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Copyright © 2020 Australian Mathematics TrustACN 083 950 341 2020 AMC AUSTRALIAN MATHEMATICS COMPETITION Junior Years 7–8 (Australian school years) THURSDAY 30 JULY 2020 NAME TIME ALLOWED: 75 MINUTES INSTRUCTIONS AND INFORMATION General 1. Do not open the booklet until told to do so by your teacher. 2. NO calculators, maths stencils, mobile phones or other calculating aids are permitted. Scribbling paper, graph paper, ruler and compasses are permitted, but are not essential. 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 response. 5. This is a competition not a test; do not expect to answer all questions. You are only competing against your own year in your own country/Australian state so different years doing the same paper are not compared. 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 1. Use only lead pencil. 2. Record your answers on the reverse of the answer sheet (not on the question paper) by FULLY colouring the circle matching your answer. 3. Your answer sheet will be scanned. The optical scanner will attempt to read all markings even if they are in the wrong places, so please be careful not to doodle or write anything extra on the answer sheet. If you want to change an answer or remove any marks, use a plastic eraser and be sure to remove all marks and smudges. Integrity of the competition The AMT reserves the right to re-examine students before deciding whether to grant official status to their score. Reminder: You may sit this competition once, in one division only, or risk no score.

Junior Division Questions 1 to 10, 3 marks each 1. How many 1 ×1 squares are in this diagram? (A) 16 (\b) 18(C) 20 (D) 24 (E) 25 2.What is half of 2020? (A) 20 (\b) 101 (C) 110 (D) 1001 (E) 1010 3. What is the perimeter of this triangle? (A) 33 m (\b) 34 m (C) 35 m (D) 36 m (E) 37 m 16 m7m 11 m \b. I stepped on the train at 8.48 am and got off at 9.21 am. How many minutes did I spend on the train? (A) 27 (\b) 33(C) 43 (D) 87 (E) 93 5.What is the value of yin this triangle? (A) 10 (\b) 30(C) 50 (D) 70 (E) 90 70 ◦ 80 ◦ y◦ 6.2− (0 −(2 −0)) = (A) −4 (\b)−2 (C) 0 (D) 2 (E) 4 7.In the grid, the total of each row is given at the end of the row, and the total of each column is given at the bottom of the column. The value of Nis (A) 1 (\b) 2 (C) 3 (D) 4 (E) 5 7 9 N 8 6 20 7 18 20 9 16

Junior Division Questions 1 to 10, 3 marks each 1. How many 1 ×1 squares are in this diagram? (A) 16 (\b) 18(C) 20 (D) 24 (E) 25 2. What is half of 2020? (A) 20 (\b) 101 (C) 110 (D) 1001 (E) 1010 3. What is the perimeter of this triangle? (A) 33 m (\b) 34 m (C) 35 m (D) 36 m (E) 37 m 16 m7m 11 m \b. I stepped on the train at 8.48 am and got off at 9.21 am. How many minutes did I spend on the train? (A) 27 (\b) 33(C) 43 (D) 87 (E) 93 5. What is the value of yin this triangle? (A) 10 (\b) 30(C) 50 (D) 70 (E) 90 70 ◦ 80 ◦ y◦ 6.2− (0 −(2 −0)) = (A) −4 (\b)−2 (C) 0 (D) 2 (E) 4 7. In the grid, the total of each row is given at the end of the row, and the total of each column is given at the bottom of the column. The value of Nis (A) 1 (\b) 2 (C) 3 (D) 4 (E) 5 7 9 N 8 6 20 718 209 16 Ju Ho n iorroD wvs DQrerot 1iQ10,vso 3m akc ×h .2v12 Q\b r2o \bQiiQ,v56 7v1rDos 3osr Do7Do so5rs r2o 5ei ve6o• •n• w ••• w ••• w ••• w • • w mo a-u-k-€-c gIoI?I. y a-u a-u-k ‚ •n• k ••• ◦ ••• a••• • • u anoƒo3esrvo5 vs r2v50v56 Q\b r,Q 53oDs ,2Qso s vs u„ e5t ,2Qso tv…oDo51o vs a€h †2o 7DQt1r Q\b ƒo3esrvo5‡s r,Q 53oDs vs •n• ˆ‰ ••• Š„••• a‰c ••• au‰ • • aku y1squreiq aa ue tnh d g?(Aq s?)6 aao n 1Q5rDm 1Q5svsrs Q\b r,Q vsie5ts es s2Q,5 Q5 r2vs e7h ‹5 sŒeDo 0viQorDosŽ vrs eDoe vs •n• 3or,oo5 a‰‰ e5t a‰‰‰ ••• 3or,oo5 a‰‰‰ e5t a‰ ‰‰‰ ••• 3or,oo5 a‰ ‰‰‰ e5t a‰‰ ‰‰‰ ••• 3or,oo5 a‰‰ ‰‰‰ e5t a ‰‰‰ ‰‰‰ • • 6DoeroD r2e5 a ‰‰‰ ‰‰‰ J uJJ nJJiJJ orDvsQetQ1 ato auk€c„ yauk€c - auk€ yauk - au ya‚ •n• kkkkk ••• a‰a‰a‰ ••• aaaaaa ••• auuuuk • • aauukk a\bo ‘vim vs u‰u‰ tems Qith ’Q, Qit ,es s2o Q5 2oD iesr 3vDr2tem• •n• € ••• c••• „ ••• “ • • ˆ 2020 Australian Mathematics Competition — Junior

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J4 19. In the grid shown, the numbers from 1 to 4 must appear once in each row and co\bumn. A\bso, the sum of numbers in each of the four regions separated by red \bines must be the same. What is the sum x+ y? (A) 8 (B) 7(C) 6 (D) 5 (E) 4 41 x y 20.Anupam has a cardboard square with a perimeter of 400 centimetres. He draws a horizonta\b \bine and a vertica\b \bine on the square and cuts a\bong these \bines to create four rectang\bes. What is the \bargest possib\be sum of the perimeters of these four rectang\bes, in centimetres? (A) 400 (B) 600 (C) 800 (D) 1000 (E) 1200 Questions 21 to 25, 5 marks each 21. The ends of the tang\bed string shown are pu\b\bed in the direction of the arrows so that the string either untang\bes or forms a simp\ber knot. Which of the fo\b\bowing best matches the knot, or otherwise, that is formed when the string is tightened? (A) (B) (C) (D) (E) 22. Mr Atkins wrote some homework questions for his c\bass to practise order of opera- tions. One of the questions was 2 + 3 ×(4 + 3), with answer 23. However, one of his students just worked from \beft to right and ignored the brackets, writing 2 + 3 = 5, 5 × 4 = 20, 20 + 3 = 23, the correct answer. Mr Atkins thought that this was fascinating, so he tried to come up with another question where working \beft to right gave the right answer. He tried 5 + 4 ×(7 + ). What number shou\bd he put in the box? (A) 2 (B) 4(C) 6 (D) 8 (E) 10 2020 Australian Mathematics Competition — Junior

J5 23. My friend and I took a maths test with 10 questions\b Question 1 was worth 1 mark, question 2 was worth 2 marks, question 3 was worth 3 marks, and so on\b Correct answers scored full marks and incorrect answers scored 0 marks\b We both scored the same number of marks and correctly answered the same number of questions\b However, we didn’t solve exactly the same set of questions as each other\b What is the maximum score that I could have received for the test? (A) 44 (B) 46(C) 48 (D) 50 (E) 52 24.A light rail network has 21 drivers, but not all of them are required at the same time: • 15 drivers are required for the Friday night shift\b • 12 drivers are required for the Saturday morning shift\b • 9 drivers are required for the Sunday morning shift\b Given that every driver must work on at least one of these shifts, what is the maximum number of drivers that can work on all three shifts? (A) 5 (B) 6(C) 7 (D) 8 (E) 9 25.A bag contains exactly 50 coins\b The coins are either worth 10 cents, 20 cents or 50 cents, and there is at least one of each\b The total value of the coins is $10\b How many different ways can this occur? (A) 2 (B) 4(C) 8 (D) 12 (E) 16 For questions 26 to 30, shade the answer as an integer \brom 0 to 999 in the space provided on the answer sheet. Questions 26–30 are worth 6, 7, 8, 9 and 10 marks, respectively. 26. The digits 1 to 9 are used exactly once each to make three 3-digit numbers\b The second number is three times the first number\b The third number is five times the first number\b What is the second number? 2020 Australian Mathematics Competition fi Junior

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2020 AMC — JUNIOR