthe points are marked as shown in the figure. What numbers can be used to markthe central point?(A) Only 0. (B) Only 1. (C) Only 2. (D) Only 0 and 1. (E) Either 0 or 1 or 2.20.Betina draws five points AA,BB,CC,DD and EE on a circle as well as the tangent tothe circle at AA, such that all five angles marked with xx are equal. (Note thatthe drawing is not to scale.) How large is the angle ∠AABBDD ?(A) 66°(B) 70.5°(C) 72°(D) 75°(E) 77.5°Part C: Each correct answer is worth 5 points21.Which pattern can we make using all five cards given below?(A) (B) (C) (D) (E)22.The numbers 1, 5, 8, 9, 10, 12 and 15 are distributed into groups with one or more numbers. The sum of thenumbers in each group is the same. What is the largest number of groups?(A) 2 (B) 3 (C) 4 (D) 5 (E) 623.My dogs have 18 more legs than noses. How many dogs do I have?(A) 4 (B) 5 (C) 6 (D) 8 (E) 924.In the picture you see 5 ladybirds.Each one sits on its flower. Their places are defined as follows: the difference of the dots on their wings is the number of the leaves and the sum of the dots on their wings is the number of the petals. Which of the following flowers has no ladybird?(A) (B) (C) (D) (E)25.On each of six faces of a cube there is one of the following six symbols: ♣, ♦, ♥, ♠, ∎ and Ο. On each facethere is a different symbol. In the picture we can see this cube shown in two different positions.Which symbol is opposite the ∎?(A) Ο(B)♦(C) ♥(D) ♠(E) ♣26.What is the greatest number of shapes of the form that can be cut out from a5 × 5 square?(A) 2 (B) 4 (C) 5 (D) 6 (E) 727.Kirsten wrote numbers in 5 of the 10 circles as shown in the figure. She wants to writea number in each of the remaining 5 circles such that the sums of the 3 numbers alongeach side of the pentagon are equal. Which number will she have to write in the circlemarked by XX?(A) 7 (B) 8 (C) 11 (D) 13 (E) 1528. A 3×3×3 cube is built from 15 black cubes and 12 white cubes. Five faces of the larger cube are shown.Which of the following is the sixth face of the large cube?(A) (B) (C) (D) (E)29.Jakob wrote down four consecutive positive integers. He then calculated the four possible totals made bytaking three of the integers at a time. None of these totals was a prime. What is the smallest integer Jakob could have written?(A) 12 (B) 10 (C) 7 (D) 6 (E) 330.Four sportsmen and sportswomen - a skier, a speed skater, a hockey player and a snowboarder - had dinnerat a round table. The skier sat at Andrea's left hand. The speed skater sat opposite Ben. Eva and Filip sat next to each other. A woman sat at the hockey player`s left hand. Which sport did Eva do?(A) speed skating (B) skiing (C) ice hockey (D) snowboarding(E) It`s not possible to find out with the given information.International Contest-Game Math Kangaroo Canada, 2016Answer KeyParents Contest。

加拿大国际袋鼠数学竞赛试题 及答案-2016年 Parents Questions

加拿大国际袋鼠数学竞赛试题 及答案-2018年

加拿大国家中小学数学竞赛( kangaroo math 袋鼠竞赛)2017年五六年级(含答案)

2016年袋鼠数学竞赛-初二

2016年5-6年级袋鼠数学竞赛

美国袋鼠数学竞赛试题及答案

2016年袋鼠数学竞赛-四年级

2016年袋鼠数学竞赛-三年级

袋鼠数学历年试题

加拿大国际袋鼠数学竞赛试题-2013年

新加坡袋鼠数学竞赛5年级考卷中文版(2016)

2016年袋鼠数学竞赛-三年级

2016年袋鼠数学竞赛-高一

加拿大国际袋鼠数学竞赛试题-2013年

加拿大国际袋鼠数学竞赛试题 -2008年

加拿大国家中小学数学竞赛( kangaroo math 袋鼠竞赛)2018年三四年级(含答案)

袋鼠数学试题

2016年袋鼠数学竞赛-一年级

加拿大国际袋鼠数学竞赛试题 -2011年

2016年袋鼠数学竞赛-Secondary-2

加拿大国际袋鼠数学竞赛试题及答案-2016年 Parents Questions

加拿大国际袋鼠数学竞赛试题及答案-2018年