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[PDF] 2019 AMC Juniors Years 7 and 8 Questions Australian Mathematics Competition [PDF]
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Copyright © 2019 Australian Mathematics Trust AMTT Limited ACN 083 950 341 AUSTRALIAN MATHEMATICS COMPETITION Junior Years 7 & 8 (Australian school years) 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. THURSDAY 1 AUGUST 2019
Junior Division Questions 1 to 10, 3 marks each 1. 201−9= (A) 111 (B) 182 (C) 188 (D) 192 (E) 198 2. This rectan\ble is 5 cm wide and 4 cm tall. What is its area in square centimetres? (A) 9 (B) 10 (C) 18 (D) 20 (E) 40 5 cm 4 cm 3.The table shows the number of boys and \birls a\bed 10 or 11 in year 5. How many boys a\bed 11 are in year 5? (A) 9 (B) 11 (C) 21 (D) 37 (E) 46 Age 10 Age 11 Total Girls 14 25 39 Boys 9 ? 46 Total 23 62 85 \b.The circles are in a re\bular rectan\bular pattern. Some circles are hidden by the card. What fraction of the circles is hidden? (A) 1 3 (B) 2 3 (C) 1 4 (D) 1 6 (E) 1 18 ♠ A♠ A♠ 5. Which one of the followin\b is the lar\best number? (A) 4.05 (B) 4.45 (C) 4.5 (D) 4.045 (E) 4.54 6. What is 25% of 1 2? (A) 1 16 (B) 1 8 (C) 1 4 (D) 1 (E) 2 2019 AMC — Junior
J2 7.We’re driving from Elizabeth to Renmark\b and as we leave we see this sign. We want to stop at a town for lunch and a break\b approximately halfway to Renmark. Which town is the best place to stop? (A) Gawler (B) Nuriootpa (C) Truro (D) Blanchetown (E) Waikerie A20 Main North Rd Gawler 15 Nuriootpa 47 Truro 60 Blanchetown 106 Waikerie 148 Renmark 230 8. This letter F is first rotated by 90 ◦clockwise and then reflected in a horizontal line. It will now look like this. (A) F (B) F (C) F (D) F (E) F 9. Edith wrote down the whole numbers from 1 to 20 on a piece of paper. How many times did she write the digit 1? (A) 9 (B) 10 (C) 11 (D) 12 (E) 13 10.Danny divided a whole number Pby another whole number Qon his calculator and got the answer 3.125. Later\b Danny forgot the two whole numbers\b but he knew that both were under 30. The value of Qis (A) 5 (B) 7(C) 8 (D) 10 (E) 25 Questions 11 to 20, 4 marks each 11. Every row and every column of this 3 ×3 square must contain each of the numbers 1\b 2 and 3. What is the value of N+M ? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 M N 2 1 2 2019 AMC — Junior
J3 12.A piece of paper is folded in three, then a semi-circular cut and a straight cut are made, as shown in the diagram\b When the paper is unfolded, what does it look like? (A) (B) (C) (D) (E) 13. What is the value of z? (A) 30 (B) 35(C) 45 (D) 50 (E) 55 50 ◦ 45 ◦ z◦ 60 ◦ 14.111111111 111 = (A) 11111 (B) 1001001 (C) 10001 (D) 10101 (E) 1001 15. Jill has the same number of brothers as she has sisters\b Her brother Jack has twice as many sisters as he has brothers\b How many children are in the family? (A) 4 (B) 5(C) 7 (D) 9 (E) 11 3 2019 AMC — Junior
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5 ffffi ffffi ff \b \b \b \b \b \b \b ff ?? ?? ?? ?? ?? ?? ? \b ? ? ?? ?? ??? ?? ?? ?? ??? ?? ?? ?? ff ?? ?? ?? ?? ?? ?? ff ff ff ? ? \b ? ? ? ?? ? ??? ?? ?? ?? ??? ?? ?? ?? ? ffff ? ? ?? \b ? ?? \b ? ? ? ?ffi \b ? ? ?? \b ? ?? ?? ??? ???? ?? ??? ?ffi ?? ?? ff ? ff? ? ? 3\b ? \b \b ? ? ? ? \b \b \b \b ? ?? ?? ??? ?? ?? ?? ??? ?? ?? ?? FRONT RIGHT SIDE FRONT RIGHT SIDE 2019 AMC — Junior
6 ffffi ffffi \b\b \b ? \b ? \b ? ? ? ?? ? ?? ?\b ? ? ? ??? ? ??? ? ff ?? ? ? ? ? ? ? ? ? not ? ? ?? ?? ?? ? ? ??? ??? ff \b ff ? ? ? ?? ff ? ? ?\b ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 2019 AMC — Junior
J7 27.A positive whole number is called stableif at least one of its digits has the same value as its position in the number\b For example, 78247 is stable because a 4 appears in the 4 th position\b How many stable 3-digit numbers are there? 28. When I divide an integer by 15, the remainder is an integer from 0 to 14\b When I divide an integer by 27, the remainder is an integer from 0 to 26\b For instance, if the integer is 100 then the remainders are 10 and 19, which are different\b How many integers from 1 to 1000 leave the same remainders after division by 15 and after division by 27? 29. In a list of numbers, an odd-sum tripleis a group of three numbers in a row that add to an odd number\b For instance, if we write the numbers from 1 to 6 in this order, 642135 then there are exactly two odd-sum triples: (4, 2,1) and (1, 3,5)\b What is the greatest number of odd-sum triples that can be made by writing the numbers from 1 to 1000 in some order? 30. The Leader of Zip decrees that the digit 0, since it represents nothing, will no longer be used in any counting number\b Only counting numbers without 0 digits are allowed\b So the counting numbers in Zip begin 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, \b \b \b , where the tenth counting number is 11\b When you write out the first one thousand allowable counting numbers in Zip, what are the last three digits of the final number? 7 2019 AMC — Junior
2019 AMC — JUNIOR SOLVE PROBLEMS. CREATE THE FUTURE. amt.edu.au Problems are part of life and we’ve made it our mission to equip young students with the skills to solve more of them. Problem solving is a life skill and by developing it, students can create more choices for themselves and the future.