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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 Upper Primary Ye a r s 5 – 6 (AUSTRALIAN  SCHOOL YEARS) 3–5 August

Upper Primary Division Questions 1 to 10, 3 marks eac\b 1. What number is two hundred and five thousand, one hundred and fifty? (A\b 150 (B\b 205 (C\b 20 150 (D\b 25 150 (E\b 205 150 2. What fraction of this picture is shaded? (A\b 1 2 (B\b 2 3 (C\b 3 4 (D\b 4 9 (E\b 5 9 3. 2220 −2022 = (A\b 18 (B\b 188 (C\b 198 (D\b 200 (E\b 202 4. Audrey wrote these three numbers in order from smallest to largest: 1.03 0. 08 0.4 In which order did she write them? (A\b 0 .08, 1.03, 0.4 (B\b 0 .08, 0.4 ,1 .03 (C\b 0 .4 ,0 .08, 1.03 (D\b 0. 4,1 .03,. 008 (E\b 1.03,0.4 ,0 .08 5. I was 7 years old when my brother turned 3. How old will I be when he turns 7? (A\b 9 (B\b 10 (C\b 11 (D\b 12 (E\b 13

Upper Primary Division Questions 1 to 10, 3 marks eac\b 1. What number is two hundred and five thousand, one hundred and fifty? (A\b 150 (B\b 205 (C\b 20 150 (D\b 25 150 (E\b 205 150 2. What fraction of this picture is shaded? (A\b 1 h (B\b 2 3 (C\b 3 4 (D\b 4 9 (E\b 5 9 3. 2220 −2022 = (A\b 18 (B\b 188 (C\b 198 (D\b 200 (E\b 202 4. Audrey wrote these three numbers in order from smallest to largest: 1.03 0. 08 0.4 In which order did she write them? (A\b 0 .08, 1.03, 0.4 (B\b 0 .08, 0.4 ,1 .03 (C\b 0 .4 ,0 .08, 1.03 (D\b 0. 4,1 .03,. 008 (E\b 1.03,0.4 ,0 .08 5. I was 7 years old when my brother turned 3. How old will I be when he turns 7? (A\b 9 (B\b 10 (C\b 11 (D\b 12 (E\b 13 2022 AUSTRALIAN MATHEMATICS COMPETITION UPPER PRIMARY

6.This shape is built from 29 squares, each 1 cm ×1 cm. What is its perimeter i\b ce\btimetres? (A) 52 (B) 58(C) 60 (D) 68 (E) 72 7.A tachometer i\bdicates how fast the cra\bkshaft i\b a car’s e\bgi\be is spi\b\bi\bg, i\b thousa\bds of revolutio\bs per mi\bute (rpm). What is the readi\bg o\b the tachometer show\b? (A) 2.2 rpm (C) 240 rpm (B) 2.4 rpm (D) 2200 rpm (E) 2400 rpm 0 1 2 3 4 5 6 7 8 x 1000 rpm 8. Joseph had a full, o\be litre bottle of water. He dra\bk 320 millilitres of it. How much was left? (A) 660 mL (B) 670 mL (C) 680 mL (D) 730 mL (E) 780 mL 9. Which of these recta\bgles have a\b area of 24 square ce\btimetres? 12cm 2 cm P 6 cm 4 cm R 24 cm 1 cm S 8 cm 3 cm Q (A) Q o\bly (B) Q a\bd R o\bly (C) R o\bly (D) S o\bly (E) P, Q, R a\bd S 6.7This apebu shlts fpirs olm2i29 mlqai2u, c1 hu 2uu.s al eu pa sWhllb e\b ?(AA po thpa is ahu bpausa aiou hu Wp2 sapma his shltum) 5B8 C(6A po 508 C(AD po 5E8 ?(DA po 578 ?(dD po 5w8 ?(6A po  97€79\b 67Q 9P‚Q ƒ.Q „ 79Q8 …Q9 Q88Q „• 79Q8 †P€Q RQP‚ P89  • 79Q8 •8. 9QQ9.  79Q8 ‡PS‚ 9 8 .S •• 79Q8 89PRSQR 66 S .  R P 667 HhiWh s3i22um is atiWu ps bi’ub\b al bp2. l2 mu. ps thiau) 5B8 508 5E8 578 5w8 67 gapmai29 pa D l2 ahu 2qoeum bi2uL Ebuou2a tpb’s epW’ p2. 1lmah i2 ahu 1lbblti29 3paaum2( 6 al ahu mi9haL d al ahu bu1aL 6 al ahu mi9haL d al ahu bu1aL p2. sl l2, D v d 6 Q A y C ? R vD vv vd ×           0 1 \b      
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6.This shape is built from 29 squares, each 1 cm ×1 cm. What is its perimeter i\b ce\btimetres? (A) 52 (B) 58(C) 60 (D) 68 (E) 72 7. A tachometer i\bdicates how fast the cra\bkshaft i\b a car’s e\bgi\be is spi\b\bi\bg, i\b thousa\bds of revolutio\bs per mi\bute (rpm). What is the readi\bg o\b the tachometer show\b? (A) 2.2 rpm (C) 240 rpm (B) 2.4 rpm (D) 2200 rpm (E) 2400 rpm 0 1 2 3 4 5 6 7 8 x 1000 rpm 8. Joseph had a full, o\be litre bottle of water. He dra\bk 320 millilitres of it. How much was left? (A) 660 mL (B) 670 mL (C) 680 mL (D) 730 mL (E) 780 mL 9. Which of these recta\bgles have a\b area of 24 square ce\btimetres? 12cm 2 cm P 6 cm 4 cm R 24cm 1 cm S 8 cm 3 cm Q (A) Q o\bly (B) Q a\bd R o\bly (C) R o\bly (D) S o\bly (E) P, Q, R a\bd S 6.7This apebu shlts fpirs olm2i29 mlqai2u, c1 hu 2uu.s al eu pa sWhllb e\b ?(AA po thpa is ahu bpausa aiou hu Wp2 sapma his shltum) 5B8 C(6A po 508 C(AD po 5E8 ?(DA po 578 ?(dD po 5w8 ?(6A po  97€79\b 67Q 9P‚Q ƒ.Q „ 79Q8 …Q9 Q88Q „• 79Q8 †P€Q RQP‚ P89  • 79Q8 •8. 9QQ9.  79Q8 ‡PS‚ 9 8 .S •• 79Q8 89PRSQR 66 S .  R P 667 HhiWh s3i22um is atiWu ps bi’ub\b al bp2. l2 mu. ps thiau) 5B8 508 5E8 578 5w8 67 gapmai29 pa D l2 ahu 2qoeum bi2uL Ebuou2a tpb’s epW’ p2. 1lmah i2 ahu 1lbblti29 3paaum2( 6 al ahu mi9haL d al ahu bu1aL 6 al ahu mi9haL d al ahu bu1aL p2. sl l2, D v d 6 Q A y C ? R vD vv vd ×           0 1 \b      
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14.I have three cardboard shapes: a square, a circle and a triangle. I glue them on top o\b each other as shown in this diagram. I then flip the glued-together shapes over. What could they look like? ••• ••• ••• ••• • • 15. What is the missing number needed to make this number sentence true? 270÷45 = ÷15 (A) 3 (B) 6 (C) 60 (D) 90 (E) 150 16. Three different squares are arranged as shown. The perimeter o\b the largest square is 32 centimetres. The area o\b the smallest square is 9 square centimetres. What is the perimeter o\b the medium- sized square? (A) 12 cm (B) 14 cm (C) 20 cm (D) 24 cm (E) 30 cm 17. Huang has a bag o\b marbles. Mei takes out one-third o\b them. Huang then takes out one-hal\b o\b those le\bt, leaving 8 marbles in the bag. How many marbles were originally in the bag? (A) 12 (B) 16 (C) 18 (D) 24 (E) 36 18. A different positive whole number is placed at each vertex of a cube. \bo two numbers joined by an edge of the cube can have a difference of 1. What is the smallest possible sum of the eight numbers? (A) 36 (B) 37(C) 38 (D) 39 (E) 40 19.George is 78 this year. He has three grandchildren: Michaela, Tom and Lucy. Michaela is 27, Tom is 23 and Lucy is 16. After how many years will George’s age be equal to the sum of his grandchildren’s ages? (A) 3 (B) 6 (C) 9 (D) 10 (E) 12 20. Ms Graham asked each student in her Year 5 class how many television sets they each have. This graph shows the results. How many television sets do the students have altogether? (A) 9 (B) 29 (C) 91 (D) 99 (E) 101 Number of TVs students have Numb er of TVs Number of students 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 Questions 21 to 25, 5 marks each 21. In a mathematics competition, 70 boys and 80 girls competed. Prizes were won by 6 boys and 15% of the girls. What percentage of the students were prize winners? (A) 10% (B) 12% (C) 15% (D) 18% (E) 20% 2022 AUSTRALIAN MATHEMATICS COMPETITION UPPER PRIMARY

14.I have three cardboard shapes: a square, a circle and a triangle. I glue them on top o\b each other as shown in this diagram. I then flip the glued-together shapes over. What could they look like? ••• ••• ••• ••• • • 15. What is the missing number needed to make this number sentence true? 270÷45 = ÷15 (A) 3 (B) 6 (C) 60 (D) 90 (E) 150 16. Three different squares are arranged as shown. The perimeter o\b the largest square is 32 centimetres. The area o\b the smallest square is 9 square centimetres. What is the perimeter o\b the medium- sized square? (A) 12 cm (B) 14 cm (C) 20 cm (D) 24 cm (E) 30 cm 17. Huang has a bag o\b marbles. Mei takes out one-third o\b them. Huang then takes out one-hal\b o\b those le\bt, leaving 8 marbles in the bag. How many marbles were originally in the bag? (A) 12 (B) 16 (C) 18 (D) 24 (E) 36 18. A different positive whole number is placed at each vertex of a cube. \bo two numbers joined by an edge of the cube can have a difference of 1. What is the smallest possible sum of the eight numbers? (A) 36 (B) 37(C) 38 (D) 39 (E) 40 19.George is 78 this year. He has three grandchildren: Michaela, Tom and Lucy. Michaela is 27, Tom is 23 and Lucy is 16. After how many years will George’s age be equal to the sum of his grandchildren’s ages? (A) 3 (B) 6 (C) 9 (D) 10 (E) 12 20. Ms Graham asked each student in her Year 5 class how many television sets they each have. This graph shows the results. How many television sets do the students have altogether? (A) 9 (B) 29 (C) 91 (D) 99 (E) 101 Number of TVs students have Numb er of TVs Number of students 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 Questions 21 to 25, 5 marks each 21. In a mathematics competition, 70 boys and 80 girls competed. Prizes were won by 6 boys and 15% of the girls. What percentage of the students were prize winners? (A) 10% (B) 12% (C) 15% (D) 18% (E) 20% 2022 AUSTRALIAN MATHEMATICS COMPETITION UPPER PRIMARY

22.Ariel writes the letters of the alphabet on a piece of paper as shown. She turns the page upside down and looks at it in her bathroom mirror. \bow many of the letters appear unchanged when viewed this way? 2  
 • • • • • •   23. The Australian Mathematical College (AMC) has 1000 students. Each student takes 6 classes a day. Each teacher teaches 5 classes per day with 25 students in each class. \bow many teachers are there at the AMC? (A) 40 (B) 48 (C) 50 (D) 200 (E) 240 24. This list pqrs, pqsr, prqs, prsq, . . . can be continued to include all 24 possible arrangements of the four letters p,q, r and s. The arrangements are listed in alphabetical order. Which one of the following is 19th in this list? (A) spqr (B)srpq (C)qpsr (D)qrps (E)rpsq 25. In this puzzle, each circle should contain an integer. Each of the five lines of four circles should add to 40. When the puzzle is completed, what is the largest number used? (A) 15 (B) 16(C) 17 (D) 18 (E) 19 7 15 8 2 9 RSTUVWXYZJKLMNOPQ ABCDEFGHI 2022 AUSTRALIAN MATHEMATICS COMPETITION UPPER PRIMARY

22.Ariel writes the letters of the alphabet on a piece of paper as shown. She turns the page upside down and looks at it in her bathroom mirror. \bow many of the letters appear unchanged when viewed this way? (A) 0 (B) 3 (C) 4 (D) 6 (E) 9 23. The Australian Mathematical College (AMC) has 1000 students. Each student takes 6 classes a day. Each teacher teaches 5 classes per day with 25 students in each class. \bow many teachers are there at the AMC? (A) 40 (B) 48 (C) 50 (D) 200 (E) 240 24. This list pqrs, pqsr, prqs, prsq, . . . can be continued to include all 24 possible arrangements of the four letters p,q, r and s. The arrangements are listed in alphabetical order. Which one of the following is 19th in this list? (A) spqr (B)srpq (C)qpsr (D)qrps (E)rpsq 25. In this puzzle, each circle should contain an integer. Each of the five lines of four circles should add to 40. When the puzzle is completed, what is the largest number used? (A) 15 (B) 16(C) 17 (D) 18 (E) 19 7 15 8 2 9 RSTUVWXYZJKLMNOPQ ABCDEFGHI 2.3 45.  .     3   .  5 3 3.  . \b\b\b    3. .   3  5.  3 .3 
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28.I choose three different numbers out of this list and add them together: 1,3 ,5 ,\b ,9 ,..., 105 How many different totals can I get? 29. The athletics clubs of Albury and Wodonga agree to send a combined team to the regional championships. They have 11 sprinters on the combined team, 5 from Albury and 6 from Wodonga. For the 4 ×100 metre relay, they agree to have a relay team with two sprinters from the Albury club and two sprinters from the Wodonga club. How many relay teams are possible? 30. The following is a net of a rectangular prism with some dimensions, in centimetres, given. 10 12 32 What is the volume of the rectangular prism in cubic centimetres? 2022 AUSTRALIAN MATHEMATICS COMPETITION UPPER PRIMARY

28.I choose three different numbers out of this list and add them together: 1,3 ,5 ,\b ,9 ,..., 105 How many different totals can I get? 29. The athletics clubs of Albury and Wodonga agree to send a combined team to the regional championships. They have 11 sprinters on the combined team, 5 from Albury and 6 from Wodonga. For the 4 ×100 metre relay, they agree to have a relay team with two sprinters from the Albury club and two sprinters from the Wodonga club. How many relay teams are possible? 30. The following is a net of a rectangular prism with some dimensions, in centimetres, given.  ‚ ‚ •. 3 .0 •90 9 .0 08  •3  88 80003

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 Upper Primary Ye a r s 5 – 6 (AUSTRALIAN  SCHOOL YEARS)