2016年5-6年级袋鼠数学竞赛
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。
2016年袋鼠数学竞赛-Secondary-1
Singapore Math Kangaroo Contest 2016Rough WorkingSection A(Correct–3points|Unanswered–0points|Wrong–deduct1point)1.How many whole numbers are there between20.16and3.17?(A)15(B)16(C)17(D)18(E)192.Which of the following traffic signs has the largest number of lines of symmetry?(A)(B)(C)(D)(E)3.What is the sum of the two marked angles?(A)150◦(B)180◦(C)270◦(D)320◦(E)360◦4.Jenny had to add26to a certain number.Instead she subtracted26and obtained-14. What number should she have obtained?(A)28(B)32(C)36(D)38(E)425.Joanna turns a card over about its lower edge and then about its right-hand edge,as shown in thefigure.What does she see?(A)(B)(C)(D)(E)6.Kanga combines555groups of9stones into a single pile.She then splits the resulting pile into groups of5stones.How many groups does she get?(A)999(B)900(C)555(D)111(E)457.In my school,60%of the teachers get to school by bike,which is45teachers.Only12%of the teachers use their car to get to school.How many teachers use their car to get to school?(A)4(B)6(C)9(D)10(E)128.What is the shaded area?(A)50(B)80(C)100(D)120(E)1509.Two pieces of rope have lengths1m and2m.Alex cuts the pieces into several parts.All the parts have equal lengths.Which of the following could not be the total number of parts he obtains?(A)6(B)8(C)9(D)12(E)1510.Four towns P,Q,R and S are connected by roads,as shown.A race uses each road exactly once.The race starts at S andfinishes at Q.How many possible routes are there for the race?(A)10(B)8(C)6(D)4(E)2Section B(Correct–4points|Unanswered–0points|Wrong–deduct1point)11.The diagram shows four identical rectangles placed inside a square.The perimeter of each rectangle is16cm.What is the perimeter of the larger square?(A)16cm(B)20cm(C)24cm(D)28cm(E)32cm12.Petra has49blue beads and one red bead.How many beads must Petra remove so that 90%of her beads are blue?(A)4(B)10(C)29(D)39(E)4013.Which of the following fractions has a value closest to12?(A)2579(B)2759(C)2957(D)5279(E)579214.Ivor writes down the results of the quarter-finals,the semi-finals and thefinal of a knock-out tournament.The results are(not necessarily in this order):Bart beat Antony,Carl beat Damien,Glen beat Henry,Glen beat Carl,Carl beat Bart,Ed beat Fred and Glen beat Ed. Which pair played in thefinal?(A)Glen and Henry(B)Glen and Carl(C)Carl and Bart(D)Glen and Ed(E)Carl and Damien15.Anne has glued some cubes together,as shown.She rotates the solid to look at it from different angles.Which of the following can she not see?(A)(B)(C)(D)(E)16.Tim,Tom and Jim are triplets(three brothers born on the same day).Their twin brothers John and James are3years younger.Which of the following numbers could be the sum of the ages of thefive brothers?(A)36(B)53(C)76(D)89(E)9217.A3cm wide rectangular strip of paper is grey on one side and white on the other.Maria folds the strip,as shown.The grey trapeziums are identical.What is the length of the original strip?(A)36cm(B)48cm(C)54cm(D)57cm(E)81cm18.Two kangaroos Jum and Per start to jump at the same time,from the same point,in the same direction.They make one jump per second.Each of Jum’s jumps is6m in length.Per’s first jump is1m in length,the second is2m,the third is3m,and so on.After how many jumps does Per catch Jum?(A)10(B)11(C)12(D)13(E)1419.Seven standard dice are glued together to make the solid shown.The faces of the dice that are glued together have the same number of dots on them.How many dots are on the surface ofthe solid?(A)24(B)90(C)95(D)105(E)12620.There are20students in a class.They sit in pairs:exactly one third of the boys sit witha girl and exactly one half of the girls sit with a boy.How many boys are there in the class?(A)9(B)12(C)15(D)16(E)18Section C(Correct–5points|Unanswered–0points|Wrong–deduct1point)21.Inside a square of area36,there are shaded regions as shown in thefigure.The total shaded area is27.What is p+q+r+s?(A)4(B)6(C)8(D)9(E)1022.Theo’s watch is10minutes slow,but he believes that it is5minutes fast.Leo’s watch is 5minutes fast,but he believes that it is10minutes slow.At the same moment,each of them looks at his own watch.Theo thinks it is12:00.What time does Leo think it is?(A)11:30(B)11:45(C)12:00(D)12:30(E)12:4523.Twelve girls met in a coffee shop.On average,they ate1.5cupcakes.None of them ate more than two cupcakes and two of them had only mineral water.How many girls ate two cupcakes?(A)2(B)5(C)6(D)7(E)824.Little Red Riding Hood is delivering waffles to three grannies.She starts with a basket full of waffles.Just before she enters each of the grannies’houses,the Big Bad Wolf eats half of the waffles in her basket.When she leaves the third granny’s house,she has no waffles left.She delivers the same number of waffles to each granny.Which of the following numbers definitely divides the number of waffles she started with?(A)4(B)5(C)6(D)7(E)925.The cube below is divided into64small cubes.Exactly one of the cubes is grey.On the first day,the grey cube changes all its neighbouring cubes to grey(two cubes are neighbours if they have a common face).On the second day,all the grey cubes do the same thing.How many grey cubes are there at the end of the second day?(A)11(B)13(C)15(D)16(E)1726.Several different positive integers are written on a blackboard.The product of the smallest two of them is16.The product of the largest two is225.What is the sum of all the integers?(A)38(B)42(C)44(D)58(E)24327.The diagram shows a pentagon.Sepideh drawsfive circles with centres A,B,C,D,E such that the two circles on each side of the pentagon touch.The lengths of the sides of the pentagon are given.Which point is the centre of the largest circle that she draws?(A)A(B)B(C)C(D)D(E)E28.Katie writes a different positive integer on each of the fourteen cubes in the pyramid. The sum of the nine integers written on the bottom cubes is equal to50.The integer written on each other cube is equal to the sum of the integers written on the four cubes underneath it. What is the greatest possible integer that can be written on the top cube?(A)80(B)98(C)104(D)110(E)11829.A train hasfive carriages,each containing at least one passenger.Two passengers are said to be”neighbours”if either they are in the same carriage or they are in two adjacent carriages. Each passenger has either exactlyfive or exactly ten”neighbours”.How many passengers are there in the train?(A)13(B)15(C)17(D)20(E)There is more than one possibility.30.A3×3×3cube is built from15black cubes and12white cubes.Five faces of the larger cube are shown.Which of the following is the sixth face of the large cube?(A)(B)(C)(D)(E)END OF PAPER。
2016年袋鼠数学竞赛-四年级
Singapore Math Kangaroo Contest 2017Primary 4 Contest PaperName:School:INSTRUCTIONS:1.Please DO NOT OPEN the contest booklet until the Proctor has given permission to start. 2.TIME : 1 hour and 30 minutes3.There are 30 questions in this paper. 3 points, 4 points and 5 points will be awarded for each correct question in Section A, Section B and Section C respectively. No points are deducted for Unanswered question. 1 point is deducted for Wrong answer. 4.Shade your answers neatly in the answer entry sheet. 5.PROCTORING : No one may help any student in any way during the contest. 6.No calculators are allowed. Name, Index number, Level and School in the 7.All students must fill and shade in your Answer sheet provided. 8.MINIMUM TIME: Students must stay in the exam hall for at least 1 hour and 15 minutes. 9.Students must show detailed working and transfer answers to the answer entry sheet. 10.No spare papers can be used in writing this contest. Enough space is provided for your working of each question. 11. Y ou must return this contest paper to the proctor. Rough WorkingSection A(Correct–3points |Unanswered –0points |Wrong –deduct 1point)Question 1Which of the pieces(A,B,C,D,E)willfit in between the two pieces below,such that the two equations formed will be true?8–3=2(A)=55–1(B)=34–2(C)=51+2(D)=45–3(E)=51+1Question2John looks through the window as shown in the picture below.He only sees half the number of kangaroos in the park.How many kangaroos are there in the park in total?(A)12(B)14(C)16(D)18(E)20Two gridded transparent sheets are darkened in some squares,as shown in the picture below.They are both placed on top of the board shown in the middle.The the pictures behind the darkenedsquares cannot be seen.Only one of the pictures can still be seen,which pictureisit?(A)(B)(C)(D)(E)Question 4A original picture of footprints(left)was rotated in a particular way.The result is shown on the rightofthe original picture.Which pair of footprints are missing?(A)(B)(C)(D)1(E)Question5What number is hidden behind the panda? – 10 = 10+ 6 = – 6 = +8 + 8 = A(A)16(B)18(C)20(D)24(E)28In the table below,the correct sums are shown.What number is in the box with the question mark?(A)10(B)12(C)13(D)15(E)16Question7Dolly accidentally broke the mirror into pieces.How many pieces have exactly four sides?(A)2(B)3(C)4(D)5(E)6Question8Which option shows the necklace below when it is untangled?(A)(B)(C)(D)(E)Section B(Correct–4points|Unanswered–0points|Wrong–deduct1point)Question9The picture below shows the front of Ann’s house.The back of her house has three windows and no door.What does Ann see when she is standing from the back of her house?(A)(B)(C)(D)(E)Question10Which option is correct?(A)(B)(C)(D)(E)Balloons are sold in packets of 5,10and 25.Marius buys exactly 70balloons.What is the smallest number of packets he could buy?(A )3(B )4(C )5(D )6(E )7Question 12Bob folded a piece of paper.He cut exactly one hole through the folded paper.Then he unfolded the piece of paper and saw the result as shown in the picture below.How did Bob fold his piece of paper?(A )(B )(C )(D )(E )Question 13There is a tournament at a pool.At first,13children signed up,and then another 19signed up.Six teams with an equal number of members are needed for the tournament.At least how many more children need to sign up so that the six teams can be form?(A )1(B )2(C )3(D )4(E )5Question 14Numbers are placed in the cells of the 4×4square shown in the picture below.Mary selects any 2×2square in 4×4square and adds up all the numbers in the four cells.What is the largest possible sum she can get?(A )11(B )12(C )13(D )14(E )15David wants to cook5dishes on a stove with only2burners.The time he needed to cook the5dishes are40mins,15mins,35mins,10mins and45mins.What is the shortest possible time in which he can cook all5dishes?(He can only remove a dish from the stove when it is fully cooked.)(A)60min(B)70min(C)75min(D)80min(E)85minQuestion16be written in the circle containing the question mark?Which number shouldSection C(Correct–5points|Unanswered–0points|Wrong–deduct1point)Question17The picture shows a group of building blocks and a plan of these blocks.Some ink has dripped onto the plan.What is the sum of the numbers covered by the ink?3411131(A)3(B)4(C)5(D)6(E)7How long is the train?340 m110 m(A)55m(B)115m(C)170m(D)220m(E)230mQuestion19George trains at his schoolfield atfive o’clock every afternoon.The journey from his house to the bus stop takes5minutes.The bus journey takes15minutes.It takes him5minutes to go from the bus stop to thefield.The bus runs every10minutes from six in the morning.What is the latest time he has to leave his house in order to arrive at thefield exactly on time?(A)(B)(C)(D)(E)Question20A small zoo has a giraffe,an elephant,a lion and a turtle.Susan wants to plan a tour where she sees 2different animals.She does not want to start with the lion.How many different tours can she plan?(A)3(B)7(C)8(D)9(E)12Four brothers have eaten11cookies in total.Each of them has eaten at least one cookie and no two of them have eaten the same number of cookies.Three of them have eaten9cookies in total and one of them has eaten exactly3cookies.What is the largest number of cookies one of the brothers has eaten?(A)3(B)4(C)5(D)6(E)7Question22Zosia has hidden some smileys in some of the squares in the table.In some of the other squares she writes the number of smileys in the neighbouring squares as shown in the picture.Two squares are said to be neighbouring if they share a common side or a common corner.How many smileys has she hidden?(A)4(B)5(C)7(D)8(E)11Question23Ten bags contain different numbers of candies from1to10in each of the bag.Five boys took two bags of candies each.Alex got5candies,Bob got7candies,Charles got9candies and Dennis got15 candies.How many candies did Eric get?(A)9(B)11(C)13(D)17(E)19Question24Kate has4flowers,one with6petals,one with7petals,one with8petals and one with11petals. Kate tears offone petal from threeflowers.She does this several times,choosing any threeflowers each time.She stops when she can no longer tear one petal from threeflowers.What is the smallest number of petals which can remain?(A)1(B)2(C)3(D)4(E)5Rough Working。
2016年袋鼠数学竞赛理工学院JC
Singapore Math Kangaroo Contest 2017Junior College Contest PaperName:School:INSTRUCTIONS:1.Please DO NOT OPEN the contest booklet until the Proctor has given permission to start.2.TIME : 1 hour and 30 minutes3.There are 30 questions in this paper. 3 points, 4 points and 5 points will be awarded for eachcorrect question in Section A, B and C respectively. Points are not deducted for unanswered questions. 1 point will be deducted for every wrong answer.4.Shade your answers neatly in the answer entry sheet.5.PROCTORING : No one may help any student in any way during the contest.6.Calculators are not allowed.7.Students are required to shade in your Name, Index number, Level and School in theAnswer sheet provided.8.MINIMUM TIME: Students must stay in the exam hall for at least 1 hour and 15 minutes.9.Students must show detailed working and transfer their final answers to the answer entry sheet.10.Any additional papers is not allowed for this contest. Sufficient space will be provided in thecontest paper.11. Y ou must return this contest paper to the proctor.Rough WorkingSection A(Correct–3points|Unanswered–0points|Wrong–deduct1point)Question120×17=2+0+1+7(A)3.4(B)17(C)34(D)201.7(E)340Question2Tom built afigurine of his brother using the ratio of1:87.If the height of thefigurine is2cm,what is actual the height of his brother?(A)1.74m(B)1.62m(C)1.86m(D)1.94m(E)1.70mQuestion3In thefigure below,we can see10islands that are connected by15bridges.If all bridges are open, what is the smallest number of bridges that must be closed in order to stop the traffic between A and B?(A)1(B)2(C)3(D)4(E)5It is given that75%of a is equal to40%of b.Which option below is always true?(A)15a=8b(B)7a=8b(C)3a=2b(D)5a=12b(E)8a=15b Question5Four of the followingfive clippings are part of the same graph of the quadratic function.Which clipping is not part of this graph?(A)(B)(C)(D)(E)Question6Given a circle with center O with diameters AB and CX such that OB=BC.What fraction of the area of the circle is the shaded?(A)25(B)13(C)27(D)38(E)411A bar consists of2white and2grey cubes glued together as shown in the picture below.Whichfigure can be built from4such bars?(A)B)C)D)E)Question8Which quadrant contains no points on the graph of the linear function f(x)=−3.5x+7?(A)I(B)II(C)III(D)IV(E)All quadrants contain points.Each of the following five boxes is filled with red and blue balls as labeled.Ben wants to take one ball out of the boxes without looking.From which box should he take the ball to have the highest probability of getting a blue ball?(A )(B )(C )(D )(E )Question 10Find the graph which has the most number of common points with the graph of the function f (x )=x ?(A )g 1(x )=x 2(B )g 2(x )=x 3(C )g 3(x )=x 4(D )g 4(x )=−x 4(E )g 5(x )=−xSection B (Correct –4points |Unanswered –0points |Wrong –deduct 1point)Question 11Three mutually tangent circles with centres A ,B ,C have the radii 3,2and 1,respectively.What is the area of the triangle ABC ?(A )6(B )4√3(C )3√2(D )9(E )2√6The positive number p is less than1,and the number q is greater than1.Which one of the following numbers is the largest?(A)p·q(B)p+q(C)pq(D)p(E)qQuestion13Two right cylinders A and B have the same volume.If the radius of the base of B is10%larger than the base of A.How much larger is the height of A than the height of B?(A)5%(B)10%(C)11%(D)20%(E)21% Question14Each face of the polyhedron shown below is either triangle or a square.Each square is surrounded by 4triangles,while each triangle is surrounded by3squares.If there are6squares in total,how many triangles are there?(A)5(B)6(C)7(D)8(E)9We have four tetrahedral dice,perfectly balanced,with their faces numbered2,0,1and7.If we roll all four of these dice,what is the probability that we can form the number2017using exactly one of the three visible numbers from each die?(A)1256(B)6364(C)81256(D)332(E)2932Question16The polynomial5x3+ax2+bx+24has integer coefficients a and b.Which of the following is certainly not a root of the polynomial?(A)1(B)-1(C)3(D)5(E)6Julia has2017chips.1009of them are black and the rest are white.She placed them in a square pattern as shown in thefigure below.How many chips of each colour are left after she has formed the largest possible square using her chips?(A)None(B)40of each(C)40black ones and41white ones(D)41of each(E)40white ones and41black onesQuestion18Two consecutive numbers are such that the sums of their digits in each of them are multiples of7. How many digits does the smaller number have?(A)3(B)4(C)5(D)6(E)7In a convex quadrilateral ABCD,the diagonals are perpendicular to each other.The sides have lengths|AB|=2017,|BC|=2018and|CD|=2019.What is the length of AD?(A)2016(B)2018(C)√20202−4(D)√20182+2(E)2020Question20Taylor attempts to be a good little Kangaroo,but lying is too much fun.Therefore,every third statement she says is a lie while the rest are true.(Sometimes she starts with a lie and sometimes with one or two true statements.)Taylor thinks of a2-digit number and tells her friend about it:”One of its digits is a2.””It is larger than50.””It is an even number.””It is less than30.””It is divisible by three.””One of its digits is a7.”What is the sum of the digits in Taylor’s number?(A)9(B)12(C)13(D)15(E)17Section C(Correct–5points|Unanswered–0points|Wrong–deduct1point)Question21When you remove the last digit in a positive integer,it is equal to1/14of the original number.How many such positive integers are there?(A)0(B)1(C)2(D)3(E)4Question22The picture shows a regular hexagon with each side lengths equal to1.Theflower was constructed with sectors of circles of radius1and centers on the vertices of the hexagon.What is the area of the flower?(A)π2(B)2π3(C)2√3−π(D)π2+√3(E)2π−3√3Question23Consider the sequence a n with a1=2017and a n+1=a n−1a n.What is the value of a2017?(A)−2017(B)−12016(C)20162017(D)1(E)2017Question24Consider a regular tetrahedron.Its four corners are cut offby four planes,each passing through the midpoints of three adjacent edges as shown in thefigure below.What is the ratio of the volume of the resulting solid to the volume of the original tetrahedron?(A)45(B)34(C)23(D)12(E)13Question25The lengths of the three sides of a right-angled triangle add up to18.The squares of the lengths of the sides add up to128.What is the area of the triangle?(A)18(B)16(C)12(D)10(E)9You are given5boxes,5black and5white balls.You choose how to put the balls in the boxes(each box has to contain at least one ball).Your opponent comes and draws one ball from one box of his choice and he wins if he draws a white ball.Otherwise,you win.How should you arrange the balls in the boxes to have the best chance to win?(A)You put one white and one black ball in each box.(B)You arrange all the black balls in three boxes,and all the white balls in two boxes.(C)You arrange all the black balls in four boxes,and all the white balls in one box.(D)You put one black ball in every box,and add all the white balls in one box.(E)You put one white ball in every box,and add all the black balls in one box.Question27Nine integers are written in the cells of a3×3table.The sum of the nine numbers is equal to500. It is known that the numbers in any two neighboring cells(with a common side)differ by1.What is the number in the central cell?(A)50(B)54(C)55(D)56(E)57Question28If|x|+x+y=5and x+|y|−y=10what is the value of x+y?(A)1(B)2(C)3(D)4(E)5How many three-digit positive integers ABC are there such that(A+B)C is a three-digit integer and an integer power of2?(A)15(B)16(C)18(D)20(E)21Question30Each of the2017people living on an island is either a liar(and always lies)or a truth-teller(and always tells the truth).More than one thousand of them take part in a banquet,all sitting together at a round table.Each of them says:”Of the two people beside me,one is a liar and the other one a truth-teller.”How many truth-tellers are there on the island at most?(A)1683(B)668(C)670(D)1344(E)1343。
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。
2016年袋鼠数学竞赛-五年级
Singapore Math Kangaroo Contest 2017Primary 5 Contest PaperName:School:INSTRUCTIONS:1.Please DO NOT OPEN the contest booklet until the Proctor has given permission to start.2.TIME : 1 hour and 30 minutes3.There are 30 questions in this paper. 3 points, 4 points and 5 points will be awarded for eachcorrect question in Section A, Section B and Section C respectively. No points are deducted for Unanswered question. 1 point is deducted for Wrong answer.4.Shade your answers neatly in the answer entry sheet.5.PROCTORING : No one may help any student in any way during the contest.6.No calculators are allowed.7.All students must fill and shade in your Name, Index number, Level and School in theAnswer sheet provided.8.MINIMUM TIME: Students must stay in the exam hall for at least 1 hour and 15 minutes.9.Students must show detailed working and transfer answers to the answer entry sheet.10.No spare papers can be used in writing this contest. Enough space is provided for yourworking of each question.11. Y ou must return this contest paper to the proctor.Rough WorkingSingapore Math Kangaroo Contest 2017–Primary 5/Grade 5Section A (Correct –3points |Unanswered –0points |Wrong –deduct 1point)Question 1Four cards lie in a row as shown in the picture below.Which card arrangement is impossible to obtainif you swap the position of 1pair of cards?20171(A )201727100127771201727101(C )20172710012710270217711(D )201727100127102721120172710012710271A fly spider has 83spiders have is thesame 9chickens (A )B )3cats cats catsAlice figure:be has?(A )(C )(D )Kalle =of 1111×(A )D )On a planet there are 10islands and 12bridges.If all bridges are open,what is the smallest number of bridges that must be closed in and B?1(A )1(B )2(C )3(D )4(E )5Question 63Rhinos named Jane,Kate and Lynn went for a walk.Jane was infront of Kate,and Lynn was behind Kate.Jane weighs 500kg more than Kate.Kate weighs 1000kg less than Lynn.Which of the following pictures shows Jane,Kate and Lynn in the right order?(A )(B )(C )(D )(E )Question 7A special dice has a number on each face.The sums of the numbers on opposite faces are all equal.Five of the numbers are 5,6,9,11and 14.What is the number on the sixth face?(A )4(B )7(C )8(D )13(E )15Martin wants to colour the squares of the rectangle so that1/3of all squares are blue and half of all squares are yellow.The rest of the squares are to be coloured red.How many squares will he colour red?(A)1(B)2(C)3(D)4(E)5Question9While Peter solves2problems in the”Kangaroo”contest,Nick manages to solve3problems.The boys solved30problems in total.How many more problems did Nick solve than Peter?(A)5(B)6(C)7(D)8(E)9Question10Bob folded a piece of paper,used a hole puncher and punched exactly one hole in the paper.Bob unfolded the paper as shown in the picture below.Which of the following shows the folded lines on the paper that Bob had intially started with?(A)(B)(C)(D)(E)Section B(Correct–4points|Unanswered–0points|Wrong–deduct1point)Question11The Modern Furniture store is selling sofas,loveseats and chairs made from identical modular pieces as shown in the picture below.Only1pair of armrests are on the sides of each furniture and all armrests have the same width.The width of the sofa is220cm and the width of the loveseat is160 cm.What is the width of the chair?sofa loveseat chair220cm160cm(A)60cm(B)80cm(C)90cm(D)100cm(E)120cm5different keys fit into the 5different padlocks in the picture below.The numbers on the keys refer to the letters on the padlocks.What is written on the lastkey?4141841248121(A )382(B )282(C )284(D )823(E )824Question 13Tom writes all the numbers from 1to 20in a row and obtains the 31-digit number:1234567891011121314151617181920Then he deletes 24of the 31digits such that the remaining number is as large as possible.Which number does he get?(A )9671819(B )9567892(C )9781920(D )9912345(E )9818192Question 14Morten wants to rebuild the construction below into a regular box.Each piece of cube that form the construction below has a length of 1cm.What is the smallest dimension of a box he can form?(A )3×3×4(B )3×5×5(C )3×4×5(D )4×4×4(E )4×4×5Question 15When we add the numbers in each row and along the columns we get the results as in the table below.Which statement is true?a b c d2143(A )a is equal to d (B )b is equal to c(C )a is greater than d(D )a is less than d(E )c is greater than bPeter went hiking in the mountains for5days.He started on Monday and his last trip was on Friday. Each dayhe walked2km more than the day before.When his trip was over,his total distance was70km.What is the distance covered by Peter on Thursday?(A)12km(B)13km(C)14km(D)15km(E)16km Question17There is a picture of a kangaroo in thefirst triangle from the left.The dotted linesact as mirrors. Thefirst2reflections are shown.What does the reflection look like in the shadedtriangle?(A)(B)(C)(D)(E)Question18Soo Ching hassome amount of money and3magic wands that he can only use once.The properties of each wand is shown below:Adds1dollar Substracts1dollar Doubles the amountIn what order must he use these wands to obtain the largest amount of money?(A)(B)(C)(D)(E)squares.The first square has a side length of 2cm.The second square has a side its vertex is placed in the center of the first square.The last square has side length is placed in the center of the second square,as shown in the picture.What is the (A )32cm 2(B )51cm 2(C )27cm 2(D )(E )Question 20Four players scored goals in a handball match.All of them scoredthe four players,Mike was the one who scored 20goals in total.What is the greatest number (A )2(B )3(C )(D )(E )Section C (Correct –5Question 21A bar consists of 2greycube can be built from 9(A )(B )((D )(E )1The 4,the following way:If a just to the right of to (A )(B )((D )6(E )88kangaroos stood in a line as shown in the diagram below.At some point,two kangaroos standing side by side and facing each other exchanged places by jumping past each other.This was repeated until no further jumps were possible.How many exchanges were made?(A)2(B)10(C)12(D)13(E)16Question24Monica has to choose5different numbers.She has to multiply some of them by2and some by3 in order to get the smallest number of different results.What is the least number of results she can obtain?(A)1(B)2(C)3(D)4(E)5Question25The squarefloor in the picture is covered by triangular and square tiles in grey or white.What is the smallest number of grey tiles,that must be swapped with white tiles,so that the pattern looks the same from each of the four directions shown by the arrows below?(A)Three triangles,one square(B)One triangle,three squares(C)One triangle,one square(D)Three triangles,three squares(E)Three triangles,two squaresQuestion26A bag contains red marbles and green marbles.For every5marbles Jackie picks,at least one marble is red.For every6marbles Jackie picks,at least one marble is green.What is the largest number of marbles that the bag can contain?(A)11(B)10(C)9(D)8(E)7Abigail likes even numbers,Betty likes numbers that are divisible by3and Celina likes numbers that are divisible by5.Each of the three girls went separately to a basket containing8balls with numbers written on them,and took all the balls with numbers they like.It turned out that Abigail collected balls with the numbers32and52,Betty collected balls with the numbers24,33and45,Celina collected balls with the numbers20,25and35.In what order did the girls approach the basket? (A)Abigail,Celina,Betty(B)Celina,Betty,Abigail(C)Betty,Abigail,Celina (D)Betty,Celina,Abigail(E)Celina,Abigail,BettyQuestion28John wants to write a whole number on each box at the diagram below,such that the sum of any two numbers in the adjacent boxes is equal to the number directly above it.What is the largest number of odd numbers that John can write?(A)4(B)5(C)6(D)7(E)8Question29Julia has four different coloured pencils.She wants to use some or all of them to colour the map of an island,divided into four nations as shown in the picture below.If the map of two nations with a common border cannot have the same colour,how many ways can she colour the map?(A)12(B)18(C)24(D)36(E)48Question30There is a lamp in each square of a6×6board.If two lamps have a common side in the board,they are known as neighbours.In the beginning,some lamps are switched on.Every minute,each lamp will be switched on if they have at least two neighboring lamps that are on.What is the minimum number of lamps that need to be switched on at the start,in order to ensure that all lamps will be lit at some point of time?(A)4(B)5(C)6(D)7(E)8。
新加坡袋鼠数学竞赛5年级考卷中文版(2016)
注意事项：
1.在监考老师宣布开始考试之前，请不要打开考卷
2.时间：1小时30分钟
3.本考卷有30个题。
第一部分每题3分，第二部分每题4分，第三部分每题5分。
不答没有分，
答错均扣一分。
4.在答题纸上清晰地涂黑选项
5.监考：在竞赛过程中，任何人不准以任何形式帮助学生。
6.不允许带计算器。
7.所有的学生必须在考卷上填写和涂黑你的名字，考号，年级和学校
8.最少时间：学生必须在考场待够1小时15分钟
9.学生必须提供详细演算过程并把答案写在答题纸上
10.不提供多余的演算纸。
每个题目已经提供足够的演算空间。
11.必须把考卷还给监考老师。
（完）。
2016年袋鼠数学竞赛-三年级
2016年袋⿏数学竞赛-三年级Singapore Math Kangaroo Contest 2017Primary 3 Contest PaperName:School:INSTRUCTIONS:1.Please DO NOT OPEN the contest booklet until the Proctor has given permission to start.2.TIME : 1 hour and 30 minutes3.There are 30 questions in this paper. 3 points, 4 points and 5 points will be awarded for eachcorrect question in Section A, Section B and Section C respectively. No points are deducted for Unanswered question. 1 point is deducted for Wrong answer.4.Shade your answers neatly in the answer entry sheet.5.PROCTORING : No one may help any student in any way during the contest.6.No calculators are allowed.7.All students must fill and shade in your Name, Index number, Level and School in theAnswer sheet provided.8.MINIMUM TIME: Students must stay in the exam hall for at least 1 hour and 15 minutes.9.Students must show detailed working and transfer answers to the answer entry sheet.10.No spare papers can be used in writing this contest. Enough space is provided for yourworking of each question.11. Y ou must return this contest paper to the proctor.Rough WorkingSection A(Correct–3points|Unanswered–0points|Wrong–deduct1point)Question1Which of the pieces(A,B,C,D,E)will?t in between the two pieces below,such that the two equations formed will be true?8–3=2(A )=55–1(B )=34–2(C )=51+2(D)=45–3(E)=51+1Question2John looks through the window as shown in the picture below.He only sees half the number of kangaroos in the park.How many kangaroos are there in the park intotal?(A)12(B)14(C)16(D)18(E)201Two gridded transparent sheets are darkened in some squares,as shown in the picture below.They are both placed on top of the board shown in the middle.The the pictures behind the darkened squares cannot be seen.Only one of the pictures can still be seen,which picture isit?Question 4original picture rotated in a particular way.The resultfootprints are missing?(A )(B )(C )1(D )1(E )Question 5What number is hidden behind the panda?– 10 = 10+ 6 =– 6 = +8 + 8 = A (A )16(B )18(C )20(D )24(E )282In the table below,the correct sums are shown.What number is in the box with the question mark?(A)10(B)12(C)13(D)15(E)16Question7Dolly accidentally broke the mirror into pieces.How many pieces have exactly four sides?(A)2(B)3(C)4(D)5(E)6Question8Which option shows the necklace below when it is untangled?(A)(B)(C)(D)(E)3Section B(Correct–4points|Unanswered–0points|Wrong–deduct1point)Question9The picture below shows the front of Ann’s house.The back of her house has three windows and no door.What does Ann see when she is standing from the back of her house?(A)(B)(C)(D)(E)Question10Which option is correct?(A)(B)(C)(D)(E)Balloons are sold in packets of5,10and25.Marius buys exactly70balloons.What is the smallest number of packets he could buy?(A)3(B)4(C)5(D)6(E)7Question12Bob folded a piece of paper.He cut exactly one hole through the folded paper.Then he unfolded the piece of paper and saw the result as shown in the picture below.How did Bob fold his piece of paper?(A)(B)(C)(D)(E)Question13There is a tournament at a pool.At?rst,13children signed up,and then another19signed up.Six teams with an equal number of members are needed for the tournament. At least how many more children need to sign up so that the six teams can be form?(A)1(B)2(C)3(D)4(E)5Question14Numbers are placed in the cells of the4×4square shown in the picture below.Mary selects any2×2 square in4×4square and adds up all the numbers in the four cells.What is the largest possible sum she can get?(A)11(B)12(C)13(D)14(E)15David wants to cook5dishes on a stove with only2burners.The time he needed to cook the5dishes are40mins,15mins,35mins,10mins and45mins.What is the shortest possible time in which he can cook all5dishes?(He can only remove a dish from the stove when it is fully cooked.)(A)60min(B)70min(C)75min(D)80min(E)85minQuestion16Which number should be(A)10(B)11(C)12(D)13(E)14Section C(Correct–5points|Unanswered–0points|Wrong–deduct1point)Question17The picture shows a group of building blocks and a plan of these blocks.Some ink has dripped onto(A)3(B)4(C)5(D)6(E)7How long is the train?(A)55m(B)115m(C)170m(D)220m(E)230mQuestion19George trains at his school?eld at?ve o’clock every afternoon.The journey from his house to the bus stop takes5minutes.The bus journey takes15minutes.It takes him5minutes to go from the bus stop to the?eld.The bus runs every10minutes from six in the morning.What is the latest time he has to leave his house in order to arrive at the?eld exactly on time?(A)(B)(C)(D)(E)Question20A small zoo has a gira?e,an elephant,a lion and a turtle.Susan wants to plan a tour where she sees 2di?erent animals.She does not want to start with the lion.How many di?erent tours can she plan? (A)3(B)7(C)8(D)9(E)12Four brothers have eaten11cookies in total.Each of them has eaten at least one cookie and no two of them have eaten the same number of cookies.Three of them have eaten9cookies in total and one of them has eaten exactly3cookies.What is the largest number of cookies one of the brothers has eaten?(A)3(B)4(C)5(D)6(E)7Question22Zosia has hidden some smileys in some of the squares in the table.In some of the other squares she writes the number of smileys in the neighbouring squares as shown in the picture.Two squares are said to be neighbouring if they share a common side or a common corner.How many smileys has she hidden?(A)4(B)5(C)7(D)8(E)11Question23Ten bags contain di?erent numbers of candies from1to10in each of the bag.Five boys took two bags of candies each.Alex got5candies,Bob got7candies,Charles got9candies and Dennis got15 candies.How many candies did Eric get?(A)9(B)11(C)13(D)17(E)19Question24Kate has4?owers,one with6petals,one with7petals,one with8petals and one with11petals. Kate tears o?one petal from three?owers.She does this several times,choosing any three?owers each time.She stops when she can no longer tear one petal from three?owers.What is the smallest number of petals which(A)1(B)2(C)3(D)4(E)5。
2016年袋鼠数学竞赛-高一
Singapore Math Kangaroo Contest 2017Secondary 4 Contest PaperName:School:INSTRUCTIONS:1.Please DO NOT OPEN the contest booklet until the Proctor has given permission to start.2.TIME : 1 hour and 30 minutes3.There are 30 questions in this paper. 3 points, 4 points and 5 points will be awarded for eachcorrect question in Section A, Section B and Section C respectively. No points are deducted for Unanswered question. 1 point is deducted for Wrong answer.4.Shade your answers neatly in the answer entry sheet.5.PROCTORING : No one may help any student in any way during the contest.6.No calculators are allowed.7.All students must fill and shade in your Name, Index number, Level and School in theAnswer sheet provided.8.MINIMUM TIME: Students must stay in the exam hall for at least 1 hour and 15 minutes.9.Students must show detailed working and transfer answers to the answer entry sheet.10.No spare papers can be used in writing this contest. Enough space is provided for yourworking of each question.11. Y ou must return this contest paper to the proctor.Rough WorkingSection A(Correct–3points|Unanswered–0points|Wrong–deduct1point)Question1In this diagram,each number is the sum of the two numbers immediately below it.What number is in the most bottom left box?(A)15(B)16(C)17(D)18(E)19Question2Peter wrote the word KANGAROO on a piece of transparent glass as shown in the picture below. What will he see if heflips the paper over to its right and then rotates it one half-turn?(A)(B)(C)(D)(E)Question3Angela made a decoration with grey and white asteroids by overlaping them from biggest at the bottom,to the smallest at the top.The areas of the asteroids are1cm2,4cm2,9cm2and16cm2. What is the total area of the visible grey regions?(A)9cm2(B)10cm2(C)11cm2(D)12cm2(E)13cm2 Question4Maria has24dollars.Every one of her3siblings has12dollars.How much does she have to give each of her siblings,such that everyone has the same amount?(A)1dollar(B)2dollars(C)3dollars(D)4dollarsj(E)6dollarsWhich option shows the path of the midpoint of the wheel when the wheel rolls along the zig-zag-curve shown?(A)(B)(C)(D)(E)Question6Some girls were dancing in a circle.Antonia was thefifth to the left from Bianca and the eighth to the right from Bianca.How many girls were in the group?(A)11(B)12(C)13(D)14(E)15Question7Circle of radius1rolls along a straight line from the point K to the point L,where KL=11π.What does the circle look like at L?LK(A(B)(C)(D(E)Question8Martin is taking part in a chess competition.He won9out of15matches.If he wins the next5 matches,what will his success rate be in the competition?(A)60%(B)65%(C)70%(D)75%(E)80%Question9One eighth of the guests at a wedding were children.Three sevenths of the adult guests were men. What fraction of the wedding guests were women?(A)12(B)13(C)15(D)17(E)37My maths teacher has a box with coloured buttons.There are203red buttons,117white buttons and28blue buttons.What is the least number of buttons he must take from the box without looking, to ensure he has at least3buttons of the same colour?(A)3(B)6(C)7(D)28(E)203Section B(Correct–4points|Unanswered–0points|Wrong–deduct1point)Question11ABCD is a trapezoid with sides AB parallel to CD,where AB=50,CD=20.E is a point on the side AB such that the segment DE divides the given trapezoid into two parts of equal area.Calculate the length AE.(A)25(B)30(C)35(D)40(E)45Question12How many positive integers A,which satisfy the property that exactly one of the numbers A or A+20 is a4-digit number?(A)19(B)20(C)38(D)39(E)40Question13Six perpendiculars lines are drawn from the midpoints on each sides of the triangle to each of the other two sides.What fraction of the area of the initial triangle does the resulting hexagon cover?(A)13(B)25(C)49(D)12(E)23The squares of three consecutive positive integers adds up to770.What is the largest of these3 integers?(A)15(B)16(C)17(D)18(E)19Question15A belt drive system consists of the wheels A,B and C,which rotate without a slippage.B turns4 full rounds when A turns5full rounds,and B turns6full rounds whenC turns7full rounds.Find the perimeter of A if the perimeter of C is30cm.(A)27cm(B)28cm(C)29cm(D)30cm(E)31cm Question16Mr Tan wants to prepare a schedule for his jogging over the next few months.Every week,he wants to jog on the same days of the week and he never wants to jog on two consecutive days.In addition, he wants to jog three times per week.How many schedules can he choose from?(A)6(B)7(C)9(D)10(E)35Question17Four brothers have different heights.Tom is shorter than Victor by x cm.Tom is taller than Peter by x cm.Oscar is shorter than Peter by by x cm.Tom is184cm tall and the average height of all the four brothers is178cm.How tall is Oscar?(A)160cm(B)166cm(C)172cm(D)184cm(E)190cm Question18It rained7times during the holiday.When it rained in the morning,it was sunny in the afternoon. When it rained in the afternoon,it was sunny in the morning.There were5sunny mornings and6 sunny afternoons.How many days did the holiday last at least?(A)7(B)8(C)9(D)10(E)11Jenny decided to write numbers in the cells of the3×3table below.The sums of the numbers in any 2×2squares are the same.The three numbers in the corner cells have already been written as shown in thefigure.Which number should she write in the bottom right corner cell?(A)5(B)4(C)1(D)0(E)Impossible to determineQuestion20Seven positive integers a,b,c,d,e,f,g are written in a row.The sum of all the seven positive integers is equals to2017;any two neighbouring numbers differ by±1.Which of the numbers can be equal to 286?(A)only a or g(B)only b or f(C)only c or e(D)only d(E)any of themSection C(Correct–5points|Unanswered–0points|Wrong–deduct1point)Question21There are4children of different ages under18.The product of their ages is882.Assuming that their ages are integers,find the sum of their ages.(A)23(B)25(C)27(D)31(E)33Question22On the faces of a given dice these numbers appear:−3,−2,−1,0,1,2.If you throw it twice and multiply the two results,what is the probability that the product is negative?(A)12(B)14(C)1136(D)1336(E)13Question23Given a two digit number ab.The six digit number ababab is divisible by?(A)2(B)5(C)7(D)9(E)11My friend wants to use a special seven digit password.The digits of the password occur exactly as many times as its digit value.The same digits of this number are always written consecutively.For example4444333or1666666.How many possible passwords can he choose from?(A)6(B)7(C)10(D)12(E)13Question25Paul wants to write a natural number in each box in the diagram such that each number is the sum of the two numbers in the boxes immediately underneath.At most how many odd numbers can Paul write?(A)13(B)14(C)15(D)16(E)17Question26Liza calculated the sum of angles of a convex polygon.She missed one of the angles and so her result was2017◦.What angle did she miss?(A)37◦(B)53◦(C)97◦(D)127◦(E)143◦Question27There are30dancers standing in a circle and facing the centre.After the”Left”command some dancers turned to the left and all the others-to the right.Those dancers who were facing each other, said”Hello”.It turned out to be10such dancers.Then after the command”Around”all the dancers made a180◦turn.Again,those dancers who were facing each other,said”Hello”.How many dancers said”Hello”?(A)10(B)20(C)8(D)15(E)impossible to determineOn a balance scale,3different masses are put at random on each pan and the result is shown in the picture.The masses are of101,102,103,104,105and106grams.What is the probability that the 106gram mass stands on the heavier(right)pan?(A)75%(B)80%(C)90%(D)95%(E)100% Question29A andB are on the circle with centre M.P B is tangent to the circle at B.The distances P A and MB are integers,P B=P A+6.How many possible values are there for MB?(A)0(B)2(C)4(D)6(E)8Question30Point D is chosen on the side AC of triangle ABC so that DC=AB.Points M and N are the midpoints of the segments AD and BC,respectively.If∠NMC=αthen∠BAC always equals to(E)60◦(A)2α(B)90◦−α(C)45◦+α(D)90◦−α2Rough Working。
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___？。
袋鼠数学澳大利亚数学竞赛题目
袋鼠数学澳大利亚数学竞赛题目（原创实用版）目录1.澳大利亚数学竞赛简介2.袋鼠数学竞赛的背景和意义3.袋鼠数学竞赛的题目类型和特点4.澳大利亚数学竞赛对学生的影响和启示正文【澳大利亚数学竞赛简介】澳大利亚数学竞赛（Australian Mathematics Competition，简称 AMC）是澳大利亚规模最大、历史最悠久的数学竞赛之一，旨在激发学生对数学的兴趣，培养学生的数学思维和解决问题的能力。
该竞赛每年吸引着成千上万的学生参加，不仅在澳大利亚境内有很高的影响力，同时也受到世界各地学生的欢迎。
【袋鼠数学竞赛的背景和意义】袋鼠数学竞赛（BMIMO，Bridge Mathematics International Olympiad）是澳大利亚数学竞赛中的一项重要赛事，其背景源于澳大利亚数学竞赛的组织者希望建立一个桥梁，将澳大利亚的学生与世界各地的学生联系起来，共同学习和探讨数学问题。
袋鼠数学竞赛的意义在于，它不仅为学生提供了一个展示自己数学才能的平台，还能激发学生对数学的兴趣，提高学生的数学素养。
【袋鼠数学竞赛的题目类型和特点】袋鼠数学竞赛的题目类型多样，包括选择题、填空题、解答题等。
题目内容涵盖了算术、代数、几何、组合等多个数学领域。
袋鼠数学竞赛的题目特点在于，它们往往具有现实意义，与生活息息相关，同时又具有一定的挑战性，需要学生运用所学的数学知识和技巧进行解答。
【澳大利亚数学竞赛对学生的影响和启示】澳大利亚数学竞赛对学生的影响是深远的。
首先，参加数学竞赛能提高学生的数学能力，激发学生对数学的兴趣。
其次，通过解决具有挑战性的数学问题，学生可以培养自己的逻辑思维、分析问题和解决问题的能力。
最后，澳大利亚数学竞赛为学生提供了一个与其他学生交流的平台，使他们能够互相学习、共同进步。
总的来说，袋鼠数学竞赛作为澳大利亚数学竞赛的一个重要组成部分，对于培养学生的数学兴趣和能力具有重要的意义。
2017年5-6年级袋鼠数学竞赛试题
假设每组的和是x，3组数的和就是3x。
6个数的和是3的倍数。 5+6+9+11+14=55
55+4=59，59不是3的倍数 55+7=62，62不是3的倍数
55+8=63，63是3的倍数 55+13=68，68不是3的倍数 55+15=63，70不是3的倍数
8.Martin把下图长方形中1/3的小正方形涂上了蓝色，一半的小正方形涂
(D) 16 cm2
(E) 6 cm2
2×2+4×4+6×6=56(cm2 )
56-1×1-2×2=51(cm2)
16. 四位球员在一场手球比赛中都有进球。他们所有人的进球数量都不同。
在四位当中，Mike 获得的进球数量最少。其余的三位总共进了 20球。
请问Mike的进球数量最大可能为多少？
(A) 2
2km 2km 2km 2km 2km 2km 2km 2km 2km 2km
70km
70-2×10=50(km) 50÷5=10(km) 10+2×3=16(km)
14. 如图所示，第一个三角形里有一只袋鼠。将虚线当作镜子。 前2个镜子的倒影已被显示 出来。 请问哪项是涂黑三角形里的袋鼠的方向？
√
4.Kalle 知道 1111 x 1111 = 1234321。请问 1111 x 2222 等于多少？
√ (A) 3456543 (B) 2345432 (C) 2234322 (D) 2468642 (E) 4321234 1 1 11×2 2 2 2 =（1 1 1 1×1 1 1 1）×2 =1 2 3 4 3 2 1×2 =24 6 8 6 4 2
从右面看： 可以确定盒子宽是4
袋鼠数学澳大利亚数学竞赛题目
袋鼠数学竞赛是澳大利亚的一个面向中学生的数学竞赛，其题目难度较高，主要考察学生的数学能力和解题技巧。
以下是一份袋鼠数学竞赛的题目样本：
题目1：在三角形ABC中，AB=AC，点D在BC上，且BD=DC。
求证：AD⊥BC。
题目2：在矩形ABCD中，点E在AD上，且CE平分∠BCD。
求证：AB=AE。
题目3：在正方形ABCD中，点E、F分别在AD、DC上，且AE=DF。
求证：CE=BF。
题目4：袋鼠A和袋鼠B在100米的直线上来回跳跃。
袋鼠A每次跳2米，而袋鼠B每次跳1米。
当其中一只袋鼠跳完100米后，另一只袋鼠还有多少米没跳完？题目5：一只蜗牛每天能爬行4米，它需要多少天才能爬完100米的直线距离？题目6：一只蜘蛛在一张网上爬行，它从网的中心开始爬行，每次爬行的距离为1厘米。
当它爬行完100厘米后，它在哪里？
这些题目考察的是学生的基础数学知识和解题能力，如三角形的中线定理、矩形的性质、正方形的性质等。
学生需要灵活运用这些知识点来解题。
同时，这些题目也注重考察学生的逻辑推理能力和空间想象能力，如通过证明来得出结论。
需要注意的是，这些题目仅为样本，实际比赛中的题目可能更加复杂和有挑战性。
因此，建议参赛者提前做好准备，熟悉各种数学知识点和解题技巧。
2016年袋鼠数学竞赛-一年级
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Question 14 Brian and William stand in a queue. Brian knows that there are 7 people in front of him. William knows that there are in total 11 people in the queue. If Brian is right in front of William, how many people are in the queue behind William?
Singapore Math Kangaroo Contest 2017
Primary 1 Contest Paper
Name: School:
INSTRUCTIONS: 1. Please DO NOT OPEN the contest booklet until the Proctor has given permission to start. 2. TIME : 1 hour and 30 minutes 3. There are 30 questions in this paper. 3 points, 4 points and 5 points will be awarded for each
(A) Adam
(B) Basil
(C) Charlie
(D) David
(E) Edgar
Question 2 In the picture below, there are 5-pointed, 6-pointed and 7-pointed stars. How many 5-pointed stars are there?
2016年袋鼠数学竞赛-Secondary-4
2016年袋⿏数学竞赛-Secondary-4Singapore Math Kangaroo Contest 2016Rough WorkingSection A(Correct–3points|Unanswered–0points|Wrong–deduct1point)1.The average of four numbers is9.What is the fourth number if three of the numbers are 5,9and12?(A)6(B)8(C)9(D)10(E)362.Which of the following numbers is the closest to the result of 17×0.3×20.16999(A)0.01(B)0.1(C)1(D)10(E)1003.On a test consisting of30questions,Ruth had50%more right answers than she had wrong answers.Each answer was either right or wrong.How many correct answers did Ruth have, assuming she answered all questions?(A)10(B)12(C)15(D)18(E)204.In a coordinate system,four of the following points are the vertices of a square.Which point is not a vertex of this square?(A)(?1,3)(B)(0,?4)(C)(?2,?1)(D)(1,1)(E)(3,?2)5.When the positive integer x is divided by6,the remainder is3.What is the remainder when3x is divided by6?(A)4(B)3(C)2(D)1(E)06.How many weeks are the same as2016hours?(A)6(B)8(C)10(D)12(E)167.Little Lucas invented his own way to write down negative numbers before he learned the usual way with the minus sign in front.Counting backwards,he’d write:...3,2,1,0,00,000, 0000,...What is the result of000+0000in his notation?(A)1(B)00000(C)000000(D)0000000(E)000000008.I have some strange dice:the faces show the numbers1to6as usual,except that the odd numbers are negative(-1,-3,-5in place of1,3,5).If I throw two such dice,which of these totals can not be achieved?(A)3(B)4(C)5(D)7(E)89.At least how many times do two directly adjacent letters have to be exchanged in order to change the word VELO into the word LOVE?(A)3(B)4(C)5(D)6(E)710.Sven wrote?ve di?erent one-digit positive integers on a blackboard.He discovered that no sum of any two numbers is equal to10.Which of the following numbers did Sven de?nitely write on the blackboard?(A)1(B)2(C)3(D)4(E)5Section B(Correct–4points|Unanswered–0points|Wrong–deduct1point)11.Let a+5=b2?1=c2+3=d?4.Which one of the numbers a,b,c,d is the largest?(A)a(B)b(C)c(D)d(E)impossible to determine12.The3×3table is divided into9squares with side length1,and two circles are inscribed in two of them(see?gure).What is the distance between the two nearest points of these circles?(A)2√2?1(B)√2+1(C)2√2(D)2(E)313.In a tennis tournament on a knock-out basis,six of the results of the quarter-?nals, the semi-?nals and the?nal were(not necessarily in this order):Bella beat Ann,Celine beat Donna,Gina beat Holly,Gina beat Celine,Celine beat Bella and Emma beat Farah.Which result is missing?(A)Gina beat Bella(B)Celine beat Ann(C)Emma beat Celine (D)Bella beat Holly(E)Gina beat Emma14.What percentage of the area of the triangle in the?gure is shaded?(A)80%(B)85%(C)88%(D)90%(E)impossible to determine15.Jill is making a magic multiplication square using the numbers1,2,4,5,10,20,25,50 and100.The products of the numbers in each row,in each column and in each of the two diagonals must all be the same.In the?gure 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)2516.Jack wants to hold six circular pipes with diameter 2cm together by a rubber band.He decided between two options as shown in the /doc/33582441988fcc22bcd126fff705cc1754275f74.html pare the lengths of the rubber bands.(A )In the left picture it is πcm shorter.(B )In the left picture it is 4cm shorter.(C )In the right picture it is πcm shorter.(D )In the right picture it is 4cm shorter.(E )Both have the same length.17.Eight identical envelopes contain the numbers:1,2,4,8,16,32,64,128.Eve chooses a fewenvelopes randomly.Alie takes the rest.Both sum up their numbers.Eve’s sum is 31more than Alie’s.How many envelopes did Eve take?(A )2(B )3(C )4(D )5(E )618.Peter wants to colour the cells of a 3×3square in such a way that each of the rows,the columns and both diagonals have three cells of three di?erent colours.What is the least number of colours Peter coulduse?(A )3(B )4(C )5(D )6(E )719.The picture shows a cube with four marked angles.What is the sum of these angles?(A )315?(B )330?(C )345?(D )360?(E )375?20.There are2016kangaroos,each of them is either grey or red and at least one of them is grey and at least one is red.For every kangaroo K we compute the fraction of the total number of kangaroos of the other colour divided by the total number of kangaroos of the same colour as K(including K).Find the sum of the fractions of all2016kangaroos.(A)2016(B)1344(C)1008(D)672(E)336Section C(Correct–5points|Unanswered–0points|Wrong–deduct1point)21.A plant wound itself exactly5times around a pole with height1m and circumference15 cm as shown in the picture.As it climbed,its height increased at a constant rate.What is the length of the plant?(A)0.75m(B)1.0m(C)1.25m(D)1.5m(E)1.75m22.What is the largest possible remainder that can be obtained when a two-digit number is divided by the sum of its digits?(A)13(B)14(C)15(D)16(E)1723.A5×5square is divided into25cells.Initially all its cells are white,as shown on the left.Neighbouring cells are those that share a common edge.On each move two neighbouring cells have their colours changed to the opposite colour(white cells become black and black ones become white).What is the minimum number of moves required in order to obtain the chess-like colouring shown on the right?(A)11(B)12(C)13(D)14(E)1524.It takes4hours for a motorboat to travel downstream along a river from X to Y.To return upstream from Y to X it takes the motorboat6hours.How many hours would it take a wooden log to be carried from X to Y by the current,assuming it is unhindered by any obstacles? (A)5(B)10(C)12(D)20(E)2425.In the Kangaroo republic,each month consists of40days,numbered1to40.Any day whose number is divisible by6is a holiday,and any day whose number is a prime is a holiday. How many times in a month does a single working day occur between two holidays?(A)1(B)2(C)3(D)4(E)526.Two of the altitudes of a triangle are10cm and11cm.Which of the following cannot be the length of the third altitude?(A)5cm(B)6cm(C)7cm(D)10cm(E)100cm27.Jakob wrote down four consecutive positive integers.He then calculated the four possible totals made by taking 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)328.Four sportsmen and sportswomen-a skier,a speed skater,a hockey player and a snow-boarder-had dinner at a round table.The skier sat at Amy’s left hand.The speed skater sat opposite Ben.Eva and Tom 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?nd out with the given information.29.Dates can be written in the form DD.MM.YYYY.For example,the date23March can be written as is23.03.2016.A date is called”surprising”if all8digits in its written form are di?erent.In what month will the next surprising date occur?(A)March(B)June(C)July(D)August(E)December30.At a conference,the2016participants are registered from P1to P2016.Each participant from P1to P2015shook hands with exactly the same number of participants as the one on their registration number.How many hands did the2016th participant shake?(A)1(B)504(C)672(D)1008(E)2015END OF PAPERRough Working。
袋鼠数学竞赛 介绍
袋鼠数学竞赛介绍
嘿嘿，大家好！我是小明，我想告诉你们一个好玩的事儿，就是袋鼠数学竞赛！这个竞赛呀，是一个很特别的数学比赛，参加的人都是小朋友。
听说它的名字是“袋鼠”，因为像袋鼠一样跳来跳去的，哈哈，好像数学也可以像袋鼠一样跳跃一样有趣呢！
袋鼠数学竞赛是一个国际性的比赛，世界上好多国家的小朋友都会参加。
竞赛的题目呀，不仅有加减法，还会有一些奇奇怪怪的图形，数字，考考你有没有观察力。
哎呀呀，有的题目好难哦！我做的时候，脑袋像要炸掉一样，哎哟！不过也好好玩儿，做出来一题，我就特别开心，觉得自己好聪明呢！
这个竞赛不需要太紧张，只要认真思考就好啦。
而且呀，竞赛的题目是分等级的，越做越难，最后就是超超级难了，但是每次做对一题，都觉得好有成就感哦！
我好喜欢袋鼠数学竞赛，下次我一定要做得更好！大家也来试试吧，数学不止是数字，它还是一个神奇的世界呢！嘻嘻！
—— 1。
袋鼠数学澳大利亚数学竞赛题目
袋鼠数学澳大利亚数学竞赛题目摘要：1.澳大利亚数学竞赛简介2.袋鼠数学竞赛的题目类型3.袋鼠数学竞赛的难度和竞赛形式4.袋鼠数学竞赛对学生的意义5.如何准备袋鼠数学竞赛正文：【澳大利亚数学竞赛简介】澳大利亚数学竞赛（Australian Mathematics Competition，简称AMC）是由澳大利亚数学协会（Australian Mathematics Trust，简称AMT）主办的一项面向全球中小学生的数学竞赛。
该竞赛自1978 年创办以来，吸引了越来越多的国家和地区的学生参与。
袋鼠数学竞赛是澳大利亚数学竞赛中的一个重要组成部分，主要面向小学生和初中生。
【袋鼠数学竞赛的题目类型】袋鼠数学竞赛的题目类型多样，涵盖了算术、代数、几何、组合等数学领域的知识。
题目设计灵活，旨在考验学生的数学应用能力和解题技巧。
竞赛题目既有选择题，也有填空题和解答题，旨在全面考察学生的数学素养。
【袋鼠数学竞赛的难度和竞赛形式】袋鼠数学竞赛的难度适中，适合小学和初中学生参加。
竞赛形式分为个人赛和团队赛，个人赛按照年级分组进行，团队赛则要求参赛选手组成团队进行合作。
这样的竞赛形式既能锻炼学生的个人能力，也能培养学生的团队协作精神。
【袋鼠数学竞赛对学生的意义】参加袋鼠数学竞赛对学生具有重要的意义。
首先，通过参加竞赛，学生可以巩固和提高自己的数学知识水平；其次，竞赛可以培养学生的逻辑思维能力和问题解决能力；最后，参加袋鼠数学竞赛可以为学生提供一个与其他学生交流和学习的平台，拓宽视野。
【如何准备袋鼠数学竞赛】要准备袋鼠数学竞赛，学生需要掌握扎实的数学基本功，多做练习题，提高解题速度和准确率。
此外，学生还可以参加培训班或请教老师，寻求专业指导。
同时，多参加模拟赛和练习赛，积累比赛经验，也是提高竞赛成绩的关键。
总之，袋鼠数学竞赛是澳大利亚数学竞赛中一项重要的赛事，对于培养学生的数学素养和团队协作精神具有重要意义。
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。
袋鼠竞赛奖项设置
袋鼠竞赛奖项设置引言袋鼠竞赛是一项具有挑战性和趣味性的比赛，旨在检验参赛者的能力、智慧和创造力。
为了激励参赛者的积极性，并推动竞赛的发展和提升，我们特设立以下奖项，以表彰在比赛中表现突出的个人和团队。
奖项设立本次袋鼠竞赛设立以下奖项：个人奖项1.最佳表现奖：该奖项将颁发给在比赛中表现最为出色的个人。
评选标准包括答题准确率、答题速度和解题思路的创新性。
获得该奖项的个人将获得奖杯和荣誉证书，并有机会获得额外的奖金。
2.进步之星奖：该奖项将颁发给在比赛中取得显著进步的个人。
评选标准是相比前一次比赛的成绩有明显提升，并展现出优秀的解题技巧和思维逻辑。
获得该奖项的个人将获得奖牌和鼓励证书。
3.全能选手奖：该奖项将颁发给在比赛中表现出色，在各个题型上均有出色表现的个人。
评选标准综合考虑各个题型的成绩，并对综合能力和全面素质进行综合评估。
获得该奖项的个人将获得奖状和奖品。
团队奖项1.团队冠军奖：该奖项将颁发给在比赛中获得总分最高的团队。
团队由3至5名参赛者组成，取团队成绩的前三名计入总分。
评选标准为团队的整体表现，包括答题准确率、答题速度和团队协作能力。
获得该奖项的团队将获得奖杯和团队荣誉证书。
2.团队创新奖：该奖项将颁发给在比赛中展现出创新思维的团队。
评选标准包括团队答题的创新解题思路、独特的解题方法和团队的合作精神。
获得该奖项的团队将获得奖牌和创新证书。
3.最佳组织奖：该奖项将颁发给在比赛组织和运营方面表现出色的团队。
评选标准包括比赛顺利进行的组织安排、比赛规则的执行和团队协作能力。
获得该奖项的团队将获得奖状和奖金。
奖项评选与颁发奖项的评选将由专业评委组成的评审团进行，他们会根据比赛结果、答题表现和解题思路等综合考虑来进行评选。
评审团将严格遵守公正、公平、公开的原则进行评选，并将评选结果及时公布。
奖项的颁发将在比赛结束后举行的颁奖典礼上进行。
颁奖典礼将由组织者精心策划和组织，以庄重、热烈的形式将奖项授予获奖个人和团队。
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(A) 1
√ (B) 2
(C) 3
(D) 5
(E) 6
6.Tom和John各使用了相同数量的立方体建了一个长方体的盒子
(每个立方体的大小相 同)。上图是Tom的盒子，下图是John的盒子的
第一层。John的盒子共有多少层？
(A) 2
(B) 3
√ (C) 4
(D) 5
(E) 6
6 ×2×2 = 24（块）
(i)第一个数字是1,
(ii)接下来的每个数字都和之前一个数字一样或更大，
(iii)所有数字的和是5。请问他共写了多少个数目？
(A) 4
√ (B) 5
(C) 6
(D) 7 (E) 8
11111
1112
1 22
113
14
20. Luigi开了一间小餐馆。他的朋友Giacomo给了他一些正方形的桌子
和一些椅子。如果他把全部桌子当单桌用，每张桌子有4把椅子，
只野猫。如果她每天给她的每一只猫吃相同数量的猫粮，祖母所买的
猫粮能维持多少夭？
√ (A) 8 (B) 7
(C) 6
(D) 5 (E) 4
4只猫
12天的猫粮
1只猫
48天的猫粮 6只猫
8天
15. BENJAMIN里的每个字母各代表数字1, 2, 3, 4, 5, 6或7其中一个。
不同的字母代表不同的数字。BENJAMIN的数目是单数并且可以
10.有五只松鼠A, B, C, D和E坐在线上。它们将会把6个有交叉标记的坚果
拾取。在同 一时刻，每只松鼠会以相同的速度向最靠近的坚果奔跑。
每当一只松鼠拾取一颗坚果后就会马上向另一颗最靠近的坚果奔跑。
请问哪只松鼠会拾取两个坚果？
(A) A (B) B
√ (C) C (D) D
(E) E
4格
4格
11.班上共有30位同学。他们一对对的坐着，每位男同学都和一位女同学
(A) 2675
√ (B) 2975 (C) 2978
(D) 258+1953+764=2975
13. Bart正在理发。他看到镜子中的时钟(如下图)。 他在十分钟前看镜子里的时钟是怎样的？
镜面对称
√
14.祖母买了足够她的四只猫吃12天的猫粮。在她回家的途中她带回了两
被3除。以下哪个数字是对应N字母？
(A) 1
(B) 2
(C) 3
BENJAMIN
√ (D) 5
(E) 7
2 3 1 4 5 6 7 1 2+3+1+4+5+6+7+1=29
2 1 3 4 5 6 7 3 2+1+3+4+5+6+7+3=31
2 1 5 4 3 6 7 5 2+1+5+4+3+6+7+5=33 2 1 7 4 3 6 5 7 2+1+7+4+3+6+5+7=35
2016袋鼠数学竞赛
等级3
1.以下哪个交通标志拥有最多的对称轴？
×√
×
2.如图，一条10cm长的线被折成几个长度相同的部分。这条线在两个作
有标记的地方被切 开。请问这三条线段的长度分别是？
√ (A) 2cm，3cm，5cm
(B) 2cm，2cm，6cm
(C) 1cm，4cm，5cm
(D)1cm，3cm，6cm (E)3cm，3cm，4cm
大长方形的周长+3个小长长方形的周长-3个红长方形的周长 30+20=50(cm) 20÷2=10(cm)
50-10=40(cm)
18.Anna把一张圆纸对折。之后她把纸对折多一次，然后再对折最后一次。 最后Anna把她 折后的纸沿着虚线剪开。这张纸打开后的形状是怎样的？
√
√
19.Richard把所有拥有以下特征的数目全部写下：
一起坐，但班上只有一半的女同学和男同学一起坐。请问班上共有多
少位男生？
(A) 25 (B) 20 (C) 15
√ (D) 10 (E) 5
30÷（2+1）=10（位）
12.号码2581953764被写在一张纸条上。John剪了纸条2次并获取3个号码.
之后他把这三个号码加起来。请问他能获得最小的和数是？
连上后形成了一个 较小的正方形。请问这个较小正方形的面积是？
(A) 10cm2 (B) 20cm2 (C)25cm2
√ (D) 40cm2 (E)50cm2
正方形的面积=对角线×对角线÷2
10×10÷2=50（cm2）
5.Alice的母亲想看见餐刀在每个盘子的右边，叉子在盘的左边。
请问Alice至少需要互换餐刀和叉子多少次以符合她母亲的要求？
3份
5份
2份
10÷（3+5+2）=1（cm） 1×3=3（cm），1×5=5（cm），1×2=2（cm）
3.在Lisa的冰箱上，有8个强力磁铁(图中黑色圆圈)支撑着一些明信片。
若不可有任何明信片落在地上，她最多能移走多少个磁铁？
(A) 2
√ (B) 3 (C)4 (D) 5 (E)6
4.Cathy画了一个边长10cm的正方形。她之后把正方形每边的中点相互
16. Tim, Tom和Jim是三胞胎(三位同一天出生的兄弟)，他们的弟弟Carl
比他们小三岁。以 下哪个数目有可能是这四位兄弟的岁数之和？
√ (A) 53
(B) 54
(C) 56 (D) 59
(E) 60
四位兄弟的岁数之和+3岁是4的倍数
5 3+ 3 = 56 56是4的倍数
54+3=57 56+3=59 60+3=63
57不是4的倍数 59不是4的倍数 63不是4的倍数
17.长方形ABCD的周长是30cm。有另三个长方形的中心为点A, B和D (如图)。这三个长方形(其中心分别为点A, B和D者)的 周长之和是20cm.请问粗线的总长度是多少？
√ (A) 50cm (B)45cm (C)40cm (D)35cm (E)30cm
24÷（3×2） = 4（层）
7.图中的这张纸被沿着虚线折成一个无盖的盒子。这个盒子被放在桌上
(顶部是无盖的)。 请问哪面是盒子的底部？
(A) A
√ (B) B
(C) C
(D) D (E) E
8.若使用两个相同的正方形粘在一起，以下哪个图形是不能被形成的？
√
9.Mary, Ann和Nata在一间幼儿园里工作。星期一至星期五的每一天正好
其中两位来上班。Mary一个星期工作3天，Ann一个星期工作4天。
请问Nata一个星期工作几天？
(A) 1 (B) 2
√ (C) 3
(D) 4
(E) 5
周一 Mar y
周二 Mar y
周三 Mar y
周四 Nata
周五 Nata
Nata
Ann Ann
Ann Ann
5×2=10（天） 10-3-4=3（天）