[PDF] 2015 Australian Mathematics Competition AMC Intermediate Years 5 and 6.pdf | Plain Text

2015 UPPER PRIMARY DIVISION AUSTRALIAN SCHOOL YEARS 5, 6 and PRIMARY 7* *SOME STATES ONLY TIME ALLOWED: 60 MINUTES 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. 3. Diagrams are NOT drawn to scale. They are intended only as aids. 4. There are 25 multiple-choice questions, each with 5 possible answers given 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. ©AMT P ublishing 2015 AMTT liMiTed Acn 0 8 3 9 5 0 3 41 A ustr Ali An M Athe MAtics c o M petition sponsored by the c o MM onwe Alth b A nk An AcTiviTy of The AusTrAliAn MATheMATics TrusT NAME YEAR TEACHER Au s Tr A l i An M A T h e M A T i c s Tr u sT

Upper Primary Division Questions 1 to 10, 3 marks eac\b 1. What does the digit 1 in 2015 represent? (A) one (B) ten (C) one h\bndred (D) one tho\bsand (E) ten tho\bsand 2.What is the val\be of 10 twenty-cent coins? (A) $1 (B) $2 (C) $5 (D) $20 (E) $50 3.What temperat\bre does this thermometer show? (A) 25 ◦ (B) 38 ◦ (C) 27 ◦ (D) 32 ◦ (E) 28 ◦ 15 20 25 30 ◦C 4.Which n\bmber do yo\b need in the box to make this n\bmber sentence tr\be? 19 + 45 = 20 + (A) 34 (B) 44 (C) 46 (D) 64 (E) 84 5.Which n\bmber has the greatest val\be? (A) 1.3 (B) 1.303 (C) 1.31 (D) 1.301 (E) 1.131

UP2 6. The perimeter of a shape is the distance around the outside. Which of these shapes has the smallest perimeter? \bA) \bB) \bC) \bD) \bE) 7.The class were shown this picture of many dinosaurs. They were asked to work out how many there were in half of the picture. •Simon wrote 6 ×10. • Carrie wrote 5 ×12. • Brian wrote 10 ×12 ÷2. • R´emy wrote 10 ÷2× 12. Who was correct? \bA) All four were correct \bB) Only Simon \bC) Only Carrie \bD) Only Brian \bE) Only R´emy 8.In the diagram, the numbers 1, 3, 5, 7 and 9 are placed in the squares so that the sum of the numbers in the row is the same as the sum of the numbers in the column. The numbers 3 and 7 are placed as shown. What could be the sum of the row? \bA) 14 \bB) 15 \bC) 12 \bD) 16 \bE) 13 7 3

UP3 9. To which square should I add a counter so that no two rows have the same number o\b counters, and no two columns have the same number o\b counters? (A) A (B) B (C) C (D) D (E) E A B C D E 10.A hal\b is one-third o\b a number. What is the number? (A) three-quarters (B) one-sixth (C) one and a third (D) five-sixths (E) one and a hal\b Questions 11 to 20, 4 marks each 11. The triangle shown is \bolded in hal\b three times without un\bolding, making another triangle each time. Which figure shows what the triangle looks like when un\bolded? (A) (B) (C) (D) (E) 12.I\bL= 100 and M=0 .1, which o\b these is largest? (A) L+ M (B)L× M (C)L÷ M (D)M÷L (E)L− M

UP4 13. You want to combine each of the shapes (A) to (E) shown be\bow separate\by with the shaded shape on the right to make a rectang\be. You are on\by a\b\bowed to turn and s\bide the shapes, not flip them over. The finished pieces wi\b\b not over\bap and wi\b\b form a rectang\be with no ho\bes. For which of the shapes is this not possib\be? (A) (B) (C) (D) (E) 14.A p\bumber has 12 \bengths of drain pipe to \boad on his ute. He knows that the pipes won’t come \boose if he bund\bes them so that the rope around them is as short as possib\be. How does he bund\be them? (A) (B) (C) (D) (E) 15.The numbers 1 to 6 are p\baced in the circ\bes so that each side of the triang\be has a sum of 10. If 1 is p\baced in the circ\be shown, which number is in the shaded circ\be? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 1

UP5 16. Follow the instructions in this flow chart. Start with 5 Subtract 2 Multi\blyby 3 Is this greater than 50? Select this answer Ye s No (A) 57 (B) 63 (C) 75 (D) 81 (E) 84 17. A square \biece of \ba\ber is folded along the dashed lines shown and then the to\b is cut off. The \ba\ber is then unfolded. Which sha\be shows the unfolded \biece? (A) (B) (C) (D) (E) 18.Sally, Li and Raheelah have birthdays on different days in the week beginning Sunday 2 August. No two birthdays are on following days and the ga\b between the first and second birthday is less than the ga\b between the second and third. Which day is definitely not one of their birthdays? (A) Monday (B) Tuesday (C) Wednesday (D) Thursday (E) Friday

UP6 19. A square of side length 3 cm is placed alongside a square of side \b cm. 3 cm \b cm What is the area, in square centimetres, of the shaded part? (A) 22.\b (B) 23 (C) 23.\b (D) 24 (E) 24.\b 20. A cube has the letters A, C, M, T, H and S on its six faces. Here are two views of this cube. C M A A M T Which one of the following could be a third view of the same cube? (A) M H T (B) A T C (C) T S C (D) H T A (E) S C M

UP7 Questions 21 to 25, 5 marks each 21. A teacher gives each of three students Asha, Betty and Cheng a card \bith a ‘secret’ number on it. Each looks at her o\bn number but does not kno\b the other t\bo numbers. Then the teacher gives them this information. All three numbers are different \bhole numbers and their sum is 13. The product of the numbers is odd. Betty and Cheng no\b kno\b \bhat the numbers are on the other t\bo cards, but Asha does not have enough information. What number is on Asha’s card? (A) 9 (B) 7 (C) 5 (D) 3 (E) 1 22.In this multiplication, L,M and Nare different digits. What is the value of L + M +N? (A) 13 (B) 15 (C) 16 (D) 17 (E) 20 L LM × M NM5M 23.A scientist \bas testing a piece of metal \bhich contains copper and zinc. He found the ratio of metals \bas 2 parts copper to 3 parts zinc. Then he melted this metal and added 120 g of copper and 40 g of zinc into it, forming a ne\b piece of metal \bhich \beighs 660 g. What is the ratio of copper and zinc in the ne\b metal? (A) 1 part copper to 3 parts zinc (B) 2 parts copper to 3 parts zinc (C) 16 parts copper to 17 parts zinc (D) 8 parts copper to 17 parts zinc (E) 8 parts copper to 33 parts zinc

UP8 24. Jason had between 50 and 200 identical square cards\b He tried to arrange them in rows of 4 but had one left over\b He tried rows of 5 and then rows of 6, but each time he had one card left over\b Finally, he discovered that he could arrange them to form one large solid square\b How many cards were on each side of this square? (A) 8 (B) 9 (C) 10 (D) 11 (E) 12 25.Eve has $400 in Australian notes in her wallet, in a mixture of 5, 10, 20 and 50 dollar notes\b As a surprise, Viv opens Eve’s wallet and replaces every note with the next larger note\b So, each $5 note is replaced by a $10 note, each $10 note is replaced by a $20 note, each $20 note is replaced by a $50 note and each $50 note is replaced by a $100 note\b Eve discovers that she now has $900\b How much of this new total is in $50 notes? (A) $50 (B) $100 (C) $200 (D) $300 (E) $500 For questions 26 to 30, shade the answer as a whole nu\bber fro\b 0 to 999 in the space provided on the answer sheet. Question 26 is 6 \barks, question 27 is 7 \barks, question 28 is 8 \barks, question 29 is 9 \barks and question 30 is 10 \barks. 26. Alex is designing a square patio, paved by putting bricks on edge using the basketweave pattern shown\b She has 999 bricks she can use, and designs her patio to be as large a square as possible\b How many bricks does she use?

UP9 27. There are many ways that you can add three different positive whole num\bers to get a total of 12. For instance, 1 + 5 + 6 = 12 is one way \but 2 + 2 + 8 = 12 is not, since 2, 2 and 8 are not all different. If you multiply these three num\bers, you get a num\ber called the product. Of all the ways to do this, what is the largest possi\ble product? 28.I have 2 watches with a 12 hour cycle. One gains 2 minutes a day and the other loses 3 minutes a day. If I set them at the correct time, how many days will it \be \before they next together tell the correct time? 29.A3×2 flag is divided into six squares, as shown. Each square is to \be coloured green or \blue, so that every square shares at least one edge with another square of the same colour. In how many different ways can this \be done? 30. The squares in a 25 ×25 grid are painted \black or white in a spiral pattern, starting with \black at the centre ∗ and spiralling out. The diagram shows how this starts. How many squares are painted \black? ∗