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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。
Singapore Math Kangaroo Contest 2017Secondary 2 Contest PaperName:School:INSTRUCTIONS:1.Please DO NOT OPEN the contest booklet until the Proctor has given permission to start.2.TIME : 1 hour and 30 minutes3.There are 30 questions in this paper. 3 points, 4 points and 5 points will be awarded for eachcorrect question in Section A, Section B and Section C respectively. No points are deducted for Unanswered question. 1 point is deducted for Wrong answer.4.Shade your answers neatly in the answer entry sheet.5.PROCTORING : No one may help any student in any way during the contest.6.No calculators are allowed.7.All students must fill and shade in your Name, Index number, Level and School in theAnswer sheet provided.8.MINIMUM TIME: Students must stay in the exam hall for at least 1 hour and 15 minutes.9.Students must show detailed working and transfer answers to the answer entry sheet.10.No spare papers can be used in writing this contest. Enough space is provided for yourworking of each question.11. Y ou must return this contest paper to the proctor.Rough WorkingSection A (Correct –3points |Unanswered –0points |Wrong –deduct 1point)Question 1What is the time 17hours after 17:00?(A )8:00(B )10:00(C )11:00(D )12:00(E )13:00Question 2A group of girls stand in a circle.Xena is the fourth on the left from Yana.She is also the seventh on the right from Yana.How many girls are in the group?(A )9(B )10(C )11(D )12(E )13Question 3What number must be subtracted from −17to obtain −33?(A )−50(B )−16(C )16(D )40(E )50Question 4The diagram shows a stripy isosceles triangle and its height.Each stripe has the same height.What fraction of the area in the triangle is white?(A )1/2(B )1/3(C )2/3(D )3/4(E )2/5Question 5Which of the following equation is correct?(A )41=1.4(B )52=2.5(C )63=3.6(D )74=4.7(E )85=5.8The diagram shows two rectangles whose sides are parallel.What is the difference in the perimeters of the two rectangles?(A)12m(B)16m(C)20m(D)21m(E)24m Question7Bob folded a piece of paper twice and then cut one hole through the folded piece of paper.When he unfolded the paper,he saw the arrangement shown in the diagram below.How did Bob fold his piece of paper?(A)(B)(C)(D)(E)Question8The sum of three different positive integers is7.What is the product of these three integers?(A)12(B)10(C)9(D)8(E)5Question9The diagram shows four overlapping hearts.The areas of the hearts are1cm2,4cm2,9cm2and16 cm2.What is the shaded area?(A)9cm2(B)10cm2(C)11cm2(D)12cm2(E)13cm2Yvonne has20dollars.Each of her four sisters has10dollars.How much does Yvonne have to give to each of her sisters,such that each of thefive girls has the same amount of money?(A)2(B)4(C)5(D)8(E)10Section B(Correct–4points|Unanswered–0points|Wrong–deduct1point)Question11Annie the Ant started at the left end of a pole and crawled 23of its length.Bob the Beetle startedat the right end of the same pole and crawled 34of its length.What fraction is the length of the polebetween Annie and Bob?(A)38(B)112(C)57(D)12(E)512Question12One sixth of the audience in a theatre were adults.Twofifths of children were boys.What fraction of the audience were girls?(A)1/2(B)1/3(C)1/4(D)1/5(E)2/5Question13In the diagram,the dashed line and the black path form seven equilateral triangles.The length of the dashed line is20.What is the length of the black path?(A)25(B)30(C)35(D)40(E)45Four cousins Ema,Iva,Rita and Zina are3,8,12and14years old,although not necessarily in that order.Ema is younger than Rita.The sum of the ages of Zina and Ema is divisible by5.The sum of the ages of Zina and Rita is also divisible by5.How old is Iva?(A)14(B)12(C)8(D)5(E)3Question15This year there were more than800runners participating in the Kangaroo Hop.Exactly35%of the runners were women and there were252more men than women.How many runners were there in total?(A)802(B)810(C)822(D)824(E)840Question16Rachel wants to write a number in each box of the diagram shown.She has already written two of the numbers.She wants the sum of all the numbers to be equal to35,the sum of the numbers in the first three boxes to equal22,and the sum of the numbers in the last three boxes to equal25.What is the product of the numbers she writes in the shaded boxes?(A)63(B)108(C)0(D)48(E)39Question17Simon wants to cut a piece of thread into nine pieces of the same length and marks his cutting points. Barbara wants to cut the same piece of thread into only eight pieces of the same length and also marks her cutting points.Carl then cuts the thread at all the cutting points that are marked.How many pieces of thread does Carl obtain?(A)15(B)16(C)17(D)18(E)19Two segments,each1cm long,are marked on opposite sides of a square of side8cm.The ends of the segments are joined as shown in the diagram.What is the shaded area,in cm2?(A)2(B)4(C)6.4(D)8(E)10Question19Tycho wants to prepare a schedule for his jogging.He wants to jog exactly twice a week,and on the same days every week.He never wants to jog on two consecutive days.How many such schedules are there?(A)16(B)14(C)12(D)10(E)8Question20Emily wants to write a number into each cell of a3×3table so that the sum of the numbers in any two cells with common sides that share an edge which is always the same.She has already written two numbers,as shown in the diagram.What is the sum of all the numbers in the table?(A)18(B)20(C)21(D)22(E)23Section C(Correct–5points|Unanswered–0points|Wrong–deduct1point)Question21The numbers of degrees in the angles in a triangle are three different integers.What is the minimum possible sum of its smallest and largest angles?(A)61◦(B)90◦(C)91◦(D)120◦(E)121◦Ten kangaroos stood in a line as shown in the picture below.At some point,two kangaroos standing side by side and facing each other exchanged places by jumping past each other.This was repeated until no further jumps were possible.How many exchanges were made?(A)15(B)16(C)18(D)20(E)21Question23Diana has nine numbers:1,2,3,4,5,6,7,8and9.She adds2to some of them,and5to all the others.What is the smallest number of different results she can obtain?(A)5(B)6(C)7(D)8(E)9Question24Buses leave the airport every3minutes to drive to the city centre.A car leaves the airport at the same time as one bus and drives to the city centre by the same route.It takes takes60minutes and 35minutes for each bus and the car respectively to drive from the airport to the city centre.How many buses does the car pass on its way to the centre,excluding the bus it left with?(A)8(B)9(C)10(D)11(E)13Question25Olesia’s tablecloth has a regular pattern,as shown in the diagram.What percentage of the tablecloth is black?(A)16(B)24(C)25(D)32(E)36Each digit in the sequence starting with2,3,6,8,8is obtained in the following way:thefirst two digits are2and3and afterwards each digit is the last digit of the product of the two preceding digits in the sequence.What is the2017th digit in the sequence?(A)2(B)3(C)4(D)6(E)8Question27Mike had125small cubes.He glued some of them together to form a big cube with nine tunnels leading through the whole cube as shown in the diagram.How many of the small cubes are there which he did not use?(A)52(B)45(C)42(D)39(E)36Question28Two runners are training on a720metre circular track.They run in opposite directions,each at constant speed.Thefirst runner takes four minutes to complete the full loop and the second runner takesfive minutes.How many metres does the second one run between two consecutive meetings of the two runners?(A)355(B)350(C)340(D)330(E)320Sarah wants to write a positive integer in each box in the diagram so that each number above the bottom row is the sum of the two numbers in the boxes immediately underneath.What is the largest number of odd numbers that Sarah can write?(A)5(B)7(C)8(D)10(E)11Question30The diagram shows parallelogram ABCD with area S.The intersection point of the diagonals of the parallelogram is O.The point M is marked on DC.The intersection point of AM and BD is E and the intersection point of BM and AC is F.The sum of the areas of the triangles AED and BF C is 13S.What is the area of the quadrilateral EOF M,in terms of S?(A)16S(B)18S(C)110S(D)112S(E)114S。
一年一度的的英国高级数学袋鼠竞赛（Senior Kangaroo）和奥林匹克数学竞赛第一轮（British Mathematical Olympiad Round 1 ，简称BMO1）一般同时进行。
今年的比赛是在11月16日，竞赛由 UKMT 主办。
The UK Mathematics Trust (UKMT) 是注册的慈善机构，主要为青少年提供数学教育，是全英国最大的数学竞赛组织。
英国奥数竞赛BMO和高级袋鼠竞赛（Senior Kangaroo）都是为英格兰和威尔士 13年级或以下的学生设计的比赛（北爱尔兰是14年级或以下，苏格兰是S6或以下）。
所以一般来说是读A Level的12-13年级（17-18岁）的学生参加，也有数学成绩优异的11年级或更小的学生参加。
今年是在英国高级数学挑战赛SMC 中取得100分以上的（约1000人）有资格晋级英国奥数竞赛第一轮（BMO1）， 76分以上的（约6000人）晋级高级袋鼠赛（Senior Kangaroo）。
英国高级袋鼠赛（Senior Kangaroo），一个小时，20道填空题，每题5分，满分100分。
直接写答案即可，不用写过程，做错不扣分。
得分最高的25%可以得到Merit证书，2022年分数达到40分以上的可以得到Merit证书。
英国奥数竞赛第一轮（ BMO1），3.5小时，六道大题，每题10分，要求写出详细的演算过程，满分60分。
成绩最好的100名学生将被邀请参加第二轮（BMO2）的决赛。
详情请点：英国奥数竞赛真题及答案。
英国奥数竞赛第二轮（ BMO2）将在2023年1月25日进行，3.5小时，四道大题，每题10分，要求写出详细的演算过程。
2022年17分以上可获得优异（Distinction）证书，10分以上获得良好（Merit）证书。
之后会从中选拔出最优秀的几十人参加集训，准备国际奥林匹克数学竞赛（International Mathematical Olympiad，简称IMO）和其它国际赛事。
袋鼠数学数学竞赛试题
题目，在一个房间里，有一只袋鼠和一只狗。
袋鼠的身高是狗的1/4，袋鼠的体重是狗的1/2。
如果袋鼠的体重增加了20%，那么袋鼠的身高将增加多少？
解答：
1. 利用代数方法解答：
设狗的身高为h，袋鼠的身高为1/4h。
袋鼠的体重为w，狗的体重为2w。
根据题意可得，袋鼠的体重增加20%，即原体重的1.2倍，即1.2w。
设袋鼠身高增加后的身高为x，则有，x = 1/4h + Δh（Δh为身高增加的值）。
根据题意可得，1.2w = 2w (x/h)^3（袋鼠体重的增加与身高的关系）。
整理方程得，(x/h)^3 = 0.6。
解方程可得，x/h ≈ 0.843。
因此，袋鼠的身高增加约为84.3%。
2. 利用比例方法解答：
根据题意可得，袋鼠的身高与狗的身高的比例为1:4，袋鼠的体重与狗的体重的比例为1:2。
设袋鼠的身高增加后的身高为x，根据比例可得，x/h = 1.2。
解方程可得，x = 1.2h。
因此，袋鼠的身高增加了20%。
3. 利用图形方法解答：
设狗的身高为h，袋鼠的身高为1/4h。
袋鼠的体重为w，狗的体重为2w。
根据题意可得，袋鼠的体重增加20%，即原体重的1.2倍，即1.2w。
画出狗和袋鼠的身高和体重的比较图，可以观察到袋鼠的身高增加了20%后，狗和袋鼠的身高之间的比例关系仍然保持不变。
综上所述，袋鼠的身高增加了约84.3%。
Singapore Math Kangaroo Contest 2017Primary 3 Contest PaperName:School:INSTRUCTIONS:1.Please DO NOT OPEN the contest booklet until the Proctor has given permission to start.2.TIME : 1 hour and 30 minutes3.There are 30 questions in this paper. 3 points, 4 points and 5 points will be awarded for eachcorrect question in Section A, Section B and Section C respectively. No points are deducted for Unanswered question. 1 point is deducted for Wrong answer.4.Shade your answers neatly in the answer entry sheet.5.PROCTORING : No one may help any student in any way during the contest.6.No calculators are allowed.7.All students must fill and shade in your Name, Index number, Level and School in theAnswer sheet provided.8.MINIMUM TIME: Students must stay in the exam hall for at least 1 hour and 15 minutes.9.Students must show detailed working and transfer answers to the answer entry sheet.10.No spare papers can be used in writing this contest. Enough space is provided for yourworking of each question.11. Y ou must return this contest paper to the proctor.Rough WorkingSection A(Correct–3points|Unanswered–0points|Wrong–deduct1point)Question1Which of the pieces(A,B,C,D,E)willfit in between the two pieces below,such that the two equations formed will be true?8–3=2(A )=55–1(B )=34–2(C)=51+2(D)=45–3(E)=51+1Question2John looks through the window as shown in the picture below.He only sees half the number of kangaroos in the park.How many kangaroos are there in the park intotal?(A)12(B)14(C)16(D)18(E)20Two gridded transparent sheets are darkened in some squares,as shown in the picture below.They are both placed on top of the board shown in the middle.The the pictures behind the darkened squares cannot be seen.Only one of the pictures can still be seen,which picture isit?Question 4original picture rotated in a particularway.The resultfootprints are missing?(A )(B )(C )(D )1(E )Question 5What number is hidden behind the panda?– 10 = 10+ 6 =– 6 = +8+ 8= A(A )16(B )18(C )20(D )24(E )28In the table below,the correct sums are shown.What number is in the box with the question mark?(A)10(B)12(C)13(D)15(E)16Question7Dolly accidentally broke the mirror into pieces.How many pieces have exactly four sides?(A)2(B)3(C)4(D)5(E)6Question8Which option shows the necklace below when it is untangled?(A)(B)(C)(D)(E)Section B(Correct–4points|Unanswered–0points|Wrong–deduct1point)Question9The picture below shows the front of Ann’s house.The back of her house has three windows and no door.What does Ann see when she is standing from the back of her house?(A)(B)(C)(D)(E)Question10Which option is correct?(A)(B)(C)(D)(E)Balloons are sold in packets of5,10and25.Marius buys exactly70balloons.What is the smallest number of packets he could buy?(A)3(B)4(C)5(D)6(E)7Question12Bob folded a piece of paper.He cut exactly one hole through the folded paper.Then he unfolded the piece of paper and saw the result as shown in the picture below.How did Bob fold his piece of paper?(A)(B)(C)(D)(E)Question13There is a tournament at a pool.Atfirst,13children signed up,and then another19signed up.Six teams with an equal number of members are needed for the tournament.At least how many more children need to sign up so that the six teams can be form?(A)1(B)2(C)3(D)4(E)5Question14Numbers are placed in the cells of the4×4square shown in the picture below.Mary selects any2×2 square in4×4square and adds up all the numbers in the four cells.What is the largest possible sum she can get?(A)11(B)12(C)13(D)14(E)15David wants to cook5dishes on a stove with only2burners.The time he needed to cook the5dishes are40mins,15mins,35mins,10mins and45mins.What is the shortest possible time in which he can cook all5dishes?(He can only remove a dish from the stove when it is fully cooked.)(A)60min(B)70min(C)75min(D)80min(E)85minQuestion16Which number should be(A)10(B)11(C)12(D)13(E)14Section C(Correct–5points|Unanswered–0points|Wrong–deduct1point)Question17The picture shows a group of building blocks and a plan of these blocks.Some ink has dripped onto(A)3(B)4(C)5(D)6(E)7How long is the train?(A)55m(B)115m(C)170m(D)220m(E)230mQuestion19George trains at his schoolfield atfive o’clock every afternoon.The journey from his house to the bus stop takes5minutes.The bus journey takes15minutes.It takes him5minutes to go from the bus stop to thefield.The bus runs every10minutes from six in the morning.What is the latest time he has to leave his house in order to arrive at thefield exactly on time?(A)(B)(C)(D)(E)Question20A small zoo has a giraffe,an elephant,a lion and a turtle.Susan wants to plan a tour where she sees 2different animals.She does not want to start with the lion.How many different tours can she plan?(A)3(B)7(C)8(D)9(E)12Four brothers have eaten11cookies in total.Each of them has eaten at least one cookie and no two of them have eaten the same number of cookies.Three of them have eaten9cookies in total and one of them has eaten exactly3cookies.What is the largest number of cookies one of the brothers has eaten?(A)3(B)4(C)5(D)6(E)7Question22Zosia has hidden some smileys in some of the squares in the table.In some of the other squares she writes the number of smileys in the neighbouring squares as shown in the picture.Two squares are said to be neighbouring if they share a common side or a common corner.How many smileys has she hidden?(A)4(B)5(C)7(D)8(E)11Question23Ten bags contain different numbers of candies from1to10in each of the bag.Five boys took two bags of candies each.Alex got5candies,Bob got7candies,Charles got9candies and Dennis got15 candies.How many candies did Eric get?(A)9(B)11(C)13(D)17(E)19Question24Kate has4flowers,one with6petals,one with7petals,one with8petals and one with11petals. Kate tears offone petal from threeflowers.She does this several times,choosing any threeflowers each time.She stops when she can no longer tear one petal from threeflowers.What is the smallest number of petals which(A)1(B)2(C)3(D)4(E)5。
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。
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。
3points#1.Four cards are in a row.We can choose any two cards and swap them.Which row of cards cannot be obtained?Empat kad disusun dalam satu baris.Kita boleh memilih mana-mana dua kad dan menukarkan kedudukan kad-kad tersebut.Baris kad yang manakah tidak boleh diperoleh?四张卡片被排成一排。
我们能选择其中两张，并对换它们的位置。
请问以下哪项是无法被获得的？201727100127102702172071(A )2017271011202172071(B )2017271001102021720711(C )2017271001102021720711(D )2017271001271027021720711(E )2017271001271027021720711#2.A fly has 6legs and a spider has 8legs.A group of 3flies and 2spiders have as many legs as a group of 9chickens and howmany cats?Seekor lalat mempunyai 6kaki dan seekor labah-labah mempunyai 8kaki.Sekumpulan 3ekor lalat dan 2ekor labah-labah mempunyai bilangan kaki yang sama dengan sekumpulan 9ekor ayam dan berapa ekor kucing?一只苍蝇有6条腿，一只蜘蛛有8条腿。
袋鼠数学竞赛题目
袋鼠数学竞赛是一项全球规模最大的青少年数学竞赛，针对1-12年级的学生。
这个竞赛的题目相比其他的数学竞赛题更具趣味性，对孩子来说也是练手的好机会。
以下是一些题目的例子：
阅读理解题：这是1、2年级的题目，你让孩子读一下，看看能否看得懂题目？第一遍看这个题目的时候有点懵，再仔细看题目、看图案，才发现，原来每只瓢虫身上都有圆点，而圆点的数量也各不一样，因此文中强调了一句“in the order of increasing number of dots”，必须要理解这句话，才能明白需要根据圆点的数量来连接瓢虫的道理。
这题的答案是D。
视觉训练题：看下面这道1、2年级的视觉训练题目，问一个图像颜色交换一下后会变成什么样子？答案是E。
等到了3、4年级，还是同样的图案，但是对孩子思维难度要求更高。
你看下面的题目，不仅仅是需要孩子将颜色交换一下，还需要将图像旋转一下，问最后变成什么样子？答案选E。
建模能力题：我们看下面这道3、4年级的题目，有4个球，分别是10g、20g、30g和40g，根据图里面的天平指示，问哪个球是30g？这道题目就需要孩子能根据图像所示建立一个数学模型，否则这道题目TA是做不出来的！这个数学模型应该是下面这个样子：第一个模型是：A+B > C+D，这对应于第一张图，表示A和B的重量比C和D的重量重。
第二个模型是：B+D = C。
这对应于第二张图，表示B和D的重量和C一样重。
有了这两个模型，孩子把数字带入进去，就比较容易得到答案了！答案是C。
2016年袋鼠数学竞赛-Primary-2Singapore Math Kangaroo Contest 2016Rough WorkingSection A(Correct–3points|Unanswered–0points|Wrong–deduct1point)1.Which letter on the board is not in the word”KOALA”?(A)R(B)L(C)K(D)N(E)O2.How many ropes are there in the picture?(A)2(B)3(C)4(D)5(E)63.Michael built a house with How many matches did he use?(A)19(B)18(C)17(D)15(E)134.In a cave,there were two horses,one bear and three ter,?ve horses,three bears and four turtles joined them.How many animals are in the cave now?(A)6(B)9(C)12(D)15(E)185.Which point can we reach if we cannot pass through walls?(A)A(B)B(C)C(D)D(E)E6.Ten friends came to John’s birthday party,six of them were girls.How many boys were there in the party?(A)4(B)5(C)6(D)7(E)87.Matt had to deliver?yers to all houses numbered from25to57.How many houses got the ?yers?(A)31(B)32(C)33(D)34(E)358.Which shape can we make with10cubes?(A)(B)(C)(D)(E)Section B(Correct–4points|Unanswered–0points|Wrong–deduct1point)9.Sophie arranges some balls on a staircase in a certain way as shown in the picture.How will the balls appear on the level with the question mark?(A)(B)(C)(D)(E)10.Agatha,the hen,lays white and brown eggs.Lisa puts six eggs in the box below.Two brown eggs cannot touch each other.At most,how many brown eggs can Lisa put in the box?(A)1(B)2(C)3(D)4(E)511.Kanga is1year and3months old now.In how many months will Kanga be2years old?(A)3(B)5(C)7(D)8(E)912.Granny went out to the yard and called all the hens and her cat.All20legs ran to her. How many hens does granny have?(A)11(B)9(C)8(D)6(E)413.In Baby Roo’s house,each room is connected to any neighboring room by a door as shown in the picture.Baby Roo wants to get from the room A to the room B.What is the least number of doors that he will need to go through?(A)3(B)4(C)5(D)6(E)714.There are twelve rooms in a building.Each room has two windows and one st evening,eighteen windows were lighted.In how many rooms was the light o??(A)2(B)3(C)4(D)5(E)615.Mary is walking along the road and she reads only the letters located on her right side. Moving from point1to point2,what is the word she will get?(A)KNAO(B)KNGO(C)KNR(D)AGRO(E)KAO16.The sum of John’s and Paul’s ages is equal to12.What will be the sum of their ages in 4years?(A)16(B)17(C)18(D)19(E)20Section C(Correct–5points|Unanswered–0points|Wrong–deduct1point)17.Which of the following pictures cannot be made by using?gures like the one given below?(A)(B)(C)(D)(E)18.Which tile?ts in the middle of the pattern?(A)((C)(D)(E)19.Amy used six equal small squares to build the?gure.What is the least number of equal small squares she should add to the obtain a larger square?(A)6(B)8(C)9(D)10(E)1220.Five sparrows sat on a wire as shown in the picture.Some of them looked to their left, others looked to their right.Each sparrow chirped only once to each bird it saw on its side. For example,third sparrow from the left chirped two times.In total,how many times did they chirp?(A)61221.Which pattern can we make using all?ve cards given below?(A)(B)(C)(D)(E)22.There are5ladybirds in the picture.Each one sits on its?ower.Their places are de?ned as follows:the di?erence of the number of dots on their wings is the number of the leaves and the sum of the number of dots on their wings is the number of the petals.Which of the following?owers has no ladybird?(A)(B)(C)(D)(E)23.On each of six faces of a cube there is one of the following six symbols:?,?,?,?, and .There is a di?erent symbol on each face.In the picture we can see this cube shown in two di?erent positions.Which symbol is opposite the ?(A) (B)?(C)?(D)?(E)?24.The numbers1,5,8,9,10,12and15are distributed into groups with one or more numbers.The sum of the numbers in each group is the same.What is the largest number of groups?(A)2(B)3(C)4(D)5(E)6END OF PAPERRough Working。
