junior division competition paper - kheradedu.irkheradedu.ir/images/inter/australia/2012/7-8.pdf ·...

JUNIOR DIVISION COMPETITION PAPER

INSTRUCTIONS AND INFORMATIONGENERAL 1. Do not open the booklet until told to do so by your teacher. 2. NO calculators, slide rules, log tables, 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 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 State or Region 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.

A U S T R A L I A N S C H O O L Y E A R S 7 A N D 8T I M E A L L O W E D : 7 5 M I N U T E S

©AMT Publishing 2012 AMTT liMiTed Acn 083 950 341

AustrAl iAn MAtheMAt ics coMpet i t ion

An AcT iv i Ty of The AusTrAl iAn MATheMAT ics TrusT

THURSDAY 2 AUGUST 2012

NAME

Junior Division

Questions 1 to 10, 3 marks each

1. The value of 99 − 2 + 1 + 102 is

(A) 0 (B) 100 (C) 198 (D) 200 (E) 202

2. The size, in degrees, of 6 Q is

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Q

R45◦P

(A) 40 (B) 55 (C) 60 (D) 80 (E) 90

3. Yesterday it rained continuously from 9:45 am until 3:10 pm. For how long did itrain?

(A) 3 hours 25 minutes (B) 3 hours 35 minutes (C) 5 hours 25 minutes

(D) 6 hours 25 minutes (E) 6 hours 35 minutes

4. The value of 8 × 3.1 is

(A) 11.1 (B) 16.8 (C) 8.31 (D) 24.1 (E) 24.8

5. The change you should receive from a $20 note after paying a bill of $9.45 is

(A) $10.55 (B) $10.45 (C) $11.55 (D) $9.55 (E) $10.65

6. Three-fifths of a number is 48. What is the number?

(A) 54 (B) 60 (C) 64 (D) 80 (E) 84

7. Which of the following is closest to 100?

(A) 99 + 2.01 (B) 98 + 3.011 (C) 97 + 4.0111 (D) 101 − 1.01 (E) 102 − 2.011

J 2

8. The adjacent sides of the decagon shown meet at right angles and all dimensionsare in metres.

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8

7

8

6

16

What is the perimeter, in metres, of this decagon?

(A) 45 (B) 60 (C) 34 (D) 90 (E) cannot be calculated

9. If5

9of the children in a choir are boys and the rest are girls, the ratio of boys to

girls is

(A) 4 : 9 (B) 4 : 5 (C) 5 : 4 (D) 9 : 4 (E) 5 : 9

10. By what number must 6 be divided to obtain1

3as a result?

(A) 18 (B)1

2(C)

1

18(D) 2 (E) 9


11. In the diagram, the sizes of three angles aregiven. Find the value of x.

(A) 90 (B) 95 (C) 100

(D) 110 (E) 120

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30◦

50◦

40◦x◦

12. A jar of mixed lollies contains 100 g of jellybeans, 30 g of licorice bullets and 20 gof bilby bears. Extra bilby bears are added to make the mix 50% bilby bears byweight. How many grams of bilby bears are added?

(A) 20 (B) 30 (C) 60 (D) 110 (E) 600

J 3

13. A square piece of paper is folded in half. The resulting rectangle has a perimeterof 18 cm. What is the area, in square centimetres, of the original square?

(A) 9 (B) 16 (C) 36 (D) 81 (E) 144

14. If 750 × 45 = p, then 750 × 44 equals

(A) p − 45 (B) p − 750 (C) p − 1 (D) 44p (E) 750p

15. The grid shown is part of a cross-number puzzle............................................................................................................................................................................................................................................................

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1 2 3

6 7

11 12 13

16 17

20 21 22

2

Clues16 across is the reverse of 2 down1 down is the sum of 16 across and 2 down7 down is the sum of the digits in 16 across

What is 7 down?

(A) 11 (B) 12 (C) 13 (D) 14 (E) 15

16. I can ride my bike 3 times as fast as Ted can jog. Ted starts 40 minutes before meand then I chase him. How long does it take me to catch Ted?

(A) 20min (B) 30min (C) 40min (D) 50min (E) 60min

17. Five towns are joined by roads, as shown in the diagram.

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Q

R

S

T

How many ways are there of travelling from town P to town T if no town can bevisited more than once?

(A) 3 (B) 5 (C) 6 (D) 7 (E) 9

J 4

18. What are the last three digits of 7777 × 9999?

(A) 223 (B) 233 (C) 333 (D) 323 (E) 343

19. In how many ways can 52 be written as the sum of three prime numbers?

(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

20. Four points P , Q, R and S are such that PQ = 10, QR = 30, RS = 15 andPS = m. If m is an integer and no three of these points lie on a straight line, whatis the number of possible values of m?

(A) 5 (B) 49 (C) 50 (D) 54 (E) 55


21. A courier company has motorbikes which can travel 300 km starting with a fulltank. Two couriers, Anna and Brian, set off from the depot together to delivera letter to Connor’s house. The only refuelling is when they stop for Anna totransfer some fuel from her tank to Brian’s tank. She then returns to the depotwhile Brian keeps going, delivers the letter and returns to the depot. What is thegreatest distance that Connor’s house could be from the depot?

(A) 180 km (B) 200 km (C) 225 km (D) 250 km (E) 300 km

22. The square PQRS has sides of 3 metres. The points X and Y divide PQ into 3equal parts.

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RS

Z

Find the area, in square metres, of 4XY Z.

(A)3

8(B)

1

2(C)

3

16(D)

1

3(E)

1

4

J 5

23. The product of three consecutive odd numbers is 226 737. What is the middlenumber?

(A) 57 (B) 59 (C) 61 (D) 63 (E) 65

24. A Meeker number is a 7-digit number of the form pqrstup, where p × q = 10r + sand s × t = 10u + p and none of the digits are zero. For example, 6 742 816 is aMeeker number. The value of s in the largest Meeker number is

(A) 2 (B) 3 (C) 5 (D) 7 (E) 8

25. Four positive integers are arranged in a 2×2 table. For each row and column of thetable, the product of the two numbers in this row or column is calculated. Whenall four such products are added together, the result is 1001. What is the largestpossible sum of two numbers in the table that are neither in the same row nor inthe same column?

(A) 33 (B) 77 (C) 91 (D) 143 (E) 500

For questions 26 to 30, shade the answer as an integer from 0 to 999 inthe 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. This cube has a different whole number on each face, and has the property thatwhichever pair of opposite faces is chosen, the two numbers multiply to give thesame result.

What is the smallest possible total of all 6 numbers on the cube?

27. How many four-digit numbers containing no zeros have the property that wheneverany one of its four digits is removed, the resulting three-digit number is divisibleby 3?

J 6

28. A rhombus-shaped tile is formed by joining two equilateral triangles together.Three of these tiles are combined edge to edge to form a variety of shapes asin the example given.

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How many different shapes can be formed? (Shapes which are reflections or rota-tions of other shapes are not considered different.)

29. Warren has a strip of paper 10 metres long. He wishes to cut from it as manypieces as possible, not necessarily using all the paper, with each piece of paper awhole number of centimetres long. The second piece must be 10 cm longer thanthe first, the third 10 cm longer than the second and so on. What is the length, incentimetres, of the largest possible piece?

30. Terry has invented a new way to extend lists of numbers. To Terryfy a list suchas [1, 8] he creates two lists [2, 9] and [3, 10], where each term is one more thanthe corresponding term in the previous list, and then joins the three lists togetherto give [1, 8, 2, 9, 3, 10]. If he starts with a list containing one number [0] andrepeatedly Terryfies it he creates the list

[0, 1, 2, 1, 2, 3, 2, 3, 4, 1, 2, 3, 2, 3, 4, 3, 4, 5, 2, 3, 4, . . . ].

What is the 2012th number in this Terryfic list?

©AMT Publishing 2012 AMTT liMiTed Acn 083 950 341

AMC SOLUTIONS AND STATISTICS

This book provides a record of the Australian Mathematics Competition Junior, Intermediate and Senior questions, solutions and statistics for 2012. It also includes details of medallists and prizewinners and provides statistical information on levels of Australian response rates and other information.

AMC Solutions and Statistics 2012 (available early 2013) can be ordered online from the Australian Mathematics Trust website where a wide range of other products are also available.

www.amt.edu.au

junior division competition paper - kheradedu.irkheradedu.ir/images/inter/australia/2012/7-8.pdf ·...

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