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Question
Free-Standing Mathematics Qualification
Foundation Level
June 2013
Mark
1
2
3
Using Spatial Techniques
4982
5
Unit 2
Friday 17 May 2013
4
6
9.00 am to 10.00 am
7
For this paper you must have:
*
a clean copy of the Data Sheet (enclosed)
*
a calculator
*
a pair of compasses
*
a protractor
*
a ruler.
8
9
10
TOTAL
Time allowed
*
1 hour
Instructions
*
Use black ink or black ball-point pen. Pencil should only be used for
drawing.
*
Fill in the boxes at the top of this page.
*
Answer all questions.
*
You must answer the questions in the spaces provided. Do not write
outside the box around each page.
*
Do all rough work in this book. Cross through any work that you do
not want to be marked.
*
You may not refer to the copy of the Data Sheet that was available
prior to this examination. A clean copy is enclosed for your use.
Information
*
The marks for questions are shown in brackets.
*
The maximum mark for this paper is 40.
*
You are expected to use a calculator where appropriate.
Advice
*
In all calculations, show clearly how you work out your answer.
(JUN13498201)
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4982
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2
Section A
Answer all questions.
Answer each question in the space provided for that question.
Use Wooden puzzle on page 2 of the Data Sheet.
1
For each shape in the table below, state:
1 (a)
the order of rotational symmetry;
(2 marks)
1 (b)
the number of lines of symmetry.
(2 marks)
Shape
Name
Order of rotational
symmetry
Number of lines of
symmetry
square
rhombus
4
2
One of the angles of this isosceles triangle is a right angle.
Calculate the size of the other two angles in this triangle.
You must show your working.
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Answer...........................................................................
(2 marks)
2
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3
3 (a)
The diagram below shows a square and eight triangles arranged in a pattern.
3 (a) (i)
Shade four triangles so that the pattern has rotational symmetry of order 4.
(1 mark)
3 (a) (ii) How many lines of symmetry does your pattern have?
Answer...........................................................................
(1 mark)
3 (b)
A square and two triangles can be arranged to give this quadrilateral.
Write down the mathematical name of this quadrilateral.
Answer...........................................................................
(1 mark)
3
s
(03)
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4
Section B
Answer all questions.
Answer each question in the space provided for that question.
Use Security guard on page 3 of the Data Sheet.
4
The diagram is a plan of the office block drawn to a scale of 1 : 500 .
D
x
C
office block
B
A
4 (a)
Measure angle x.
Answer x ¼ ..................................................................
(1 mark)
4 (b) (i)
Measure the length AB on the diagram.
Give your answer in centimetres.
Answer...........................................................................
(1 mark)
4 (b) (ii) Calculate the length of side AB of the actual office block.
Give your answer in metres.
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Answer...........................................................................
(3 marks)
5
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5
5
The diagram below shows the workshop and car park.
car park
y
workshop
The security guard walks across the car park along the bisector of angle y.
Using a pencil, ruler and a pair of compasses only, construct the bisector of
angle y on the diagram above. Show ALL your construction lines.
(3 marks)
3
6
The diagram shows the dimensions of the boundary fence.
48 m
46 m
Calculate the perimeter.
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Answer...........................................................................
(2 marks)
2
s
(05)
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6
Section C
Answer all questions.
Answer each question in the space provided for that question.
Use Cans on page 3 of the Data Sheet.
7
The diameter of a cylindrical can is 8.6 cm.
8.6 cm
Not to scale
7 (a)
Calculate the circumference of the circular base.
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.............................................................................................................................................
Answer...........................................................................
(2 marks)
7 (b)
The label for the can is just long enough to go around the can.
The ends of the label do not overlap.
The height of the label is 4 cm.
Use your answer to part (a) to find the area of the label.
Not to scale
label
4 cm
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Answer...........................................................................
(2 marks)
4
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7
8
The diagram shows the dimensions of another can.
Not to scale
10.2 cm
7.4 cm
8 (a)
Calculate the area of the circular base of this can.
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Answer...........................................................................
(3 marks)
8 (b)
Calculate the volume of this can.
State the units of your answer.
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Answer...........................................................................
(3 marks)
6
s
(07)
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8
Section D
Answer all questions.
Answer each question in the space provided for that question.
Use Bird boxes on page 4 of the Data Sheet.
9
The diagram below shows the dimensions of one bird box.
The front of the bird box has one line of symmetry.
The circular hole has radius 1.4 cm and its centre is 13.8 cm above the base.
1.4 cm
10.4 cm
Not to scale
1.4 cm
1.4 cm
22 cm
17 cm
13.8 cm
15 cm
16 cm
On the page opposite, draw an accurate front elevation of the bird box from the
direction of the arrow.
Use a scale of 1 : 2 .
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Space for working
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(6 marks)
6
s
(09)
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10
10
The diagram below shows the dimensions of the back of the bird box.
Not to scale
22 cm
17 cm
16 cm
Calculate the area of the back of the bird box.
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Answer...........................................................................
(5 marks)
5
END OF QUESTIONS
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