加拿大国际袋鼠数学竞赛试题-2013年

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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°。

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

加拿⼤国际袋⿏数学竞赛试题及答案-2016年ParentsQuestionsCanadian 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 5 stones. 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, eighteen windows 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 different digits. 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 face there 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。

袋鼠思维数学竞赛报名历年题目

选择题在袋鼠思维数学竞赛中，若一个等差数列的前n项和为S_n，且S_3 = 6，S_6 = 21，则S_9等于：A. 45B. 54（正确答案）C. 63D. 72竞赛题目：设f(x) = x3 - 3x2 + 2x，则f(f(x)) = 0的实数根个数为：A. 3B. 4C. 5（正确答案）D. 6袋鼠思维数学竞赛中，若一个直角三角形的两条直角边长度分别为a和b，且满足a2 + b2 = 100，c为斜边，则c的取值范围是：A. (0, 10)B. [10, +∞)C. (10, 10√2]（正确答案）D. [10√2, +∞)竞赛中，若一个圆的半径为r，内接于一个边长为a的正三角形中，则该圆的面积与正三角形面积之比为：A. π/3B. π/4C. π/(3√3)（正确答案）D. π/6在袋鼠思维数学竞赛的数列问题中，若数列{a_n}满足a_1 = 1，a_{n+1} = a_n + 2n，则a_10等于：A. 81B. 90C. 99D. 100（正确答案）竞赛题目：若一个长方体的长、宽、高分别为a、b、c，且满足a + b + c = 6，则长方体的体积V的最大值为：A. 8B. 27/8C. 27/4D. 27（正确答案）在袋鼠思维数学竞赛的几何问题中，若一个等腰三角形的底边长为2a，底角为θ，则三角形的面积S关于θ的表达式为：A. a2sin(θ)B. a2cos(θ)C. a2sin(2θ)/2（正确答案）D. a2cos(2θ)/2竞赛中，若一个函数的图像在x轴上方，且其导函数在x=0处取得极小值，则该函数在x=0处：A. 一定有拐点B. 一定有极值点C. 可能有拐点也可能有极值点（正确答案）D. 既无拐点也无极值点在袋鼠思维数学竞赛的组合数学问题中，从1到9的九个数字中任选三个不同的数字，组成一个没有重复数字的三位数，且这个三位数是3的倍数，这样的三位数共有多少个？A. 120B. 168（正确答案）C. 216D. 288。

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

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。

2013 -美国袋鼠数学一二年级竞赛练习题

SAMPLE QUESTION FOR 3 POINTSWhich digits are missing on the right?A) 3 and 5 B) 4 and 8 C) 2 and 0 D) 6 and 9 E) 7 and 1SAMPLE QUESTION FOR 4 POINTSGeorge has 2 cats of the same weight. What is the weight of one cat if George weighs 30 kilograms?A) 1 kilogram B) 2 kilograms C) 3 kilogramsD) 4 kilograms E) 5 kilogramsSAMPLE QUESTION FOR 5 POINTSIn a certain game it is possible to make the following exchanges:Adam has 6 pears. How many strawberries will Adam have after he trades all his pears for just strawberries?A) 12 B) 36 C) 18 D) 24 E) 6SAMPLE QUESTION FOR 3 POINTSWhich digits are missing on the right?A) 3 and 5 B) 4 and 8 C) 2 and 0 D) 6 and 9E) 7 and 1SAMPLE QUESTION FOR 4 POINTSGeorge has 2 cats of the same weight. What is the weight of one cat if George weighs 30 kilograms?A) 1 kilogram B) 2 kilograms C) 3 kilogramsD) 4 kilograms E) 5 kilogramsSAMPLE QUESTION FOR 5 POINTSIn a certain game it is possible to make the following exchanges:Adam has 6 pears. How many strawberries will Adam have after he trades all his pears for just strawberries?A) 12 B) 36 C) 18D) 24 E) 6SAMPLE QUESTION FOR 3 POINTSIn which figure is the number of black kangaroos larger than the number of white kangaroos?SAMPLE QUESTION FOR 4 POINTSEach time Pinocchio lies, his nose gets 6 cm longer. Each time he tells the truth, his nose gets 2 cm shorter. After 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 cmSAMPLE QUESTION FOR 5 POINTSJoining the midpoints of the sides of the triangle in the drawing we obtain a smaller triangle. We repeat this one more time with the smaller triangle. How many triangles of the same size as the smallest resulting triangle fit in the original drawing?A) 5 B) 8 C) 10 D) 16 E) 32SAMPLE QUESTION FOR 3 POINTSIn which figure is the number of black kangaroos larger than the number of white kangaroos?SAMPLE QUESTION FOR 4 POINTSEach time Pinocchio lies, his nose gets 6 cm longer. Each time he tells the truth, his nose gets 2 cm shorter. After 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 cmSAMPLE QUESTION FOR 5 POINTSJoining the midpoints of the sides of the triangle in the drawing we obtain a smaller triangle. We repeat this one more time with the smaller triangle. How many triangles of the same size as the smallest resulting triangle fit in the original drawing?A) 5 B) 8 C) 10 D) 16E) 32SAMPLE QUESTION FOR 3 POINTSNathalie wanted to build the same cube as Diana had (Figure 1). However, Nathalie ran out of small cubes and built only a part of the cube, as you can see in Figure 2. How many small cubes must be added to Figure 2 to form Figure 1?A) 5 B) 6 C) 7 D) 8 E) 9SAMPLE QUESTION FOR 4 POINTSMary shades various shapes on square sheets of paper, as shown.How many of these shapes have the same perimeter as the sheet of paper itself?A) 2 B) 3 C) 4 D) 5 E) 6SAMPLE QUESTION FOR 5 POINTSThere are four buttons in a row as shown below. Two of them show happy faces, and two of them show sad faces. If we press on a face, its expression turns to the opposite (e.g. a happy face turns into a sad face). In addition to this, the adjacent buttons also change their expressions to the opposite. What is the least number of times you need to press the buttons in order to get all happy faces?A) 2 B) 3 C) 4 D) 5 E) 6SAMPLE QUESTION FOR 3 POINTSNathalie wanted to build the same cube as Diana had (Figure 1). However, Nathalie ran out of small cubes and built only a part of the cube, as you can see in Figure 2. How many small cubes must be added to Figure 2 to form Figure 1?A) 5 B) 6 C) 7D) 8 E) 9SAMPLE QUESTION FOR 4 POINTSMary shades various shapes on square sheets of paper, as shown.How many of these shapes have the same perimeter as the sheet of paper itself?A) 2 B) 3 C) 4D) 5 E) 6SAMPLE QUESTION FOR 5 POINTSThere are four buttons in a row as shown below. Two of them show happy faces, and two of them show sad faces. If we press on a face, its expression turns to the opposite (e.g. a happy face turns into a sad face). In addition to this, the adjacent buttons also change their expressions to the opposite. What is the least number of times you need to press the buttons in order to get all happy faces?A) 2 B) 3C) 4 D) 5 E) 6SAMPLE QUESTION FOR 3 POINTSIn the picture, the big triangle is equilateral and has an area of 9. The lines are parallel to the sides and divide the sides into three equal parts. What is the area of the shaded part?A) 1 B) 4 C) 5 D) 6 E) 7SAMPLE QUESTION FOR 4 POINTSVasya wrote down several consecutive integers. Which of the following could not be the percentage of odd numbers among them?A) 40 B) 45 C) 48 D) 50 E) 60SAMPLE QUESTION FOR 5 POINTSThe diagram shows a shaded quadrilateral KLMN drawn on a grid. Each cell of the grid has sides of length 2 cm. What is the area of KLMN?A) 96 cm2B) 84 cm2C) 76 cm2D) 88 cm2E) 104 cm2SAMPLE QUESTION FOR 3 POINTSIn the picture, the big triangle is equilateral and has an area of 9. The lines are parallel to the sides and divide the sides into three equal parts. What is the area of the shaded part?A) 1 B) 4 C) 5 D) 6E) 7SAMPLE QUESTION FOR 4 POINTSVasya wrote down several consecutive integers. Which of the following could not be the percentage of odd numbers among them?A) 40 B) 45C) 48 D) 50 E) 60SAMPLE QUESTION FOR 5 POINTSThe diagram shows a shaded quadrilateral KLMN drawn on a grid. Each cell of the grid has sides of length 2 cm. What is the area of KLMN?A) 96 cm2B) 84 cm2C) 76 cm2D) 88 cm2E) 104 cm2SAMPLE QUESTION FOR 3 POINTSThe number 200013 – 2013 is not divisible byA) 2. B) 3. C) 5. D) 7. E) 11.SAMPLE QUESTION FOR 4 POINTSThe points P and Q are opposite vertices of a regular hexagon and the points R and S are the midpoints of opposite edges, as shown. The area of the hexagon is 60 cm2. What is the product of the lengths of PQ and RS?A) 40 cm2B) 50 cm2C) 60 cm2D) 80 cm2E) 100 cm2SAMPLE QUESTION FOR 5 POINTSHow many positive integers are multiples of 2013 and have exactly 2013 divisors (including 1 and the number itself)?A) 0 B) 1 C) 3 D) 6 E) other answerSAMPLE QUESTION FOR 3 POINTSThe number 200013 – 2013 is not divisible byA) 2. B) 3. C) 5. D) 7.E) 11.SAMPLE QUESTION FOR 4 POINTSThe points P and Q are opposite vertices of a regular hexagon and the points R and S are the midpoints of opposite edges, as shown. The area of the hexagon is 60 cm2. What is the product of the lengths of PQ and RS?A) 40 cm2B) 50 cm2C) 60 cm2D) 80 cm2E) 100 cm2SAMPLE QUESTION FOR 5 POINTSHow many positive integers are multiples of 2013 and have exactly 2013 divisors (including 1 and the number itself)?A) 0 B) 1 C) 3 D) 6E) other answerLEVELS 11 AND 12SAMPLE QUESTION FOR 3 POINTSWhich of the following numbers is the largest?A) 2013 B) 20+13C) 2013 D) 2013E) 20 ·13SAMPLE QUESTION FOR 4 POINTSRadu has identical plastic pieces in the shape of a regular pentagon. He glues them edge to edge to complete a circle, as shown in the picture. How many pieces are there in this circle?A) 8 B) 9 C) 10 D) 12 E) 15SAMPLE QUESTION FOR 5 POINTSHow 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) 8LEVELS 11 AND 12 ANSWERSSAMPLE QUESTION FOR 3 POINTSWhich of the following numbers is the largest?A) 2013 B) 20+13C) 2013 D) 2013E) 20 ·13SAMPLE QUESTION FOR 4 POINTSRadu has identical plastic pieces in the shape of a regular pentagon. He glues them edge to edge to complete a circle, as shown in the picture. How many pieces are there in this circle?A) 8 B) 9 C) 10D) 12 E) 15SAMPLE QUESTION FOR 5 POINTSHow many pairs (x, y) of integers with x < y exist such that their product equals 5 times their sum?A) 4B) 5 C) 6 D) 7 E) 8。

袋鼠数学 GRADE1-2(2014)

CANADIAN MATH KANGAROO CONTEST 2014 Grade 1 and 2 Questions and AnswersYear 2014Grade 1-2 2014Copyright © Canadian Math Kangaroo Contest. All rights reserved.Canadian Math Kangaroo ContestPROBLEMSPart A: Each correct answer is worth 3 points 1.A ladybug will sit on a flower that has five petals and three leaves. On which of the following flowers will the ladybug sit?(A) (B) (C) (D) (E)2.A square was made of 25 small squares, but some of these small squares were lost. How many small squares were lost?(A) 6 (B) 7 (C) 8(D) 10(E) 123.The kangaroo is inside how many circles?(A) 1(B) 2(C) 3(D) 4(E) 54.Seven sticks lie on top of each other. Stick number 2 is at the bottom. Stick number 6 is at the top. Which stick is in the middle?(A) 1 (B) 3 (C) 4(D) 5(E) 7Grade 1-22014Copyright © Canadian Math Kangaroo Contest. All rights reserved.5. Alan is five years old. His sister Bethany is seven years older than him. What is the sum of their ages?(A) 11 (B) 12 (C) 13 (D) 15 (E) 17 6.What numbers of dots are hidden behind the cat and the dog in the equations?(A) 8 and 2 (B) 9 and 2 (C) 9 and 3 (D) 8 and 3 (E) 7 and 4Part B: Each correct answer is worth 4 points7.The first two scales in the picture are balanced. How many ducks are needed on the right side of the third scale, to balance with the crocodile?(A)(B)(C)(D)(E)8.Which of the shapes below should be placed on top of the shapeto make a rectangle?(A) (B) (C)(D) (E)9. How many numbers between 10 and 31 (including 31) can be written using only the digits 1, 2 and 3? You can repeat digits. (A) 2 (B) 4 (C) 6 (D) 7 (E) 8==Grade 1-2 2014Copyright © Canadian Math Kangaroo Contest. All rights reserved.10. My rabbit eats only cabbage and carrots. Last week he ate either 10carrots or 2 heads of cabbage each day. If he ate a total of 6 heads of cabbage last week, how many carrots did he eat? (A) 20 (B) 30 (C) 34 (D) 40 (E) 5011. Mary has 13 flowers, five of which are roses. The rest are tulips. Six of theflowers are white, and the remaining flowers are red. At least how many tulips are red? (A) 1 (B) 2 (C) 3 (D) 4 (E) 512. Six little elephants, A, B, C, D, E, F, are lining up to buy tickets. F is after Aand before D and he is also between B and C; B is the first in the line; and E is the last in the line. Which elephant is F?(A) the 2nd (B) the 3rd(C) the 4th(D) the 5th(E) the 6thPart C: Each correct answer is worth 5 points13. A square was cut into four parts as shown in the picture.Which of the following shapes cannot be made with these 4 parts?(A) (B) (C) (D)(E)14. Place the digits 2, 3, 4, and 5 in the squares so that the sum is as large aspossible. What is this sum?(A) 68(B) 77(C) 86(D) 95(E) 971st23 41Grade 1-2 2014Copyright © Canadian Math Kangaroo Contest. All rights reserved.15. Fedya has 4 red cubes, 3 blue cubes, 2 green cubes, and 1 yellow cube. He isbuilding a tower (see the picture) in such a way that no two cubes touching each other have the same colour. What is the colour of the cube with the question mark?(A) red (B) blue (C) green (D) yellow (E) impossible to determine16. Gear A is about to make one complete turn in the direction shown in Figure 1.The piece “x ” moved to one of the positions a , b , c , d, e shown in Figure 2.To which position did “x ” move?(A) a (B) b (C) c(D) d(E) e17. How many triangles are there in the picture?(A) 15 (B) 17 (C) 19(D) 21(E) 2518. John wrote the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 on a whiteboard. Johnthen erased some of the numbers and added up the remaining ones. He got a sum of 24. At most how many numbers were left on the whiteboard? (A) 3 (B) 4 (C) 5 (D) 6(E) 7Grade 1-2 2014International Contest-GameMath Kangaroo Canada, 2014Answer 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 E14 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 E11 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 E Copyright © Canadian Math Kangaroo Contest. All rights reserved.。

袋鼠数学数学竞赛中文试题

袋鼠数学数学竞赛中文试题袋鼠数学数学竞赛中文试题Ⅰ.选择题（每题2分，共10分）1. 下列哪个数是一个素数？A. 25B. 31C. 42D. 502. A、B、C三个人分别携带了2本、3本、5本书，他们总共带了多少本书？A. 6B. 10C. 9D. 73. 一些苹果在3个篮子中平均分配，每个篮子得到10个苹果，若再将这些苹果平均分配到6个篮子中，则每个篮子得到多少个苹果？A. 5B. 10C. 15D. 204. 甲、乙、丙三个人分别花费400元、600元、800元购买了一些物品，他们所花费的总金额是多少元？A. 800B. 1200C. 1800D. 16005. 若9+4x=25，则x的值是多少？A. 4B. 3C. 5D. 2Ⅱ.填空题（每题3分，共15分）1. 一个整数减去两个负整数之和能是正整数吗？为什么？________________________________________________2. 一个多边形的内角和是2160°，这个多边形有多少个角？________________________________________________3. 甲、乙两个容器分别装有2升和3升的水，如何只用这两个容器倒水，可以得到1升的水？________________________________________________4. 如果一个数的平方加上这个数的2倍等于18，求出这个数。

________________________________________________5. 某树在一年内的生长长度是150厘米，第一季度它的生长长度是前两个季度长度之和的1.5倍，第二季度它的生长长度是前两个季度长度之和的0.5倍，求出第三季度它的生长长度。

________________________________________________Ⅲ.解答题（每题10分，共30分）1. 中国的国旗是由什么颜色组成的？每种颜色的面积占比是多少？________________________________________________2. 一辆火车从A站出发，以每小时100千米的速度前进，过了1小时到达B站。

加拿大国际袋鼠数学竞赛试题 -2004年

Back to All Problems PageMATH KANGAROO 2004 in USALevel of Grades 3 - 43 points each1. 2001+ 2002 + 2003 + 2004 + 2005 =A) 1,015 B) 5,010 C) 10,150 D) 11,005 E) 10,0152. Marek was 4 years old when his sister was born. Today he blew out all 9 candles on his birthday cake. What is the difference between Marek’s and his sister’s age today?A) 4 years B) 5 years C) 9 years D) 13 years E) 14 years3. The picture below shows a road from town A to town B (indicated by solid line) and a detour (marked by a dash line) caused by renovation of the section CD. How many kilometres longer is the road from town A to town B because of the detour now?A) 3 km B) 5 km C) 6 km D) 10 km E) This cannot be calculated.4. Which of the results below is not identical to the difference 671 – 389?A) 771 – 489 B) 681 – 399 C) 669 – 391 D) 1871 – 1589 E) 600 –3185. There were some birds sitting on the telegraph wire. At one moment, 5 of them flied away and after some time, 3 birds came back. At that time there were 12 birds sitting on the wire. How many birds were there at the very beginning?A) 8 B) 9 C) 10 D) 12 E) 146. Which numbers are inside a rectangle and inside a circle but not inside a triangle at the same time?A) 5 and 11 B) 1 and 10 C) 13 D) 3 and 9 E)6, 7 and 47. Buildings on Color Street are numbered from 1 to 5 (see the picture).Each building is colored with one of the following colors: blue, red,yellow, pink, and green. It is known that:– The red building neighbours with the blue one only.– The blue building is between the red one and the green one.What is the color of the building numbered with 3?A) Blue B) Red C) Yellow D) Pink E) Green8. How many white squares need to be shaded so that the number ofshaded squares equals exactly to half of the number of white squares?A) 2 B) 3 C) 4 D) 6 E) It isimpossible to calculate it.4 points each9. Five identical sheets of a plastic rectangles were dividedinto white and black squares. Which of the sheets from A to Ehas to be covered with the sheet to the right in order to gettotally black rectangle?A: B: C: D:E:10. The scales in the pictures had been balanced. There are pencils and a pen on the arms of the scales. What is the weight of the pen in grams?A) 6 g B) 7 g C) 8 g D) 9 g E) 10 g11. I notice four clocks on the wall (see the picture). Only one of them shows correct time. One of them is 20 minutes ahead, another is 20 minutes late, and the other is stopped. What is the time at the moment?among them. There are 14 students on Mathew’s left, and Maria is among them. There are 7 students between Maria and Mathew. How many students are in this class?A) 37 B) 30 C) 23 D) 22 E) 1620. The sum of the digits of the 10-digit number is 9.What is the product of the digits of this number?A) 0 B) 1 C) 45 D) 9 x 8 x 7 x…..x 2 x 1E) 1021. Out of 125 small, white and black cubes, the big cube was formed (see the picture). Every twoadjacent cubes have different colors. The vertices of the big cube are black. How many white cubesdoes the big cube contain?A) 62 B) 63 C) 64 D) 65 E) 6822. A lottery-ticket was 4 dollars. Three boys: Paul, Peter, and Robert made a contribiution and bought two tickets. Paul gave 1 dollar, Peter gave 3 dollars, and Robert gave 4 dollars. One of the tickets they bought was worth 1000 dollars. Boys shared the award fairly, meaning, proportionally to their contributions. How much did Peter receive?A) 300 B) 375 C) 250 D) 750 E) 42523. In three soccer games the Dziobak’s team scored three goals and lost one. For every game won the team gets 3 points, fora tie it gets 1 point, and for the game lost it gets 0 points. For sure, the number of points the team earned in those three games was not equal to which of the following numbers?A) 7 B) 6 C) 5 D) 4 E) 324. In every white section of a diagram, the products of two numbers from grey sections – one fromabove and one from the left – was placed (for example: 42 = 7 • 6 ). Some of these products arerepresented by letters. Which two letters represent the same number?A) L and M B) T and N C) R and P D) K and P E) M and Sback to all problems page。

加拿大国家中小学数学竞赛( kangaroo math 袋鼠竞赛)2018年一二年级(含答案)

袋鼠数学竞赛历年真题中文

袋鼠数学竞赛历年真题中文一、2008年1、给定4个正整数a，b，c，d，请解决：$$\frac{a}{b}+\frac{c}{d}=?$$2、证明：若正整数m，n满足$m \cdot n= 85$，则$m + n \le 19$二、2009年1、圆锥曲线的方程为$${x^2} + {y^2} = 16{x^2}，$$试求它的渐近线的方程？2、已知正方形ABCD的面积为36，点E在BC边上，DE=4。

求正三角形ABE的面积？三、2010年1、设$a,b \in R$，试证明下列结论：若$a^2+b^2=1$，$a \ne 0$，则$\frac{1}{a}+\frac{1}{b} \ge 2$2、三棱锥的一边角为$\frac{\pi }{3}$，其余直角三角形的斜边长分别为1，2，3，求这个三棱锥的体积。

四、2011年1、在正四面体ABCD中，AB=a，BC=b，AD=c，则其表面积为____2、若$a$,$b$,$c$为不相等的正数，$a+b+c=1$，请证明：$a^3+b^3+c^3 \ge abc$五、2012年1、设$m, n$是正整数，$m \ge n$，试证明:$m+n \le m^2-mn+n^2$2、设正方形$ABCD$中，$B(-3,2)$，$AD=8$，试求$ABCD$的外接圆的方程？六、2013年1、求函数$f(x)=x^2(x-1)^2$的最大值？2、求$\frac{1}{2}x(x+1)(x-1)$的三个零点的和？七、2014年1、已知变量$x,y$满足$x+y=100$，试求$f(x,y)=20x^2-44xy+90y^2$的最大值？2、设函数$f(x)=\frac{1}{{1 + 2x}} + 3e^x$的定义域为$[2,3]$，试求$f(x)$在定义域中的最小值？八、2015年1、若$x,y,z\in R^+$，满足$x^2+y^2+z^2=14$，求证：$xy+yz+zx \ge 6\sqrt {3}$2、若$ab+bc+ca=36，a \ge b \ge c$，求$a,b,c$的值？九、2016年1、求函数$y=\frac{x^2+15x+50}{x^2+10x+25}$的零点？2、若$a,b,c$满足$2a^2+b+c=15$, $b+c\ge 9$，求证：$bc \ge 6$？十、2017年1、若$3x^2+2xy+7y^2-13xy=0$，求$x,y$的最大值？2、圆锥曲线$x^2+y^2=16x^2$的双曲线半径为___？。

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。

数学竞赛袋鼠试题及答案

数学竞赛袋鼠试题及答案试题一：小明有5个苹果，他决定将它们平均分给3个朋友。

如果每个朋友得到的苹果数量相等，那么每个朋友会得到多少苹果？答案：小明有5个苹果，要平均分给3个朋友。

5除以3等于1余2。

所以，每个朋友可以得到1个苹果，剩下2个苹果无法平均分配。

试题二：一个长方形的长是宽的两倍，如果长是10厘米，那么这个长方形的面积是多少？答案：长方形的长是宽的两倍，所以宽是10除以2，等于5厘米。

长方形的面积是长乘以宽，即10厘米乘以5厘米，等于50平方厘米。

试题三：如果一个数的平方等于这个数本身，那么这个数可以是什么？答案：一个数的平方等于这个数本身，这个数可以是0或1。

因为0的平方是0，1的平方是1。

试题四：在一个圆中，半径增加了10%，那么圆的面积增加了多少百分比？答案：设原圆的半径为r，增加后的半径为1.1r。

原圆的面积为πr²，新圆的面积为π(1.1r)²=1.21πr²。

面积增加了(1.21πr² - πr²) / πr² = 0.21，即增加了21%。

试题五：一个班级有40名学生，如果每个学生都至少参加一个兴趣小组，并且每个兴趣小组最多只能有10名学生，那么至少需要多少个兴趣小组？答案：如果每个兴趣小组最多有10名学生，那么40名学生至少需要40/10=4个兴趣小组。

但是，如果每个学生都至少参加一个兴趣小组，那么至少需要5个兴趣小组，因为4个兴趣小组只能容纳40名学生，而最后一个兴趣小组至少需要1名学生。

结束语：以上是数学竞赛袋鼠试题及答案，希望这些题目能够帮助你更好地理解数学问题，并提高解题能力。

数学是一种美妙的语言，通过不断的练习和思考，你将能够发现它的魅力。

袋鼠数学竞赛试题及答案

袋鼠数学竞赛试题及答案1. 基础计算题：计算下列各题的结果。

- 题目一：$ 56 + 78 - 39 $- 题目二：$ 48 \times 25 $- 题目三：$ 3200 ÷ 40 + 76 $2. 逻辑推理题：小明有5个不同颜色的球，他想从这些球中选出3个来玩。

请问小明有多少种不同的选法？3. 几何题：一个正方形的边长为10厘米，求其周长和面积。

4. 应用题：一家商店出售T恤衫，每件T恤衫的进价是50元，标价是100元。

如果商店决定打8折销售，那么每件T恤衫的利润是多少？5. 数列题：一个等差数列的首项是3，公差是2，求这个数列的第10项。

6. 概率题：一个袋子里有5个红球和3个蓝球，随机抽取一个球，求抽到红球的概率。

7. 组合题：一个班级有30个学生，需要选出5个学生代表班级参加比赛。

如果不考虑顺序，有多少种不同的选法？8. 代数题：解下列方程：$ 3x - 7 = 26 $9. 统计题：一组数据是：4, 7, 2, 9, 5, 8。

求这组数据的平均数和中位数。

10. 智力题：一个数字去掉第一位是42，去掉最后一位是32，这个数字是什么？答案1. 基础计算题- 题目一：$ 56 + 78 - 39 = 95 $- 题目二：$ 48 \times 25 = 1200 $- 题目三：$ 3200 ÷ 40 + 76 = 95 $2. 逻辑推理题：小明有5个不同颜色的球，选择3个球的选法是$ C(5, 3) = 5! / (3! \times (5-3)!) = 10 $ 种。

3. 几何题：正方形的周长是 $ 4 \times 10 = 40 $ 厘米，面积是$ 10 \times 10 = 100 $ 平方厘米。

4. 应用题：打8折后，T恤衫售价为 $ 100 \times 0.8 = 80 $ 元，利润是 $ 80 - 50 = 30 $ 元。

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 。

袋鼠数学国际数学竞赛题

袋鼠数学国际数学竞赛题摘要：一、袋鼠数学竞赛简介1.袋鼠数学竞赛的起源2.竞赛面向的年龄段和级别3.竞赛的宗旨和目标二、袋鼠数学竞赛的特点1.题目趣味性强2.题目涉及多个领域3.鼓励学生用不同方法解题三、袋鼠数学竞赛的题目类型1.选择题2.填空题3.解答题四、袋鼠数学竞赛的评分标准1.正确率2.解题过程3.创意性解题五、参加袋鼠数学竞赛的意义1.提升数学能力2.培养逻辑思维3.激发学习兴趣正文：袋鼠数学国际数学竞赛（Kangaroo Mathematics Competition）是一项在全球范围内举办的青少年数学竞赛，起源于澳大利亚，现在已经发展成为一个国际性的数学竞赛。

该竞赛主要面向小学四年级至高中的学生，根据学生的年龄和年级分为不同级别。

竞赛旨在激发学生对数学的兴趣，提高他们的数学能力，培养他们的逻辑思维和创新能力。

袋鼠数学竞赛的特点在于题目的趣味性强，题目设置不拘泥于传统数学题目，而是涉及到多个领域，如几何、组合、逻辑等。

竞赛鼓励学生用不同的方法解题，注重培养学生的发散性思维。

题目类型包括选择题、填空题和解答题，让学生在各种题型中锻炼自己的数学能力。

袋鼠数学竞赛的评分标准不仅看重学生的正确率，还看重学生的解题过程和创意性解题。

这意味着学生在解题过程中，即使答案不正确，但若能给出有创意的解题思路，也有可能获得一定分数。

这样的评分方式旨在鼓励学生勇于尝试，不怕失败，培养他们独立思考和创新的能力。

参加袋鼠数学竞赛对学生有很多意义。

首先，通过参加竞赛，学生可以提升自己的数学能力，掌握更多数学知识。

其次，竞赛中的题目设置可以培养学生的逻辑思维能力，让他们在面对问题时能更加冷静、理性地分析。

最后，袋鼠数学竞赛的趣味性和挑战性可以激发学生对数学的兴趣，让他们在学习中找到乐趣，为未来的学习打下坚实的基础。

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(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?
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?
strawberries?
(A) 12
(B) 36
(C) 18
(D) 24
(E) 6
16. 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) 20
(B) 30
(C) 40
(D) 50
(E) 60
11. There is a house on each corner of the streets. The houses
are shown on the map. Two new houses will be built on
each street between the corner houses. How many houses
Grade 1-2
International Contest-Game MATH KANGAROO
Part A: Each correct answer is worth 3 points. 1. Which digits are missing?
Year 2013
(A) 3 and 5 (B) 4 and 8
with 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) 24
(E) 26
Grade 3-4
Year 2013
6. There are three families in my neighbourhood with three children each; two of the families have
(B) 2
(C) 3
(D) 4
(E) 5
10. 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 a
number less than 60. Who am I?
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) 7
(B) 9
(C) 10
(D) 30
(E) 8
4. How many triangles of all sizes can be seen in the picture below?
(A) 9
(B) 10
(C) 11
(D) 13
(E) 12
5. In London 2012, the USA won the most medals: 46 gold, 29 silver and 29 bronze. China was second
How many sandwiches can she prepare from two and a half packages of bread?
(A) 24
(B) 30
(C) 48
(D) 34
(E) 26
8. About the number 325, five boys said:
Andrei: "This is a 3-digit number"
Year 2013
9. 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
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Grade 1-2
15. In a game it is possible to make the following exchanges:
Year 2013
Adam has 6 pears. How many strawberries will Adam have, when he trades all his pears for just
(B)
(C)
(D)
(E)
3. Monica arrived in the Kangaroo Camp on July 25th in the morning and left the camp on August 3rd in
the afternoon. How many nights did she sleep in the camp?
(A) 50
(B) 51
(C) 55
(D) 60
(E) 62
17. 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?
will there be in all?
(A) 8
(B) 12
(C) 16
(D) 20
(E) Other answer
12. 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 sisters
Part C: Each correct answer is worth 5 points.
. Jim has
. Bob has
. Who is Barb?

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