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Transcript of Mathematics paper H

HPAPER

DO NOT OPEN THIS BOOKLET UNTIL INSTRUCTED.

STUDENT’S NAME:

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 may use a ruler and spare paper.A CALCULATOR is required.

Practice

Questions

international competitions and assessments for schools

ICAS Mathematics Practice Questions Paper H © EAA 2

1. In which picture does the slice match the missing part of the cake?

cake

slice

slice

slice

slice

(A) (B)

(C) (D)

cake

cake cake

2. This is a diagram of a triangle.

NOT TO SCALE

x y(A) 70 120(B) 50 120(C) 70 100(D) 50 100

Which of these cannot be values for x and y ?

NOT TO SCALE

x y(A) 70 120(B) 50 120(C) 70 100(D) 50 100

3. This is a sector graph (pie graph).

carsKey

trucksmotorbikesbicycles

Vehicles Passing the School

90

21

159

What is the angle at the centre for the number of cars passing this school?

(A) 296°(B) 284°(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.

When the car travels one metre, the back wheels go around 6 times.

How many times do the front wheels go around when the car travels one metre?

(A) 4(B) 6(C) 9(D) 12

3 ICAS Mathematics Practice Questions Paper H © EAA

5. How many numbers between 301 and 400 are divisible by both 3 and 4?

(A) 6(B) 8(C) 12(D) 25

6. Alan and Bill want to make a bottle that will hold about twice as much as the one shown.

height

diameter

Alan wanted to double the height of the bottle. Bill wanted to double the diameter of the bottle.

Who was correct?

(A) neither of them(B) both of them(C) Bill only(D) Alan only

7. This picture is based on the style of the Dutch artist Piet Mondrian (1872–1944).

2

NOT TO SCALE

26

6

4

4

Which expression gives the total area of the three coloured rectangles in the picture?

(A) 6a2 + 48ab – 32b2(B) 20a2 + 24b2(C) 4a2 + 36ab – 24b2(D) 6a2 + 16b2

8. A very large number is represented as shown.

What is the last digit (unit) of this number?

(A) 1(B) 3(C) 7(D) 9

ICAS Mathematics Practice Questions Paper H © EAA 4

9. Ricky is thinking of a positive 3-digit 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.If I subtract 11 from the number,the result will be divisible by 11.’

What is the lowest possible number Ricky is thinking of?

10. Katya has a set of Russian dolls. The heights of her dolls are shown. They increase by a fixed ratio.

128

mm

96 m

m

72 m

m

54 m

m

40.5

mm

1.1603 � 10x mm

The smallest doll fits in the next larger doll. They both fit inside the next doll. The largest doll shown fits all four of the other dolls inside it.

Katya calculates the height of the doll that can fit exactly 700 dolls inside it, including the dolls shown.

128

mm

96 m

m

72 m

m

54 m

m

40.5

mm

1.1603 � 10x mm

What is the value of x?

END OF PAPER

5 ICAS Mathematics Practice Questions Paper H © EAA

HPAPER

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

Singapore secondary 3

THE UNIVERSITY OF NEW SOUTH WALES

Educational Assessment Australia eaa.unsw.edu.au

© 2010 educational assessment australia. eaa is an education group of UNsW Global Pty Limited, a not-for-profit provider of education, training and consulting services and a wholly owned enterprise of the University of New south Wales. aBN 62 086 418 582

Acknowledgmentcopyright 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.

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FIRST NAME to appear on certificate LAST NAME to appear on certificate

Are you male or female? Male Female

Does anyone in your home usually speak a language other than English? Yes No

School name:

Town / suburb:

Today’s date: Postcode:

CLASSDATE OF BIRTHDay Month Year

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HOW TO FILL OUT THIS SHEET:

• Ruboutallmistakescompletely.• Printyourdetailsclearly intheboxesprovided.• Makesureyoufillinonly oneovalineachcolumn.

EXAMPLE 1: Debbie BachFIRST NAME LAST NAME

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EXAMPLE 2: Chan Ai BengFIRST NAME LAST NAME

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EXAMPLE 3: Jamal bin AbasFIRST NAME LAST NAME

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M THE UNIVERSITY OF NEW SOUTH WALES

International Competit ions and Assessments for Schools

PRACTICE QUESTIO

NS

*045910*

PaPer

H

DCBA

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Your privacy is assured as EAA fully complies with appropriate Australian privacy legislation. Visit www.eaa.unsw.edu.au for more details.

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International Competit ions and Assessments for SchoolsM

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MULTIPLE CHOICE FREE RESPONSE

Example: 4+6= Example:6+6=

DCBA

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ICAS Mathematics Practice Questions Paper H © EAA

QUESTION KEY SOLUTION STRAND LEVEL OF DIFFICULTY

1 CThe missing part in C is one third which matches the slice (one third); altogether they complete one whole.

Space and Geometry Easy

2 A The sum of x and y adds to 190° which is more than the angle sum of a triangle (180°).

Space and Geometry Easy

3 D

The total number of vehicles = 135

The angle at the centre for cars = 90135

× 360°

= 240°

Chance and Data Medium

4 C

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 = 1Circumference of the big wheel is πD, therefore the equation can be presented as:6 × πD = 1….(Equation 1).

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:

6Dxd

= 1 6Dd

x = 6 × 3 2x = = 9 , make x the subject of the equation:

6Dxd

= 1 6Dd

x = 6 × 3 2x = = 9

Substitute D= 3/2 d

6Dxd

= 1 6Dd

x = 6 × 3 2x = = 9 .

Measurement Medium

5 B

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 until you reach 396 (the last number before 400).Therefore, the numbers are 312, 324, 336, 348, 360, 372, 384, 396. There are 8 numbers.

Number and Arithmetic Medium/Hard

ICAS Mathematics Practice Questions Paper H © EAA

6 D

d 2V = π × h

d 2

V = π × 4 × × h

2d 2V = π × h 2d

2 V = π × hd 2V = π × h where d is the diameter, h is

the height of the bottle.Alan suggested doubling the height, therefore the new volume will be: d

2V = π × h

d 2

V = π × 4 × × h

2d 2V = π × h 2d

2 V = π × hd 2V = π × h.

This is twice the original volume. In other words, by doubling the height of the bottle it will hold twice as much content.Bill suggested doubling the diameter, therefore the new volume will be:

d 2V = π × h

d 2

V = π × 4 × × h

2d 2V = π × h 2d

2 V = π × hd 2V = π × h

.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.

Space and Geometry Hard

7 A

The green area is 2a × a = 2a2The orange area is 4a × a = 4a2The blue area is = length × width = (6b + 2b) × (6a − 4b)= 8b × (6a − 4b)= 48ab − 32b2Therefore the total area that is coloured is = green + orange + blue= 2a2 + 4a2 + 48ab − 32b2= 6a2 + 48ab − 32b2

Algebra and Pattern Hard

ICAS Mathematics Practice Questions Paper H © EAA

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

8 A

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 = 1111112 = 123211113 = 1367631It is clear that the last digit of 111 to the powerof 444 is 1.For powers of 3 there is a different pattern:31 = 332 = 933 = 2734 = 8135 = 24336 = 72937 = 218738 = 6561From this pattern every 4th power of 3 results ina 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.

Number and Arithmetic Hard

9 990 990 is the lowest common multiple of 9, 10 and 11.

Number and Arithmetic Hard

10 89

Height of smallest doll is 40.5mm.Rate of increase in height of successive dolls is 12896

12896

700

.

Height of doll with 700 dolls inside

= 40.5 × 12896

12896

700

= 1.1603 × 1089 mmTherefore, the value of x is 89.

Number and Arithmetic Hard