[PDF] 2020 Australian Mathematics Competition AMC Upper Primary Years 5 - 6 and 7.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 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. Mobile phones are not permitted. 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. 2020 AMC AUSTRALIAN MATHEMATICS COMPETITION Upper Primary Years 5–7* (*Australian school years, some states only)

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UP3 8. The graph shows the number of eggs laid by ba\bkyard \bhi\bkens Nony and Cera for the first six months of the year. Eggs Month 0 10 20 30 Jan Feb Mar Apr May Jun Nony \bera In how many months did Nony lay more eggs than Cera? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 9. A \blass of 24 students, all of different heights, is standing in a line from tallest to shortest. Mary is the 8th tallest and John is the 6th shortest. How many students are standing between them in the line? (A) 6 (B) 7 (C) 8 (D) 9 (E) 10 10. Maria divided a re\btangle into a number of identi\bal squares and \boloured some of them in, as shown. She wants three-quarters of the re\btangle’s area to be \boloured in altogether. How many more squares does she need to \bolour in? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4 2020 Australian Mathematics Competition — Upper Primary

UP3 8. The graph shows the number of eggs laid by ba\bkyard \bhi\bkens Nony and Cera for the first six months of the year. Eggs Month 0 10 20 30 Jan FebMar AprMay Jun Nony \bera In how many months did Nony lay more eggs than Cera? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 9. A \blass of 24 students, all of different heights, is standing in a line from tallest to shortest. Mary is the 8th tallest and John is the 6th shortest. How many students are standing between them in the line? (A) 6 (B) 7 (C) 8 (D) 9 (E) 10 10. Maria divided a re\btangle into a number of identi\bal squares and \boloured some of them in, as shown. She wants three-quarters of the re\btangle’s area to be \boloured in altogether. How many more squares does she need to \bolour in? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4 UP3 8.9101  0   1 9  Th heg gra ps o wotg ps tonumgbf lgi eob dy tonumgbf \bpno eob k ora Nton eob 3C fipx tor. tonumgb tIbh lgi wi?g uo(A hp eib snigrab is heg. xorh hp bhonh heg rg)h wotg xihe or g1Iom rItugn go(eB 2TD y 24D E 25D , 2\bD k 2ffD M  8r heg wniaf heg hphom ps go(e npx ib wi?gr oh heg gra ps heg npxf ora heg hphom ps go(e (pmItr ib wi?gr oh heg uphhpt ps heg (pmItrC Jeg ?omIg ps Eib 2TD d 24D 6 25D H 2\bD 3 2ffD y , M E k E 67 , dk 67 M dE  Th eib uinheao. 9onh.f 0i(A. ora eib snigrab xgon bhni9. 9o9gn eohb ir heg beo9g ps o (prgf ob bepxr pr heg mgshC Tshgn heg 9onh.f 0i(A. toAgb o bhnoiweh (Ih ir prg ps heg eohb omm heg xo. I9 hp heg 9pirh oh heg hp9f ob bepxr pr heg niwehC U UP3TP he gPr ehaahp3so wrtg nugTPrt pPug gPr Pug p3aa ahhm a3mr pPrs b3Tmf luggrst 3g hig hs gPr guward y\bk yNk yCk yfik yxk 2020 Australian Mathematics Competition — Upper Primary

UP5 14. Emma is going to write all the numbers from 1 to 50 in order\b She writes 25 digits on the first line of her page\b What was the last number she wrote on this line? (A) 13 (B) 15 (C) 17 (D) 19 (E) 21 15. The playing card shown is flipped over along edge band then flipped over again along edge c\b What does it look like now? 7 ♣ 7 ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ a b c d (A) 7 ♣ 7 ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ (B) 7 ♣ 7 ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ (C) 7 ♣ 7 ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ (D) 7 ♣ 7 ♣ ♣ ♣ ♣♣ ♣ ♣ ♣ (E) 7 ♣ 7 ♣ ♣♣ ♣ ♣ ♣ ♣ ♣ 2020 Australian Mathematics Competition — Upper Primary

UP5 14. Emma is going to write all the numbers from 1 to 50 in order\b She writes 25 digits on the first line of her page\b What was the last number she wrote on this line? (A) 13 (B) 15 (C) 17 (D) 19 (E) 21 15. The playing card shown is flipped over along edge band then flipped over again along edge c\b What does it look like now? 7 ♣ 7 ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ a b c d (A) 7 ♣ 7 ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ (B) 7 ♣ 7 ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ (C) 7 ♣ 7 ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ (D) 7 ♣ 7 ♣ ♣ ♣ ♣♣ ♣ ♣ ♣ (E) 7 ♣ 7 ♣ ♣♣ ♣ ♣ ♣ ♣ ♣ UP 6 16. Which labelled counter should you remove so that no two rows have the same number of counters and no two columns have the same number of counters\b (A) A (B) B(C) C (D) D (E) E h W U P 6 17.Aidan puts a range of 3D shapes on his desk at school. This is the view from his side of the desk: Nadia is sitting on the opposite side of the desk facing Aidan. Which of the following diagrams best represents the view from Nadia’s side of the desk\b (A) (C) (B) (D) (E) 2020 Australian Mathematics Competition — Upper Primary

UP7 18. The area of each of the five equilateral tri- angles in the diagra\b is 1 square \betre. What is the shaded area? (A) 1 .5\b 2 (B) 2 \b 2 (C) 2 .5\b 2 (D) 3 \b 2 (E) 3 .5\b 2 19. Kayla is 5 years old and Ryan is 13 years younger than Cody. One year ago, Cody’s age was twice the su\b of Kayla’s and Ryan’s age. Find the su\b of the three children’s current ages. (A) 10 (B) 22 (C) 26 (D) 30 (E) 36 20. Mary has a piece of paper. She folds it exactly in half. Then she folds it in half again. She finishes up with this shape. Which of the shapes P, QandRshown below could have been her starting shape? P T h (A) only P(B) only Q(C) only R(D) only Pand R(E) all three 2020 Australian Mathematics Competition — Upper Primary

UP7 18. The area of each of the five equilateral tri- angles in the diagra\b is 1 square \betre. What is the shaded area? (A) 1 .5\b 2 (B) 2 \b 2 (C) 2 .5\b 2 (D) 3 \b 2 (E) 3 .5\b 2 19. Kayla is 5 years old and Ryan is 13 years younger than Cody. One year ago, Cody’s age was twice the su\b of Kayla’s and Ryan’s age. Find the su\b of the three children’s current ages. (A) 10 (B) 22 (C) 26 (D) 30 (E) 36 20. Mary has a piece of paper. She folds it exactly in half. Then she folds it in half again. She finishes up with this shape. Which of the shapes P, QandRshown below could have been her starting shape? P QR (A) only P(B) only Q(C) only R(D) only Pand R(E) all three UP 8 Questions 21 to 25, 5 marks each 21. Four positive whole numbers are placed at the vertices of a s\buare. On each edge, the difference between the two numbers at the vertices is written. The four edge numbers are 1, 2, 3 and 4 in some order. What is the smallest possible sum of the numbers at the vertices? 3EK )y 3RK )) 3OK )5 3,K )B 3’K )2 22. The large rectangle shown has been divided into 4 smaller rectangles. The perimeters of three of these are 10 cm, 16 cm and 20 cm. The fourth rectangle does not have the largest or the smallest perimeter of the four smaller rectangles. Cqnc? fi gfiicflficafio? fo cqfi rfiaflficfia hd cqfi unaWfi afigcniWufiD 3EK 5w 3RK By 3OK B5 3,K Bw 3’K 2w 2020 Australian Mathematics Competition — Upper Primary

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UP10 For questions 26 to 30, shade the answer as a whole number from 0 to \b\b\b in the space provided on the answer sheet. Questions 26–30 are worth 6, 7, 8, \b and 10 marks, respectively. ri7 A numb er is oddtasticif all of its digits are odd. For exam\ble, 9, 57 and 313 are oddtastic. However, 50 and 787 are not oddtastic, since 0 and 8 are even digits. How many of the numbers from 1 to 999 are oddtastic? 27. On my chicken farm where I have 24 \bens, the \bens were a bit crowded. So I built 6 more \bens, and the number of chickens in each \ben reduced by 6. How many chickens do I have? 28. How many even three-digit numbers are there where the digits add u\b to 8? 2\b. Madeleine ty\bes her three-digit Personal Identifica- tion Number (PIN) into this key\bad. All three digits are different, but the buttons for the first and second digits share an edge, and the buttons for the second and third digits share an edge. For instance, 563 is a \bossible PIN, but 536 is not, since 5 and 3 do not share an edge. How many \bossibilities are there for Madeleine’s PIN? 0 P 1 0 A n u m b e 30. Writing one digitevery second, you have half an hour to list as many of the counting numbers as you can, starting 1, 2, 3, . . . . At the end of half an hour, what number have you just finished writing? UP1 For 0 Anum be rni snf Am mnamf Ai n rblom tf d gnio. Ai n sbF tf x gnio nfg Ai n ormm\b tf ,d gnio9 0 enl5ml rno dd Anumo be rni nfg bfm rblom. bfm sbF nfg bfm ormm\b ab emmg9 7bF 5nfi gnio Ftuu rto Anumo unoa3 c0H dw cvH dd c8H dy chH d? cOH dk Fqr Irto lmsanf2um to x? s5 ubf29 4a to sSa tfab aFb \btmsmo nfg lmnllnf2mg ab ebl5 n o6Snlm. no orbFf9 x? s5 3 -rna to arm rmt2ra be arm blt2tfnu lmsanf2um3 c0H ,y s5 cvH ,? s5 c8H ,k s5 chH dw s5 cOH dy s5 Fur 0 Abaaum Ftar n omnumg utg sbfantfo ob5m Fnaml9 Irm gtn2ln5 orbFo arto Abaaum S\b arm lt2ra Fni nfg S\botgm gbFf9 7bF eSuu to arm Abaaum3 ,d s5 d, s5 ,M s5 c0H , d cvH y fi c8H M fi chH d x cOH 1 ,y 2020 Australian Mathematics Competition — Upper Primary

2020 AMC — UPPER PRIMARY