美国国际袋鼠数学竞赛试题

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%。

美国袋鼠数学竞赛试题及答案一、选择题（每题2分，共10分）1. 如果一个数的平方等于81，那么这个数是：A. 9B. -9C. 3D. -32. 下列哪个分数是最接近0.5的？A. 0.49B. 0.51C. 0.48D. 0.523. 如果一个圆的半径是5厘米，那么它的周长是多少厘米？A. 15πB. 10πC. 20πD. 25π4. 一个班级有30名学生，其中1/3是男生，其余是女生。

这个班级有多少名女生？A. 20B. 10C. 15D. 55. 一个数的立方是-27，这个数是：A. -3B. 3C. -27D. 27二、填空题（每题3分，共15分）6. 如果一个数的平方根是4，那么这个数是______。

7. 一个直角三角形的两条直角边分别是3和4，那么它的斜边长度是______。

8. 一个数的1/4加上5等于10，这个数是______。

9. 如果一个数的1/5是2，那么这个数是______。

10. 一个数的2倍加上3等于11，这个数是______。

三、解答题（每题5分，共20分）11. 一个长方形的长是20厘米，宽是10厘米，求它的面积。

12. 如果一个数的平方加上这个数等于10，求这个数。

13. 一个圆的直径是14厘米，求它的面积。

14. 一个数的立方加上这个数的平方再加上这个数等于64，求这个数。

答案1. B（-9的平方是81）2. B（0.51最接近0.5）3. C（周长=2πr，r=5，所以周长=2*π*5=10π）4. A（女生人数=30*(2/3)=20）5. A（-3的立方是-27）6. 16（4的平方是16）7. 5（根据勾股定理，斜边=√(3^2+4^2)=5）8. 36（设这个数为x，x/4+5=10，解得x=36）9. 10（设这个数为x，x/5=2，解得x=10）10. 4（设这个数为x，2x+3=11，解得x=4）11. 面积=长*宽=20*10=200平方厘米12. 设这个数为x，x^2+x=10，解得x=(-1+√41)/2 或 x=(-1-√41)/2（舍去负根）13. 面积=πr^2，r=直径/2=7，所以面积=π*7^2=49π平方厘米14. 设这个数为x，x^3+x^2+x=64，解得x=4结束语希望这份试题能够帮助同学们更好地准备美国袋鼠数学竞赛，同时也能够激发大家学习数学的热情。

SAMPLE QUESTION FOR 3 POINTSWhich digits are missing on the right?A) 3 and 5 B) 4 and 8 C) 2 and 0 D) 6 and 9 E) 7 and 1SAMPLE QUESTION FOR 4 POINTSGeorge has 2 cats of the same weight. What is the weight of one cat if George weighs 30 kilograms?A) 1 kilogram B) 2 kilograms C) 3 kilogramsD) 4 kilograms E) 5 kilogramsSAMPLE QUESTION FOR 5 POINTSIn a certain game it is possible to make the following exchanges:Adam has 6 pears. How many strawberries will Adam have after he trades all his pears for just strawberries?A) 12 B) 36 C) 18 D) 24 E) 6SAMPLE QUESTION FOR 3 POINTSWhich digits are missing on the right?A) 3 and 5 B) 4 and 8 C) 2 and 0 D) 6 and 9E) 7 and 1SAMPLE QUESTION FOR 4 POINTSGeorge has 2 cats of the same weight. What is the weight of one cat if George weighs 30 kilograms?A) 1 kilogram B) 2 kilograms C) 3 kilogramsD) 4 kilograms E) 5 kilogramsSAMPLE QUESTION FOR 5 POINTSIn a certain game it is possible to make the following exchanges:Adam has 6 pears. How many strawberries will Adam have after he trades all his pears for just strawberries?A) 12 B) 36 C) 18D) 24 E) 6SAMPLE QUESTION FOR 3 POINTSIn which figure is the number of black kangaroos larger than the number of white kangaroos?SAMPLE QUESTION FOR 4 POINTSEach time Pinocchio lies, his nose gets 6 cm longer. Each time he tells the truth, his nose gets 2 cm shorter. After his nose was 9 cm long, he told three lies and made two true statements. How long was Pinocchio's nose afterwards?A) 14 cm B) 15 cm C) 19 cm D) 23 cm E) 31 cmSAMPLE QUESTION FOR 5 POINTSJoining the midpoints of the sides of the triangle in the drawing we obtain a smaller triangle. We repeat this one more time with the smaller triangle. How many triangles of the same size as the smallest resulting triangle fit in the original drawing?A) 5 B) 8 C) 10 D) 16 E) 32SAMPLE QUESTION FOR 3 POINTSIn which figure is the number of black kangaroos larger than the number of white kangaroos?SAMPLE QUESTION FOR 4 POINTSEach time Pinocchio lies, his nose gets 6 cm longer. Each time he tells the truth, his nose gets 2 cm shorter. After his nose was 9 cm long, he told three lies and made two true statements. How long was Pinocchio's nose afterwards?A) 14 cm B) 15 cm C) 19 cm D) 23 cm E) 31 cmSAMPLE QUESTION FOR 5 POINTSJoining the midpoints of the sides of the triangle in the drawing we obtain a smaller triangle. We repeat this one more time with the smaller triangle. How many triangles of the same size as the smallest resulting triangle fit in the original drawing?A) 5 B) 8 C) 10 D) 16E) 32SAMPLE QUESTION FOR 3 POINTSNathalie wanted to build the same cube as Diana had (Figure 1). However, Nathalie ran out of small cubes and built only a part of the cube, as you can see in Figure 2. How many small cubes must be added to Figure 2 to form Figure 1?A) 5 B) 6 C) 7 D) 8 E) 9SAMPLE QUESTION FOR 4 POINTSMary shades various shapes on square sheets of paper, as shown.How many of these shapes have the same perimeter as the sheet of paper itself?A) 2 B) 3 C) 4 D) 5 E) 6SAMPLE QUESTION FOR 5 POINTSThere are four buttons in a row as shown below. Two of them show happy faces, and two of them show sad faces. If we press on a face, its expression turns to the opposite (e.g. a happy face turns into a sad face). In addition to this, the adjacent buttons also change their expressions to the opposite. What is the least number of times you need to press the buttons in order to get all happy faces?A) 2 B) 3 C) 4 D) 5 E) 6SAMPLE QUESTION FOR 3 POINTSNathalie wanted to build the same cube as Diana had (Figure 1). 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The lines are parallel to the sides and divide the sides into three equal parts. What is the area of the shaded part?A) 1 B) 4 C) 5 D) 6 E) 7SAMPLE QUESTION FOR 4 POINTSVasya wrote down several consecutive integers. Which of the following could not be the percentage of odd numbers among them?A) 40 B) 45 C) 48 D) 50 E) 60SAMPLE QUESTION FOR 5 POINTSThe diagram shows a shaded quadrilateral KLMN drawn on a grid. Each cell of the grid has sides of length 2 cm. What is the area of KLMN?A) 96 cm2B) 84 cm2C) 76 cm2D) 88 cm2E) 104 cm2SAMPLE QUESTION FOR 3 POINTSIn the picture, the big triangle is equilateral and has an area of 9. The lines are parallel to the sides and divide the sides into three equal parts. What is the area of the shaded part?A) 1 B) 4 C) 5 D) 6E) 7SAMPLE QUESTION FOR 4 POINTSVasya wrote down several consecutive integers. Which of the following could not be the percentage of odd numbers among them?A) 40 B) 45C) 48 D) 50 E) 60SAMPLE QUESTION FOR 5 POINTSThe diagram shows a shaded quadrilateral KLMN drawn on a grid. Each cell of the grid has sides of length 2 cm. What is the area of KLMN?A) 96 cm2B) 84 cm2C) 76 cm2D) 88 cm2E) 104 cm2SAMPLE QUESTION FOR 3 POINTSThe number 200013 – 2013 is not divisible byA) 2. B) 3. C) 5. D) 7. E) 11.SAMPLE QUESTION FOR 4 POINTSThe points P and Q are opposite vertices of a regular hexagon and the points R and S are the midpoints of opposite edges, as shown. The area of the hexagon is 60 cm2. What is the product of the lengths of PQ and RS?A) 40 cm2B) 50 cm2C) 60 cm2D) 80 cm2E) 100 cm2SAMPLE QUESTION FOR 5 POINTSHow many positive integers are multiples of 2013 and have exactly 2013 divisors (including 1 and the number itself)?A) 0 B) 1 C) 3 D) 6 E) other answerSAMPLE QUESTION FOR 3 POINTSThe number 200013 – 2013 is not divisible byA) 2. B) 3. C) 5. 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How many pieces are there in this circle?A) 8 B) 9 C) 10 D) 12 E) 15SAMPLE QUESTION FOR 5 POINTSHow many pairs (x, y) of integers with x < y exist such that their product equals 5 times their sum?A) 4 B) 5 C) 6 D) 7 E) 8LEVELS 11 AND 12 ANSWERSSAMPLE QUESTION FOR 3 POINTSWhich of the following numbers is the largest?A) 2013 B) 20+13C) 2013 D) 2013E) 20 ·13SAMPLE QUESTION FOR 4 POINTSRadu has identical plastic pieces in the shape of a regular pentagon. He glues them edge to edge to complete a circle, as shown in the picture. How many pieces are there in this circle?A) 8 B) 9 C) 10D) 12 E) 15SAMPLE QUESTION FOR 5 POINTSHow many pairs (x, y) of integers with x < y exist such that their product equals 5 times their sum?A) 4B) 5 C) 6 D) 7 E) 8。

袋鼠数学数学竞赛试题袋鼠数学数学竞赛试题（详细版）第一部分：选择题（共10道题，每题4分，共40分）1. 若方程组 $2x+3y=7$，$5x-4y=8$ 的解为 $(a,b)$ ，求 $a+b$ 的值。

A. 1B. 2C. 3D. 42. 在一个等边三角形的内部有一个圆，圆与三角形的边相切，圆的半径为 4 cm。

求该等边三角形的边长。

A. 8 cmB. 12 cmC. 16 cmD. 24 cm3. 数列 $\{a_n\}$ 满足 $a_1=1$，$a_2=2$，$a_3=4$，$a_n=a_{n-1}+a_{n-2}+a_{n-3}$ （$n \geq 4$）。

则 $a_8$ 的值为多少？A. 29B. 32C. 33D. 364. 已知正方形 $ABCD$ 的边长为 8 cm，点 $P$ 在边 $AB$ 上，点$Q$ 在边 $CD$ 上，且 $AP=3$ cm，$CQ=4$ cm。

连接 $PQ$ ，求$PQ$ 的长度。

A. 3 cmB. 4 cmC. 5 cmD. 6 cm5. 在等差数列 $\{a_n\}$ 中，$a_1=3$，$a_5=11$。

求 $a_{10}$ 的值。

A. 19B. 20C. 21D. 226. 若 $a$ 的值满足 $a^3-7a^2+16a-12=0$，求 $a^2-3a+6$ 的值。

A. 8B. 10C. 12D. 147. 已知 $\triangle ABC$ 的三边分别为 $AB=8$ cm，$AC=6$ cm，$BC=10$ cm。

点 $D$ 在边 $BC$ 上，且 $BD=4$ cm。

若 $\angle DAB=60^\circ$，求 $\angle ACD$ 的度数。

A. $30^\circ$B. $45^\circ$C. $60^\circ$D. $75^\circ$8. 函数 $f(x)$ 为实数域上的线性函数，且满足 $f(3)=-4$，$f(5)=6$。

SAMPLE QUESTION FOR 3 POINTS6. The pink tower is taller than the red tower but shorter than the green tower. The silver tower is taller than the green tower. Which tower is the tallest?(A) pink tower (B) green tower (C) red tower (D) silver tower(E) We don’t know.SAMPLE QUESTION FOR 4 POINTS15. The picture shows the five houses of five friends and their school. The school is the largest building in the picture. To go to school, Doris and Ali walk past Leo’s house. Eva walks past Chole’s house. Which is Eva’s house?(A) (B) (C) (D) (E) SAMPLE QUESTION FOR 5 POINTS18. Every time the witch has 3 apples, she turns them into 1 banana. Every time she has3 bananas, she turns them into 1 apple. What will she end up with if she starts with4 apples and5 bananas?(A) (B) (C) (D) (E)SAMPLE QUESTION FOR 3 POINTS6. The pink tower is taller than the red tower but shorter than the green tower. The silver tower is taller than the green tower. Which tower is the tallest?(A) pink tower (B) green tower (C) red tower (D) silver tower(E) We don’t know.SAMPLE QUESTION FOR 4 POINTS15. The picture shows the five houses of five friends and their school. The school is the largest building in the picture. To go to school, Doris and Ali walk past Leo’s house. Eva walks past Chole’s house. Which is Eva’s house?(A) (B)(C) (D) (E) SAMPLE QUESTION FOR 5 POINTS18. Every time the witch has 3 apples, she turns them into 1 banana. Every time she has3 bananas, she turns them into 1 apple. What will she end up with if she starts with4 apples and5 bananas?(A)(B) (C) (D) (E)SAMPLE QUESTION FOR 3 POINTS2. How many fish will have their heads pointing towards the ring when we straighten the line?(A) 3 (B) 5 (C) 6 (D) 7 (E) 8SAMPLE QUESTION FOR 4 POINTS15. On a tall building there are 4 fire escape ladders, as shown. The heightsof 3 ladders are at their tops. What is the height of the shortest ladder?(A) 12 (B) 14 (C) 16 (D) 20 (E) 22SAMPLE QUESTION FOR 5 POINTS23. Elena wants to write the numbers from 1 to 9 in the squares shown. The arrows always point from a smaller number to a larger one. She has already written 5 and 7. Which number should she write instead of the question mark?(A) 2 (B) 3 (C) 4 (D) 6 (E) 8SAMPLE QUESTION FOR 3 POINTS2. How many fish will have their heads pointing towards the ring when we straighten the line?(A) 3 (B) 5 (C) 6 (D) 7 (E) 8SAMPLE QUESTION FOR 4 POINTS15. On a tall building there are 4 fire escape ladders, as shown. The heightsof 3 ladders are at their tops. What is the height of the shortest ladder?(A) 12 (B) 14 (C) 16 (D) 20 (E) 22SAMPLE QUESTION FOR 5 POINTS23. Elena wants to write the numbers from 1 to 9 in the squares shown. The arrows always point from a smaller number to a larger one. She has already written 5 and 7. Which number should she write instead of the question mark?(A) 2 (B) 3 (C) 4 (D) 6 (E) 8SAMPLE QUESTION FOR 3 POINTS10. There is a square with line segments drawn inside it. The line segments are drawn either from the vertices or the midpoints of other line segments. We colored 18 of the large square. Which one is our coloring?(A) (B) (C) (D) (E)SAMPLE QUESTION FOR 4 POINTS13. Rosa wants to start at the arrow, follow the line, and get out at the other arrow. Which piece, if placed in the middle, cannot produce this? Note: The piece can be rotated.(A) (B) (C) (D) (E)SAMPLE QUESTION FOR 5 POINTS29. 10 elves and trolls each were given a token with a different number from 1 to 10 written on it. They were each asked what number was on their token and all answered with a number from 1 to 10. The sum of the answers was 36. Each troll told a lie and each elf told the truth. What is the smallest number of trolls there could be in the group?(A) 1 (B) 3 (C) 4 (D) 5 (E) 7SAMPLE QUESTION FOR 3 POINTS10. There is a square with line segments drawn inside it. The line segments are drawn either from the vertices or the midpoints of other line segments. We colored 18 of the large square. Which one is our coloring?(A) (B) (C) (D)(E)SAMPLE QUESTION FOR 4 POINTS13. Rosa wants to start at the arrow, follow the line, and get out at the other arrow. Which piece, if placed in the middle, cannot produce this? Note: The piece can be rotated.(A) (B) (C) (D) (E)SAMPLE QUESTION FOR 5 POINTS29. 10 elves and trolls each were given a token with a different number from 1 to 10 written on it. They were each asked what number was on their token and all answered with a number from 1 to 10. The sum of the answers was 36. Each troll told a lie and each elf told the truth. What is the smallest number of trolls there could be in the group?(A) 1 (B) 3 (C) 4 (D) 5 (E) 7SAMPLE QUESTION FOR 3 POINTS5. When the five pieces shown fit together correctly, the result is a rectangle with a calculationwritten on it. What is the result of this calculation?(A) –100 (B) –8 (C) –1 (D) 199 (E) 208SAMPLE QUESTION FOR 4 POINTS13. The area of the large square is 16 cm 2 and the area of each small square is 1 cm 2. What is the total area of the black flower?(A) 3 cm 2(B) 72 cm 2(C) 4 cm 2(D) 112 cm 2(E) 6 cm 2SAMPLE QUESTION FOR 5 POINTS26. 2021 colored kangaroos are arranged in a row and are numbered from 1 to 2021. Eachkangaroo is colored red, gray, or blue. Among any three consecutive kangaroos, there are always kangaroos of all three colors. Bruce guesses the colors of five kangaroos. These are his guesses: Kangaroo 2 is gray; Kangaroo 20 is blue; Kangaroo 202 is red; Kangaroo 1002 is blue; Kangaroo 2021 is gray. Only one of his guesses is wrong. What is the number of the kangaroo whose color he guessed incorrectly?(A) 2 (B) 20 (C) 202 (D) 1002 (E) 2021SAMPLE QUESTION FOR 3 POINTS5. When the five pieces shown fit together correctly, the result is a rectangle with a calculation written on it. What is the result of this calculation?(A) –100 (B) –8 (C) –1 (D) 199 (E) 208SAMPLE QUESTION FOR 4 POINTS13. The area of the large square is 16 cm2 and the area of each smallsquare is 1 cm2. What is the total area of the black flower?(A) 3 cm2(B) 72 cm2(C) 4 cm2(D) 112 cm2(E) 6 cm2SAMPLE QUESTION FOR 5 POINTS26. 2021 colored kangaroos are arranged in a row and are numbered from 1 to 2021. Each kangaroo is colored red, gray, or blue. Among any three consecutive kangaroos, there are always kangaroos of all three colors. Bruce guesses the colors of five kangaroos. These are his guesses: Kangaroo 2 is gray; Kangaroo 20 is blue; Kangaroo 202 is red; Kangaroo 1002 is blue; Kangaroo 2021 is gray. Only one of his guesses is wrong. What is the number of the kangaroo whose color he guessed incorrectly?(A) 2 (B) 20 (C) 202 (D) 1002 (E) 2021SAMPLE QUESTION FOR 3 POINTS1. Each year, the third Thursday in March is named Kangaroo Day. The dates of Kangaroo Day for the next few years are shown below, with one error. Which date is wrong?(A) March 17, 2022 (B) March 16, 2023 (C) March 14, 2024(D) March 20, 2025 (E) March 19, 2026SAMPLE QUESTION FOR 4 POINTS13. The numbers from 1 to 6 are placed in the circles at the intersections of three rings.The position of number 6 is shown. The sums of the numbers on each ring are the same. What number is placed in the circle with the question mark?(A) 1 (B) 2 (C) 3 (D) 4 (E) 5SAMPLE QUESTION FOR 5 POINTS25. The smaller square in the picture has an area of 16 and the gray triangle has an area of 1. What is the area of the larger square?(A) 17 (B) 18 (C) 19 (D) 20 (E) 21SAMPLE QUESTION FOR 3 POINTS1. Each year, the third Thursday in March is named Kangaroo Day. The dates of Kangaroo Day for the next few years are shown below, with one error. Which date is wrong?(A) March 17, 2022 (B) March 16, 2023 (C) March 14, 2024(D) March 20, 2025 (E) March 19, 2026SAMPLE QUESTION FOR 4 POINTS13. The numbers from 1 to 6 are placed in the circles at the intersections of three rings.The position of number 6 is shown. The sums of the numbers on each ring are the same. What number is placed in the circle with the question mark?(A) 1 (B) 2 (C) 3 (D) 4 (E) 5SAMPLE QUESTION FOR 5 POINTS25. The smaller square in the picture has an area of 16 and the gray triangle has an area of 1. What is the area of the larger square?(A) 17 (B) 18 (C) 19 (D) 20 (E) 21LEVELS 11 AND 12SAMPLE QUESTION FOR 3 POINTS1. Paula’s weather app shows a diagram of the predicted weather and maximum temperatures for the next seven days, as shown. Which of the following represents the corresponding graph of maximum temperatures?(A) (B) (C)(D) (E)SAMPLE QUESTION FOR 4 POINTS19. A naughty puppy grabs the end of a roll of toilet paper and walks away at a constant speed. Which of the functions below best describes the thickness y of the roll as a function of the unrolled part x?(A) (B) (C)(D) (E)SAMPLE QUESTION FOR 5 POINTS30. A certain game is won when one player gets 3 points ahead. Two players A and B are playingthe game and at a particular point, A is 1 point ahead. Each player has an equal probability of winning each point. What is the probability that A wins the game?(A) 12(B) 23(C) 34(D) 45(E) 56LEVELS 11 AND 12 ANSWERSSAMPLE QUESTION FOR 3 POINTS1. Paula’s weather app shows a diagram of the predicted weather and maximum temperatures for the next seven days, as shown. Which of the following represents the corresponding graph of maximum temperatures?(A) (B) (C)(D) (E)SAMPLE QUESTION FOR 4 POINTS19. A naughty puppy grabs the end of a roll of toilet paper and walks away at a constant speed. Which of the functions below best describes the thickness y of the roll as a function of the unrolled part x?(A) (B) (C)(D) (E)SAMPLE QUESTION FOR 5 POINTS30. A certain game is won when one player gets 3 points ahead. Two players A and B are playingthe game and at a particular point, A is 1 point ahead. Each player has an equal probability of winning each point. What is the probability that A wins the game?(A) 12(B)23(C) 34(D) 45(E) 56。

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。

LEVELS 1 AND 2SAMPLE QUESTION FOR 3 POINTSWhich toy comes before the 5th toy?A) B) C) D) E)SAMPLE QUESTION FOR 4 POINTSWhich letter is missing from each of the words below? SCHOL BOK PRBLEM QUESTINA) A B) E C) O D) I E) USAMPLE QUESTION FOR 5 POINTSWhich number should replace the question mark in the pyramid?A) 10 B) 14 C) 22 D) 24 E) 34LEVELS 1 AND 2 ANSWERSSAMPLE QUESTION FOR 3 POINTSWhich toy comes before the 5th toy?A) B) C) D)E)SAMPLE QUESTION FOR 4 POINTSWhich letter is missing from each of the words below? SCHOL BOK PRBLEM QUESTINA) A B) E C) O D) I E) USAMPLE QUESTION FOR 5 POINTSWhich number should replace the question mark in the pyramid?A) 10 B) 14 C) 22 D) 24E) 34LEVELS 3 AND 4SAMPLE QUESTION FOR 3 POINTSNot taking any steps backwards, Anna travelled toward the car using a path shown in the picture, and picked up numbers she encountered along her way. Which set of the numbers below could she pick up?A) 1, 2, 4 B) 2, 3, 4 C) 2, 3, 5 D) 1, 5, 6 E) 1, 2, 5SAMPLE QUESTION FOR 4 POINTSThe square shown in the picture must be filled in such a way that each of thedigits 1, 2, and 3 appears in each row and in each column once and onlyonce. If Harry started to fill in the square as shown, what number can hewrite in the square marked with the question mark?A) 1 B) 2 C) 3 D) 1 or 2 E) 1, 2 or 3SAMPLE QUESTION FOR 5 POINTSHow many digits have to be written in order to write down every number from 1 to 100 inclusive?A) 100 B) 150 C) 190 D) 192 E) 200LEVELS 3 AND 4 ANSWERSSAMPLE QUESTION FOR 3 POINTSNot taking any steps backwards, Anna travelled toward the car using a path shown in the picture, and picked up numbers she encountered along her way. Which set of the numbers below could she pick up?A) 1, 2, 4 B) 2, 3, 4 C) 2, 3, 5D) 1, 5, 6 E) 1, 2, 5SAMPLE QUESTION FOR 4 POINTSThe square shown in the picture must be filled in such a way that each of thedigits 1, 2, and 3 appears in each row and in each column once and onlyonce. If Harry started to fill in the square as shown, what number can hewrite in the square marked with the question mark?A) 1 B) 2 C) 3D) 1 or 2 E) 1, 2 or 3SAMPLE QUESTION FOR 5 POINTSHow many digits have to be written in order to write down every number from 1 to 100 inclusive?A) 100 B) 150 C) 190 D) 192E) 200LEVELS 5 AND 6SAMPLE QUESTION FOR 3 POINTSEvaluate 2007 ÷ (2 + 0 + 0 + 7) – 2 × 0 × 0 × 7A) 1 B) 9 C) 214 D) 223 E) 2007SAMPLE QUESTION FOR 4 POINTSAlex, Ben, Carl, and Daniel each participates in a different sport: karate, soccer, volleyball, and judo. Alex does not like sports played with a ball. Ben practices judo and often attends soccer games to watch his friend play. Which of the following statements is true?A) Alex plays volleyball.B) Ben plays soccer.C) Carl plays volleyball.D) Daniel does karate.E) Alex does judo.SAMPLE QUESTION FOR 5 POINTSTo the right of a certain two-digit number the same number has been written, creating a four-digit number. How many times is the new four-digit number greater than the original two-digit number?A) 100 B) 101 C) 1000 D) 1001 E) 10LEVELS 5 AND 6 ANSWERSSAMPLE QUESTION FOR 3 POINTSEvaluate 2007 ÷ (2 + 0 + 0 + 7) – 2 × 0 × 0 × 7A) 1 B) 9 C) 214 D) 223E) 2007SAMPLE QUESTION FOR 4 POINTSAlex, Ben, Carl, and Daniel each participates in a different sport: karate, soccer, volleyball, and judo. Alex does not like sports played with a ball. Ben practices judo and often attends soccer games to watch his friend play. Which of the following statements is true?A) Alex plays volleyball.B) Ben plays soccer.C) Carl plays volleyball.D) Daniel does karate.E) Alex does judo.SAMPLE QUESTION FOR 5 POINTSTo the right of a certain two-digit number the same number has been written, creating a four-digit number. How many times is the new four-digit number greater than the original two-digit number?A) 100 B) 101C) 1000 D) 1001 E) 10LEVELS 7 AND 8SAMPLE QUESTION FOR 3 POINTSRose bushes are planted in a line on both sides of a path. The distance between the bushes is 2 m. What is the largest number of bushes that can be planted if the path is 20 m long?A) 22 B) 20 C) 12 D) 11 E) 10SAMPLE QUESTION FOR 4 POINTSx is a strictly negative integer. Which of the expressions is the greatest?A) x + 1 B) 2x C) −2x D) 6x + 2 E) x − 2SAMPLE QUESTION FOR 5 POINTSA certain broken calculator does not display the digit 1. For example, if we type in the number 3131, only the number 33 is displayed, with no spaces. Mike typed a 6-digit number into that calculator, but only 2007 appeared on the display. How many different numbers could Mike have typed?A) 12 B) 13 C) 14 D) 15 E) 16LEVELS 7 AND 8 ANSWERSSAMPLE QUESTION FOR 3 POINTSRose bushes are planted in a line on both sides of a path. The distance between the bushes is 2 m. What is the largest number of bushes that can be planted if the path is 20 m long?A) 22B) 20 C) 12 D) 11 E) 10SAMPLE QUESTION FOR 4 POINTSx is a strictly negative integer. Which of the expressions is the greatest?A) x + 1 B) 2x C) −2x D) 6x + 2 E) x − 2SAMPLE QUESTION FOR 5 POINTSA certain broken calculator does not display the digit 1. For example, if we type in the number 3131, only the number 33 is displayed, with no spaces. Mike typed a 6-digit number into that calculator, but only 2007 appeared on the display. How many different numbers could Mike have typed?A) 12 B) 13 C) 14 D) 15E) 16LEVELS 9 AND 10SAMPLE QUESTION FOR 3 POINTSIn the picture, what is the sum of the number of dots on the faces of the dice which you cannot see?A) 15 B) 12 C) 7 D) 27 E) another answerSAMPLE QUESTION FOR 4 POINTSTo fill in the table, we need to write 0 or 1 in each cell in such a way that the sum of numbers of each row and of each column is equal to 2. What are x and y ? A) x = 1, y = 1 B) x = 1, y = 0 C) x = 0, y = 1D) x = 0, y = 0 E) It is impossible to determine.SAMPLE QUESTION FOR 5 POINTSA certain island is inhabited by liars and truth-tellers (the liars always lie and the truth-tellers always tell the truth). One day 12 islanders, both liars and truth-tellers, gathered together and issued a few statements. Two people said: “Exactly two people among us twelve are liars.” Four other people said: “Exactly four people among us twelve are liars.” The other six people said: “Exactly six people among us twelve are liars.” How many liars were there? A) 2 B) 4 C) 6 D) 8 E) 10LEVELS 9 AND 10 ANSWERSSAMPLE QUESTION FOR 3 POINTSIn the picture, what is the sum of the number of dots on the faces of the dice which you cannot see?A) 15 B) 12C) 7D) 27E) another answerSAMPLE QUESTION FOR 4 POINTSTo fill in the table, we need to write 0 or 1 in each cell in such a way that the sum of numbers of each row and of each column is equal to 2. What are x and y ? A) x = 1, y = 1 B) x = 1, y = 0C) x = 0, y = 1D) x = 0, y = 0 E) It is impossible to determine.SAMPLE QUESTION FOR 5 POINTSA certain island is inhabited by liars and truth-tellers (the liars always lie and the truth-tellers always tell the truth). One day 12 islanders, both liars and truth-tellers, gathered together and issued a few statements. Two people said: “Exactly two people among us twelve are liars.” Four other people said: “Exactly four people among us twelve are liars.” The other six people said: “Exactly six people among us twelve are liars.” How many liars were there? A) 2 B) 4C) 6D) 8E) 10LEVELS 11 AND 12SAMPLE QUESTION FOR 3 POINTSA billiard ball always bounces off the side of a billiard table at an angle of 45° as shown. If it continues on the path shown, which pocket will the ball fall into?A) A B) B C) C D) DE) The ball will not fall into any pocket.SAMPLE QUESTION FOR 4 POINTSThe square ABCD lies in a plane and its edge measures 1. Consider all squares that share at least two vertices with the square ABCD. What is the area of the region covered by all of such squares, not including ABCD?A) 5 B) 6 C) 7 D) 8 E) 9SAMPLE QUESTION FOR 5 POINTSWhat is the measure of the acute angle of a rhombus with side of length equal to the geometric mean of its diagonals?A) 15° B) 30° C) 45° D) 60° E) 75°LEVELS 11 AND 12 ANSWERSSAMPLE QUESTION FOR 3 POINTSA billiard ball always bounces off the side of a billiard table at an angle of 45° as shown. If it continues on the path shown, which pocket will the ball fall into?A) A B) B C) C D) DE) The ball will not fall into any pocket.SAMPLE QUESTION FOR 4 POINTSThe square ABCD lies in a plane and its edge measures 1. Consider all squares that share at least two vertices with the square ABCD. What is the area of the region covered by all of such squares, not including ABCD?A) 5 B) 6 C) 7D) 8 E) 9SAMPLE QUESTION FOR 5 POINTSWhat is the measure of the acute angle of a rhombus with side of length equal to the geometric mean of its diagonals?A) 15° B) 30°C) 45° D) 60° E) 75°。

2024袋鼠数学试卷一、选择题（每题3分，共30分）1. 小明有10颗糖，给了小红3颗，又给了小刚2颗，小明还剩下几颗糖？（）A. 5颗B. 4颗C. 6颗D. 7颗。

2. 一个三角形的内角和是（）（人教版数学知识）A. 180°B. 360°C. 90°D. 270°.3. 计算：25×4÷2= （）A. 50B. 40C. 60D. 80.4. 在1 - 100这些自然数中，能被5整除的数有多少个？（）A. 19个B. 20个C. 21个D. 18个。

5. 一个正方形的边长为5厘米，它的面积是（）平方厘米。

A. 10B. 15C. 20D. 25.6. 观察下面的数列：1，3，5，7，9，……，这个数列的第10项是（）A. 19B. 21C. 17D. 23.7. 把(3)/(4)化成小数是（）A. 0.7B. 0.75C. 0.8D. 0.6.8. 直角三角形的两条直角边分别为3厘米和4厘米，它的斜边长为（）厘米。

（根据勾股定理，人教版知识）A. 5B. 6C. 7D. 8.9. 一桶油重10千克，用去了(3)/(5)，用去了多少千克？（）A. 6千克B. 4千克C. 8千克D. 5千克。

10. 一个圆柱的底面半径是2厘米，高是5厘米，它的侧面积是（）平方厘米。

（π取3.14）A. 62.8B. 31.4C. 125.6D. 94.2.二、填空题（每题4分，共20分）1. 3.14 +2.71 = _______。

2. 最小的质数是_______。

3. 一个数除以8，商是12，余数是5，这个数是_______。

4. 1小时20分钟 = _______分钟。

5. 从一副扑克牌（54张）中任意抽出一张，抽到黑桃的概率是_______（结果用最简分数表示）。

三、解答题（每题10分，共50分）1. 学校图书馆有故事书300本，科技书的数量是故事书的(2)/(3)，漫画书的数量是科技书的(3)/(4)，漫画书有多少本？2. 一个长方形的长是12厘米，宽是8厘米，求这个长方形的周长和面积。

袋鼠数学国际数学竞赛题摘要：1.代码外提的背景和意义2.代码外提的基本概念3.代码外提的实践方法和技巧4.代码外提的实际应用案例5.代码外提的未来发展趋势和挑战正文：一、代码外提的背景和意义随着互联网技术的飞速发展，软件开发行业也迎来了黄金时期。

在这个过程中，代码质量、开发效率和协同能力成为了软件开发团队的核心竞争力。

为了满足市场需求，提高软件开发的效率，代码外提应运而生。

代码外提，即提取代码中的关键部分，将其独立为一个模块或者函数，以实现代码复用和优化。

二、代码外提的基本概念代码外提主要包括以下几个方面的内容：1.提取函数：将重复出现的代码片段提取为函数，以实现代码复用。

2.模块化：将复杂的项目结构进行模块化处理，提高代码的可读性和可维护性。

3.抽象：将具体实现抽象为接口或者抽象类，降低模块间的耦合度。

三、代码外提的实践方法和技巧进行代码外提时，可以采用以下方法和技巧：1.识别重复代码：通过代码审查、静态分析等手段，找出重复出现的代码片段。

2.选择合适的抽象层次：根据项目的需求和架构，选择合适的抽象层次，如接口、抽象类等。

3.优化命名规范：遵循命名规范，提高代码的可读性。

4.编写详尽的注释：为提取的代码添加详细的注释，方便其他开发者理解和使用。

四、代码外提的实际应用案例代码外提在实际项目中的应用案例如下：1.提取登录验证功能：将登录验证功能从主函数中提取为一个独立的函数，实现代码复用。

2.模块化处理：将一个大型项目按照功能模块进行划分，提高项目的可读性和可维护性。

3.抽象为接口：将具体的数据操作类抽象为接口，降低不同模块间的耦合度。

五、代码外提的未来发展趋势和挑战随着软件开发技术的不断发展，代码外提将面临以下趋势和挑战：1.自动化：借助人工智能、机器学习等技术，实现代码外提的自动化。

2.智能化：结合代码分析工具，提供更智能的代码外提建议。

3.挑战：如何在保证代码外提质量的同时，提高开发效率和协同能力，将是一个长期的挑战。

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。

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

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

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

SAMPLE QUESTION FOR 3 POINTSAlice draws a figure connecting all the ladybugs in the order of increasing number of dots. She starts with the ladybug with one dot. Which figure will she get?SAMPLE QUESTION FOR 4 POINTSPeter drew a pattern twice, as in the picture. Which point will he reach when he draws the third pattern?A) A B) B C) C D) D E) ESAMPLE QUESTION FOR 5 POINTSThe number of dwarfs that can fit under a mushroom is equal to the number of dots on the mushroom cap. The picture below shows one side of each mushroom. The number of dots on the other side is the same. If 30 dwarfs are seeking shelter from the rain, how many dwarfs will get wet?A) 2 B) 3 C) 4 D) 5 E) 6SAMPLE QUESTION FOR 3 POINTSAlice draws a figure connecting all the ladybugs in the order of increasing number of dots. She starts with the ladybug with one dot. Which figure will she get?SAMPLE QUESTION FOR 4 POINTSPeter drew a pattern twice, as in the picture. Which point will he reach when he draws the third pattern?A) A B) B C) CD) DE) ESAMPLE QUESTION FOR 5 POINTSThe number of dwarfs that can fit under a mushroom is equal to the number of dots on themushroom cap. The picture below shows one side of each mushroom. The number of dots on the other side is the same. If 30 dwarfs are seeking shelter from the rain, how many dwarfs will get wet?A) 2 B) 3 C) 4 D) 5E) 6SAMPLE QUESTION FOR 3 POINTSThe picture shows 3 arrows that are flying and 9 balloons that can't move. When an arrow hits a balloon, the balloon pops, and the arrow keeps flying in the same direction. How many balloons will be hit by the flying arrows?A) 2 B) 3 C) 4 D) 5 E) 6SAMPLE QUESTION FOR 4 POINTSToby glues 10 cubes together to make the structure shown to the right. He paints the whole structure, even the bottom. How many cubes are painted on exactly 4 of their faces?A) 6 B) 7 C) 8 D) 9 E) 10SAMPLE QUESTION FOR 5 POINTSLeon wants to write the numbers from 1 to 7 in the grid shown. Two consecutive numbers cannot be written in two neighboring cells. Neighboring cells are those that meet at the edge or at a corner. What numbers can he write in the cell marked with the question mark?A) all seven numbersB) all of the odd numbersC) all of the even numbersD) only the number 4E) only the numbers 1 or 7SAMPLE QUESTION FOR 3 POINTSThe picture shows 3 arrows that are flying and 9 balloons that can't move. When an arrow hits a balloon, the balloon pops, and the arrow keeps flying in the same direction. How many balloons will be hit by the flying arrows?A) 2 B) 3 C) 4 D) 5 E) 6SAMPLE QUESTION FOR 4 POINTSToby glues 10 cubes together to make the structure shown to the right. He paints the whole structure, even the bottom. How many cubes are painted on exactly 4 of their faces?A) 6 B) 7 C) 8D) 9 E) 10SAMPLE QUESTION FOR 5 POINTSLeon wants to write the numbers from 1 to 7 in the grid shown. Two consecutive numbers cannot be written in two neighboring cells. Neighboring cells are those that meet at the edge or at a corner. What numbers can he write in the cell marked with the question mark?A) all seven numbersB) all of the odd numbersC) all of the even numbersD) only the number 4E) only the numbers 1 or 7SAMPLE QUESTION FOR 3 POINTSAlice subtracted two 2-digit numbers. Then she paintedtwo cells. What is the sum of the two digits in the painted cells?A)8 B) 9 C) 12 D) 13 E) 15SAMPLE QUESTION FOR 4 POINTSEmily wants to enter a number into each cell of the triangular table. The sum of the numbers in any two cells with a common edge must be the same. She has already entered two numbers. What is the sum of all the numbers in the table?A) 18 B) 20 C) 21 D) 22 E) impossible to determineSAMPLE QUESTION FOR 5 POINTSFive balls, A, B, C, D, and E, weigh 30 g, 50 g, 50 g, 50 g, and 80 g each, not necessarily in that order. Which ball weighs 30 g?A) A B) B C) C D) D E) ESAMPLE QUESTION FOR 3 POINTSAlice subtracted two 2-digit numbers. Then she painted two cells. What is the sum of the two digits in the painted cells?B)8 B) 9 C) 12 D) 13E) 15SAMPLE QUESTION FOR 4 POINTSEmily wants to enter a number into each cell of the triangular table. The sum of the numbers in any two cells with a common edge must be the same. She has already entered two numbers. What is the sum of all the numbers in the table?A) 18 B) 20 C) 21D) 22 E) impossible to determineSAMPLE QUESTION FOR 5 POINTSFive balls, A, B, C, D, and E, weigh 30 g, 50 g, 50 g, 50 g, and 80 g each, not necessarily in that order. Which ball weighs 30 g?A) A B) B C) C D) D E) ESAMPLE QUESTION FOR 3 POINTSWhen the letters of the word MAMA are written vertically above one another, the word has a vertical line of symmetry. Which of these words also has a vertical line of symmetry when written in the same way?A) ROOT B) BOOM C) BOOT D) LOOT E) TOOTSAMPLE QUESTION FOR 4 POINTSA rectangle is divided into 40 identical squares. The rectangle contains more than one row of squares. Andrew found the middle row of squares and colored it in. How many squares did he not color?A) 20 B) 30 C) 32 D) 35 E) 39SAMPLE QUESTION FOR 5 POINTSDomino tiles are said to be arranged correctly if the number of dots at the ends that touch are the same. Peter laid six dominoes in a line as shown in the diagram. He can make a move by either swapping the position of any two dominoes or by rotating one domino. What is the smallest number of moves he needs to make to arrange all the tiles correctly?A) 1 B) 2C) 3D) 4E) It is impossible to do.SAMPLE QUESTION FOR 3 POINTSWhen the letters of the word MAMA are written vertically above one another, the word has a vertical line of symmetry. Which of these words also has a vertical line of symmetry when written in the same way?A) ROOT B) BOOM C) BOOT D) LOOT E) TOOTSAMPLE QUESTION FOR 4 POINTSA rectangle is divided into 40 identical squares. The rectangle contains more than one row of squares. Andrew found the middle row of squares and colored it in. How many squares did he not color?A) 20 B) 30 C) 32 D) 35 E) 39SAMPLE QUESTION FOR 5 POINTSDomino tiles are said to be arranged correctly if the number of dots at the ends that touch are the same. Paulius laid six dominoes in a line as shown in the diagram. He can make a move by either swapping the position of any two dominoes or by rotating one domino. What is the smallest number of moves he needs to make to arrange all the tiles correctly?A) 1 B) 2C) 3D) 4E) It is impossible to do.SAMPLE QUESTION FOR 3 POINTSIn my family each child has at least two brothers and at least one sister. What is the smallest possible number of children in my family?A) 3 B) 4 C) 5 D) 6 E) 7SAMPLE QUESTION FOR 4 POINTSEight congruent semicircles are drawn inside a square with a side length of 4. What is the area of the non-shaded part of the square?A) 2πB) 8 C) 6 + πD) 3π– 2 E) 3πSAMPLE QUESTION FOR 5 POINTSDiana draws a rectangular grid of 12 squares on squared paper. Some of the squares are painted black. In each blank square she writes the number of black squares that share a side with it. The figure shows an example. Now she does the same in a rectangular grid with 2018 squares. What is the maximum value that she can obtain as the result of the sum of all the numbers in the grid?A) 1262 B) 2016 C) 2018 D) 3025 E) 3027SAMPLE QUESTION FOR 3 POINTSIn my family each child has at least two brothers and at least one sister. What is the smallest possible number of children in my family?A) 3 B) 4 C) 5D) 6 E) 7SAMPLE QUESTION FOR 4 POINTSEight congruent semicircles are drawn inside a square with a side length of 4. What is the area of the non-shaded part of the square?A) 2πB) 8C) 6 + πD) 3π– 2 E) 3πSAMPLE QUESTION FOR 5 POINTSDiana draws a rectangular grid of 12 squares on squared paper. Some of the squares are painted black. In each blank square she writes the number of black squares that share a side with it. The figure shows an example. Now she does the same in a rectangular grid with 2018 squares. What is the maximum value that she can obtain as the result of the sum of all the numbers in the grid?A) 1262 B) 2016 C) 2018 D) 3025E) 3027LEVELS 11 AND 12SAMPLE QUESTION FOR 3 POINTSThe figure shows the floor plan of Renate's house. Renate enters her house from the porch and walks through each door exactly once. In which room does she end up?A) 1 B) 2 C) 3 D) 4 E) 5SAMPLE QUESTION FOR 4 POINTSA vase is filled up to the top with water, at a constant rate. The graph shows the height h of the water as a function of time t.Which of the following can be the shape of the vase?A) B) C) D) E)SAMPLE QUESTION FOR 5 POINTSThere are 40% more girls than boys in a class. How many pupils are in this class if the probability that a two-person delegation selected at random consists of a girl and a boy equals 1/2?A) 20 B) 24 C) 36 D) 38 E) This situation is not possible.LEVELS 11 AND 12 ANSWERSSAMPLE QUESTION FOR 3 POINTSThe figure shows the floor plan of Renate's house. Renate enters her house from the porch and walks through each door exactly once. In which room does she end up?A) 1 B) 2C) 3 D) 4 E) 5SAMPLE QUESTION FOR 4 POINTSA vase is filled up to the top with water, at a constant rate. The graph shows the height h of the water as a function of time t.Which of the following can be the shape of the vase?B) B) C) D) E)SAMPLE QUESTION FOR 5 POINTSThere are 40% more girls than boys in a class. How many pupils are in this class if the probabilitythat a two-person delegation selected at random consists of a girl and a boy equals 1/2?A) 20 B) 24 C) 36D) 38 E) This situation is not possible.。

SAMPLE QUESTION FOR 3 POINTSIn the picture there are stars with 5 points, stars with 6 points and stars with 7 points. How many stars that have only 5 points are there?A) 2 B) 3 C) 4 D) 5 E) 9SAMPLE QUESTION FOR 4 POINTSIn which picture are there twice as many apples as carrots and twice as many carrots as pears?SAMPLE QUESTION FOR 5 POINTSIn Old McDonald's Barn there is one horse, two cows and three pigs. How many more cows does Old McDonald's Barn need so that the number of all the animals is twice the number of cows?A) 0 B) 1 C) 2 D) 3 E) 4SAMPLE QUESTION FOR 3 POINTSIn the picture there are stars with 5 points, stars with 6 points and stars with 7 points. How many stars that have only 5 points are there?A) 2 B) 3 C) 4 D) 5 E) 9SAMPLE QUESTION FOR 4 POINTSIn which picture are there twice as many apples as carrots and twice as many carrots as pears?SAMPLE QUESTION FOR 5 POINTSIn Old McDonald's Barn there is one horse, two cows and three pigs. How many more cows does Old McDonald's Barn need so that the number of all the animals is twice the number of cows?A) 0 B) 1 C) 2 D) 3 E) 4SAMPLE QUESTION FOR 3 POINTSJohn looks out the window. He sees half of the kangaroos in the park (see picture). How many kangaroos are there in the park?A) 12 B) 14 C) 16 D) 18 E) 20SAMPLE QUESTION FOR 4 POINTSDavid wants to prepare a meal with 5 dishes using a stove with only 2 burners. The times needed to cook the 5 dishes are 40 min, 15 min, 35 min, 10 min and 45 min. What is the shortest time in which he can do it? (He may only remove a dish from the stove when it is done cooking.)A) 60 min B) 70 min C) 75 min D) 80 min E) 85 minSAMPLE QUESTION FOR 5 POINTSEach of ten bags contains a different number of pieces of candy. The number of pieces of candy in each bag ranges from 1 to 10. Each of five boys took two bags of candy. Alex got 5 pieces of candy, Bob got 7 pieces, Charles got 9 pieces, and Dennis got 15 pieces. How many pieces of candy did Eric get?A) 9 B) 11 C) 13 D) 17 E) 19SAMPLE QUESTION FOR 3 POINTSJohn looks out the window. He sees half of the kangaroos in the park (see picture). How many kangaroos are there in the park?A) 12B) 14 C) 16 D) 18 E) 20SAMPLE QUESTION FOR 4 POINTSDavid wants to prepare a meal with 5 dishes using a stove with only 2 burners. The times needed to cook the 5 dishes are 40 min, 15 min, 35 min, 10 min and 45 min. What is the shortest time in which he can do it? (He may only remove a dish from the stove when it is done cooking.)A) 60 min B) 70 min C) 75 min D) 80 min E) 85 minSAMPLE QUESTION FOR 5 POINTSEach of ten bags contains a different number of pieces of candy. The number of pieces of candy in each bag ranges from 1 to 10. Each of five boys took two bags of candy. Alex got 5 pieces of candy, Bob got 7 pieces, Charles got 9 pieces, and Dennis got 15 pieces. How many pieces of candy did Eric get?A) 9 B) 11 C) 13 D) 17 E) 19SAMPLE QUESTION FOR 3 POINTSA special die has a number on each face. The sums of the numbers on opposite faces are all equal. Five of the numbers are 5, 6, 9, 11 and 14. What number is on the sixth face?A) 4 B) 7 C) 8 D) 13 E) 15SAMPLE QUESTION FOR 4 POINTSThe Modern Furniture store is selling sofas, loveseats, and chairs made from identical modular pieces as shown in the picture. Including the armrests, the width of the sofa is 220 cm and the width of the loveseat is 160 cm. What is the width of the chair?A)60 cm B) 80 cm C) 90 cm D) 100 cm E) 120 cmSAMPLE QUESTION FOR 5 POINTSJohn wants to write a natural number in each box in the diagram in such a way 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 John can write?A) 4 B) 5 C) 6 D) 7 E) 8SAMPLE QUESTION FOR 3 POINTSA special die has a number on each face. The sums of the numbers on opposite faces are all equal. Five of the numbers are 5, 6, 9, 11 and 14. What number is on the sixth face?A) 4 B) 7 C) 8 D) 13 E) 15SAMPLE QUESTION FOR 4 POINTSThe Modern Furniture store is selling sofas, loveseats, and chairs made from identical modular pieces as shown in the picture. Including the armrests, the width of the sofa is 220 cm and the width of the loveseat is 160 cm. What is the width of the chair?B)60 cm B) 80 cm C) 90 cm D) 100 cm E) 120 cmSAMPLE QUESTION FOR 5 POINTSJohn wants to write a natural number in each box in the diagram in such a way 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 John can write?A) 4 B) 5 C) 6 D) 7E) 8SAMPLE QUESTION FOR 3 POINTSA group of girls stands in a circle. Xena is the fourth to the left from Yana and the seventh to the right from Yana. How many girls are in the group?A) 9 B) 10 C) 11 D) 12 E) 13SAMPLE QUESTION FOR 4 POINTSAnnie the Ant started at the left end of a pole and crawled 2/3 of its length. Bob the Beetle started at the right end of the same pole and crawled ¾ of its length. What fraction of the length of the pole are Annie and Bob now apart?A)3/8 B) 1/12 C) 5/7 D) 1/2 E) 5/12SAMPLE QUESTION FOR 5 POINTSTen kangaroos stood in a line as shown in the diagram. At some point, two kangaroos standing side by side and facing each other exchanged places by jumping past each other. This was repeated until no further jumps were possible. How many exchanges were made?A) 15 B) 16 C) 18 D) 20 E) 21SAMPLE QUESTION FOR 3 POINTSA group of girls stands in a circle. Xena is the fourth to the left from Yana and the seventh to the right from Yana. How many girls are in the group?A) 9 B) 10 C) 11D) 12 E) 13SAMPLE QUESTION FOR 4 POINTSAnnie the Ant started at the left end of a pole and crawled 2/3 of its length. Bob the Beetle started at the right end of the same pole and crawled ¾ of its length. What fraction of the length of the pole are Annie and Bob now apart?B)3/8 B) 1/12 C) 5/7 D) 1/2 E) 5/12SAMPLE QUESTION FOR 5 POINTSTen kangaroos stood in a line as shown in the diagram. At some point, two kangaroos standing side by side and facing each other exchanged places by jumping past each other. This was repeated until no further jumps were possible. How many exchanges were made?A) 15 B) 16 C) 18D) 20 E) 21SAMPLE QUESTION FOR 3 POINTSWhich of the following pictures shows the path of the center of the wheel when the wheel rolls along the zig-zag line shown?SAMPLE QUESTION FOR 4 POINTSABCD is a trapezoid with side AB parallel to CD, where AB = 50 and CD =20. E is a point on side AB with the property that the segment DE divides thegiven trapezoid into two parts of equal area (see figure). Calculate the lengthAE.A) 25 B) 30 C) 35 D) 40 E) 45SAMPLE QUESTION FOR 5 POINTSThere are 4 children of different integer ages under 18. The product of their ages is 882. What is the sum of their ages?A)23 B) 25 C) 27 D) 31 E) 33SAMPLE QUESTION FOR 3 POINTSWhich of the following pictures shows the path of the center of the wheel when the wheel rolls along the zig-zag line shown?SAMPLE QUESTION FOR 4 POINTSABCD is a trapezoid with side AB parallel to CD , where AB = 50 and CD = 20. E is a point on side AB with the property that the segment DE divides the given trapezoid into two parts of equal area (see figure). Calculate the length AE .A) 25 B) 30 C) 35 D) 40 E) 45SAMPLE QUESTION FOR 5 POINTSThere are 4 children of different integer ages under 18. The product of their ages is 882. What is the sum of their ages?B) 23 B) 25 C) 27 D) 31 E) 33LEVELS 11 AND 12SAMPLE QUESTION FOR 3 POINTSBen likes to play with his H0-model railroad. He modeled some things in the H0-ratio of 1:87, even a 2 cm high model of his brother. How tall is Ben's brother?A)1.74 m B) 1.62 m C) 1.86 m D) 1.94 m E) 1.70 mSAMPLE QUESTION FOR 4 POINTSThree mutually externally tangent circles with centers A, B, and C have theradii of 3, 2, and 1, respectively. What is the area of the triangle ABC?A) 6 B) 4√3C) 3√2D) 9 E) 2√6SAMPLE QUESTION FOR 5 POINTSThe sum of the lengths of the three sides of a right triangle is equal to 18 and the sum of the squares of the lengths of the three sides is equal to 128. What is the area of the triangle?A) 18 B) 16 C) 12 D) 10 E) 9LEVELS 11 AND 12 ANSWERSSAMPLE QUESTION FOR 3 POINTSBen likes to play with his H0-model railroad. He modeled some things in the H0-ratio of 1:87, even a 2 cm high model of his brother. How tall is Ben's brother?A)1.74 m B) 1.62 m C) 1.86 m D) 1.94 m E) 1.70 mSAMPLE QUESTION FOR 4 POINTSThree mutually externally tangent circles with centers A, B, and C have theradii of 3, 2, and 1, respectively. What is the area of the triangle ABC?A) 6B) 4√3C) 3√2D) 9 E) 2√6SAMPLE QUESTION FOR 5 POINTSThe sum of the lengths of the three sides of a right triangle is equal to 18 and the sum of the squares of the lengths of the three sides is equal to 128. What is the area of the triangle?A) 18 B) 16 C) 12 D) 10 E) 9。

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。

袋鼠数学试题袋鼠数学试题第一部分：选择题1. 已知等差数列的首项为14，公差为6，求第十项的值。

A) 54 B) 42 C) 68 D) 902. 某家庭每月固定收入为3000元，每月固定支出为2000元。

若家庭每月剩余收入为200元，家庭每月可用剩余收入购买书籍数量为：A) 10本 B) 20本 C) 30本 D) 40本3. 已知长方形的长为5cm，宽为3cm，求其面积。

A) 5cm² B) 8cm² C) 15cm² D) 18cm²4. 下列哪个图形是正方形？A) 长方形 B) 梯形 C) 圆形 D) 正方形5. 若甲数为8，乙数为-4，丙数为12，则甲数与乙数的和与丙数之和的差为：A) 0 B) 4 C) 8 D) 126. 若某数的1/6等于4，求这个数。

A) 24 B) 18 C) 22 D) 287. A、B 和 C 三人一起去买礼物，共花费500元。

C用自己的1/4的份额和A说，他受到了严重的财务困境，无法支付自己的份额，于是A和 B各多支付了25元。

现在 C只给了A和B各100元，请问礼物的总价格为多少元？A) 750 B) 600 C) 400 D) 3508. 若一周7天中，星期日这天是第几天？A) 第2天 B) 第6天 C) 第7天 D) 第1天9. 若一个圆的半径为4cm，求其周长。

A) 16cm B) 8πcm C) 4πcm D) 8cm10. 30除以一个数得到3，求这个数。

A) 1 B) 2 C) 3 D) 10第二部分：填空题1. 一年有____个星期。

2. 平行线上的对应角度相等，这是____定理。

3. 同底数相乘，底数不变，指数____.4. 值为负数的根不存在，是因为____.5. 一个正方形的面积是4cm²，其边长是____cm.6. 一个数减去它的5倍等于____.7. 余角是____角与给定角度的差.8. 若两个角的和为90°，则这两个角互为____角.9. 圆心角等于____角.10. √2是一个____数.第三部分：解答题1. 一个分数的分母是6，如果分子减去2是分母的2倍，求这个分数是多少？2. 某数减去2的四次方等于20，求这个数。

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

该竞赛主要面向小学四年级至高中的学生，根据学生的年龄和年级分为不同级别。

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

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

竞赛鼓励学生用不同的方法解题，注重培养学生的发散性思维。

题目类型包括选择题、填空题和解答题，让学生在各种题型中锻炼自己的数学能力。

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

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

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

参加袋鼠数学竞赛对学生有很多意义。

首先，通过参加竞赛，学生可以提升自己的数学能力，掌握更多数学知识。

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

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

1.Which square is cut into 2different shapes?请问哪个正方形被划分为两个不同的形状2024袋鼠B 真题试卷及答案？答案：E2.What is the smallest number of ladders the firefghter must use to reach the fire without jumping?在不跳跃的情况下，消防员最少要用多少把梯子才能去救火?(A)4(B)5(C)6(D)7(E)8答案：C3.The table consists of 28white cells:Ira paints 2rows and 1column.A row is from left to right.A column is from top to bottom.How many cells will remain white?下表由28个白色方格组成，小艾为其中2行和1列方格涂色。

行是从左到右，列是从上到下。

请问最后还剩多少个白色方格?(A)8(B)10(C)12(D)14(E)17答案：C4.Soccer players numbered1to11stand in a circle.Each player kicks the ball to the third player on their left.Player1starts.This kicking pattern continues until a player has the ball for the second time.What is the number of the player who kicked the ball last?编号为1到11的足球运动员站成一个圆圈，每名球员把球踢给自己左边的第三名球员。

从1号球员开始踢球。

这种踢球方式一直持续到出现一名球员第二次拿到球为止。