加拿大国际袋鼠数学竞赛试题 及答案-2016年 Parents Questions

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 EI 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 teamGrade 3-42018 Canadian Math Kangaroo ContestPart 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 but in 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 EI 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 E5-121.You have 75 minutes to solve 30 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 theonly sheet that is marked, so make sure you have all your answers transferred to that form before giving it back to the contest supervisor. 3.The problems are arranged in three groups. A correct answer of the first10 problems is worth 3 points. A correct answer of problems 11 -20 isworth 4 points. A correct answer of problems 21-30 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 30 points. The maximum score possible is 150.4.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 forillustration purposes.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.The drawing shows 3flying arrows and 9fixed balloons. Whenan arrow hits a balloon, it bursts, and the arrow flies further inthe same direction. How many balloons will not be hit byarrows?(A) 3 (B) 2(C) 6(D) 5(E) 42.The image shows a structure made of three objects.What does Peter see if he looks at the structure from above?(A)(B)(C) (D) (E)3.Diana played darts throwing arrows toward a target with three sections. First she got 14 points with twoarrows on the target. The second time she got 16 points. How many points did she get the third time?(A) 17(B) 18(C) 19 (D) 20 (E) 22 4. A garden is divided into identical squares. A fast snail and a slow snail move along the perimeter of thegarden starting simultaneously from the corner S but in different directions. The slow snail moves at the speed of 1 metre per hour (1 m/h) and the fast one at 2 metres per hour (2 m/h).At what point will the two snails meet?(A) A (B) B (C) C (D) D(E) E 14 points16 points ? A B CDE S 1 m/h2 m/h5.In which of the four squares is the fraction of the black area the largest?(A) A (B) B (C) C (D) D (E) they are all the same6. A star is made out of four equilateral triangles and a square. The perimeter of thesquare is 36 cm. What is the perimeter of the star?(A) 144 cm (B) 120 cm (C) 104 cm (D) 90 cm (E) 72 cm7.From the list 3, 5, 2, 6, 1, 4, 7 Masha chose 3 different numbers whose sum is 8. From the same list Dashachose 3 different numbers whose sum is 7. How many common numbers have been chosen by both girls?(A) none (B) 1 (C) 2 (D) 3 (E) impossible to determine8.We move a bead along a piece of wire. What shall we see when the beadcomes to the end of the wire?(A) (B) (C)(D) (E)9.There are 3squares in the figure. The side length of the smallest square is 6 cm.What is the side length of the biggest square?(A) 8(B) 10(C) 12(D) 14(E) 1610.In the following figure, the circles are light bulbs connected to some other lightbulbs. Initially, all light bulbs are off. When you touch a light bulb, this light bulband all its neighbours (e.g., the light bulbs connected to it) are lit.At least how many light bulbs do you have to touch to turn on all the light bulbs?(A) 2 (B) 3 (C) 4 (D) 5 (E) 6Part B: Each correct answer is worth 4 points11.Each square contains one of the numbers 1, 2, 3, 4, or 5, so that both of thecalculations following the arrows are correct. A number may be used morethan once. What number goes into the box with the question mark?(A) 1 (B) 2 (C) 3 (D) 4 (E) 5 12. Nine cars arrive at a crossroads and drive off as indicated by the arrows. Which figure shows these cars after leaving the crossroads?(A)(B) (C) (D) (E) 13. The faces of a cube are painted black, white or grey so that opposite faces are of different colour. Which of the following is not a possible net of this cube?(A)(B) (C) (D) (E)14.In a box there are many one-euro, two-euro and five-euro coins. A dispenser draws coins out of the box – one at a time, and stops when three identical coins are taken out. What is the largest possible amount that can be withdrawn? (A) 24 (B) 23 (C) 22 (D) 21 (E) 1515.Two girls, Eva and Olga and three boys, Adam, Isaac and Urban play with a ball. When a girl has the ball, she throws it to the other girl or to a boy. When a boy has the ball, he throws it to another boy but never to the boy from whom he just received it. Eva starts by throwing the ball to Adam. Who will do the fifth throw?(A) Adam (B) Eva (C) Isaac (D) Olga (E) Urban16.Emily wants to enter a number into each cell of the triangular table. The sum of thenumbers in any two cells with a common edge must be the same. She has alreadyentered two numbers. What is the sum of all the numbers in the table?(A) 18 (B) 20 (C) 21 (D) 22 (E) impossible to determine17.John coded a correct addition calculation naming the digits AA , BB , CC and DD .Which digit is represented by BB ?(A) 0 (B) 2 (C) 4 (D) 5(E) 6 + A B C C B A D D DD18.On Monday Alexandra shares a picture with 5 friends. For several days, everybody who receives thepicture, sends it once on the next day to two friends. On which day does the number of people who have seen the picture (including Alexandra) become greater than 75, if it is known that no one receives the picture more than once?(A) Wednesday (B) Thursday (C) Friday (D) Saturday (E) Sunday 19.The sum of the ages of Kate and her mother is 36, and the sum of the ages of her mother and her grandmother is 81. How old was the grandmother when Kate was born? (A) 28 (B) 38 (C) 45 (D) 53 (E) 56 20.Annie replaced the letters with numbers in the word KANGAROO (identical letters with the same digits, different letters with different digits) so that she got the largest possible 8-digit number, which is not a multiple of 4. What is the sum of the last three digits replacing the word ROO? (A) 13 (B) 14 (C) 12 (D) 15 (E) 11Part C: Each correct answer is worth 5 points21.Captain Hook has plundered a safe that contains 2520 gold coins. During the night, each of his pirates secretly took out some coins just for themselves. The first one took out �12�of the coins, the second one�13�of the remaining coins, the third one �14�of the remaining coins and so on. When Captain Hook opened the safe in the morning, he found only 252 coins inside. How many pirates are commanded by Captain Hook?(A) 8 (B) 9 (C) 10 (D) 11 (E) 12 22.In the figure on the right, the five balls A, B, C, D and E weigh 30, 50, 50, 50 and 80 grams, but not necessarily in this order. Which ball weighs 30 grams? (A) A (B) B (C) C (D) D (E) E23.If A, B, C are distinct digits, which of the following numbers cannot be the largest possible 6-digit number written using three digits A, two digits B, and one digit C? (A) AAABBC (B) CAAABB (C) BBAAAC (D) AAABCB (E) AAACBB 24.In the World of Numbers, there are many number-machines, which work in the following way: the machine adds the two beginning digits of the number and replaces them by their sum. For example, beginning with the number 87312 and using six such machines we obtain:How many such machines should be used in order to get the number times509...9 from the numbertimes1009...9? (A) 50(B) 60(C) 100(D) 80(E) Not possible to obtain this number8731215312 6312 91210212 3Page 525.Nick wants to arrange the numbers 2, 3, 4, ..., 10 into several groups such that the sum of the numbers in each group is the same. What is the largest number of groups he can get?(A) 2 (B) 3 (C) 4 (D) 6 (E) other answer 26.Peter cut an 8-cm wide wooden plank with a saw into 9 parts across the width of the plank.One piece was a square, the other were rectangles. Then he arranged all the pieces together as shown in the picture. What was the length of the plank?(A) 150 cm (B) 168 cm (C) 196 cm (D) 200 cm (E) 232 cm 27.Write 0 or 1 in each cell of the 5×5 table so that each 2×2 square of the 5×5 table contains exactly 3 equal numbers. What is the largest possible sum of all the numbers in the table?(A) 22 (B) 21 (C) 19 (D) 17 (E) 1528.14 people are seated at a round table.Each person is either a liar or tells the truth. Everybody says: "Both my neighbours are liars". What is themaximum number of liars at the table?(A) 7 (B) 8 (C) 9(D) 10(E) 1429.There are eight domino tiles on the table (pic 1). One half of one tile is covered. The 8 tiles can be arranged into a 4×4 square (pic 2), so that the number of dots in each row and column is the same.How many dots are on the covered part? (A) 1 (B) 2 (C) 3 (D) 4(E) 530.Four ladybugs sit on different cells of a 4×4 grid.One of them is sleeping and does not move. Each time you whistle, the other three ladybugs move toa free neighbouring cell. They can move up, down,right or left but they are not allowed to go back tothe cell they just came from. Which of the following images might show the result after the fourth whistle?(A)(B)(C)(D)(E)pic 1pic 2initial position after firstwhistleafter second whistle after third whistle Both my neighboursare liars.International Contest-GameMath Kangaroo Canada, 2018Answer KeyGrade 5-61 A B C D E 11 A B C D E21 A B C D E2 A B C D E 12 A B C D E 22 A B C D E3 A B C D E 13 A B C D E23 A B C D E4 A B C D E 14 A B C D E 24 A B C D E5 A B C D E15 A B C D E 25 A B C D E6 A B C D E16 A B C D E 26 A B C D E7 A B C D E 17 A B C D E 27 A B C D E8 A B C D E 18 A B C D E 28 A B C D E9 A B C D E 19 A B C D E 29 A B C D E10 A B C D E 20 A B C D E30 A B C D EI 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 E5-121.You have 75 minutes to solve 30 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 theonly sheet that is marked, so make sure you have all your answers transferred to that form before giving it back to the contest supervisor. 3.The problems are arranged in three groups. A correct answer of the first10 problems is worth 3 points. A correct answer of problems 11 -20 isworth 4 points. A correct answer of problems 21-30 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 30 points. The maximum score possible is 150.4.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 forillustration purposes.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 teamPage 1Canadian Math Kangaroo ContestPart A: Each correct answer is worth 3 points1.When 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) TOOT2.A triangle has sides of length 6, 10 and 11. An equilateral triangle has the same perimeter. What is the length of each side of the equilateral triangle?(A) 6 (B) 9 (C) 10 (D) 11 (E) 273.Which number should replace ∗in the equation 2 ∙ 18 ∙ 14 = 6 ∙ ∗ ∙ 7to make it correct?(A) 8 (B) 9 (C) 10 (D) 12 (E) 154.The panels of Fergus' fence are full of holes. One morning, one of the panels fell flat on the floor.Which of the following could Fergus see as he approaches his fence?(A) (B) (C) (D) (E)5.How many possible routes are there to go from A to B in the direction indicated by the arrows?(A) 2 (B) 3 (C) 4 (D) 5 (E) 66.Martha multiplied two 2-digit numbers correctly on a piece of paper.Then she scribbled out three digits as shown.What is the sum of the three digits she scribbled out? (A) 5 (B) 6 (C) 9 (D) 12 (E) 14 7.A large rectangle is made up of nine identical rectangles whose longest sides are 10 cm long. What is the perimeter of the large rectangle?(A) 40 cm(B) 48 cm(C) 76 cm(D) 81 cm(E) 90 cm8. A hotel on an island in the Caribbean advertises using the slogan "350 days of sun every year!''. According tothe advert, what is the smallest number of days Willi Burn has to stay at the hotel in 2018 to be certain of having two consecutive days of sun?(A) 17 (B) 21 (C) 31 (D) 32 (E) 359.The diagram shows a rectangle of dimensions 7 × 11 containing two circles eachtouching three of the sides of the rectangle. What is the distance between the centres of the two circles?(A) 1 (B) 2(C) 3(D) 4 (E) 510.Only one of the digits in the year 2018 is a prime number. How many years will pass till the next year whenall of the digits in the year number are prime numbers?(A) 201 (B) 202 (C) 203 (D) 204 (E) 205Part B: Each correct answer is worth 4 points11.Square AAAAAAAA has sides of length 3 cm. The points MM and NN lie on AAAA and AAAA so that AAMMand AANN split the square into three pieces of the same area. What is the length of AAMM?(A) 0.5 cm (B) 1 cm (C) 1.5 cm (D) 2 cm (E) 2.5 cm12.A rectangle is divided into 40 identical squares. The rectangle contains more than one row of squares. Avacoloured the middle row. What is the largest possible number of squares that remain uncoloured?(A) 20 (B) 30 (C) 32 (D) 35 (E) 3913.A lion is hidden in one of three rooms. A note on the door of room 1 reads "The lion is here". A note on thedoor of room 2 reads "The lion is not here". A note on the door of room 3 reads "2+3=2×3". Only one of these statements is true. In which room is the lion hidden?(A) In room 1 (B) In room 2 (C) In room 3 (D) It may be in any room(E) It may be in either room 1 or room 214.Valeriu draws a zig-zag line inside a rectangle, creating angles of 10°,14°,33°, and 26°as shown.What is the size of angle θθ?(A) 11°(B) 12°(C) 16°(D) 17°(E)33°。

I N T ER N A T I ON A L CO N T E S T-GA M EM A TH KA N GA RO OC A N A DA, 2017INSTRUCTIONSGRADE 5-61.You have 75 minutes to solve 30 multiple choice problems. For each problem, circle onlyone 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 sheet that ismarked, so make sure you have all your answers transferred here by the end of the contest.3.The problems are arranged in three groups. A correct answer of the first 10 problems isworth 3 points. A correct answer of problems 11-20 is worth 4 points. A correct answer of problems 21-30 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 30 points. The maximum score possible is 150.4.Calculators and graph paper are not permitted. You are allowed to use rough paper for draftwork.5.The figures are not drawn to scale. They should be used only for illustration.6.Remember, you have about 2-3 minutes for each problem; hence, if a problem appears tobe too difficult, save it for later and move on to the other problems.7.At the end of the allotted time, please submit the response form to the contest supervisor.Please do not forget to pick up your Certificate of Participation!Good luck! Canadian Math Kangaroo Contest team2017 CMKC locations: Algoma University; Bishop's University; Brandon University; Brock University; Carlton University; Concordia University; Concordia University of Edmonton; Coquitlam City Library; Dalhousie University; Evergreen Park School; F.H. Sherman Recreation & Learning Centre; GAD Elementary School; Grande Prairie Regional College; Humber College; Lakehead University (Orillia and Thunder Bay); Laurentian University; MacEwan University; Memorial University of Newfoundland; Mount Allison University; Mount Royal University; Nipissing University; St. Mary’s University (Calgary); St. Peter’s College; The Renert School at Royal Vista; Trent University; University of Alberta-Augustana Campus; University of British Columbia (Okanagan); University of Guelph; University of Lethbridge; University of New Brunswick; University of Prince Edward Island; University of Quebec at Chicoutimi; University of Quebec at Rimouski; University of Regina; University of Toronto Mississauga; University of Toronto Scarborough; University of Toronto St. George; University of Windsor; The University of Western Ontario; University of Winnipeg; Vancouver Island University; Walter Murray Collegiate, Wilfrid Laurier University; YES Education Centre; York University; Yukon College.2017 CMKC supporters: Laurentian University; Canadian Mathematical Society; IEEE; PIMS.Canadian Math Kangaroo ContestPart A: Each correct answer is worth 3 points1.A fly has 6 legs, a spider has 8 legs. Together, 3 flies and 2 spiders have as many legs as 9 chickens andseveral cats. How many cats are there?(A) 2 cats (B) 3 cats (C) 4 cats (D) 5 cats (E) 6 cats2.Alice has 4 pieces of this shape: . Which picture can she not make from these four pieces?(A) (B) (C)(D) (E)3.Kalle knows that 1111 × 1111 = 1234321. What is the answer of 1111 × 2222?(A) 3456543 (B) 2346642 (C)2457642 (D) 2468642 (E) 43212344.There are 10 islands and 12 bridges, as depicted in the figure. All bridgesare open for traffic right now. What is the smallest number of bridges thatmust be closed in order to stop the traffic between A and B?(A) 1 (B) 2 (C) 3 (D) 4 (E) 55.Martin wants to colour the squares of the rectangle so that 1/3 of allsquares are blue and half of all squares are yellow. The rest of the squaresare to be coloured red.How many squares will he colour red?(A) 1 (B) 2 (C) 3 (D) 4 (E) 56.When the car wheels make one full rotation the car moves forward by about 1.8 meters. Approximatelyhow many kilometres will the car move forward after 10,000 full rotations of the wheels?(A) 1.8 (B) 18 (C) 180 (D) 1 800 (E) 18 0007.There are 32 students in Mrs. Vicky’s class. Part of the students took one pencil each from the box withpencils on the teacher’s desk. Then a third of the remaining students took 3 pencils each, and there were no more pencils left in the box. How many pencils were there in the box at first?(A) 16 (B) 24 (C) 32 (D) 43 (E) 648.Three rhinoceroses Jane, Kate and Lynn go for a walk: Jane first, Kate in the middle, and Lynn – last. Janeweighs 500 kg more than Kate. Kate weighs 1000 kg less than Lynn. Which of the following pictures may show Jane, Kate and Lynn in the order they walked?(A) (B)(C) (D)(E)9.Peter and Nick are both working on "Kangaroo" contest problems. For every two problems that Petersolves, Nick manages to solve three problems. In total, the boys solved 30 problems. How many problems did Nick solve more than Peter?(A) 5 (B) 6 (C) 7 (D) 8 (E) 910.Bob folded a piece of paper, used a hole puncher and punched exactly one hole in the folded paper.Then, he unfolded the piece of paper, which looked as shown below.Which of the following pictures shows the lines along which Bob folded the piece of paper?(A) (B) (C) (D) (E)Part B: Each correct answer is worth 4 points11.A special die has a number on each of its six faces. 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) 15 12.Tom wrote all the numbers from 1 to 20 in a row and obtained the 31‐digit number1234567891011121314151617181920.Then he deleted 24 of the 31 digits, so that the remaining number was as large as possible. Which number was it? (A) 9671819 (B) 9567892 (C) 9781920 (D) 9912345 (E) 981819213.Peter went hiking in the mountains for 5 days. He started on Monday and his last trip was on Friday. Each day he walked 2km more than the day before. The total distance he walked during the five days was 70km. What distance did Peter walk on Thursday? (A) 12 km (B) 13 km (C) 14 km (D) 15 km (E) 16 km14.In a chocolate store, one chocolate costs $3. One day the store had a deal: “Buy two and get a third one free” and Adam decided to take 49 chocolates. How much did he pay for the chocolates? (A) $75 (B) $98 (C) $99 (D) $102 (E) $14715.Eight 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) 2 (B) 10 (C) 12 (D) 13 (E) 1616.The 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 cmsofa loveseatchair220 cm160cm17.There are five padlocks and 5 keys – one for each of them (see the figure). The number code on each key has been modified into a letter code on the corresponding padlock. Equal digits have been replaced by the same letter, and different digits – by different letters. What is the number code on the fifth key?(A) 382(B) 282 (C) 284 (D) 823 (E) 82418.Boris has an amount of money and three magic wands that he can use only once. Wand A adds $1. Wand S subtracts $1. Wand D doubles the amount. In which order must he use these wands to obtain the largest amount of money? (A) DAS (B) ASD (C) DSA (D) ADS (E) SAD19.A vase weighs 600 g when one third of it is filled with water. The same vase weighs 800 g when two thirds of it are filled with water. What is the weight of the vase when it is empty? (A) 100 g (B) 200 g (C) 300 g (D) 400 g (E) 500 g20.Rafael has three squares. The first one has side length 2 cm. The second one has side length 4 cm and a vertex is placed in the centre of the first square. The last one has side length 6 cm and a vertex is placed in the centre of the second square, as shown in the picture. What is the area of the figure? (A) 32 cm 2 (B) 51 cm 2 (C) 27 cm 2 (D) 16 cm 2 (E) 6 cm 2Part C: Each correct answer is worth 5 points21.The natural numbers are arranged in the form of a triangle: 1 is in the first row, 2 and 3 are in the second row, 4, 5 and 6 are in the third row, and so on. What is the sum of the numbers written in the 10‐th row?(A) 490(B) 495 (C) 500(D) 505 (E) 5101 2 3 456.. .22.There are eight balls numbered with the numbers 40, 80, 100, 101, 190, 200, 260 and 292 in a bag.Martina takes four balls out of the bag and calculates the sum of the numbers on these balls. It appears that this sum is half of the sum of the numbers on the balls that remain in the bag. What is the greatest number written on the balls taken out?(A) 101 (B) 200 (C) 260 (D) 190 (E) 29223.The structure on the figure is made of unit cubes glued together. Morten wants toput it into a rectangular box. What are the dimensions (length, width and height)of the smallest box he can use?(A) 3 × 3 × 4 (B) 3 × 5 × 5 (C) 3 × 4 × 5 (D) 4 × 4 × 4 (E) 4 × 4 × 524.Four players scored goals in a handball game. All of them scored a different number of goals. One of theplayers, Mike, scored the least number of goals. The other three players scored 20 goals in total. What is the largest number of goals Mike could have scored?(A) 2 (B) 3 (C) 4 (D) 5 (E) 625.Ala likes even numbers, Beata likes numbers divisible by 3, Celina likes numbers divisible by 5. Each ofthese three girls went separately to a basket containing 8 balls with numbers written on them, and took all the balls with numbers she liked. It turned out that Ala collected balls with numbers 32 and 52, Beata ‐ 24,33 and 45, Celina ‐ 20, 25 and 35. In what order did the girls approach the basket?(A) Ala, Celina, Beata (B) Celina, Beata, Ala (C) Beata, Ala, Celina(D) Beata, Celina, Ala (E) Celina, Ala, Beata26.The picture of a kangaroo in the first (leftmost) triangle was reflected across the dotted lines, as in mirrors.The first two reflections are shown.What does the reflection look like in the shaded triangle?(A) (B) (C) (D) (E)27.The numbers 1, 2, 3, 4, and 5 must be written in the five cells in the figure, respecting the following rules:-If a number is just below another number, it must be greater.-If a number is just to the right of another number, it must be greater.In how many ways can this be done?(A) 3 (B) 4 (C) 5 (D) 6 (E) 828.John wrote a natural number in each of the four boxes in the bottom row of the diagram. Then he wrote ineach of the other boxes the sum of the two numbers in the boxes immediately underneath. What is the largest number of odd numbers that could appear in the completed diagram?(A) 4 (B) 5 (C) 6 (D) 7 (E) 829.Julia has four pencils of different colours and wants to use some or all of them to paint the map of anisland divided into four countries, as in the picture. Any two countries with a common border must be coloured differently on the map. How many different colourings of this map are possible? (Twocolourings are considered different if at least one of the countries is coloured differently).(A) 12 (B) 18 (C) 24 (D) 36 (E) 4830.A bar consists of two grey cubes and one white cube glued together as shown in the figure.Which cube can be built from nine such bars?(A) (B) (C) (D) (E)International Contest-GameMath Kangaroo Canada, 2017Answer KeyGrade 5-61 A B C D E 11 A B C D E21 A B C D E2 A B C D E12 A B C D E 22 A B C D E3 A B C D E 13 A B C D E23 A B C D E4 A B C D E 14 A B C D E 24 A B C D E5 A B C D E 15 A B C D E 25 A B C D E6 A B C D E 16 A B C D E 26 A B C D E7 A B C D E 17 A B C D E 27 A B C D E8 A B C D E 18 A B C D E 28 A B C D E9 A B C D E 19 A B C D E 29 A B C D E10 A B C D E 20 A B C D E 30 A B C D E。

Singapore Math Kangaroo Contest 2017Secondary 2 Contest PaperName:School:INSTRUCTIONS:1.Please DO NOT OPEN the contest booklet until the Proctor has given permission to start.2.TIME : 1 hour and 30 minutes3.There are 30 questions in this paper. 3 points, 4 points and 5 points will be awarded for eachcorrect question in Section A, Section B and Section C respectively. No points are deducted for Unanswered question. 1 point is deducted for Wrong answer.4.Shade your answers neatly in the answer entry sheet.5.PROCTORING : No one may help any student in any way during the contest.6.No calculators are allowed.7.All students must fill and shade in your Name, Index number, Level and School in theAnswer sheet provided.8.MINIMUM TIME: Students must stay in the exam hall for at least 1 hour and 15 minutes.9.Students must show detailed working and transfer answers to the answer entry sheet.10.No spare papers can be used in writing this contest. Enough space is provided for yourworking of each question.11. Y ou must return this contest paper to the proctor.Rough WorkingSection A (Correct –3points |Unanswered –0points |Wrong –deduct 1point)Question 1What is the time 17hours after 17:00?(A )8:00(B )10:00(C )11:00(D )12:00(E )13:00Question 2A group of girls stand in a circle.Xena is the fourth on the left from Yana.She is also the seventh on the right from Yana.How many girls are in the group?(A )9(B )10(C )11(D )12(E )13Question 3What number must be subtracted from −17to obtain −33?(A )−50(B )−16(C )16(D )40(E )50Question 4The diagram shows a stripy isosceles triangle and its height.Each stripe has the same height.What fraction of the area in the triangle is white?(A )1/2(B )1/3(C )2/3(D )3/4(E )2/5Question 5Which of the following equation is correct?(A )41=1.4(B )52=2.5(C )63=3.6(D )74=4.7(E )85=5.8The diagram shows two rectangles whose sides are parallel.What is the difference in the perimeters of the two rectangles?(A)12m(B)16m(C)20m(D)21m(E)24m Question7Bob folded a piece of paper twice and then cut one hole through the folded piece of paper.When he unfolded the paper,he saw the arrangement shown in the diagram below.How did Bob fold his piece of paper?(A)(B)(C)(D)(E)Question8The sum of three different positive integers is7.What is the product of these three integers?(A)12(B)10(C)9(D)8(E)5Question9The diagram shows four overlapping hearts.The areas of the hearts are1cm2,4cm2,9cm2and16 cm2.What is the shaded area?(A)9cm2(B)10cm2(C)11cm2(D)12cm2(E)13cm2Yvonne has20dollars.Each of her four sisters has10dollars.How much does Yvonne have to give to each of her sisters,such that each of thefive girls has the same amount of money?(A)2(B)4(C)5(D)8(E)10Section B(Correct–4points|Unanswered–0points|Wrong–deduct1point)Question11Annie the Ant started at the left end of a pole and crawled 23of its length.Bob the Beetle startedat the right end of the same pole and crawled 34of its length.What fraction is the length of the polebetween Annie and Bob?(A)38(B)112(C)57(D)12(E)512Question12One sixth of the audience in a theatre were adults.Twofifths of children were boys.What fraction of the audience were girls?(A)1/2(B)1/3(C)1/4(D)1/5(E)2/5Question13In the diagram,the dashed line and the black path form seven equilateral triangles.The length of the dashed line is20.What is the length of the black path?(A)25(B)30(C)35(D)40(E)45Four cousins Ema,Iva,Rita and Zina are3,8,12and14years old,although not necessarily in that order.Ema is younger than Rita.The sum of the ages of Zina and Ema is divisible by5.The sum of the ages of Zina and Rita is also divisible by5.How old is Iva?(A)14(B)12(C)8(D)5(E)3Question15This year there were more than800runners participating in the Kangaroo Hop.Exactly35%of the runners were women and there were252more men than women.How many runners were there in total?(A)802(B)810(C)822(D)824(E)840Question16Rachel wants to write a number in each box of the diagram shown.She has already written two of the numbers.She wants the sum of all the numbers to be equal to35,the sum of the numbers in the first three boxes to equal22,and the sum of the numbers in the last three boxes to equal25.What is the product of the numbers she writes in the shaded boxes?(A)63(B)108(C)0(D)48(E)39Question17Simon wants to cut a piece of thread into nine pieces of the same length and marks his cutting points. Barbara wants to cut the same piece of thread into only eight pieces of the same length and also marks her cutting points.Carl then cuts the thread at all the cutting points that are marked.How many pieces of thread does Carl obtain?(A)15(B)16(C)17(D)18(E)19Two segments,each1cm long,are marked on opposite sides of a square of side8cm.The ends of the segments are joined as shown in the diagram.What is the shaded area,in cm2?(A)2(B)4(C)6.4(D)8(E)10Question19Tycho wants to prepare a schedule for his jogging.He wants to jog exactly twice a week,and on the same days every week.He never wants to jog on two consecutive days.How many such schedules are there?(A)16(B)14(C)12(D)10(E)8Question20Emily wants to write a number into each cell of a3×3table so that the sum of the numbers in any two cells with common sides that share an edge which is always the same.She has already written two numbers,as shown in the diagram.What is the sum of all the numbers in the table?(A)18(B)20(C)21(D)22(E)23Section C(Correct–5points|Unanswered–0points|Wrong–deduct1point)Question21The numbers of degrees in the angles in a triangle are three different integers.What is the minimum possible sum of its smallest and largest angles?(A)61◦(B)90◦(C)91◦(D)120◦(E)121◦Ten kangaroos stood in a line as shown in the picture below.At some point,two kangaroos standing side by side and facing each other exchanged places by jumping past each other.This was repeated until no further jumps were possible.How many exchanges were made?(A)15(B)16(C)18(D)20(E)21Question23Diana has nine numbers:1,2,3,4,5,6,7,8and9.She adds2to some of them,and5to all the others.What is the smallest number of different results she can obtain?(A)5(B)6(C)7(D)8(E)9Question24Buses leave the airport every3minutes to drive to the city centre.A car leaves the airport at the same time as one bus and drives to the city centre by the same route.It takes takes60minutes and 35minutes for each bus and the car respectively to drive from the airport to the city centre.How many buses does the car pass on its way to the centre,excluding the bus it left with?(A)8(B)9(C)10(D)11(E)13Question25Olesia’s tablecloth has a regular pattern,as shown in the diagram.What percentage of the tablecloth is black?(A)16(B)24(C)25(D)32(E)36Each digit in the sequence starting with2,3,6,8,8is obtained in the following way:thefirst two digits are2and3and afterwards each digit is the last digit of the product of the two preceding digits in the sequence.What is the2017th digit in the sequence?(A)2(B)3(C)4(D)6(E)8Question27Mike had125small cubes.He glued some of them together to form a big cube with nine tunnels leading through the whole cube as shown in the diagram.How many of the small cubes are there which he did not use?(A)52(B)45(C)42(D)39(E)36Question28Two runners are training on a720metre circular track.They run in opposite directions,each at constant speed.Thefirst runner takes four minutes to complete the full loop and the second runner takesfive minutes.How many metres does the second one run between two consecutive meetings of the two runners?(A)355(B)350(C)340(D)330(E)320Sarah wants to write a positive integer in each box in the diagram so that each number above the bottom row is the sum of the two numbers in the boxes immediately underneath.What is the largest number of odd numbers that Sarah can write?(A)5(B)7(C)8(D)10(E)11Question30The diagram shows parallelogram ABCD with area S.The intersection point of the diagonals of the parallelogram is O.The point M is marked on DC.The intersection point of AM and BD is E and the intersection point of BM and AC is F.The sum of the areas of the triangles AED and BF C is 13S.What is the area of the quadrilateral EOF M,in terms of S?(A)16S(B)18S(C)110S(D)112S(E)114S。

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。

Singapore Math Kangaroo Contest 2017Primary 4 Contest PaperName:School:INSTRUCTIONS:1.Please DO NOT OPEN the contest booklet until the Proctor has given permission to start. 2.TIME : 1 hour and 30 minutes3.There are 30 questions in this paper. 3 points, 4 points and 5 points will be awarded for each correct question in Section A, Section B and Section C respectively. No points are deducted for Unanswered question. 1 point is deducted for Wrong answer. 4.Shade your answers neatly in the answer entry sheet. 5.PROCTORING : No one may help any student in any way during the contest. 6.No calculators are allowed. Name, Index number, Level and School in the 7.All students must fill and shade in your Answer sheet provided. 8.MINIMUM TIME: Students must stay in the exam hall for at least 1 hour and 15 minutes. 9.Students must show detailed working and transfer answers to the answer entry sheet. 10.No spare papers can be used in writing this contest. Enough space is provided for your working of each question. 11. Y ou must return this contest paper to the proctor. Rough WorkingSection A(Correct–3points |Unanswered –0points |Wrong –deduct 1point)Question 1Which of the pieces(A,B,C,D,E)willfit in between the two pieces below,such that the two equations formed will be true?8–3=2(A)=55–1(B)=34–2(C)=51+2(D)=45–3(E)=51+1Question2John looks through the window as shown in the picture below.He only sees half the number of kangaroos in the park.How many kangaroos are there in the park in total?(A)12(B)14(C)16(D)18(E)20Two gridded transparent sheets are darkened in some squares,as shown in the picture below.They are both placed on top of the board shown in the middle.The the pictures behind the darkenedsquares cannot be seen.Only one of the pictures can still be seen,which pictureisit?(A)(B)(C)(D)(E)Question 4A original picture of footprints(left)was rotated in a particular way.The result is shown on the rightofthe original picture.Which pair of footprints are missing?(A)(B)(C)(D)1(E)Question5What number is hidden behind the panda? – 10 = 10+ 6 = – 6 = +8 + 8 = A(A)16(B)18(C)20(D)24(E)28In the table below,the correct sums are shown.What number is in the box with the question mark?(A)10(B)12(C)13(D)15(E)16Question7Dolly accidentally broke the mirror into pieces.How many pieces have exactly four sides?(A)2(B)3(C)4(D)5(E)6Question8Which option shows the necklace below when it is untangled?(A)(B)(C)(D)(E)Section B(Correct–4points|Unanswered–0points|Wrong–deduct1point)Question9The picture below shows the front of Ann’s house.The back of her house has three windows and no door.What does Ann see when she is standing from the back of her house?(A)(B)(C)(D)(E)Question10Which option is correct?(A)(B)(C)(D)(E)Balloons are sold in packets of 5,10and 25.Marius buys exactly 70balloons.What is the smallest number of packets he could buy?(A )3(B )4(C )5(D )6(E )7Question 12Bob folded a piece of paper.He cut exactly one hole through the folded paper.Then he unfolded the piece of paper and saw the result as shown in the picture below.How did Bob fold his piece of paper?(A )(B )(C )(D )(E )Question 13There is a tournament at a pool.At first,13children signed up,and then another 19signed up.Six teams with an equal number of members are needed for the tournament.At least how many more children need to sign up so that the six teams can be form?(A )1(B )2(C )3(D )4(E )5Question 14Numbers are placed in the cells of the 4×4square shown in the picture below.Mary selects any 2×2square in 4×4square and adds up all the numbers in the four cells.What is the largest possible sum she can get?(A )11(B )12(C )13(D )14(E )15David wants to cook5dishes on a stove with only2burners.The time he needed to cook the5dishes are40mins,15mins,35mins,10mins and45mins.What is the shortest possible time in which he can cook all5dishes?(He can only remove a dish from the stove when it is fully cooked.)(A)60min(B)70min(C)75min(D)80min(E)85minQuestion16be written in the circle containing the question mark?Which number shouldSection C(Correct–5points|Unanswered–0points|Wrong–deduct1point)Question17The picture shows a group of building blocks and a plan of these blocks.Some ink has dripped onto the plan.What is the sum of the numbers covered by the ink?3411131(A)3(B)4(C)5(D)6(E)7How long is the train?340 m110 m(A)55m(B)115m(C)170m(D)220m(E)230mQuestion19George trains at his schoolfield atfive o’clock every afternoon.The journey from his house to the bus stop takes5minutes.The bus journey takes15minutes.It takes him5minutes to go from the bus stop to thefield.The bus runs every10minutes from six in the morning.What is the latest time he has to leave his house in order to arrive at thefield exactly on time?(A)(B)(C)(D)(E)Question20A small zoo has a giraffe,an elephant,a lion and a turtle.Susan wants to plan a tour where she sees 2different animals.She does not want to start with the lion.How many different tours can she plan?(A)3(B)7(C)8(D)9(E)12Four brothers have eaten11cookies in total.Each of them has eaten at least one cookie and no two of them have eaten the same number of cookies.Three of them have eaten9cookies in total and one of them has eaten exactly3cookies.What is the largest number of cookies one of the brothers has eaten?(A)3(B)4(C)5(D)6(E)7Question22Zosia has hidden some smileys in some of the squares in the table.In some of the other squares she writes the number of smileys in the neighbouring squares as shown in the picture.Two squares are said to be neighbouring if they share a common side or a common corner.How many smileys has she hidden?(A)4(B)5(C)7(D)8(E)11Question23Ten bags contain different numbers of candies from1to10in each of the bag.Five boys took two bags of candies each.Alex got5candies,Bob got7candies,Charles got9candies and Dennis got15 candies.How many candies did Eric get?(A)9(B)11(C)13(D)17(E)19Question24Kate has4flowers,one with6petals,one with7petals,one with8petals and one with11petals. Kate tears offone petal from threeflowers.She does this several times,choosing any threeflowers each time.She stops when she can no longer tear one petal from threeflowers.What is the smallest number of petals which can remain?(A)1(B)2(C)3(D)4(E)5Rough Working。

Singapore Math Kangaroo Contest 2017Primary 3 Contest PaperName:School:INSTRUCTIONS:1.Please DO NOT OPEN the contest booklet until the Proctor has given permission to start.2.TIME : 1 hour and 30 minutes3.There are 30 questions in this paper. 3 points, 4 points and 5 points will be awarded for eachcorrect question in Section A, Section B and Section C respectively. No points are deducted for Unanswered question. 1 point is deducted for Wrong answer.4.Shade your answers neatly in the answer entry sheet.5.PROCTORING : No one may help any student in any way during the contest.6.No calculators are allowed.7.All students must fill and shade in your Name, Index number, Level and School in theAnswer sheet provided.8.MINIMUM TIME: Students must stay in the exam hall for at least 1 hour and 15 minutes.9.Students must show detailed working and transfer answers to the answer entry sheet.10.No spare papers can be used in writing this contest. Enough space is provided for yourworking of each question.11. Y ou must return this contest paper to the proctor.Rough WorkingSection A(Correct–3points|Unanswered–0points|Wrong–deduct1point)Question1Which of the pieces(A,B,C,D,E)willfit in between the two pieces below,such that the two equations formed will be true?8–3=2(A )=55–1(B )=34–2(C)=51+2(D)=45–3(E)=51+1Question2John looks through the window as shown in the picture below.He only sees half the number of kangaroos in the park.How many kangaroos are there in the park intotal?(A)12(B)14(C)16(D)18(E)20Two gridded transparent sheets are darkened in some squares,as shown in the picture below.They are both placed on top of the board shown in the middle.The the pictures behind the darkened squares cannot be seen.Only one of the pictures can still be seen,which picture isit?Question 4original picture rotated in a particularway.The resultfootprints are missing?(A )(B )(C )(D )1(E )Question 5What number is hidden behind the panda?– 10 = 10+ 6 =– 6 = +8+ 8= A(A )16(B )18(C )20(D )24(E )28In the table below,the correct sums are shown.What number is in the box with the question mark?(A)10(B)12(C)13(D)15(E)16Question7Dolly accidentally broke the mirror into pieces.How many pieces have exactly four sides?(A)2(B)3(C)4(D)5(E)6Question8Which option shows the necklace below when it is untangled?(A)(B)(C)(D)(E)Section B(Correct–4points|Unanswered–0points|Wrong–deduct1point)Question9The picture below shows the front of Ann’s house.The back of her house has three windows and no door.What does Ann see when she is standing from the back of her house?(A)(B)(C)(D)(E)Question10Which option is correct?(A)(B)(C)(D)(E)Balloons are sold in packets of5,10and25.Marius buys exactly70balloons.What is the smallest number of packets he could buy?(A)3(B)4(C)5(D)6(E)7Question12Bob folded a piece of paper.He cut exactly one hole through the folded paper.Then he unfolded the piece of paper and saw the result as shown in the picture below.How did Bob fold his piece of paper?(A)(B)(C)(D)(E)Question13There is a tournament at a pool.Atfirst,13children signed up,and then another19signed up.Six teams with an equal number of members are needed for the tournament.At least how many more children need to sign up so that the six teams can be form?(A)1(B)2(C)3(D)4(E)5Question14Numbers are placed in the cells of the4×4square shown in the picture below.Mary selects any2×2 square in4×4square and adds up all the numbers in the four cells.What is the largest possible sum she can get?(A)11(B)12(C)13(D)14(E)15David wants to cook5dishes on a stove with only2burners.The time he needed to cook the5dishes are40mins,15mins,35mins,10mins and45mins.What is the shortest possible time in which he can cook all5dishes?(He can only remove a dish from the stove when it is fully cooked.)(A)60min(B)70min(C)75min(D)80min(E)85minQuestion16Which number should be(A)10(B)11(C)12(D)13(E)14Section C(Correct–5points|Unanswered–0points|Wrong–deduct1point)Question17The picture shows a group of building blocks and a plan of these blocks.Some ink has dripped onto(A)3(B)4(C)5(D)6(E)7How long is the train?(A)55m(B)115m(C)170m(D)220m(E)230mQuestion19George trains at his schoolfield atfive o’clock every afternoon.The journey from his house to the bus stop takes5minutes.The bus journey takes15minutes.It takes him5minutes to go from the bus stop to thefield.The bus runs every10minutes from six in the morning.What is the latest time he has to leave his house in order to arrive at thefield exactly on time?(A)(B)(C)(D)(E)Question20A small zoo has a giraffe,an elephant,a lion and a turtle.Susan wants to plan a tour where she sees 2different animals.She does not want to start with the lion.How many different tours can she plan?(A)3(B)7(C)8(D)9(E)12Four brothers have eaten11cookies in total.Each of them has eaten at least one cookie and no two of them have eaten the same number of cookies.Three of them have eaten9cookies in total and one of them has eaten exactly3cookies.What is the largest number of cookies one of the brothers has eaten?(A)3(B)4(C)5(D)6(E)7Question22Zosia has hidden some smileys in some of the squares in the table.In some of the other squares she writes the number of smileys in the neighbouring squares as shown in the picture.Two squares are said to be neighbouring if they share a common side or a common corner.How many smileys has she hidden?(A)4(B)5(C)7(D)8(E)11Question23Ten bags contain different numbers of candies from1to10in each of the bag.Five boys took two bags of candies each.Alex got5candies,Bob got7candies,Charles got9candies and Dennis got15 candies.How many candies did Eric get?(A)9(B)11(C)13(D)17(E)19Question24Kate has4flowers,one with6petals,one with7petals,one with8petals and one with11petals. Kate tears offone petal from threeflowers.She does this several times,choosing any threeflowers each time.She stops when she can no longer tear one petal from threeflowers.What is the smallest number of petals which(A)1(B)2(C)3(D)4(E)5。

袋鼠数学历年试题今天咱们来聊聊袋鼠数学的历年试题呀。

袋鼠数学竞赛可有趣啦。

它的试题就像一个个小挑战，等着我们去攻克。

我做过一些历年的试题，那里面的题目可真是五花八门。

比如说有一道关于小动物分果子的题目。

就像在一个大森林里，小兔子有一堆果子，它要分给小松鼠和小猴子一些。

题目里告诉我们小兔子有多少个果子，小松鼠想要几个，小猴子又想要几个。

然后问我们小兔子还剩下几个果子呢。

这就像我们平时和小伙伴分小零食一样呀。

我当时就想着我和我的好朋友分糖果的情景，就很容易算出答案啦。

还有那种关于图形的题目。

就像我们在玩拼图游戏。

有一个大的图形，然后又给了我们几个小的图形，问我们怎么把小图形拼到大图形里面去呢。

我记得有一次是一个像房子形状的大图形，小图形有三角形、正方形。

我就想象着我在搭积木盖房子，把那些小图形一块一块地放在合适的位置。

这让我觉得做试题就像在玩游戏一样。

在历年试题里，也有关于数字排队的题目。

就好比小动物们排队领东西，数字们也要排队。

它会告诉我们一些数字的位置，然后问另一个数字应该在什么地方。

我想到了我们在学校排队做早操，我站在某个同学后面，那另一个同学又该站哪里呢？这样想的话，题目就变得很简单了。

这些试题不仅仅是为了考试，还让我们学会用有趣的方式思考数学问题。

我每次做完一些试题，就感觉自己像一个聪明的小探险家，又发现了数学世界里的一个小秘密。

而且当我做对一道题的时候，那种开心就像我在学校跑步比赛得了第一名一样。

虽然有时候也会遇到很难的题目，就像爬山遇到很陡的坡。

但是只要我们不放弃，再仔细看看题目，就像在山上找另外的小路一样，总会找到解决的办法的。

我特别喜欢做袋鼠数学的历年试题，因为它让数学变得不再那么枯燥。

你们要是有机会做这些试题，一定会像我一样，发现数学原来是这么好玩的东西呢。

它就像一个充满惊喜的大盒子，每一道试题都是一个小惊喜在等着我们去打开。

注意事项：
1.在监考老师宣布开始考试之前，请不要打开考卷
2.时间：1小时30分钟
3.本考卷有30个题。

第一部分每题3分，第二部分每题4分，第三部分每题5分。

不答没有分，
答错均扣一分。

4.在答题纸上清晰地涂黑选项
5.监考：在竞赛过程中，任何人不准以任何形式帮助学生。

6.不允许带计算器。

7.所有的学生必须在考卷上填写和涂黑你的名字，考号，年级和学校
8.最少时间：学生必须在考场待够1小时15分钟
9.学生必须提供详细演算过程并把答案写在答题纸上
10.不提供多余的演算纸。

每个题目已经提供足够的演算空间。

11.必须把考卷还给监考老师。

（完）。