加拿大国际袋鼠数学竞赛试题 及答案-2018年

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%。

袋鼠数学题，也被称为“袋鼠数学竞赛”，是一个面向中
学生的数学竞赛，其题目以问题解决和数学应用为主。

以下
是一份袋鼠数学竞赛的样题：
选择题
1. 如果一只袋鼠一年跳300次，那么五只袋鼠跳多少次？
A. 1500次
B. 1400次
C. 1300次
D. 1200次
E. 1100次
2. 在一个等边三角形中，一个顶点到一个对边的中点的
距离是3米，那么这个三角形的边长是多少？
A. 3米
B. 4米
C. 5米
D. 6米
E. 8米
3. 一个圆和一个扇形的半径相等。

已知圆的面积是50平
方厘米，而扇形所在圆的面积是200平方厘米，这个扇形的
圆心角是多少度？
A. 72度
B. 108度
C. 180度
D. 360度
E. 720度
答案：A，C，B。

解释：第一题根据比例关系计算；第二题利用勾股定理计算；第三题根据面积比计算圆心角。

通过这些题目可以看出，袋鼠数学竞赛的题目强调数学的应用和问题解决能力，而不仅仅是理论知识和计算能力。

因此，想要在袋鼠数学竞赛中取得好成绩，需要具备广泛的数学知识、敏锐的观察力和良好的思维习惯。

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. 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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。

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

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

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

袋鼠数学竞赛题在我国，数学一直被视为学科中的重头戏。

为了提高孩子们的数学素养和思维能力，许多学校和机构举办了各种各样的数学比赛。

袋鼠数学竞赛就是其中之一，它的名称来源于袋鼠在澳大利亚是一种非常普遍的动物，象征着这个竞赛适合广大学生参加。

下面我将带您了解一下袋鼠数学竞赛的特点及其挑战性的数学问题。

袋鼠数学竞赛是一个国际性的数学竞赛，始于1980年，至今已有40年历史。

为了鼓励学生对数学的兴趣和探究，竞赛制定了一套独特而有趣的考题，不仅能考察学生的数学知识，更能考察他们的逻辑思维和问题解决能力。

与其他数学竞赛不同的是，袋鼠数学竞赛有三个不同的组别：普及组、提高组和国际组，每个组别的试题难度和题型也不同。

普及组的题目结构比较简单，主要考察学生在基础数学知识的掌握程度上。

而提高组的题目就相对难一些，主要考察学生在更加高级的数学知识和技能上的掌握情况。

而在国际组的竞赛中，一些挑战性的数学问题会让参赛选手挑战自我、超越自我。

在袋鼠数学竞赛中，题目形式多样，短问题、选择题、填空题、计算题、解决问题和证明题都会出现。

每个题目都有一定深度和难度，一些题目还要求学生在短时间内分析和解决，是一种很好的对数学运用和思考能力的考验。

接下来，我们来看看几道典型的袋鼠数学竞赛题目。

第一道题目是普及组中的一道计算题：小李要从1元、2元、5元三种面额的货币中选择70元钱，共有多少种不同的选择方法？这道题主要考察了学生的组合数学基础。

第二道选自提高组的题目：一个正整数被九除余八，被水平线翻转后得到一个六位正整数，求这个六位正整数的值。

这道题主要考察了学生在数论和数字推理中的能力。

此外，还有一道难度较大的题目：有100个棋子，其中有99个正常重量，还有1个轻重袋子。

通过使用一个只能测3次的天平，你能找到轻重袋子吗？这道题考察了学生的逻辑思维和问题解决能力，是一道非常挑战性的数学题目。

总的来说，袋鼠数学竞赛是一种很好的对学生数学能力的考察和锻炼。

I N T E R N A T I O N A L C O N T E S T-G A M EM A T H K A N G A R O OC A N AD A,2018I N S T R U C T I O N SG R A D E1-21.You have 45 minutes to solve 18 multiple choice problems. For eachproblem, circle only one of the proposed five choices. If you circle more than one choice, your response will be marked as wrong.2.Record your answers in the response form. Remember that this is the onlysheet that is marked, so make sure you have all your answers transferred to the response form before giving it back to the contest supervisor.3.The problems are arranged in three groups. A correct answer of the first 6problems is worth 3 points. A correct answer of the problems 7-12 is worth4 points. A correct answer of the problems 13-18 is worth5 points. Foreach incorrect answer, one point is deducted from your score. Each unanswered question is worth 0 points. To avoid negative scores, you start from 18 points. The maximum score possible is 90.4.The use of external material or aid of any kind is not permitted.5.The figures are not drawn to scale. They should be used only for illustrationpurposes.6.Remember, you have about 2 to 3 minutes for each problem; hence, if aproblem appears to be too difficult, save it for later and move on to another problem.7.At the end of the allotted time, please give the response form to thecontest supervisor.8.Do not forget to pick up your Certificate of Participation on your way out!Good luck!Canadian Math Kangaroo Contest teamCanadian Math Kangaroo ContestPart A: Each correct answer is worth 3 points1.Which shape cannot be formed using and ?(A) (B) (C) (D) (E)2.At least how many 4-ray stars like this are glued together tomake this shape ?(A) 5 (B) 6 (C) 7 (D) 8 (E) 93.This pizza was divided into equal slices.How many slices are missing?(A) 1 (B) 2 (C) 3 (D) 4 (E) 54.How many kangaroos must be moved from one park to the other in order toget the same number of kangaroos in each park?(A) 4 (B) 5 (C) 6 (D) 8 (E) 95.Which of these ladybugs has to fly away so that the rest of them have 20dots in total?(A) (B) (C) (D) (E)6.Emilie builds towers in the following patternWhich one will be the tower number 6?(A) (B) (C) (D) (E)Part B: Each correct answer is worth 4 points7.If ◊+ ◊ = 4 and ∆ + ∆ + ∆ = 9, what is the value of ◊ + ∆ = ?(A) 2 (B) 3 (C) 4 (D) 5 (E) 68.Lisa has 4 pieces , but she only needs 3 forcompleting her puzzle frame . Which piece will be left over?(A)(B)(C)(D) (E)or9.How many right hands are in this picture?(A) 3 (B) 4 (C) 5 (D) 6 (E) 710.The dog went to its food following a path. In total it made 3 right turns and2 left turns. Which path did the dog follow?(A) (B) (C)(D) (E)11.What number is in the box marked "?" ?(A) 6 (B) 13 (C) 24 (D) 29 (E) Some other number12.Charles cut a rope in three equal pieces and then made some equal knotswith them. Which figure correctly shows the three pieces with the knots?(A) (B)(C) (D)(E)Part C: Each correct answer is worth 5 points13.How many circles and how many squares are covered by the blot in thepicture?(A) 1 circle and 3 squares(B) 2 circles and 1 square(C) 3 circles and 1 square(D) 1 circles and 2 squares(E) 2 circles and 2 squares14.Diana shoots three arrows at a target.On her first try, she gets 6 points and the arrows land like this: 6 pointsOn her second try, she gets 8 points and the arrows land like this: 8 pointsOn her third try, the arrows land like this:? points How many points will she get the third time?(A) 8 (B) 10 (C) 12 (D) 14 (E) 1615.How many different numbers greater than 10 and smaller than 25 with distinct digits can we make by using any two of the digits 2, 0, 1, and 8?(A) 4 (B) 5 (C) 6 (D) 7 (E) 816.Mark had some sticks of length 5 cm and width 1 cm.With the sticks he constructed the fence below.What is the length of the fence?(A) 20 cm(B) 21 cm(C) 22 cm (D) 23 cm (E) 25 cmlength17.The road from Anna's house to Mary's house is 16 km long.The road from Mary's house to John's house is 20 km long.The road from the crossroad to Mary's house is 9 km long.How long is the road from Anna’s house to John's house?(A) 7 km (B) 9 km (C) 11 km (D) 16 km (E) 18 km18.There are four ladybugs on a 4×4 board. Two are asleep and do not move.The other two ladybugs move one square every minute (up, down, left, or right). Here are pictures of the board for the first four minutes:Minute 1 Minute 2 Minute 3 Minute 4Which of these is a picture of the fifth minute (Minute 5)?(A) (B) (C) (D) (E)International Contest-GameMath Kangaroo Canada, 2018Answer KeyGrade 1-21 A B C D E 7 A B C D E 13 A B C D E2 A B C D E 8 A B C D E 14 A B C D E3 A B C D E 9 A B C D E 15 A B C D E4 A B C D E 10 A B C D E 16 A B C D E5 A B C D E 11 A B C D E 17 A B C D E6 A B C D E 12 A B C D E 18 A B C D E。

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

Singapore Math Kangaroo Contest 2018Rough Working–0points|Wrong–deduct1point)has one of the digits:0,1,2,3,4,5,6,7,8and9.Sheas shown below.How many stamps does she use?810320(A)5(B)6(C)7(D)9(E)10Question2The picture shows3flying arrows and9fixed balloons.When an arrow hits a balloon,it bursts, and the arrowflies further in the same direction.How many balloons will be hit by the arrows?(A)2(B)3(C)4(D)5(E)6Question3Susan is6years old.Her sister is one year younger and her brother is one year older.What is the sum of the ages of the three siblings?(A)10(B)15(C)18(D)21(E)30Question4The picture showsfive screws in a block.Among the5screws,only1of them is shorter than the other4screws.Which screw is the shortest?(A)1(B)2(C)3(D)4(E)5Question5The picture of the ladybird is shown below.Which option is not the same ladybird?(A)(B)(C)(D)(E)Question6Lucy folds a sheet of paper in half.Then she cuts a piece out of it as shown in the picture below. What will she see when she unfolds the paper?(A)(B)(C)(D)(E)Question7In herfirst try,Diana scores12points in total with three arrows.On her second try she scores15 points.How much points does(A)18(B)19(C)20(D)21(E)22Question8Mike sets the table for8guests as shown in the picture below.He wants to serve each guest with the correct arrangement,which means a fork on the left of each plate and a knife on the right.How many guest will have the correct(A)5(B)4(C)6(D)2(E)3|Wrong–deduct1point)Question9Roberto makes designs using tiles like this.How many of the5designs can he make?(A)1(B)2(C)3(D)4(E)5Question10Albertfills the grid below withfivefigures.Eachfigure appears exactly once in every column and every row.Whichfigure must mark?(A(B)(C)(D)(E)Question11Tom wants to cover the boat completely using the2types of shapes,a square and a trapezium as shown in the picture below.If no shapes can overlap each other,what is the least number of square and trapezium pieces does Tom needs to cover the boat completely?(A)5(B)6(C)7(D)8(E)9The colours in the picture below are inverted.Then the picture was rotated.What does the new picture looklike?(A )11111Question 13A rabbit has 20carrots.It eats 2carrots every day.If it ate the 12th carrot on Wednesday,which day did the rabbit start eating the carrots?(A )Monday (B )Tuesday (C )Wednesday (D )Thursday (E )Friday Question 14Toby glues 10cubes together to make the structure shown below.He paints the surface of the structure,including the bottom.How many cubes 4faces painted?(A )6(B )7(C )8(D )9(E )10Question 15There are 8flowers on a rose bush.There are no more than one insect per flower.More than half of the flowers are occupied.The number of butterflies on the flowers is twice the number of dragonflies on the flowers.How many butterflies are on the flowers?(A )2(B )3(C )4(D )5(E )6Kook wants to sail from the island called Easter through every island on the map and back to The total journey is 100km long.Some of the distances between each island have been written in the picture as shown below.For example,the distance between Easter Island andVolcano Island is 17km.The distance between Desert Island and Lake Island is the sameas the distance between Easter Island and Flower Island through Volcano Island.What is the distance between Easter Island and Lake Island?(A )17km (B )23km (C )26km (D )33km (E )35kmSection C (Correct –5points |Unanswered –0points |Wrong –deduct 1point)Question 17The rooms in Kanga’s house are numbered from 1to 14.Baby Roo enters the main door as indicated by the arrow show in the picture below.He passes through some rooms before leaving the house in one of the doors labeled A,B,C,D and E.The numbers of the rooms that he visits are always increasing.Through which door does he leave the house?(A )A (B )B (C )C (D )D (E )EQuestion 18Four balls each weigh 10,weighs 30?(A )A(B )B (C )C (D )D(E )It could be A or B2018–Primary 3/Grade 3in five ways.How much longer is the band fastened (A )4cm (B )8cm (C )10cm (D )16cm (E )20cmQuestion 20In an ancient language the symbolsIt is knownthat:represent the followingnumbers 1,2,3,4,and 5.Nobody knows which symbol represents which number.We know that:It is known that:Which (A )t is known that:It is known that:It is known that:It is known that:)It is known that:(A )(B )(C )(D )(E )Singapore Math Kangaroo Contest 2018–Primary 3/Grade 3Question 22The large rectangle is made up of different sized squares as shown in the picture below.The 3small squares each have an area of 1.1(A )165(B )176(C )187(D )198(E )200Question 23Loes wants to write the numbers from 1to 7in the boxes shown below.Two consecutive numbers cannot be written in twoneighbouring boxes.Neighbouring boxes share a common side.What numbers can she write in the box marked with a question mark?(A )all seven numbers (B )only odd numbers (C )only even numbers (D )only number 4(E )only the numbers 1or 7Question 24To defeat a dragon Mathias has to cut offall the dragon’s heads.If he can cut off3dragon’s heads,one new head immediately grows.Mathias defeats the dragon by cutting off13heads in total.How many heads did the dragon have in the beginning?(A )8(B )9(C )10(D )11(E )12Rough Working。

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

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

5除以3等于1余2。

所以，每个朋友可以得到1个苹果，剩下2个苹果无法平均分配。

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

长方形的面积是长乘以宽，即10厘米乘以5厘米，等于50平方厘米。

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

因为0的平方是0，1的平方是1。

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

原圆的面积为πr²，新圆的面积为π(1.1r)²=1.21πr²。

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

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

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

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

数学是一种美妙的语言，通过不断的练习和思考，你将能够发现它的魅力。

袋鼠数学竞赛试题及答案1. 基础计算题：计算下列各题的结果。

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

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

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

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

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

7. 组合题：一个班级有30个学生，需要选出5个学生代表班级参加比赛。

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

求这组数据的平均数和中位数。

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

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

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