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(1)Middle Primary Division Questions 1 to 10, 3 marks each 1.. How many dots are on the plate? (A) 10. (B) 12. (C) 13. (D) 14. 2.. Jill had 15 grapes. She ate 5. How many are left? (A) 7. 3.. (E) 15. (B) 8. (C) 9. This grid gives the position of different shapes. For example, a ♢ is in position B4. Which shape is in position D2?. A ⊕. (A) ♢. C ⊙. (B) ⊕. 1. (E) △. 1 2. (B) (D). 1 5. 1 3. (C) (E). 2. 1 6. 1 4. 3. 4. ♡ ♡ ⊙ ♢. ⊙ ⊕ ♡. D △ ♡. What fraction of this shape is shaded? (A). (E) 11. B △ . (C) ♡. (D) ⊙. 4.. (D) 10. ⊕ △.

(2) MP 2. 5.. On this spinner, which shape are you most likely to spin? (A) N (D) ♠. 6.. •. (C) ⋆. (B). N. (E) •. ⋆ •. ♠. What time is shown on this clock?. 11 12 1. (A) twelve o’clock. 10 9 8. (B) a quarter to nine (C) a quarter past three. 2 3 4 7 6 5. (D) a quarter past twelve (E) three o’clock. 7.. The graph below shows the number of pets owned by the students in a Year 4 class. Pets in Year 4 8 6 4 2 0. Cats. Dogs. Fish. Rabbits. How many pets does this class have altogether? (A) 24. (B) 22. (C) 21. (D) 14. (E) 4.

(3) MP 3. 8.. Which number do you need in the box to make this number sentence true? 19 + 45 = 20 + (A) 34. 9.. (B) 44. (C) 46. (D) 64. (E) 84. How many 2 by 1 rectangles will fit exactly into an 8 by 7 rectangle? (A) 14. (B) 28. (C) 36. (D) 56. (E) 63. 10. Five swimmers were in a 50 m race. The time each swimmer took to finish the race is shown in this graph. Who won the race? George Ethan Franco Henry Ivan 0 (A) George. 10. 20. (B) Ethan. 30. 40 Time in seconds. (C) Franco. (D) Henry. (E) Ivan.

(4) MP 4. Questions 11 to 20, 4 marks each 11. Cianna is stringing beads for a necklace, starting with two round beads, then a square bead, and then repeating this pattern of three beads.. She finished her necklace with a round bead, which happens to be the 18th round bead. How many square beads are on her necklace? (A) 10. (B) 12. (C) 18. (D) 6. (E) 8. 12. The triangle shown is folded in half three times without unfolding, making another triangle each time.. Which figure shows what the triangle looks like when unfolded? (A). (B). (C). (D). (E). 13. When complete, each row, column and diagonal in this diagram has a sum of 15. What is the sum of the numbers in the shaded squares? (A) 20. (B) 25. (C) 27. (D) 30. (E) 45. 4 5 5.

(5) MP 5. 14. To which square should I add a counter so that no two rows have the same number of counters, and no two columns have the same number of counters? (A) A. (B) B. (C) C. (D) D. A B. C D E. (E) E. 15. John wrote his name on his book. Martha said he wrote with a black pen. Aaron said it was a brown pencil. Frankie said it was a black crayon. If each of John’s friends were half right, what did he really use to write his name? (A) a brown pen. (B) a brown crayon. (D) a black pen. (C) a brown pencil. (E) a black pencil. 16. Follow the instructions in this flow chart.. Start with 5. Subtract 2. Multiply by 3. Is this greater than 50?. Yes. Select this answer. No. (A) 57. (B) 63. (C) 75. (D) 81. (E) 84.

(6) MP 6. 17. A square piece of paper is folded along the dashed lines shown and then the top is cut off. . The paper is then unfolded. Which shape shows the unfolded piece? (A). (B). (C). (D). (E). 18. Rod had fewer than 100 blocks. When he made five equal rows, he had one block left over. With four equal rows, he had one block left over. With nine equal rows, there were no blocks left over. How many blocks did he have? (A) 18. (B) 49. (C) 81. 19. Simon has some 24 cm long strips. Each strip is made from a different number of equal-sized tiles. Simon took 1 tile from each strip to make a new strip. How long is the new strip? (A) 18 cm. (B) 20 cm. (D) 24 cm. (C) 23 cm. (E) 33 cm. (D) 91. (E) 99.

(7) MP 7. 20. The numbers 1 to 6 are placed in the circles so that each side of the triangle has a sum of 10. If 1 is placed in the circle shown, which number is in the shaded circle? (A) 2. (B) 3. (C) 4. (D) 5. 1. (E) 6. Questions 21 to 25, 5 marks each 21. Grandpa had $400 in his wallet. He gave half the money to his wife. From what was left, he then gave one-quarter to his son. Half of the remainder went to his grandson. How much money did his grandson receive? (A) $50. (B) $125. (C) $100. (D) $200. (E) $75. 22. The numbers 40, 19, 37, 33, 12, 25, 46, 18, 39, 21 are matched in pairs so that the sum of each pair is the same. Which number is paired with 39? (A) 19. (B) 33. 23. This shape is made from two overlapping rectangles. What is its area in square centimetres? (A) 35 (C) 39. (B) 37 (D) 41 (E) 43. (C) 21. (D) 18. (E) 25. 6 cm. 4 cm. 3 cm 4 cm 3 cm 2 cm 5 cm.

(8) MP 8. 24. Molly is thinking of a number. Twice her number take away seven is the same as her number plus five. What is her number? (A) 19. (B) 17. (C) 15. (D) 12. (E) 10. iGloo. iGloo. iGloo. iGloo. iGloo. 25. Tom borrowed some items from the stationery cupboard. He found that 5 glue sticks weigh the same as 2 staplers, and that 3 staplers weigh the same as 20 erasers.. How many glue sticks balance with how many erasers? (A) 3 glue sticks with 8 erasers (B) 3 glue sticks with 50 erasers (C) 1 glue stick with 6 erasers (D) 3 glue sticks with 17 erasers (E) 7 glue sticks with 23 erasers. For questions 26 to 30, shade the answer as a whole number from 0 to 999 in the space provided on the answer sheet. Question 26 is 6 marks, question 27 is 7 marks, question 28 is 8 marks, question 29 is 9 marks and question 30 is 10 marks.. 26. Jill has three large piles of coins: 10c, 20c and 50c. In how many different ways can she make one dollar?.

(9) MP 9. 27. A newspaper open on the table had page 42 opposite page 55 because someone had removed some pages from the centre. What is the number of the last page of the newspaper?. 28. Alex is designing a square patio, paved by putting bricks on edge using the basketweave pattern shown. She has 999 bricks she can use, and designs her patio to be as large a square as possible. How many bricks does she use?. 29. There are many ways that you can add three different positive whole numbers to get a total of 12. For instance, 1 + 5 + 6 = 12 is one way but 2 + 2 + 8 = 12 is not, since 2, 2 and 8 are not all different. If you multiply these three numbers, you get a number called the product. Of all the ways to do this, what is the largest possible product?. 30. A 3 × 2 flag is divided into six squares, as shown. Each square is to be coloured green or blue, so that every square shares at least one edge with another square of the same colour. In how many different ways can this be done?.

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(18) Middle Primary Division Questions 1 to 10, 3 marks each 1.. The value of 2 + 0 + 1 + 7 is (A) 10. 2.. 4.. (C) 37. (D) 208. (E) 2017. Jillian has her 9th birthday in 2017. In which year was she born? (A) 2006. 3.. (B) 19. (B) 2007. (C) 2008. What is the value of the 2 in 213? (A) 0.02 (B) 0.2 (C) 2. The squirrel’s tree is on square L3. To get there from square K1, the squirrel must move (A) (B) (C) (D) (E). two squares right and one square down one square left and two squares down three squares left and two squares down three squares right and one square down one square right and two squares down. (D) 2009. (E) 2010. (D) 20. (E) 200. 1 J K L M. 2. 3. 4.

(19) MP 2. 5.. Lincoln went to buy some fruit at the school canteen. He bought 4 apples which cost 30 cents each. How much did the 4 apples cost? (A) 60c. 6.. (B) 80c. 3 4. (B) (D). 2 5. 1 2. (C) (E). (E) $1.60. (B) 13. 2 3. 3 5. Zara was cycling. She came to a T-intersection in the road where she saw this sign. The road to Smithton passes through Marytown. How many kilometres is it from Marytown to Smithton? (A) 8. 8.. (D) $1.20. Five dice were rolled, and the results were as shown. What fraction of the dice showed a two on top? (A). 7.. (C) $1.00. 28 km Janesville Marytown 15 km Smithton. (C) 38. 23 km. (D) 43. (E) 51. Riverside Primary School has 235 staff and students. Each bus can fit 50 people. What is the least number of buses they need for a whole school excursion? (A) 2 (B) 3 (C) 5 (D) 6 (E) 7.

(20) MP 3. 9.. Which of these shapes are pentagons? 1. 2. 3. 4 (A) all of the shapes. 5 (B) shape 3 only. (D) shapes 1 and 3. (C) shapes 3 and 4. (E) none of the shapes. 10. Fred gave half of his apples to Beth, and then half of what was left to Sally, leaving him with just one apple. How many did he have to start with? (A) 12 (B) 8 (C) 6 (D) 4 (E) 2. Questions 11 to 20, 4 marks each 11. Which of the shaded areas below is the largest? (A). (B). (C). (D). (E). 12. Helen is adding some numbers and gets the total 157. Then she realises that she has written one of the numbers as 73 rather than 37. What should the total be? (A) 110 (B) 121 (C) 124 (D) 131 (E) 751.

(21) MP 4. 4c. 3c. 4c. 3c. (C) 18c. 3c. ? 4c. 4c. (B) 8c. 3c. (A) 3c. 4c. 13. In the year 3017, the Australian Mint recycled its coins to make new coins. Each 50c coin was cut into six triangles, six squares, and one hexagon. The triangles were each worth 3c and the squares were each worth 4c. How much should the value of the hexagon be to make the total still worth 50c?. 3c. 4c. (D) 20c. 3c. (E) 43c. 14. At the supermarket Ashan noticed that her favourite biscuits were on special, with one-third extra for free in the packet. If this special packet contained 24 biscuits, how many biscuits would be in the normal packet? (A) 12. (B) 16. (C) 18. (D) 20. 15. Greg sees a clock in the mirror, where it looks like this. What is the actual time? (A) 4:10 (B) 4:50 (C) 5:10 (D) 6:50. (E) 7:10. 16. Jonathan made this shape with rectangular cards 2 cm long and 1 cm wide. What is the perimeter of the shape? (A) 6 cm. (B) 12 cm. (D) 24 cm. (C) 18 cm (E) 36 cm. (E) 32. 21.

(22) MP 5. 17. In these two number sentences +. +. +. = 12. +. +. +. = 20. what is the value of (A) 1. (B) 2. ? (C) 3. (D) 4. (E) 5. 18. One year in June, there were four Wednesdays and five Tuesdays. On which day was the first of June? (A) Monday (B) Tuesday (C) Thursday (D) Friday (E) Saturday. 19. In the 4 by 4 square shown, I am filling in the 16 small squares with the numbers 1, 2, 3 and 4 so that each row and each column has one of each of these numbers. I have filled in some of the squares as shown. What do the two squares marked ∗ add to? (A) 3. (B) 4. (D) 6. (C) 5. (E) 7. 20. On these scales, two of the cubes balance with three of the balls. How many cubes need to be added to the right-hand side to make the scales balance? (A) 5 (B) 6 (C) 8 (D) 12. (E) 13. 1. * *. 4 2. 4. 3. 2. 1.

(23) MP 6. Questions 21 to 25, 5 marks each 21. This shape can be folded up to make a cube. Which cube could it make?. (A). (B). (D). (C). (E). 22. How many three-digit numbers contain only the digits 2 and 3, and each of them at least once? (A) 2 (B) 4 (C) 6 (D) 8 (E) 32. 23. Which one of the patterns below would be created with these folds and cuts?. (A). (B). (C). (D). (E).

(24) MP 7. 24. I have a rectangular block of cheese that I can cut into 12 identical 1 cm cubes, with none left over. How many differently-shaped blocks of cheese could I have started with? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6. 25. A clockface can be divided with two straight lines into three regions so that the sum of the numbers in each region is the same. What is this sum? (A) 20. (B) 22 (D) 26. (C) 24. 11 12 1 10. 2. 9 8. 3 4 7 6. 5. (E) 28. For questions 26 to 30, shade the answer as a whole number from 0 to 999 in the space provided on the answer sheet. Question 26 is 6 marks, question 27 is 7 marks, question 28 is 8 marks, question 29 is 9 marks and question 30 is 10 marks.. 26. In a three-digit number, one of the digits is 7 and the difference between any two of the digits is 4 or less. What is the smallest this number could be?.

(25) MP 8. 27. Julie has 5 steps up to her classroom, where step 5 is the floor of the classroom. Each day she tries to think of a different way of climbing up these steps. She does not have to touch each step, but the biggest distance she can reach is 3 steps. How many different ways are there of going up the steps?. 28. Zhipu has an unusual construction set, consisting of square tiles which only connect together if they are joined with half a side touching. That is, the corner of one connects with the midpoint of the other, as in the diagram. In how many ways can he connect three tiles? (Two arrangements are not different if they can be rotated or reflected to look the same.). 29. Old Clarrie has three dogs. The oldest is Bob, next comes Rex and Fido is the youngest. Fido is 10 years younger than Bob, and none of the dogs are the same age. When Clarrie adds their ages together they come to 28 years. When Clarrie multiplies their ages together, he gets a number. What is the smallest that this number could be?. 30. All of the digits from 0 to 9 are used to form two 5-digit numbers. What is the smallest possible difference between these two numbers?.

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(35) 注意：允許學生個人、非營利性的圖書館或公立學校合理使用本基金會網站所提供之各項試題及其解答。可直接下載而不須申請。. 重版、系統地複製或大量重製這些資料的任何部分，必須獲得財團法人臺北市九章數學教育基金會的授權許可。申請此項授權請電郵 ccmp@seed.net.tw Notice: Individual students, nonprofit libraries, or schools are permitted to make fair use of the papers and its solutions. Republication, systematic copying, or multiple reproduction of any part of this material is permitted only under license from the Chiuchang Mathematics Foundation. Requests for such permission should be made by e-mailing Mr. Wen-Hsien SUN. ccmp@seed.net.tw.

(36) Middle Primary. 1. Middle Primary Division Questions 1 to 10, 3 marks each How many eggs are in these cartons? (A) 12 (B) 15 (C) 16 (D) 18. 2.. Which one of the following is the largest number? (A) 401. 3.. 4.. (E) 21. (B) 410. (C) 14. (D) 140. (E) 44. Which of the following is equal to 3 m? (A) 3 cm (B) 30 cm (C) 300 cm. (D) 3000 cm. (E) 36 cm. A bowl has 8 peaches. After the children take one each, there is one peach left. How many children are there? (A) 5 (B) 6 (C) 7 (D) 8. 5.. (E) 9. A Runnyball team has 5 players. This graph shows the number of goals each player scored in a tournament. Who scored the second-highest number of goals? (A) Ali. (B) Beth. (D) Dan. AMC2019: Final for translation. (C) Caz (E) Evan. Goals. 1.. 8 7 6 5 4 3 2 1 0. Ali. Beth Caz Dan Evan Player. 12/5/2019.

(37) Middle Primary. The next counting number after 1089 is. r r r. r. A r. 5 r. 2 r. r r. 5. r. (E) 1009. rr r r. 3 r. 4 r. A r. r r r. 4r Ar 5r 3r 2r Ar 4r 5r 3r 2r 2r 4r Ar 3r 5r Ar 2r 3r 4r 5r 2r 3r 4r 5r Ar. The table shows the pets six children own. Which boy owns a dog?. Girls. (A) Alex. Boys Teejay Finn Alex. (B) Chris. (C) Finn. Jo. Sam. AMC2019: Final for translation. W. E. 5th Avenue. S 4th Avenue. S 3rd Avenue. 2nd Avenue. E. 4th Street. east, 3 blocks north west, 4 blocks north west, 2 blocks north east, 2 blocks north north, 2 blocks south. N N. 3rd Street. blocks blocks blocks blocks blocks. Chris. 2nd Street. 4 3 4 3 2. Dog Fish. (E) Teejay. Sophia is at the corner of 1st Street and 1st Avenue. Her school is at the corner of 4th Street and 3rd Avenue. To get there, she walks (A) (B) (C) (D) (E). Cat. 1st Street. (D) Jo. 9.. (D) 1900. These cards were dropped on the table, one at a time. In which order were they dropped? (A) (B) (C) (D) (E). 8.. (C) 1910. 4 r 2 r. 7.. (B) 10810. 3 r. (A) 1090. r r. 6.. 2. 1st Avenue. 12/5/2019.

(38) Middle Primary. 3. 10. Jake is playing a card game, and these are his cards. Elena chooses one card from Jake at random. Which of the following is Elena most likely to choose?. r r ♣ rr♠♣r♣ ♣. JA♠ r4r ♣ ♣ r♣ r r r r. r. 7K. (D) a picture card (J, Q or K). ♣. (B) a diamond (q). ♣3 ♠♣ ♠9. (A) a heart (r). 9 3 K ♣7 r ♠ ♠♣♠ J 4♣ ♣ ♣ A r r. (C) a spade (♠). (E) an even-numbered card. Questions 11 to 20, 4 marks each 11. In Jacqui’s puzzle, a number is put in each box. In each circle, the four numbers must add to 13. Which number goes in the top box? (A) 2 (B) 3 (C) 4 (D) 5. ?. 1 5. 3. 7. (E) 6. 12. Noah follows the instructions in this flow chart. What number does he end with? Start with 8. Subtract 5. Multiply by 5 No. (A) 120. (B) 150. AMC2019: Final for translation. (C) 200. Greater Yes than 100?. (D) 225. End. (E) 250. 12/5/2019.

(39) Middle Primary. 4. 13. On this number line, where would the number 0 (A) A. A. B. C. (B) B. D. be? 2. E. (C) C. 14. When Bessie puts a mirror next to her calculator, the digits sometimes spell words in the mirror. Which number spells ‘BESSIE’ in the mirror? (A) 315538 (B) 835513 (C) 832213 (D) 815312 (E) 312238. 1 2. (D) D. (E) E. 7. 8. 9. ÷. ÷. 9. 8. 7. 4. 5. 6. ×. ×. 6. 5. 4. 1. 2 .. 3. −. −. 3. 1. =. +. +. =. 2 .. 0. 15. Looking at this view of four dice, how many dots cannot be seen? (A) 21 (B) 28 (C) 32 (D) 36. (E) 45. 16. A pencil costs 25 cents and a ruler costs 80 cents. With $5 I bought one ruler and as many pencils as I could afford. What change did I get? (A) 25 cents (B) 20 cents (C) 15 cents (D) 10 cents (E) 5 cents 17. 27 identical cubes are used to make this 3 × 3 × 3 cube. How many more are needed to make a 4 × 4 × 4 cube? (A) 1 (B) 25 (C) 27 (D) 36. AMC2019: Final for translation. (E) 37. 12/5/2019. 0.

(40) Middle Primary. 5. 18. Meena has a $50 gift voucher to spend in a toyshop, but they won’t give change from the voucher. Here is a short list of toys she would like. She tried to spend as much of the $50 as possible.. $24. $14. $6. $39. If she buys no more than one of each toy, how much of the voucher will not get used? (A) $1 (B) $3 (C) $5 (D) $7 (E) $9. . 19. A square piece of paper is folded twice along its diagonals, as shown in the diagram. Two corners are then cut off. When the paper is unfolded, what will it look like?. . (A). (B). (D). AMC2019: Final for translation. (C). (E). 12/5/2019.

(41) Middle Primary. 6. 20. It takes Preeti 30 minutes to walk to school. Sometimes she goes on her bike and she cycles twice as fast as she walks. Occasionally, her mother takes her in the car, which goes three times as fast as her bike. How many minutes does it take to get to school in the car? (A) 2 (B) 4 (C) 5 (D) 10 (E) 15 Questions 21 to 25, 5 marks each 21. In my dance class, 14 students are taller than Bob, and 12 are shorter than Alice. Four students are both shorter than Alice and taller than Bob. How many students are in my dance class? (A) 22 (B) 24 (C) 26 (D) 28 (E) 30 22. My sister and I are playing a game where she picks two counting numbers and I have to guess them. When I tell her a number, she multiplies my number by her first number and then adds her second number. When I say 15, she says 50. When I say 2, she says 11. If I say 6, what should she say? (A) 23 (B) 27 (C) 35 (D) 41 (E) 61 23. A year 6 student saved 100 cents in 5 days, each day saving 5 cents more than the previous day. How many cents did she save on the fifth day? (A) 20 cents (B) 25 cents (C) 30 cents (D) 40 cents (E) 50 cents. (B) E. AMC2019: Final for translation. (C). (D). F. A. C D A. E. (A) D. F. 24. A cube has the letters A, M, C, D, E and F on its six faces. Two different views of the cube are shown. I place the cube on the table so that the front shows C . If I look at the back of the cube, what will I see?. E. (E) F. 12/5/2019.

(42) Middle Primary. 7. 25. Shirley has six pieces of her construction kit: two red, two blue and two green. She wants to build a square using four of the pieces.. Shirley considers Square 1 below to be the same as Square 2, since the colours match once Square 2 is turned over and rotated. However she considers Square 3 to be different from Square 1, since no matter how it is turned, the two red sides are always opposite, and cannot match Square 1.. Square 2. Square 3. Blue. Blue. Red. Green. Green. Red. Red. Red. Square 1. Green. Red. Blue. Red. How many different squares could she build? (A) 4. (B) 8. (C) 12. (D) 16. (E) 18. For questions 26 to 30, shade the answer as a whole number from 0 to 999 in the space provided on the answer sheet.. A C KET. AMC2019: Final for translation. KE. TI. 26. At my local greengrocer, you take a ticket from the machine and wait until your number is called. The roll of tickets goes from 000 up to 999. When I was there last week with my neighbour, we took two tickets in a row and our two numbers added to 777. What was the next ticket number after ours?. TA. Questions 26–30 are worth 6, 7, 8, 9 and 10 marks, respectively.. 12/5/2019.

(43) Middle Primary. 8. 27. There are 390 children at a summer camp. One-third of the number of girls is equal to one-half of the number of boys. How many girls are there?. 28. How many of the numbers from 100 to 999 have exactly one zero digit?. 29. A tower is built from exactly 2019 equal rods. Starting with 3 rods as a triangular base, more rods are added to form a regular octahedron with this base as one of its faces. The top face is then the base of the next octahedron. The diagram shows the construction of the first three octahedra. How many octahedra are in the tower when it is finished?. 30. John is one year older than his wife Mary. They have three children, whose ages are two years apart. The product of John and Mary’s ages is less than 2019. The product of the three children’s ages is also less than 2019. Next year both these products will be greater than 2020. This year, what is the sum of all five ages?. AMC2019: Final for translation. 12/5/2019.

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