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Question
Free-Standing Mathematics Qualification
Higher Level
June 2013
Mark
1
2
3
Shape and Space
4985
5
Unit 5
Friday 17 May 2013
4
6
9.00 am to 10.15 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
11
12
Time allowed
*
1 hour 15 minutes
TOTAL
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 50.
*
You are expected to use a calculator where appropriate.
Advice
*
In all calculations, show clearly how you work out your answer.
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2
Section A
Answer all questions.
Answer each question in the space provided for that question.
Use Computer games on page 2 of the Data Sheet.
1
Two shapes used in computer games are shown below.
Shape A
1 (a) (i)
Shape B
State the order of rotational symmetry for Shape A.
Answer...........................................................................
(1 mark)
1 (a) (ii) Draw any lines of symmetry on Shape A.
(1 mark)
1 (b) (i)
State the order of rotational symmetry for Shape B.
Answer...........................................................................
(1 mark)
1 (b) (ii) Draw any lines of symmetry on Shape B.
(1 mark)
4
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2
Complete the diagram below by reflecting the given shape in the line AB.
A
B
(2 marks)
2
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3
A and B are similar shapes.
A
0.3 cm
1.4 cm
Not to scale
B
2.1 cm
The total width of Shape A is 1.4 cm.
The distance between the eyes in Shape A is 0.3 cm.
The total width of Shape B is 2.1 cm.
Find the distance between the eyes in Shape B.
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Answer...........................................................................
(3 marks)
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5
Section B
Answer all questions.
Answer each question in the space provided for that question.
Use Gardens on page 3 of the Data Sheet.
4
A scale diagram of a garden layout, using a scale of 1: 50, is shown below.
R
P
4 (a) (i)
Q
Measure the length PQ on the diagram in centimetres.
Answer...........................................................................
(1 mark)
4 (a) (ii) Calculate the length represented by PQ in the actual garden, in metres.
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Answer...........................................................................
(2 marks)
4 (b)
What is the size of angle PQR in the actual garden?
Answer...........................................................................
(1 mark)
4
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5
The flower bed shown below is made up of rectangles and semicircles.
It has two lines of symmetry.
Find the perimeter of the flower bed.
6m
2.6 m
1.8 m
Not to
scale
1.5 m
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Answer...........................................................................
(4 marks)
4
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6
ABCD is a square lawn.
The length of the diagonal AC is 25 feet 8 inches.
Reuben wants to mow the lawn with an electric lawnmower.
The lawnmower can reach a maximum distance of 8 m from the point A.
Use the following conversions to show that the lawnmower will reach every part of
the lawn:
1 foot ¼ 12 inches
1 inch ¼ 2.54 cm
D
A
25 ft 8 in
C
B
Answer
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(3 marks)
3
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A garden layout is shown below.
7
13 m
Q
P
4.6 m
7.2 m
S
Not to
scale
R
A
C
7 (a)
B
State the mathematical name of the shape PQRS.
Answer...........................................................................
(1 mark)
7 (b)
Find the area of PQRS.
State the units of your answer.
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Answer...........................................................................
(4 marks)
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7 (c)
In the triangle ABC, AC ¼ 5.2 m and BC ¼ 11.0 m.
These measurements are correct to the nearest 10 cm.
Find an upper bound for the length AB.
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Answer...........................................................................
(4 marks)
9
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8
A gardener, Sue, wants to cover a circular flower bed with an even layer of compost.
The radius of the flower bed is 2.8 m.
The thickness of the layer of compost is to be 2 cm.
2.8 m
8 (a)
Express 2 cm in metres.
Answer...........................................................................
(1 mark)
8 (b)
Sue has a bag containing 0.5 m3 of compost.
Is this enough compost to cover the whole flower bed?
You must show all your working.
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(3 marks)
4
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Turn over for the next question
DO NOT WRITE ON THIS PAGE
ANSWER IN THE SPACES PROVIDED
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12
Section C
Answer all questions.
Answer each question in the space provided for that question.
Use Bookcases on page 3 of the Data Sheet.
9
The
The
The
The
The
The
diagram below shows a bookcase with two vertical planes of symmetry.
bookcase is made of wood 2 cm thick.
base and the top of the bookcase stick out 1.5 cm at the sides, front and back.
bookcase is 70 cm high, 28 cm deep and 80 cm wide.
top of the shelf is at a height of 40 cm above the ground.
bookcase is open at the back.
80
Not to
scale
2
2
All
measurements
in cm
2
2
70
40
1.5
28
1.5
2
On the opposite page, draw a side elevation of this bookcase viewed from the
direction shown by the arrow.
Make your drawing to a scale of 1: 5 and show all hidden detail.
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(5 marks)
5
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A point P and a line AB have been drawn below.
10
Using pencil, ruler and a pair of compasses only, construct a perpendicular
from P to line AB. Show all construction arcs clearly.
P
.
B
A
(3 marks)
3
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Section D
Answer all questions.
Answer each question in the space provided for that question.
Use Glasses on page 4 of the Data Sheet.
11
A cylindrical glass has a volume of 330 cm3 and a height of 12 cm.
The thickness of the glass can be ignored.
11 (a)
Find the area of the circular base of the glass.
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Answer...........................................................................
(2 marks)
11 (b)
Find the radius of the base of the glass.
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Answer...........................................................................
(3 marks)
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12
Not to scale
Glass A
Glass B
The two glasses shown here are similar in shape.
Glass B contains exactly twice as much liquid as Glass A when both are full.
The height of Glass A is 11.9 cm.
Explain, using suitable calculations, why the height of Glass B must be 15.0 cm
correct to three significant figures.
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(4 marks)
4
END OF QUESTIONS
ACKNOWLEDGEMENT OF COPYRIGHT-HOLDERS AND PUBLISHERS
Section D:
John Lewis
ª Thinkstock
Copyright ª 2013 AQA and its licensors. All rights reserved.
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