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MatheMaticsMark only ONE answer for each question.Your score will be the number of correct answers.Marks are NOT deducted for incorrect answers.
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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 G © EAA 2
1. The plans for a new school hall are on display. These plans show a front view, a side view and a top view of the hall.
top viewside viewfront view
(A) (B)
(C) (D)
Which of the diagrams shows a correct three-dimensional view of the new hall?
top viewside viewfront view
(A) (B)
(C) (D)
2. A rotary clothes line is 180 cm from the ground at its lowest level and 210 cm when it is at its highest.
When the handle is given one full turn, the height of the clothes line increases by 30 mm.
How many full turns of the handle will it take to raise the clothes line from its lowest to its highest level?
(A) 10 (B) 30 (C) 100 (D) 300
3. Henry made a pattern with blocks, as shown.
Stage Picture
1
2
3
4
In Stage 2 Henry used a total of five blocks.
How many blocks does Henry need for Stage 5?
(A) 16(B) 17(C) 18(D) 21
3 ICAS Mathematics Practice Questions Paper G © EAA
4. Sandra has these pictures on her website.
Picture 1 uses 7.25 Kb of memory.
Picture 2 uses 3.323 Kb of memory.
Approximately how much memory does Picture 2 use as a percentage of the memory used by Picture 1?
(A) 54%(B) 46%(C) 43%(D) 39%
5. The two spinners shown have the numbers 2, 4, 6 and 8 written on them.
22
88
66
44
22
88 44
66The arrows are spun on both to get two numbers. The numbers are then added to get a score.
The picture shows a score of 6 + 2 = 8.
What is the most likely score when the spinners are used this way?
(A) 10(B) 12(C) 14(D) 16
6. Here are the prices of seven houses sold on Saturday.
House Prices
$460 000
$290 000
$660 000
$350 000
$590 000
$210 000
$590 000
What was the median house price?
(A) $350000(B) $450000(C) $460000(D) $590000
7. 5 910 393 387 ÷ 454 645 645 = 13 with remainder 2
What is the next larger number that will also give a remainder of 2 when divided by 454 645 645?
(A) 5 001 102 047 (B) 5 455 747 742(C) 6 365 039 032(D) 6 819 684 677
ICAS Mathematics Practice Questions Paper G © EAA 4
8. Here is a picture of a fan.
NOT TO SCALE
diameter of fan8 cm
The paper part of this fan is a semicircle from which a smaller semicircle has been cut. The smaller semicircle has a diameter of 8 cm. The paper part of the fan has an area of 140 cm2.
What is the diameter of the fan, in cm, correct to one decimal place?
(A) 7.8(B) 10.3(C) 15.6(D) 20.5
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. Lin cut this square picture out of a magazine.
She made an enlarged copy that was still square but twice as wide.
Lin cut off a rectangle from the right of the picture.
The picture was now a rectangle whosewidth was 2
3 of the height.
She then doubled the width of the picture.
The area of the rectangle was now 139 968 mm2.
How high, in mm, was the original picture?
QUESTIONS9AND10AREFREERESPONSE.WriteyouranswerintheboxesprovidedontheANSWERSHEETandfillintheovalsthatmatchyouranswer.
END OF PAPER
5 ICAS Mathematics Practice Questions Paper G © EAA
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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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M THE UNIVERSITY OF NEW SOUTH WALES
International Competit ions and Assessments for Schools
PRACTICE QUESTIO
NS
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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=
(A) 2 ●Theansweris12,soWRITEyour (B) 9 answerintheboxes. (C) 10 ●WriteonlyONEdigitineachbox, (D) 24 asshown,andfillinthecorrectoval, asshown.Theansweris10,sofillintheoval,asshown.C
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ICAS Mathematics Practice Questions Paper G © EAA
QUESTION KEY SOLUTION STRAND LEVEL OF DIFFICULTY
1 A
Option A correctly matches the front, side and top views.Option B does not match the front view or the top view.Option C does not match the front view or the side view.Option D does not match any view.
Space and Geometry Easy
2 A
The difference between the clothes line highest and lowest level is 210 − 180 = 30 cmConvert this to mm is 30 × 10 = 300 mm.One full turn of the handle increases the height by 30 mm; therefore we need to divide 300 by 30 which equals 10.It will take 10 full turns of the handle to raise the clothes line from its lowest to its highest level.
Measurement Easy
3 B
The number of blocks used in the stages shows a pattern: 1, 5, 9, 13…The pattern is continued by adding four blocks to the previous term.So Stage 5 will contain 13 + 4 = 17 blocks.
Algebra and Patterns Medium
4 B
3.323 Kb as a percentage of 7.25 Kb is calculated as (3.323 ÷ 7.25) × 100% = 45.83427%.This is 46% when rounded up.
Number and Arithmetic Medium
5 A
Each spinner has an equal chance of landing on 2, 4, 6 or 8.This table shows the possible sums, given in the options, and the combinations of numbers which give these sums.
Sum Combination Ways10 2 + 8; 8 + 2; 4 + 6; 6 + 4 412 4 + 8; 8 + 4 214 6 + 8; 8 + 6 216 8 + 8 1
The sum 10 can be obtained in 4 different ways. All other sums can be obtained in fewer than 4 ways. Hence, 10 is the most likely score.
Chance and Data Medium
6 C
To find the median we need to arrange the values from smallest to largest: 210 000, 290 000, 350 000, 460 000, 590 000, 590 000, 660 000.Since we have seven values (odd number) the middle value, the fourth in this case, is the median. Hence, the median is 460 000.
Chance and Data Medium/Hard
ICAS Mathematics Practice Questions Paper G © EAA
7 C
A good understanding of division, multiplication and remainders is important to be able to recognise what you need to do in this question.
In division, when a number is divided by a divisor, we are left with the quotient and the remainder.let’s use small numbers as an example9 ÷ 2 = 4 r 1.2 is the divisor, 4 is the quotient and 1 is the remainder.
Intuitively, this means that4 × 2 + 1 = 9quotient × divisor + remainder = number
To get a new number with the same remainder and divisor, we can simply change the quotient.For example, if we change the quotient from 4 to 5, we now get the next number that gives a remainder of 1 when divided by 2 which is 11.5 × 2 + 1 = 11
Likewise, for this question; the quotient is 13 and it can be written as:13 × 454 645 645 + 2 = 5 910 393 387for the next largest number that will give the same remainder 2 when divided by 454 645 645 we need to go up to the next quotient which is 14. The calculation can be written as:14 × 454 645 645 + 2 = 6 365 039 032
Number and Arithmetic Medium/Hard
8 D
The semicircular fan of unknown diameter is comprised of two parts: the smaller semicircle of diameter 8 cm, and the paper section with area 140 cm2.
We can write this as a mathematical equation.Let r be the radius of the fan.The small semicircle has a diameter of 8 cm. Hence, its radius is 4 cm.
= + 140π × 42
2π × r2
2
r2 = 16 + 280π
π × r2 = 16 × π + 280
r = √105.126781...
r = 10.25313455As this is the radius, the diameter is twice this amount. So the diameter rounded to 1 decimal place is 20.5.
Measurement Hard
9 990 990 is the lowest common multiple of 9, 10 and 11.
Number and Arithmetic Hard
ICAS Mathematics Practice Questions Paper G © 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
10 162
Let x be the side length of the original picture.
After the first transformation, the picture is still a square, but now with a side length of 2x.After cutting off a rectangle from the right of the picture, the picture is now a rectangle with height 2x and width
2x × =139 9688x3
= 139 96816x2
3
x2 = 139 968 × 316
x = √26 244
x =
23
43
83
of 2x which equals
2x × =139 9688x3
= 139 96816x2
3
x2 = 139 968 × 316
x = √26 244
x =
23
43
83
x.
After the final transformation, the width is doubled,
2x × =139 9688x3
= 139 96816x2
3
x2 = 139 968 × 316
x = √26 244
x =
23
43
83 x, but the height stays the same, 2x.
The area of the picture is now 139 968 mm2. Hence,
2x × =139 9688x3
= 139 96816x2
3
x2 = 139 968 × 316
x = √26 244
x =
23
43
83
Number and Arithmetic Hard
![2015 SRJC H2 Mathematics Prelim Paper 2 - A Level JC · PDF file1 2015 SRJC H2 Mathematics Prelim Paper 2 Section A: Pure Mathematics [40 marks] 1 Functions f and g are defined as](https://img.pdfslide.us/doc/110x75/5a7b63007f8b9a0a668c0536/2015-srjc-h2-mathematics-prelim-paper-2-a-level-jc-2015-srjc-h2-mathematics.jpg)
