Mathematics Pap Erg

8/9/2019 Mathematics Pap Erg

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DO NOT OPEN THIS BOOKLET UNTIL INSTRUCTED.

STUDENT’S NAME:

Read the instructions on the ANSWER SHEET and fill in yourNAME, 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.

MMMark only ONE answer for each question.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 fromthe 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.

P r a c t i c e

Q u e s t i o n s

nternationalompetitionsand ssessments for chools


http://slidepdf.com/reader/full/mathematics-pap-erg 2/11ICAS Mathematics Practice Questions Paper G © 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

Which of these cannot be values for

x and y ?

x y

(A) 70 120

(B) 50 120

(C) 70 100

(D) 50 100

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

cars

Key

trucks

motorbikes

bicycles

Vehicles Passing the School

90

21

15

9

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


http://slidepdf.com/reader/full/mathematics-pap-erg 3/113 ICAS Mathematics Practice Questions Paper G © 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


http://slidepdf.com/reader/full/mathematics-pap-erg 4/11ICAS Mathematics Practice Questions Paper G © 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.

1 2 8

m m

9 6 m

m

7 2 m m

5 4 m m

4 0 . 5 m

m

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 dollthat can fit exactly 700 dolls inside it,

including the dolls shown.

She writes the answer as:

1.1603 10 x

mm

What is the value of x

?

END OF PAPER

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QUESTION KEY SOLUTION STRANDLEVEL OFDIFFICULTY

1 CThe missing part in C is one third whichmatches the slice (one third); altogether theycomplete one whole.

Space andGeometry

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 =90

135× 360°

= 240°

Chance andData

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 makes6 turns. Therefore, 6 × the circumference of the big wheel = 1

Circumference of the big wheel is π D,therefore the equation can be presented as:

6 × π D = 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 × π d = 1…. (Equation 2)

Dividing Equation 1 by Equation 2:

6 D

xd= 1 , make x the subject of the equation:

6 D

d x =

Substitute D= 3/2 d

6 × 3

2 x = = 9 .

Measurement Medium

5 B

If the number is to be divisible by 3 and by 4, ithas to be divisible by 12. The first number thatis divisible by 12 between 300 and 400 is 312.Then continue to add 12 to get the nextnumber until you reach 396 (the last numberbefore 400).Therefore, the numbers are 312, 324, 336,348, 360, 372, 384, 396.

There are 8 numbers.

Number and Arithmetic

Medium/Hard


http://slidepdf.com/reader/full/mathematics-pap-erg 10/11ICAS Mathematics Practice Questions Paper G © EAA

6 D

where d is the diameter, h is

the height of the bottle.

Alan suggested doubling the height, therefore

the new volume will be: .

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:

.

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 andGeometry

Hard

7 A

The green area is 2 a × a = 2 a 2

The orange area is 4 a × a = 4 a 2

The blue area is = length × width = (6b + 2b)

× (6 a − 4b)

= 8b × (6 a − 4b)

= 48 ab − 32b 2

Therefore the total area that is coloured is =green + orange + blue

= 2 a 2 + 4 a 2 + 48 ab − 32b 2

= 6 a 2 + 48 ab − 32b 2

Algebra andPattern

Hard



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 apattern: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 = 6561

From 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 endin 1. If we multiply this number by 111444

(which also ends with the digit 1), the result will also end with 1.


Hard

9 990990 is the lowest common multiple of 9, 10and 11.


Hard

10 89

Height of smallest doll is 40.5mm.

Rate of increase in height of successive dollsis 128

96.

Height of doll with 700 dolls inside

= 40.5 × 128

96

700

= 1.1603 × 1089 mm

Therefore, the value of x is 89.


Hard

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Mathematics Pap Erg