[PDF] 2013 Australian Mathematics Competition AMC Middle Primary Years 3 and 4.pdf | Plain Text

Middle Primary Division Questions 1 to 10, 3 marks each 1. Ten years after the year 2013 will be (A) 2003 (B) 2013 (C) 2014 (D) 2023 (E) 2113 2. How many edges does a cube have? (A) 4 (B) 6 (C) 8 (D) 9 (E) 12 3. Each lap of Laura's school running track is 400 metres long. She runs 3 laps. How far does she run? (A) 300 m (B) 600 m (C) 800 m (D) 1200 m (E) 3000 m 4. What fraction of this rectangle is shaded? (A) one- fth (B) two- fths (C) two-thirds (D) one-third (E) three- fths

MP 2 5. What is three times the di erence between 9 and 3? (A) 6 (B) 9 (C) 18 (D) 36 (E) 81 6. Jenny's hat has the words COTTON CLUB written on it. What does she see on her hat when she looks in the mirror? (A) CLUB N COTTO (B) B COTTON CLU (C) BUL C N COTTO (D) COTTON CLUB (E) UBL C N COTTO 7. Sally is playing a board game where you throw a dice numbered from 1 to 6, move along a numbered board and then follow the instructions on each square you land on. On one turn, she throws a 6 and lands on a square which tells her to go back 4 squares. This puts her on a square which tells her to go forward 3 squares. She nishes up on square 7. What square did she start that turn on? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 8. Joel is in the centre of a maze which lls a 10-metre square. He knows he can get out of the maze if he follows the path in the spiral pattern below. The maze has exits on the boundary at A, B, C, D and E. By which exit will Joel leave the maze? A C DE B (A) A (B)B (C)C (D)D (E)E

MP 3 9. What is the di erence between the largest and smallest 3-digit num- bers which can be made from rearranging the 3 digit cards below? 1 2 3 (A) 198 (B) 200 (C) 202 (D) 298 (E) 302 10. Brad thinks of a number, doubles it and adds 2. His result is 14. What was the number he thought of at the start? (A) 6 (B) 7 (C) 8 (D) 12 (E) 30 Questions 11 to 20, 4 marks each 11. Alice has two 50c coins, three 20c coins and eight 5c coins. David has four 20c coins and six 10c coins. How much more money does Alice have than David? (A) 40c (B) 60c (C) 80c (D) $1.40 (E) $2.00 12. Jim is one year older than his brother and one year younger than his sister. The sum of their three ages is 30. How old is his sister? (A) 8 (B) 9 (C) 10 (D) 11 (E) 12 13. Mary counts on in 3s starting at 30 whilst John counts on in 5s starting at 20. If they say each number out loud together, starting at the same time, what same number will they both say together? (A) 30 (B) 40 (C) 45 (D) 50 (E) 60 14. Given a 2-digit number, a new 3-digit number is formed by putting the digit 1 after it. The new number is (A) the original number plus 1 (B) ten times the original number plus 1 (C) one hundred plus the original number (D) one hundred times the original number (E) one hundred times the original number plus 1

MP 4 15. How many triangles are in the following picture? (A) 9 (B) 10 (C) 13 (D) 14 (E) 17 16. To mix concrete you need 4 shovelfuls of sand, 2 shovelfuls of gravel and 1 shovelful of cement. If 56 shovelfuls are put into a mixer, how many would be of gravel? (A) 7 (B) 16 (C) 20 (D) 32 (E) 40 17. A train from Brisbane to Cairns leaves at 1:25 pm on Tuesday, and arrives at 7:35 pm on Wednesday. How long was the trip? (A) 6 h 10 min (B) 24 h 50 min (C) 18 h 10 min (D) 29 h 10 min (E) 30 h 10 min18. An online poll asked the question, `Is Maths your favourite sub ject?' The results of the poll are as follows: 6 out of every 10 voted yes. 3 out of every 10 voted no. 1 out of every 10 was undecided. If 120 people answered yes, how many of those polled were undecided? (A) 20 (B) 24 (C) 30 (D) 45 (E) 70

MP 5 19. George is planning a garden bed which is to be 1 metre wide and a whole number of metres long. It is to be surrounded by 1 metre 1 metre pavers as shown in the diagrams below. As the design for the garden gets longer, the number of pavers needs to increase. Which of the following best describes the number of pavers required for each garden bed design? (A) The number of pavers needed is 8 times the length of the garden bed. (B) The number of pavers needed is 6 times the length of the garden bed plus 2. (C) The number of pavers needed is 4 times the length of the garden bed. (D) The number of pavers needed is 4 times the length of the garden bed plus 2. (E) The number of pavers needed is 2 times the length of the garden bed plus 6. 20. Each triangle in the diagram is equilateral. What fraction of the largest triangle is shaded? (A) 1 4 (B) 15 64 (C) 1 3 (D) 3 16 (E) 7 32

MP 6 Questions 21 to 25, 5 marks each 21. Kathy plays Eddie in a game with 12 rounds. In each round the winner scores 5 points and the loser scores 3 points. When the game ends, Eddie's total score is 46 points. How many rounds did Kathy win? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 22. Nine cards numbered 1 to 9 are set out as in the diagram. The sum of the numbers in the vertical column is equal to the sum of the numbers in the horizontal row. How many di erent numbers could be used in the central square of the diagram? 146 2573 89 (A) 1 (B) 3 (C) 5 (D) 7 (E) 9 23. There are thirty 20c coins in a row. I replace every second coin with a 50c coin. Next, I replace every third coin with a $1 coin. Finally, I replace every fourth coin with a $2 coin. The value of the thirty coins is now (A) $18.50 (B) $22.80 (C) $25.60 (D) $26.50 (E) $27.80

MP 7 24. There is a shaded square inside a rectangle as shown. From Ato B is 6 cm and from Cto Dis 8 cm. What is the perimeter of the large rectangle? C D BA (A) 28 cm (B) 27 cm (C) 26 cm (D) 25 cm (E) 24 cm 25. Jake and Joe wanted to buy the same magazine. Jake needed $2.80 more to buy it, while Joe needed $2.60 more. So they put their money together and bought the magazine. They had $2.60 left. How much was the magazine? (A) $10 (B) $9 (C) $8 (D) $7 (E) $6 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. I take 2 vitamin C tablets every day. If I increase my dose to 3 tablets a day, a full bottle would last 8 days less. How many tablets are in a full bottle?

MP 8 27. Each side of this large square is 30 cm. The middle of each side is joined to a corner as shown. What area, in square centimetres, has been shaded? 28. Starting at 100 and going through to 999, how many numbers have two or more digits the same? 29. In how many ways can three di erent numbers be selected from the numbers 1 to 12, so that their sum can be exactly divided by 3? 30. Adam, Barney and Joe carry 999 books out of the library. Adam works for 3 hours, Barney works for 4 hours and Joe works for 5 hours. They work at di erent speeds, with Adam carrying 5 books for every 3 books Barney carries and every 2 books Joe carries. How many books did Adam carry?