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2020 AUSTRALIAN MATHEMATICS COMPETITION Instructions and Information General 1. Do not open the booklet until told to do so by your teacher. 2. You may use any teaching aids normally available in your classroom, such as MAB  blocks, counters, currency, calculators, play money etc. You are allowed to work on  scrap paper and teachers may explain the meaning of words in the paper. Mobile  phones are not permitted. 3. Diagrams are NOT drawn to scale. They are intended only as aids. 4. There are 25 multiple-choice questions, each requiring a single answer, and 5  questions that require a whole number answer between 0 and 999. The questions  generally get harder as you work through the paper. There is no penalty for an  incorrect answer. 5. This is not a test so do not worry if you can’t answer all the questions. However, try  to answer as many as you can — you do not lose marks for incorrect answers. 6. Read the instructions on the answer sheet carefully. Ensure your name, school  name and school year are entered. It is your responsibility to correctly code your  answer sheet. 7. When your teacher gives the signal, begin working on the problems. The answer sheet Your answer sheet will be scanned. To make sure the scanner reads your paper  correctly, there are some DOs and DON’Ts: DO: •  use only a lead pencil •  record your answers on the answer sheet (not on the question paper) •  for questions 1–25, fully colour the circle matching your answer — keep within  the lines •  for questions 26–30, write your 3-digit answer in the box — make sure your  writing does not touch the box •  use an eraser if you want to change an answer or remove any marks or smudges. D O N O T: •  doodle or write anything extra on the answer sheet •  colour in the QR codes on the corners of the answer sheet. Integrity of the competition The AMT reserves the right to re-examine students before deciding whether to grant  of  cial status to their score. Reminder You may sit this competition once, in one division only, or risk no score. Copyright © 2022 Australian Mathematics Trust | ACN 083 950 341 2022 DAT E TIME ALLOWED 60 minutes Middle Primary Ye a r s 3 – 4 (AUSTRALIAN  SCHOOL YEARS) 3–5 August

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6.Which shape is notused in this snowman picture? (A) circle (B) oval (\b) triangle (D) square (E) rectangle 7.Eve starts at 20 and counts up by twos: 20, 22, 24 and so on. What is the tenth number she counts? (A) 30 (B) 32 (\b) 34 (D) 36 (E) 38 8. This graph was made by a Year 3 class. How many students chose either Saturday or Sunday as their favourite day? (A) 5 (B) 8 (\b) 10 (D) 12 (E) 20 Favourite day of the week Day Numb er of students 0 1 2 3 4 5 Mon Tu e s W ed Thurs Fri Sat Sun 9. I went for a bike ride this morning. These clocks show my start and finish times. In minutes, how long was my ride? (A) 9 (B) 13 (\b) 47 (D) 52 (E) 62 12 3 45 6 \b8 9 1011 12 Start 12 3 45 6 \b8 9 1011 12 Finish 10.Edie and Louie are standing in a line with other children. Edie is fourth from the front and Louie is fourth from the back of the line. There are 15 children in the line. How many children are between Edie and Louie? (A) 7 (B) 8 (\b) 10 (D) 11 (E) 12 6.not789o 11 t8 0  o n 11 Whici sci ap eiudniue ntouw ou mr ?ou( ?oAAr )su( sul Bv e\biuerdniue ntouw ou mr )gDi ?oAAr )su(q Et\b mDnh mtuir lt 2 hs0i sgetAiehicb y:, 4.qa3 y6, 4pqp3 y8, 4TBqY3 yH, 4TaqS3 yf, 4pp3 Fav012 345M 31on T34uu esWnT 4on 5nndnd h1 e13runhn hFiT u4oSn esWna t6\b 8 t9\b  t\b  t\b • t•\b •• Fov•T 634ui Woi5ST •• Thie•noT h1 TF4on n•s4uuM 4315S Fno eu4TT 1  •- Thsdn5hT€ 012 345M Thie•noT 2iuu TFn F4‚n un h 1‚noa t6\b - t9\b  t\b • t\b ƒ t•\b • Fuv „FiT e4od iT …irrnd 1‚no ihT oiSFh†F45d ndSn 45d hFn5 …irrnd 4S4i5 1‚no ihT W1hh13 ndSn€ ‡F4h d1nT hFn e4od u11• ui•n 512a t6\b t9\b t\b t\b t•\b 2022 AUSTRALIAN MATHEMATICS COMPETITION MIDDLE PRIMARY

6.Which shape is notused in this snowman picture? (A) circle (B) oval (\b) triangle (D) square (E) rectangle 7.Eve starts at 20 and counts up by twos: 20, 22, 24 and so on. What is the tenth number she counts? (A) 30 (B) 32 (\b) 34 (D) 36 (E) 38 8. This graph was made by a Year 3 class. How many students chose either Saturday or Sunday as their favourite day? (A) 5 (B) 8 (\b) 10 (D) 12 (E) 20 Favourite day of the week Day Numb er of students 0 1 2 3 4 5 Mon Tu e s W ed Thurs Fri Sat Sun 9. I went for a bike ride this morning. These clocks show my start and finish times. In minutes, how long was my ride? (A) 9 (B) 13 (\b) 47 (D) 52 (E) 62 12 3 45 6 \b8 9 1011 12 Start 12 3 45 6 \b8 9 1011 12 Finish 10.Edie and Louie are standing in a line with other children. Edie is fourth from the front and Louie is fourth from the back of the line. There are 15 children in the line. How many children are between Edie and Louie? (A) 7 (B) 8 (\b) 10 (D) 11 (E) 12 6.not789o 11 t8 0  o n 11 Whici sci ap eiudniue ntouw ou mr ?ou( ?oAAr )su( sul Bv e\biuerdniue ntouw ou mr )gDi ?oAAr )su(q Et\b mDnh mtuir lt 2 hs0i sgetAiehicb y:, 4.qa3 y6, 4pqp3 y8, 4TBqY3 yH, 4TaqS3 yf, 4pp3 Fav012 345M 31on T34uu esWnT 4on 5nndnd h1 e13runhn hFiT u4oSn esWna t6\b 8 t9\b  t\b  t\b • t•\b •• Fov•T 634ui Woi5ST •• Thie•noT h1 TF4on n•s4uuM 4315S Fno eu4TT 1  •- Thsdn5hT€ 012 345M Thie•noT 2iuu TFn F4‚n un h 1‚noa t6\b - t9\b  t\b • t\b ƒ t•\b • Fuv „FiT e4od iT …irrnd 1‚no ihT oiSFh†F45d ndSn 45d hFn5 …irrnd 4S4i5 1‚no ihT W1hh13 ndSn€ ‡F4h d1nT hFn e4od u11• ui•n 512a t6\b t9\b t\b t\b t•\b 2022 AUSTRALIAN MATHEMATICS COMPETITION MIDDLE PRIMARY

15.Chris wants to use the same number in both boxes to make this number sentence true. What number should she use? 7\b  =11 −  (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 16. Sally says to her brother, ‘You are 10 years older than me’. Her brother says, ‘You are right, and I am three times your age’. How old is Sally? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 17. How many of the small coloured tiles are needed to cover the large cross shape shown? (A) 10 (B) 15 (C) 20 (D) 36 (E) 40 tile 18.Siobhan has seven cards, numbered 1 to 7. She places six of them correctly in the three number sentences. Which card does she have left over? 1 2 3 4 5 6 7 × \b − = 12 = 11 =1 (A) 1 (B) 2 (C) 3 (D) 5 (E) 7 19. A long rectangular room 10 m long and 2 m wide has mirrors on all four walls. Any \beam of light hitting these mirrors \bounces \back at the same angle as shown \below. A guard standing at one end of the room shines a torch at an angle of 45 ◦ to the walls, making a narrow \beam that \bounces off the mirrors several times, stopping when it returns to her. How many times does the \beam of light \bounce off the mirrors? 4CE 5 4SE y 4,E mb 4‘E mm 4YE kk 20. A can filled with 30 mar\bles weighs 115 g. The same can with 20 mar\bles weighs 85 g. How much does the empty can weigh? (A) 10 g (B) 20 g (C) 25 g (D) 30 g (E) 55 g Questions 21 to 25, 5 marks each 21. Peter wants to \buy a length of ri\b\bon to wrap around a \box as shown. The \box is 20 cm long, 20 cm wide and 20 cm high. It takes an extra 80 cm of ri\b\bon to tie the \bow. What is the \best estimate of the amount of ri\b\bon that Peter needs to \buy to tie around the \box? 1. 2.3. 4. 5.6. (A) 160 cm (B) 180 cm (C) 240 cm (D) 280 cm (E) 320 cm 22. In week 1, Hamish and Eliza open \bank accounts for their savings. Hamish saves $12 every two weeks, starting in week 1. Eliza saves $32 in week 1 and then $4 every week after that. When will they first have the same amount of money in the \bank? (A) week 3 (B) week 5 (C) week 7 (D) week 9 (E) week 11 2022 AUSTRALIAN MATHEMATICS COMPETITION MIDDLE PRIMARY

15.Chris wants to use the same number in both boxes to make this number sentence true. What number should she use? 7\b  =11 −  (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 16. Sally says to her brother, ‘You are 10 years older than me’. Her brother says, ‘You are right, and I am three times your age’. How old is Sally? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 17. How many of the small coloured tiles are needed to cover the large cross shape shown? (A) 10 (B) 15 (C) 20 (D) 36 (E) 40 tile 18.Siobhan has seven cards, numbered 1 to 7. She places six of them correctly in the three number sentences. Which card does she have left over? 1 2 3 4 5 6 7 × \b − = 12 = 11 =1 (A) 1 (B) 2 (C) 3 (D) 5 (E) 7 19. A long rectangular room 10 m long and 2 m wide has mirrors on all four walls. Any \beam of light hitting these mirrors \bounces \back at the same angle as shown \below. A guard standing at one end of the room shines a torch at an angle of 45 ◦ to the walls, making a narrow \beam that \bounces off the mirrors several times, stopping when it returns to her. How many times does the \beam of light \bounce off the mirrors? •t• • •••   •-•  •€•  •‚•  20. A can filled with 30 mar\bles weighs 115 g. The same can with 20 mar\bles weighs 85 g. How much does the empty can weigh? (A) 10 g (B) 20 g (C) 25 g (D) 30 g (E) 55 g Questions 21 to 25, 5 marks each 21. Peter wants to \buy a length of ri\b\bon to wrap around a \box as shown. The \box is 20 cm long, 20 cm wide and 20 cm high. It takes an extra 80 cm of ri\b\bon to tie the \bow. What is the \best estimate of the amount of ri\b\bon that Peter needs to \buy to tie around the \box? 1. 2. 3. 4. 5.6. (A) 160 cm (B) 180 cm (C) 240 cm (D) 280 cm (E) 320 cm 22.In week 1, Hamish and Eliza open \bank accounts for their savings. Hamish saves $12 every two weeks, starting in week 1. Eliza saves $32 in week 1 and then $4 every week after that. When will they first have the same amount of money in the \bank? (A) week 3 (B) week 5 (C) week 7 (D) week 9 (E) week 11 2022 AUSTRALIAN MATHEMATICS COMPETITION MIDDLE PRIMARY

23.A different whole number is placed in each corner of a square. Two numbers \boined by an edge must have a difference of more than 1. When the four numbers are added together, what is the smallest possible total? (A) 10 (B) 11(C) 12 (D) 13 (E) 14 24.Three whole numbers add to 21. When these same three numbers are multiplied together they equal 280. What is the smallest of these three numbers? (A) 1 (B) 2 (C) 4 (D) 7 (E) 10 25. Steven made this cube from a paper net, then pushed a pin through it as shown. He then removed the pin, leaving holes in the cube, and unfolded the cube back to its net. Which of the following could be the net of Steven’s cube? (A) (B) (C) (D) (E) 2022 AUSTRALIAN MATHEMATICS COMPETITION MIDDLE PRIMARY

23.A different whole number is placed in each corner of a square. Two numbers \boined by an edge must have a difference of more than 1. When the four numbers are added together, what is the smallest possible total? (A) 10 (B) 11(C) 12 (D) 13 (E) 14 24.Three whole numbers add to 21. When these same three numbers are multiplied together they equal 280. What is the smallest of these three numbers? (A) 1 (B) 2 (C) 4 (D) 7 (E) 10 25. Steven made this cube from a paper net, then pushed a pin through it as shown. He then removed the pin, leaving holes in the cube, and unfolded the cube back to its net. Which of the following could be the net of Steven’s cube? (A) (B) (C) (D) (E) For questions 26 to 30, shade the answer as a whole number from 0 to \b\b\b in the space provided on the answer sheet. Questions 26–30 are worth 6, 7, 8, \b and 10 marks, respectively. ol1 I notice that my electricity meter currently reads 896 754 units, \bhere all the digits are different. Ho\b many more units of electricity \bill I need to use before all the digits are again different? 8 9 6 7 5 4 27. Ho\b many \bhole numbers bet\been 200 and 500 contain the digit 3? 28.On a digital display, a combination of bars light up to represent each digit as sho\bn: In some special numbers, the number of bars \bhich light up in the digits is the same as the sum of the digits. For example, in 373 the number of bars is 5 + 3 + 5 = 13 \bhich is the equal to 3 + 7 + 3 = 13. What is the largest such three-digit number? 2\b. Nguyen \brites do\bn some numbers according to the follo\bing rules. Starting \bith the number 1, he doubles the number and adds 4, so the second number he \brites is 6. He no\b repeats this process, starting \bith the last number \britten, doubling and then adding 4, but he doesn’t \brite the hundreds digit if the number is bigger than 100. What is the 2022nd number that Nguyen \brites do\bn? 30. I choose three different numbers out of this list and add them together: 1,3 ,5 ,7 ,9 ,..., 105 Ho\b many different totals can I get? 2022 AUSTRALIAN MATHEMATICS COMPETITION MIDDLE PRIMARY





CORRECTLY RECORDING YOUR ANSWER (QUESTIONS 1–25) Only use a lead pencil to record your answer. When recording your answer on the sheet, fi ll in the bubble completely. The example below shows the answer to Question 1 was recorded as ‘B’\ . DO NOT record your answers as shown below. They cannot be read accurately by the scanner and you may not receive a mark for the question. Use an eraser if you want to change an answer or remove any pencil marks or smudges. DO NOT cross out one answer and fi ll in another answer, as the scanner cannot determine which one is your answer. Correct CORRECTLY WRITING YOUR ANSWER (QUESTIONS 26–30) For questions 26–30, write your answer in the boxes as shown below. 2 + 3 = 20 + 21 = 200 + 38 = WRITING SAMPLES 0 12 3 45 6 78 9 Your numbers MUST NOT touch the edges of the box or go outside it. The number one must only be written as above, otherwise the scanner migh\ t interpret it as a seven. DO NOT doodle or write anything extra on the answer sheet or colour in the QR \ codes on the corners of the answer sheet, as this will interfere with the scanner. Incorrect Incorrect Incorrect Incorrect Incorrect Incorrect this one! 1 digit 2 digits 3 digits 54 l 2 3 8 0 Correct l Correct 3 Correct 4 6 Correct 7 9 Correct 1 Incorrect 3 0 6 9 4 7 Correct Correct 2 Correct 5 Correct 8 Correct 5 2 8 2 36 5 4 0 5 8 1 Middle Primary Ye a r s 3 – 4 (AUSTRALIAN  SCHOOL YEARS)