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PP1/43603H
General Certificate of Secondary EducationHigher Tier
GCSE Mathematics
Unit 3 Higher Tier
Practice Paper Set 1 Specification 4360
Time allowed 1 hour 30 minutes
Instructions Use black ink or black ball-point pen. Draw diagrams in pencil. Fill in the boxes at the top of this page. Answer all questions. You must answer the questions in the space provided. Do not write outside the
box around each page or on blank pages. Do all rough work in this book. Cross through any work that you do not want to
be marked. If your calculator does not have a button, take the value of to be
3.14 unless another value is given in the question.
Information The marks for questions are shown in brackets. The maximum mark for this paper is 80. The quality of your written communication is specifically assessed
in questions 4 and 9 and 17.These questions are indicated with an asterisk ()
You may ask for more answer paper and graph paper.These must be tagged securely to this answer booklet.
Advice In all calculations, show clearly how you work out your answer.
43603H
H
Practice Paper Set 1/43603H
For Examiner’s Use
Examiner’s Initials
Pages Mark
3
4 - 5
6 - 7
8 - 9
10 - 11
12 - 13
14 - 15
16 - 17
18 - 19
20 - 21
22
TOTAL
For this paper you must have:
mathematical instruments.
You may use a calculator
PP1/43603H
Volume of prism = area of cross-section × length
Area of trapezium =2
1(a + b)h h
a
b
length
cross-section
Formulae Sheet: Higher Tier
Volume of sphere =3
4r3
Surface area of sphere = 4r2
r
r
hl
Volume of cone =3
1r2 h
Curved surface area of cone = r l
In any triangle ABC
Area of triangle =2
1ab sin C
Sine ruleA
a
sin=
B
b
sin=
C
c
sin
Cosine rule a2= b2
+ c2– 2bc cos A
The Quadratic Equation
The solutions of ax2+ bx + c = 0, where a 0, are given by
x =a
acbb
2
)4_(_ 2±
A B
C
ab
c
3
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PP1/43603H
Answer all questions in the spaces provided.
1 Calculate the circumference of a circle with a diameter of 9 cm.
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Answer ................................................................. cm (2 marks)
2 Here are an expression, an equation, a formula and an identity
Write down which is which
3x + 8 = 5 ................................................................
3(x + 5) 3x +15 ................................................................
P = 2l + 2w .................................................................
15x – 7y .................................................................. (3 marks)
Do not writeoutside the
box
5
Not drawnaccurately
9cm
4
PP1/43603H
3 Shapes are made from squares and semi-circles.
For example
The area of a square is S.
The area of a semi-circle is D.
The shape has an area of S + D.
The shape has an area of S – D.
3 (a) Use a diagram to show that 2D is less than S.
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(1 mark)
5
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PP1/43603H
3 (b) Write down the shaded area of these shapes in terms of S and D.
Give your answers in their simplest form.
3 (b) (i)
Answer .................................................................... (2 marks)
3 (b) (ii)
Answer...................................................................... (2 marks)
Do not writeoutside the
box
5
6
PP1/43603H
4 Five footpaths meet at O.
D is due South of O.
4 (a) (i) Kate is at O and walks towards B.
On what bearing does she walk?
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Answer ................................................................... ° (2 marks)
4 (a) (ii) Ben is at B and walks to meet Kate.
On what bearing does he walk?
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Answer ................................................................... ° (2 marks)
4 (b) Frank is walking from A to O.
When he gets to O what angle clockwise does he need to turn through to continue to C?
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Answer ................................................................... ° (2 marks)
Do not writeoutside the
box
N
Not drawnaccurately
80°
60°40°
O
AB
E
D
C
N
7
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PP1/43603H
5 Sally is buying a radiator for her bedroom.
The room is 2.4 metres high.
Plan View
You can work out the heat output in Watts (W) of a radiator in a room using this formula.
.
Heat output (W) = Volume in cubic metres × 42
This table shows heat output and cost of radiators.
Radiator Heat output(W)
Cost (£)
A 1070 200
B 1148 215
C 1365 220
D 1404 230
E 1638 245
Work out the cost of the most suitable radiator.
You must show your working.
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Answer £.....………………….…….…..(5 marks)
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box
4.2m
3.1m
Not drawnaccurately
11
8
PP1/43603H
6 (a) Complete the table for the quadratic equation y = x2 + 2xfor x values from –4 to 3
x –4 –3 –2 –1 0 1 2 3
y 8 0 –1 0 3 8
(2 marks)
6 (b) Use the table to complete the graph of y = x2 + 2x for –4 x 3
(2 marks)
6 (c) Use the graph to find the value of y when x = 1.5
Answer ............................................................................. (1 mark)
Do not writeoutside the
box
y
x
9
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PP1/43603H
7 Use ruler and compasses only.
Show all construction lines and arcs.
7 (a) Construct the perpendicular bisector of AB.
(2 marks)
7 (b) Construct the angle bisector of the angle XYZ.
(2 marks)
Do not writeoutside the
box
X
Y
Z
A
B
9
10
PP1/43603H
8 The diagram shows an isosceles trapezium.
8 (a) Work out the value of x.
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Answer ......................................................... degrees (1 mark)
8 (b) Work out the area of the trapezium.
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Answer .............................................................. cm2
(2 marks)
Do not writeoutside the
box
10 cm
14cm
7.5cm
x
75°
Not drawnaccurately
11
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PP1/43603H
8 (c) Some of these trapeziums are put together to make a regular shape.
The diagram below is incomplete.
How many exterior sides does the shape have?
You must show your working
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Answer ...................................................................... (3 marks)
Not drawn
accurately
Do not writeoutside the
box
6
Not drawnaccurately
12
PP1/43603H
9 Use trial and improvement to find the solution to the equation
x3 + 2x = 56
Give your answer to 1 decimal place.
x x3 + 2x Comment
3 33 Too low
Answer x = ................................................................ (4 marks)
13
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PP1/43603H
10 ABCD is a quadrilateral.
Angles A and B are in the ratio 1 : 2
Angle C is 30 more than angle B.
Angle D is a right angle.
Work out the size of angles A,B and C
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angle A……………….degrees
angle B……………….degrees
angle C……………….degrees (4 marks)
Do not writeoutside the
box
Not drawnaccurately
A
DC
B
8
14
PP1/43603H
11 Two radio stations at A and B pick up a distress call from a boat at sea.
The station at A can tell that the boat is between 60 km and 80 km from A.
The station at B can tell that the boat is between a bearing of 050° and 060° from B.
Show clearly, using compasses and a protractor, the region where the boat will befound.
(3 marks)
Do not writeoutside the
box
SEA
LAND
N
A
B
Scale: 1cm represents 10 km.N
15
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12 Calculate the size of angle x.
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Answer ....................................................... degrees (3 marks)
Turn over for the next question
Not drawnaccurately
10cm
4 cm
x
6
16
PP1/43603H
13 Two rectangles have the following dimensions
Perimeter equals 21 cm Perimeter equals 43 cm
Work out x and y
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x = ………… y = …………… (3 marks)
14 Solve the equation 2x2– 5x – 5 = 0
Give your answers to 2 decimal places.
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Answers .................................................................... (3 marks)
Do not writeoutside the
box
2y
3x
6y
5x
17
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PP1/43603H
15 1000 bacteria are put into a Petri dish.
After 1 hour there are 2000 bacteria in the dish.
The bacteria continue to double in quantity every hour.
15(a) Draw a fully labelled graph to show the number of bacteria in the dish for the first 4 hours.
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(3 marks)
15(b) How many bacteria will be in the dish after 12 hours?
Show your working.
Give your answer to an appropriate degree of accuracy.
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Answer ..................................................................... (3 marks)
Do not writeoutside the
box
0 1 2 3 4Hours after start
Number ofbacteria
12
18
PP1/43603H
16 Fred is marking a sector of a circle on a sports field as shown.
He puts tape around the perimeter.
Tape comes in 3 metre rolls.
How many rolls does he need?
You must show your working.
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Answer ................................................................ (5 marks)
Do not writeoutside the
box
40 m
50°
A
B CNot drawnaccurately
19
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PP1/43603H
Turn over for the next question
5
20
PP1/43603H
17 (a) Here is a circle with centre O.
Write down the value of x.
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Answer ......................................................... degrees (1 mark)
17(b) Here is a different circle.
Write down the value of y.
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Answer ......................................................... degrees (1 mark)
Do not writeoutside the
box
Not drawnaccurately
OB
x
104°
Not drawnaccurately
40°
28°
y
21
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PP1/43603H
17(c) ABCD is a cyclic quadrilateral within a circle centre O.
XY is the tangent to the circle at A.
Angle XAB = 58°
Angle BAD = 78°
Angle DBC = 34°
Prove that AB is parallel to CD.
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(5 marks)
Do not writeoutside the
box
Not drawnaccurately
B
C
D
YX
A
34°
78°58°
7
22
PP1/43603H
18 ABCD is a quadrilateral.
AB = 7cm, BC = 8cm and CD = 6cm
Angle ABC = 80° and angle ADC = 90°
Work out the area of the quadrilateral ABCD.
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Answer ................................................................ cm2
(6 marks)
END OF QUESTIONS
Do not writeoutside the
box
6
7 cm
PP1/43603H
There are no questions printed on this page
DO NOT WRITE ON THIS PAGEANSWER IN THE SPACES PROVIDED
PP1/43603H
There are no questions printed on this page
DO NOT WRITE ON THIS PAGEANSWER IN THE SPACES PROVIDED
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