[PDF] 2020 Australian Mathematics Competition AMC Middle Primary Years 3 and 4.pdf | Plain Text

Copyright © 2020 Australian Mathematics TrustACN 083 950 341 THURSDAY 30 JULY 2020 NAME TIME ALLOWED: 60 MINUTES INSTRUCTIONS AND INFORMATION General 1. Do not open the booklet until t old to do so by your teacher. 2. Y ou 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. Diagr ams are NOT drawn to scale. They are intended only as aids. 4. T here 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. T his 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. R ead 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. W hen your teacher gives the signal, begin working on the problems. The answer sheet 1. Use only lead pencil. 2. R ecord your answers on the reverse of the answer sheet (not on the question paper) by FULLY colouring the circle matching your answer. 3. Y our 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. 2020 AMC AUSTRALIAN MATHEMATICS COMPETITION Middle Primary Years 3–4 (Australian school years)

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MP6 19. Aidan puts a range of 3D shapes on his desk at school\b This is the view from his side of the desk: Nadia is sitting on the opposite side of the desk facing Aidan\b Which of the following diagrams best represents the view from Nadia’s side of the desk? (A) (C) (B) (D) (E) 20. I have five 50c coins, five $1 coins and five $2 coins\b In how many different ways can I make up $5? (A) 4 (B) 6 (C) 8 (D) 10 (E) 12 MP6 19.202  0   2 .  Aidan dpa untd srgeoadna ei dpa tfpeeg fnett3feDhdnk nDhc Padnl \blt tafehT gltdv wh dpa hamd srgeoadna tpa olhl:aT de eNandlsa taNah nDhhantv wh dpa dprnT srgeoadnac d\be nDhhant eNandees panv wh dpa uhlg srgeoa3 dnac tpa WlttaT ar:pd nDhhantc bDd ieDn edpan nDhhant eNandees panv ’pa uhrtpaT hrhdpv ?e\b olhk \bana rh dpa nlfa( )AC BE )IC Bfi )5C B0 ),C $1 )2C $B  w iegT DW dprt had de olsa l fDbav w dpah oDgdrWgk dpa hDobant eh eWWetrda ilfat de :ad dpnaa hDobantv ypa gln:atd ei dpata rt )AC B$ )IC BE )5C Bfi ),C $ff )2C 41 B$4 8 Eff  2olhDag \benst rh l bDtk natdlDnlhd \bltprh: Trtpatv 2lfp Trndk Wglda ineo dpa tdlfs eh dpa gaid dlsat B orhDda de \bltp lhT Tnkc baiena barh: WglfaT eh deW ei dpa fgalh tdlfs eh dpa nr:pdv Aidan 6 orhDdatc lhT aNank 6 orhDdat ineo dpah ehc l \blrdan bnrh:t ff oena Trndk Wgldat lhT lTTt dpao de dpa deW ei dpa Trndk tdlfsv BE Trndk Wgldat 4 fgalh Wgldat MP6 AidA ia nAp anuts Pr tgpue ogunpa 6Ape nAp tPgPf3pD ogunp ia hpied 6uaApDk cl\b Tv cw\b Tm c:\b TN cW\b b’ c?\b bb 2020 Australian Mathematics Competition — Middle Primary

MP6 19. Aidan puts a range of 3D shapes on his desk at school\b This is the view from his side of the desk: Nadia is sitting on the opposite side of the desk facing Aidan\b Which of the following diagrams best represents the view from Nadia’s side of the desk? (A) (C) (B) (D) (E) 20. I have five 50c coins, five $1 coins and five $2 coins\b In how many different ways can I make up $5? (A) 4 (B) 6 (C) 8 (D) 10 (E) 12 MP6 19.202  0   2 .  Aidan dpa untd srgeoadna ei dpa tfpeeg fnett3feDhdnk nDhc Padnl \blt tafehT gltdv wh dpa hamd srgeoadna tpa olhl:aT de eNandlsa taNah nDhhantv wh dpa dprnT srgeoadnac d\be nDhhant eNandees panv wh dpa uhlg srgeoa3 dnac tpa WlttaT ar:pd nDhhantc bDd ieDn edpan nDhhant eNandees panv ’pa uhrtpaT hrhdpv ?e\b olhk \bana rh dpa nlfa( )AC BE )IC Bfi )5C B0 ),C $1 )2C $B  w iegT DW dprt had de olsa l fDbav w dpah oDgdrWgk dpa hDobant eh eWWetrda ilfat de :ad dpnaa hDobantv ypa gln:atd ei dpata rt )AC B$ )IC BE )5C Bfi ),C $ff )2C 41 B$4 8 Eff  2olhDag \benst rh l bDtk natdlDnlhd \bltprh: Trtpatv 2lfp Trndk Wglda ineo dpa tdlfs eh dpa gaid dlsat B orhDda de \bltp lhT Tnkc baiena barh: WglfaT eh deW ei dpa fgalh tdlfs eh dpa nr:pdv Aidan 6 orhDdatc lhT aNank 6 orhDdat ineo dpah ehc l \blrdan bnrh:t ff oena Trndk Wgldat lhT lTTt dpao de dpa deW ei dpa Trndk tdlfsv BE Trndk Wgldat 4 fgalh Wgldat MP6 AidA ia nAp anuts Pr tgpue ogunpa 6Ape nAp tPgPf3pD ogunp ia hpied 6uaApDk cl\b Tv cw\b Tm c:\b TN cW\b b’ c?\b bb 2020 Australian Mathematics Competition — Middle Primary

MP8 24. A primary school has 400 students and they each have one vote \bor a school captain. They voted \bor Jordan, Evie and Emily. Jordan got 3 times as many votes as Emily. Evie got 20 \bewer votes than Jordan. How many votes did Evie get? (A) 20 (B) 60 (C) 100 (D) 140 (E) 160 25. Karl likes to avoid walking on the cracks in the \bootpath by taking three equally spaced steps \bor every two blocks. Every third block o\b the \bootpath is darker than the others, as shown. In his first 100 steps, how many times does Karl’s le\bt \boot step on a darker block? (A) 11 (B) 16 (C) 21 (D) 25 (E) 33 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. Questions 26–30 are worth 6, 7, 8, 9 and 10 \barks, respectively. 26. Janine thinks o\b three numbers. Between them, they use the digits 1, 3, 5, 6, 7, 8 and 9, with each digit being used exactly once. The second number is 2 times the first number. The third number is 4 times the first number. What is the third number? MP 9 27. In the following diagram, you enter at the square la\belled entryand exit at the square la\belled exit. You can move horizontally and vertically along the white squares, \but must stay off the coloured squares. Each square can only \be visited once. By moving this way and adding the num\bers in the squares you pass through, what is the highest sum you can get? 60 50 5055 50 45150 5050 55 556025 55 30 70 entry exit 28. A \bale of hay can \be eaten \by a horse in 2 days, \by a cow in 3 days and \by a sheep in 12 days. A farmer has 22 \bales of hay and one horse, one cow and one sheep to feed. How many days will his \bales last? 29. A num\b er is oddtasticif all of its digits are odd. For example, 9, 57 and 313 are oddtastic. However, 50 and 787 are not oddtastic, since 0 and 8 are even digits. How many of the num\bers from 1 to 999 are oddtastic? 30. Oliver used small cu\bes to \build a set of solid shapes as shown. In the first shape, he used 1 cu\be; in the second shape, he used 6 cu\bes; in the third shape, he used 19 cu\bes. How many cu\bes did Oliver use to \build his fifth shape? 2020 Australian Mathematics Competition — Middle Primary

MP8 24. A primary school has 400 students and they each have one vote \bor a school captain. They voted \bor Jordan, Evie and Emily. Jordan got 3 times as many votes as Emily. Evie got 20 \bewer votes than Jordan. How many votes did Evie get? (A) 20 (B) 60 (C) 100 (D) 140 (E) 160 25. Karl likes to avoid walking on the cracks in the \bootpath by taking three equally spaced steps \bor every two blocks. Every third block o\b the \bootpath is darker than the others, as shown. In his first 100 steps, how many times does Karl’s le\bt \boot step on a darker block? (A) 11 (B) 16 (C) 21 (D) 25 (E) 33 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. Questions 26–30 are worth 6, 7, 8, 9 and 10 \barks, respectively. 26. Janine thinks o\b three numbers. Between them, they use the digits 1, 3, 5, 6, 7, 8 and 9, with each digit being used exactly once. The second number is 2 times the first number. The third number is 4 times the first number. What is the third number? MP 9 27. In the following diagram, you enter at the square la\belled entryand exit at the square la\belled exit. You can move horizontally and vertically along the white squares, \but must stay off the coloured squares. Each square can only \be visited once. By moving this way and adding the num\bers in the squares you pass through, what is the highest sum you can get? () B) B)BB B)6BCB) B) B) BBBB() 1BBB D) K) entry exit 28. A \bale of hay can \be eaten \by a horse in 2 days, \by a cow in 3 days and \by a sheep in 12 days. A farmer has 22 \bales of hay and one horse, one cow and one sheep to feed. How many days will his \bales last? 29. A num\b er is oddtasticif all of its digits are odd. For example, 9, 57 and 313 are oddtastic. However, 50 and 787 are not oddtastic, since 0 and 8 are even digits. How many of the num\bers from 1 to 999 are oddtastic? 30. Oliver used small cu\bes to \build a set of solid shapes as shown. In the first shape, he used 1 cu\be; in the second shape, he used 6 cu\bes; in the third shape, he used 19 cu\bes. How many cu\bes did Oliver use to \build his fifth shape? 2020 Australian Mathematics Competition — Middle Primary

2020 AMC — MIDDLE PRIMARY