Icas Math Specimen Paper G 26576j
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PAPER
G
e c i t c Pra stions Que
Inter national Competitions and Assessments for Schools
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 MUST record your answers on the ANSWER SHEET.
Mathematics
Mark 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 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.
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. side view side view
A rotary clothes line is 180 cm from the ground at its lowest level and 210 cm when it is at its highest.
top view top view
FP FP
front view front view
2.
Which of the diagrams shows a correct three-dimensional view of the new hall?
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) (A)
(A) 10 (B) 30 (C) 100 (D) 300
(B) (B)
3. (C) (C)
Henry made a pattern with blocks, as shown.
(D) (D)
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) (B) (C) (D) ICAS Mathematics Practice Questions Paper G © EAA
2
16 17 18 21
4.
QUESTION 5 IS FREE RESPONSE.
Sandra has these pictures on her website.
Write your answer in the boxes provided on the ANSWER SHEET and fill in the ovals that match your answer. 5.
Lin cut this square picture out of a magazine.
Picture 1 uses 7.25 Kb of memory.
She made an enlarged copy that was still square but twice as wide.
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) (B) (C) (D)
Lin cut off a rectangle from the right of the picture.
54% 46% 43% 39%
The picture was now a rectangle whose 2 of the height. width was 3 She then doubled the width of the picture.
The area of the rectangle was now 2 139 968 mm . How high, in mm, was the original picture? END OF PAPER 3
ICAS Mathematics Practice Questions Paper G © EAA
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 9
Brunei
Form 4
Hong Kong
Form 3
Indonesia
Year 10
Malaysia
Form 3
New Zealand
Year 10 Year 9
Singapore South Africa
Secondary 2
PAPER
G
Grade 9
THE UNIVERSITY OF NEW SOUTH WALES
Educational Assessment Australia eaa.unsw.edu.au
© 2012 Educational Assessment Australia. EAA is an education group of UNSW Global Pty training and consulting services and a wholly owned enterprise of the University of New South Wales. ABN 62 086 418 582
Paper
G
M
Inter national Competitions THE UNIVERSITY OF NEW SOUTH WALES
and Assessments for Schools
HOW TO FILL OUT THIS SHEET:
EXAMPLE 1: Debbie Bach
EXAMPLE 2: Chan Ai Beng
EXAMPLE 3: Jamal bin Abas
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FIRST NAME
LAST NAME
LAST NAME
LAST NAME
• Rub out all mistakes completely. • Print your details clearly in the boxes provided. • Make sure you fill in only one oval in each column.
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DATE OF BIRTH
Are you male or female? Male Female
Day
*045909*
Does anyone in your home usually speak a language other than English? Yes No School name: Town / suburb: Today’s date:
Postcode:
Month Year
CLASS
(optional)
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TO ANSWER THE QUESTIONS MULTIPLE CHOICE
FREE RESPONSE
Example:
6+4=
Example:
START
(A) (B) (C) (D)
2 9 10 24
The answer is 10, so A
B
C
● The answer is 12, so WRITE your answer in the boxes. ● Write only ONE digit in each box, as shown, and in the correct oval, as shown. in the oval
C
, as shown.
D
1
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PAPER
Your privacy is assured as EAA fully complies with appropriate Australian privacy legislation. Visit www.eaa.unsw.edu.au for more details.
G M
Inter national Competitions and Assessments for Schools
QUESTION
1
2
3
4
SOLUTION
STRAND
LEVEL OF DIFFICULTY
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
A
The difference between the clothes line highest and lowest level is 210 − 180 = 30 cm Convert 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
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
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
KEY
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
2 3
8 2 of342x which equals 3 3
4 3
After the final transformation, the width is8x 8x 2x ×
5
162
=139 968
2x ×
x. 38
=139 968
8 2 4 doubled, x, but stays the same, 16x 2x. 8 the height 16x 32 3 43 = 139 968 Number and = 139 968 3 3 3 3 3 2 139 968 × Arithmetic 3 139 968 × 3 The 8area the picture isx now 139 968 mmx .= x =139of = 16 16 2x × 968 3 Hence, x = √26 244 x = √26 244 16x = 139 968 3 8x x= x= 2x × 139=139 968 × 3 968 x =3 16 2 x =x√26 244 16 = 139 968 x3 = ×3 x2 = 139 968 16
3
3
2
2
2
2
Hard
2
2
x = √26 244 x = 162
ICAS Mathematics Practice Questions Paper G © EAA
4 3
2 3
8 3
4 3 8x =139 968 3 2 16x = 139 968 3 ×3 2 x = 139 968 16
2x ×
8 3
2 3
8x =139 968 3 16x2 = 139 968 3 ×3 x2 = 139 968 16
2x ×
x = √26 244 x =
x = √26 244 x =
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 G © EAA
G
e c i t c Pra stions Que
Inter national Competitions and Assessments for Schools
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 MUST record your answers on the ANSWER SHEET.
Mathematics
Mark 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 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.
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. side view side view
A rotary clothes line is 180 cm from the ground at its lowest level and 210 cm when it is at its highest.
top view top view
FP FP
front view front view
2.
Which of the diagrams shows a correct three-dimensional view of the new hall?
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) (A)
(A) 10 (B) 30 (C) 100 (D) 300
(B) (B)
3. (C) (C)
Henry made a pattern with blocks, as shown.
(D) (D)
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) (B) (C) (D) ICAS Mathematics Practice Questions Paper G © EAA
2
16 17 18 21
4.
QUESTION 5 IS FREE RESPONSE.
Sandra has these pictures on her website.
Write your answer in the boxes provided on the ANSWER SHEET and fill in the ovals that match your answer. 5.
Lin cut this square picture out of a magazine.
Picture 1 uses 7.25 Kb of memory.
She made an enlarged copy that was still square but twice as wide.
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) (B) (C) (D)
Lin cut off a rectangle from the right of the picture.
54% 46% 43% 39%
The picture was now a rectangle whose 2 of the height. width was 3 She then doubled the width of the picture.
The area of the rectangle was now 2 139 968 mm . How high, in mm, was the original picture? END OF PAPER 3
ICAS Mathematics Practice Questions Paper G © EAA
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 9
Brunei
Form 4
Hong Kong
Form 3
Indonesia
Year 10
Malaysia
Form 3
New Zealand
Year 10 Year 9
Singapore South Africa
Secondary 2
PAPER
G
Grade 9
THE UNIVERSITY OF NEW SOUTH WALES
Educational Assessment Australia eaa.unsw.edu.au
© 2012 Educational Assessment Australia. EAA is an education group of UNSW Global Pty training and consulting services and a wholly owned enterprise of the University of New South Wales. ABN 62 086 418 582
Paper
G
M
Inter national Competitions THE UNIVERSITY OF NEW SOUTH WALES
and Assessments for Schools
HOW TO FILL OUT THIS SHEET:
EXAMPLE 1: Debbie Bach
EXAMPLE 2: Chan Ai Beng
EXAMPLE 3: Jamal bin Abas
FIRST NAME
FIRST NAME
FIRST NAME
LAST NAME
LAST NAME
LAST NAME
• Rub out all mistakes completely. • Print your details clearly in the boxes provided. • Make sure you fill in only one oval in each column.
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
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DATE OF BIRTH
Are you male or female? Male Female
Day
*045909*
Does anyone in your home usually speak a language other than English? Yes No School name: Town / suburb: Today’s date:
Postcode:
Month Year
CLASS
(optional)
0
0
0
0
0
0
A
1
1
1
1
1
1
B
K L
2
2
2
2
2
C
M
3
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3
D
N
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E
O
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G
Q
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R
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J
T
TO ANSWER THE QUESTIONS MULTIPLE CHOICE
FREE RESPONSE
Example:
6+4=
Example:
START
(A) (B) (C) (D)
2 9 10 24
The answer is 10, so A
B
C
● The answer is 12, so WRITE your answer in the boxes. ● Write only ONE digit in each box, as shown, and in the correct oval, as shown. in the oval
C
, as shown.
D
1
A
B
C
D
2
A
B
C
D
3
A
B
C
D
4
A
B
C
D
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6+6=
1 2 0
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PAPER
Your privacy is assured as EAA fully complies with appropriate Australian privacy legislation. Visit www.eaa.unsw.edu.au for more details.
G M
Inter national Competitions and Assessments for Schools
QUESTION
1
2
3
4
SOLUTION
STRAND
LEVEL OF DIFFICULTY
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
A
The difference between the clothes line highest and lowest level is 210 − 180 = 30 cm Convert 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
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
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
KEY
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
2 3
8 2 of342x which equals 3 3
4 3
After the final transformation, the width is8x 8x 2x ×
5
162
=139 968
2x ×
x. 38
=139 968
8 2 4 doubled, x, but stays the same, 16x 2x. 8 the height 16x 32 3 43 = 139 968 Number and = 139 968 3 3 3 3 3 2 139 968 × Arithmetic 3 139 968 × 3 The 8area the picture isx now 139 968 mmx .= x =139of = 16 16 2x × 968 3 Hence, x = √26 244 x = √26 244 16x = 139 968 3 8x x= x= 2x × 139=139 968 × 3 968 x =3 16 2 x =x√26 244 16 = 139 968 x3 = ×3 x2 = 139 968 16
3
3
2
2
2
2
Hard
2
2
x = √26 244 x = 162
ICAS Mathematics Practice Questions Paper G © EAA
4 3
2 3
8 3
4 3 8x =139 968 3 2 16x = 139 968 3 ×3 2 x = 139 968 16
2x ×
8 3
2 3
8x =139 968 3 16x2 = 139 968 3 ×3 x2 = 139 968 16
2x ×
x = √26 244 x =
x = √26 244 x =
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 G © EAA
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