Mathematics A Paper 4h Answers

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1. PAPER H ctice s Pra stion Que inter national DO NOT OPEN THIS BOOKLET UNTIL INSTRUCTED. competitions STUDENT'S NAME: and assessments for schools Read the instructions on the ANSWER SHEET and fill in your NAME, SCHOOL and OTHER INFORMATION. Use a 2B or B pencil. Do NOT use a pen. Rub out any mistakes completely. You MUST record your answers on the ANSWER SHEET. Mark only ONE answer for each question. MatheMatics Your score will be the number of correct answers. Marks are NOT deducted for incorrect answers. MULTIPLE-CHOICE QUESTIONS: Use the information provided to choose the BEST answer from the four possible options. On your ANSWER SHEET fill in the oval that matches your answer. FREE-RESPONSE QUESTIONS: Write your answer in the boxes provided on the ANSWER SHEET and fill in the oval that matches your answer You may use a ruler and spare paper. A CALCULATOR is required.
2. 1. In which picture does the slice match the 3. This is a sector graph (pie graph). missing part of the cake? Vehicles Passing the School cake cake 15 9 slice slice Key (A) (B) 21 cars trucks 90 cake cake motorbikes bicycles slice What is the angle at the centre for the slice number of cars passing this school? (C) (D) (A) 296° (B) 284° 2. This is a diagram of a triangle. (C) 257° (D) 240° 4. In the toy car shown, the diameters of the back wheels are one-and-a-half times the diameters of the front wheels. NOT TO SCALE Which of these cannot be values for NOT TO SCALE x and y ? x y (A) 70 120 (B) x 50 y120 When the car travels one metre, the (A) 70 120 back wheels go around 6 times. (C) 70 100 (B) 50 120 (D) 50 100 How many times do the front wheels go (C) 70 100 around when the car travels one metre? (D) 50 100 (A) 4 (B) 6 (C) 9 (D) 12 ICAS Mathematics Practice Questions Paper H © EAA 2
3. 5. How many numbers between 301 and 400 7. This picture is based on the style of the are divisible by both 3 and 4? Dutch artist Piet Mondrian (1872–1944). (A) 6 6 2 (B) 8 2 (C) 12 (D) 25 4 6 6. Alan and Bill want to make a bottle that will hold about twice as much as the 4 one shown. NOT TO SCALE height Which expression gives the total area of the three coloured rectangles in the picture? (A) 6a2 + 48ab – 32b2 (B) 20a2 + 24b2 diameter (C) 4a2 + 36ab – 24b2 (D) 6a2 + 16b2 Alan wanted to double the height of the bottle. Bill wanted to double the diameter of the bottle. 8. A very large number is represented as shown. Who was correct? (A) neither of them (B) both of them (C) Bill only (D) Alan only What is the last digit (unit) of this number? (A) 1 (B) 3 (C) 7 (D) 9 3 ICAS Mathematics Practice Questions Paper H © EAA
4. QUESTIONS 9 AND 10 ARE FREE RESPONSE. 10. Katya has a set of Russian dolls. Write your answer in the boxes provided on The heights of her dolls are shown. the ANSWER SHEET and fill in the ovals that They increase by a fixed ratio. match your answer. 128 mm 9. Ricky is thinking of a positive 3-digit 96 mm 40.5 mm 72 mm 54 mm number. 'If I subtract 9 from the number, the result will be divisible by 9. If I subtract 10 from the number, the result will be divisible by 10. The smallest doll fits in the next larger doll. If I subtract 11 from the number, They both fit inside the next doll. the result will be divisible by 11.' 128 mm x The largest doll shown fits all four of the 1.1603 10 mm 96 mm 40.5 mm 72 mm other dolls inside it. 54 mm Katya calculates the height of the doll that can fit exactly 700 dolls inside it, including the dolls shown. She writes the answer as: 1.1603 10 x mm What is the lowest possible number What is the value of x? Ricky is thinking of? END OF PAPER ICAS Mathematics Practice Questions Paper H © EAA 4
5. This page may be used for working. 5 ICAS Mathematics Practice Questions Paper H © EAA
6. Acknowledgment copyright in this booklet is owned by educational assessment australia, UNsW Global Pty Limited, unless otherwise indicated. every effort has been made to trace and acknowledge copyright. educational assessment australia apologises for any accidental infringement and welcomes information to redress the situation. The following year levels should sit THIS Paper: Australia Year 10 Brunei Form 5 Hong Kong Form 4 Indonesia Year 11 Malaysia Form 4 New Zealand Year 11 Pacific Year 10 PAPER Singapore secondary 3 H South Africa Grade 10 Educational © 2010 educational assessment australia. eaa is an education group of UNsW Global Pty Assessment Limited, a not-for-profit provider of education, THE UNIVERSITY OF NEW SOUTH WALES Australia training and consulting services and a wholly owned enterprise of the University of New eaa.unsw.edu.au south Wales. aBN 62 086 418 582
7. PaPer H M Inter national Competitions and Assessments THE UNIVERSITY OF NEW SOUTH WALES for Schools HOW TO FILL OUT THIS SHEET: EXAMPLE 1: Debbie Bach EXAMPLE 2: Chan Ai Beng EXAMPLE 3: Jamal bin Abas FIRST NAME LAST NAME FIRST NAME LAST NAME FIRST NAME LAST NAME • Rub out all mistakes completely. • Print your details clearly A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A in the boxes provided. B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C • Make sure you fill in only D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D one oval in each column. FIRST NAME to appear on certificate LAST NAME to appear on certificate A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B S C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C N D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E IO F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G T H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H S I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I E J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K U L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L Q M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N E O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P I C Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R T S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S C T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T A U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V R W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W P X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / DATE OF BIRTH CLASS Day Month Year (optional) Are you male or female? Male Female *045910* 0 1 0 1 0 1 0 1 0 1 0 1 A B K L Does anyone in your home usually speak a language other than English? 2 2 2 2 2 C M Yes No 3 3 3 3 3 D N 4 4 4 4 E O School name: 5 5 5 5 F P 6 6 6 6 G Q Town / suburb: 7 7 7 7 H R 8 8 8 8 I S Today's date: Postcode: 9 9 9 9 J T
8. TO ANSWER THE QUESTIONS MULTIPLE CHOICE FREE RESPONSE Example: 4 + 6 = Example: 6 + 6 = (A) 2 ● The answer is 12, so WRITE your 1 2 (B) 9 answer in the boxes. 0 0 0 (C) 10 ● Write only ONE digit in each box, 1 1 1 2 2 2 (D) 24 as shown, and fill in the correct oval, 3 3 3 as shown. 4 4 4 5 5 5 The answer is 10, so fill in the oval , as shown. C 6 6 6 7 7 7 A B C D 8 8 8 9 9 9 START 1 A B C D 2 A B C D 3 A B C D 4 A B C D 5 A B C D 6 A B C D 7 A B C D 8 A B C D 9 10 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 9 9 9 9 9 9 PaPer H M Inter national Competitions Your privacy is assured as EAA fully complies and Assessments with appropriate Australian privacy legislation. for Schools Visit www.eaa.unsw.edu.au for more details.
9. LEVEL OF QUESTION KEY SOLUTION STRAND DIFFICULTY The missing part in C is one third which Space and 1 C matches the slice (one third); altogether they Easy Geometry complete one whole. The sum of x and y adds to 190° which is more Space and 2 A Easy than the angle sum of a triangle (180°). Geometry The total number of vehicles = 135 90 Chance and 3 D The angle at the centre for cars = × 360° Medium 135 Data = 240° Let D be the diameter of the big wheel (back wheel). Let d be the diameter of the small wheel (front wheel). According to the question information, D = 3/2 × d. When the car travels 1 m, the big wheel makes 6 turns. Therefore, 6 × the circumference of the big wheel = 1 Circumference of the big wheel is πD, therefore the equation can be presented as: 6 × πD = 1….(Equation 1). 4 C Measurement Medium Let x be the number of turns the small wheel makes when the car travels 1m. Using the same logic, we can form the equation x × πd = 1…. (Equation 2) Dividing Equation 1 by Equation 2: 6D 6D 6×3 = 1, make x = subject of x = equation: 9 the the = xd d 2 6D =1 x = 6D x= 6×3 =9 xd d 2 Substitute D= 3/2 d 6D =1 x = 6D x= 6×3 =9. xd d 2 If the number is to be divisible by 3 and by 4, it has to be divisible by 12. The first number that is divisible by 12 between 300 and 400 is 312. Then continue to add 12 to get the next Number and 5 B number until you reach 396 (the last number Medium/Hard Arithmetic before 400). Therefore, the numbers are 312, 324, 336, 348, 360, 372, 384, 396. There are 8 numbers. ICAS Mathematics Practice Questions Paper H © EAA
10. V = π d  × h where dπis d  × h h is 2d V =  the diameter, V = π  × h 2 2 2 2 the height of the bottle. d V = π × 4 ×  × h Alan suggested doubling the height, therefore 2 V = π d  will be: V = π d  × h . the new volume × h 2d  V = π  × h 2 2 2 This is twice the original volume. In other d V = π × 4 ×  × h words, by doubling the height of the bottle it 2 will hold twice as much content. Bill suggested doubling the diameter, therefore Space and 6 D Hard Geometry the new volume will be: d  × h V = π d  ×  h 2d 2d V = π V = π  × h  × h 2 2 2 2 V = π × 4 ×  × h . d 2 This is 4 times the original volume. In other words, the bottle then will hold 4 times as much content. Therefore, only Alan was correct. The green area is 2a × a = 2a2 The orange area is 4a × a = 4a2 The blue area is = length × width = (6b + 2b) × (6a − 4b) = 8b × (6a − 4b) Algebra and 7 A Hard = 48ab − 32b2 Pattern Therefore the total area that is coloured is = green + orange + blue = 2a2 + 4a2 + 48ab − 32b2 = 6a2 + 48ab − 32b2 ICAS Mathematics Practice Questions Paper H © EAA
11. This question relies on looking for a pattern. 333444 = (3 × 111)444 = 3444 × 111444 Let's look at powers of 111 and try to find a pattern: 1111 = 111 1112 = 12321 1113 = 1367631 It is clear that the last digit of 111 to the power of 444 is 1. For powers of 3 there is a different pattern: 31 = 3 32 = 9 Number and 8 A Hard 33 = 27 Arithmetic 34 = 81 35 = 243 36 = 729 37 = 2187 38 = 6561 From this pattern every 4th power of 3 results in a number with the digit 1 in the units place. Since 444 is a multiple of 4, then 3444 will end in 1. If we multiply this number by 111444 (which also ends with the digit 1), the result will also end with 1. 990 is the lowest common multiple of 9, 10 Number and 9 990 Hard and 11. Arithmetic Height of smallest doll is 40.5mm. Rate of increase in height of successive dolls 700 is 128 . 128 96 96 Height of doll with 700 dolls inside Number and 10 89 Hard 700 Arithmetic 128 = 40.5 × 128 96 96 = 1.1603 × 1089 mm Therefore, the value of x is 89. Level of difficulty refers to the expected level of difficulty for the question. Easy more than 70% of candidates will choose the correct option Medium about 50–70% of candidates will choose the correct option Medium/Hard about 30–50% of candidates will choose the correct option Hard less than 30% of candidates will choose the correct option ICAS Mathematics Practice Questions Paper H © EAA