2016年袋鼠数学竞赛-四年级

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2015年5-6年级袋鼠数学竞赛试题

(A) 23
(B) 25
(C) 27
√ (D) 29 (E) 31
3 3 3 3 3 3 3 3 3 27
4 2 4 2 4 2 4 2 4 28
51
51
51
51
5 29
15. Lucy和她的妈妈共同在一月份出生。今天，3月26日2015年，
Lucy把她出生的年份、她妈妈出生的年份、她的年龄与她妈妈的
2015袋鼠数学竞赛
等级3
1. 以下哪个图中的灰格是占据整个图形的一半？
√
2.作者的雨伞上印有KANGAROO的字母（如图）。请问以下图中哪一支雨伞不是作者的？
√
3. Sam在图中的9个格子中涂上黑色，灰色和白色（如图）。
请问他最少需要再重新涂上颜色以便没有任何两个相邻的格子有着相同
的颜色？
若BC长为10cm,请问AB的长度是？
(A) 40
(B) 30
√ (C) 20
(D) 10
(E) 5
A
B
10cm
宽是长的一半
D
C
13. 以下哪个不能组成一个锥体？
√
14. 在Jump Street，一排共有9间屋子。每间最少一人居住。任何两间相邻
的屋子加起来最多可住6人。请问Jump Street最多可住多少人？
(A) 2
√ (B) 3
(C) 4
(D) 5
(E) 6
19.在以下加法算式中，相同的字母代表相同的号码，不同的字母代表
不同的号码。请问X代表什么号码？
(A) 2 (B) 3
(C) 4 (D) 5
√ (E) 6
6 6
99
11 1
20. Jane买了3个玩具。在付第一个玩具的钱时她付了身上一半又加EUR1

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。

袋鼠数学竞赛四年级66分

袋鼠数学竞赛四年级66分袋鼠数学竞赛四年级66分1. 竞赛介绍袋鼠数学竞赛是一项专门为孩子们量身打造的数学竞赛。

它不仅考察了学生掌握数学知识的程度，还挑战了学生的逻辑思维和创新能力，尤其是对于小学生来说，更是一项不容忽视的竞赛。

2. 活动背景春节期间，我带着孩子一起参加了袋鼠数学竞赛四年级组的比赛。

这个组别的考题主要涵盖了加减乘除、面积周长等基本的数学概念，以及逻辑推理和图形识别等更高阶的数学技能。

3. 孩子的表现我家孩子参加竞赛的表现可谓是非常出色的。

此前，家长们也曾经提醒过，这个竞赛可不是一场轻松的比赛，而是需要花费大量时间和精力去准备的。

为此，我也和孩子一起进行了长时间的复习和准备。

4. 学习的过程在竞赛前一个月，我就和孩子一起跟着袋鼠数学竞赛的复习资料进行有针对性的复习。

对于孩子来说，一些看似简单的概念，在正确的引导和提示下，也能够更好地被掌握和运用。

5. 竞赛的体验早上7点的比赛开始前，我们便到达了考场。

看到整个考场内挤满了孩子和家长，我不禁感触良多，为这种注重孩子学科全面发展的竞赛形式点赞。

在竞赛过程中，孩子们应对起来也表现得非常镇定自若，呈现出了过硬的数学知识和优秀的逻辑思维能力。

6. 取得的成绩几天后，我们收到了孩子的竞赛成绩，66分。

对于我们来说，虽然并不是最优秀的成绩，但考虑到我们孩子与竞赛初次接触的情况下，这个成绩已经非常不错了。

同时，通过这个竞赛，我们也意识到了孩子在数学学习上需要重点加强的地方，将针对这些地方进行更加有针对性的学习和练习。

7. 总结袋鼠数学竞赛是一场极具挑战性的比赛，要想在里面获得出色的成绩，需要经过专门的学习和准备。

孩子们在这场比赛中所取得的成绩不单单只是数字上的表现，更是对于他们数学知识和思维能力的全方位考核。

因此，我们家长也要给予孩子足够的支持和鼓励，引导他们更好地面对挑战，不断进步。

2016年5-6年级袋鼠数学竞赛

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

澳大利亚kangaroo袋鼠数学竞赛试题及答案grade1-11 2015年

(A) 16
(B) 15
(C) 12
(D) 8
(E) 7
Mathematical Kangaroo 2015 Group Ecolier (Grade 3 and 4)
Austria – 23. 3. 2015
‐ 3 point questions ‐
1.
(A) 6
(B) 7
(C) 8
(D) 10
(A) 24 meters (B) 48 meters (C) 72 meters (D) 80 meters (E) 88 meters
15. Some pirates are climbing onto a ship one after the other using a rope. Their leader is exactly in the middle. He is the eighth pirate to climb onto the ship. How many pirates board the ship?
(C)
(D)
(E)
2. How many triangles can you find in the picture?
(A) 7 (B) 6 (C) 5 (D) 4
(E) 3
3. Which part of the house is missing?
(A)
(B)
(C)
(D)
(E)
4. How many dots do all ladybirds have together? (A) 17 (B) 18 (C) 19 (D) 20 (E) 21
(A) 10
(B) 12
(C) 13
(D) 14

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。

袋鼠数学2018真题(3-4年级)

has one of the digits:0,1,2,3,4,5,6,7,8below.How many stamps does she use?salah satu digit berikut:0,1,2,3,4,Kangaroo seperti berikut.Berapakah bilangan cop yang digunakan?Leonie有10个橡皮图章。

每个图章拥有0，1，2，3，4，5，6，7，8，9的其中一个数字。

如下图所示，她把Kangaroo比赛的日期印了出来。

请问她一共用了多少个图章？85032011(A)5(B)6(C)7(D)9(E)10#2.The picture shows3ﬂying arrows and9ﬁxed balloons.When an arrow hits a balloon, the balloon bursts and the arrowﬂies further in the same direction.How many balloons in total are hit by arrows?Gambar berikut menunjukkan3anak panah yang berterbangan dan9belon yang tidak bergerak.Apabila suatu anak panah mengenai suatu belon,belon tersebut akan pecah dan anak panah tersebut akan terus terbang pada arah yang sama.Berapakah jumlah bilangan belon yang akan dipecahkan oleh anak panah?下图显示3支飞箭和9粒固定的气球。

当一支箭击中一粒气球，那粒气球会爆裂，而箭会继续往同样的方向飞行。

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。

16届wmo初赛试题四年级

16届WMO初赛试题四年级1. 引言本文档旨在介绍16届WMO初赛四年级的试题内容和相关要求。

该试题涉及多个学科的知识，包括数学、语文、英语等。

通过参与该试题，学生能够提高自己的综合素养和解决问题的能力。

2. 数学试题2.1 题目描述一辆货车总共装了300件商品，其中有60件是苹果，50件是梨子，剩余的是桃子。

已知桃子的数量是苹果和梨子数量之和的2倍，求货车上桃子的数量。

2.2 解答要求要求学生使用代数的方法解题，写出方程并求解。

然后，用文字描述解题过程，说明每一步的数学推理。

2.3 评分标准正确列出代数方程：30分正确求解方程并得出答案：30分正确描述解题过程并进行数学推理：40分3. 语文试题3.1 题目描述阅读下面的短文，根据短文内容回答问题。

北方的冬天真的很冷，特别是当风一吹过来时，仿佛能将人的骨头都冻住。

小明不怕冷，每天都会到外面玩耍。

小明最喜欢的活动是堆雪人。

他用手捏起一团雪，然后再给雪人加上眼睛、鼻子和嘴巴，最后给雪人梳头，整个过程非常有趣。

问题：小明最喜欢的活动是什么？3.2 解答要求要求学生根据短文的描述，准确回答问题，并用简洁的语言表达。

3.3 评分标准正确回答问题：40分清晰简洁的语言表达：60分4. 英语试题4.1 题目描述根据句子意思，在方框中选择合适的单词填空，使句子完整正确。

1.— Do you like _______? —Yes, I do. It’s my favoritefruit.A. appleB. orangeC. banana2.— Where is _______ bag? —It’s under the desk.A. myB. IC. me4.2 解答要求要求学生根据句子的意思，选择正确的单词填空，并写出自己选择的理由。

4.3 评分标准正确选择填空的单词：40分正确写出理由并解释选择的依据：60分5. 结语本文档介绍了16届WMO初赛四年级的试题内容和相关要求。

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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 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。