BBC bitesize non calculator (higher)

Maths exam calculator (higher)

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GCSE BITESIZE examinations
General Certificate of Secondary Education
Specimen paper
MATHEMATICS
HIGHER TIER
©2005
Paper 1 Non-calculator
Time allowed: 2 hours
You must not use a calculator.
Answer all questions in the space provided.
Mark allocations are shown in brackets.
The maximum mark for this paper is 99.
Show clearly how you work out your answer.
In addition to this paper, you will require:
- mathematical instruments
1

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Formula sheet: Higher Tier
You may use the following formulas:
Volume of prism = area of cross section × length
4
Volume of sphere = r³
3
Surface area of sphere = 4 r²
1
Volume of cone = r²h
3
Curved surface area of cone = rl
In any triangle ABC
1
Area of triangle = ab sin C
2
a b c
Sine rule = =
sin A sin B sin C
Cosine rule a² = b² + c² -2bc cos A
The…read more

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Answer all questions in the spaces provided.
1. (a) Give prime factorisations of 432 and 522.
432 = .......................................
522 = ....................................... (1 mark)
(b) Hence, or otherwise, find the Highest Common Factor of 432 and 522'
HCF = ....................................... (2 marks)
2. The diameter AB of the circle is 10cm. The
length of BC is 6cm. Calculate the length of
AC.
AC = ..............................…read more

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State the nth term of each of the following sequences:
(i) 3, 7, 11, 15, 19, ....
Answer:................................................................ (1 mark)
1 1 1 1
(ii) 1, , , , , ...
4 9 16 25
Answer:................................................................ (1 mark)
(iii) 4, 7, 12, 19, 28......
Answer:.............................................................. (1 mark)
(b) Given that u n = 5u n -1 + 1 and that u1 = 3 , find the value of u 4
Answer:....................................................................... .…read more

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Sketch the net of a triangular-based pyramid. (2 marks)
(b) Here are the plan, front elevation and side elevation of a 3-D shape:
Draw a sketch of the 3-D shape.…read more

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Write as a decimal.
8
Answer:....................................................................... . (1 mark)
(b) Write as a fraction in its lowest terms.
Show all your working.
Answer:....................................................................... .…read more

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Factorise fully 3a 3 b + 12a 2 b 2 + 9a 5 b 3
................................................................................. (1 mark)
(b) Give the value of x when 2 x 2 - x - 6 = 0
................................................................................. (2 marks)
3x + 2
(c) Solve the equation +3= 4
x -1
.................................................................................…read more

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The histogram shows the price distribution of houses in an area of Manchester.
Prices are given in thousands of pounds (to the nearest thousand).
Price
0 x < 100 100 x <250 250 x <300 300 x <350 350 x <500
£(x)000s
Frequency 60
(a) Add a bar to the histogram showing the frequency density for the interval
350-499. (2 marks)
(b) Complete the table above, showing the frequencies for each interval.…read more

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Using a ruler and compasses only, and making sure you leave all construction
lines visible:
(a) Construct a triangle of side lengths 4cm, 5cm and 6cm (2 marks)
(b). Construct a square of side length 5cm.…read more

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Enlarge shape A with a scale factor of -½, centre O. (2 marks)
10. (a) Solve the inequality 5 x + 3 3 x - 6
................................................................................. (1 mark)
(b) Given that x is an integer and - 3 < x + 1 4 list the possible values of x .
................................................................................. (1 mark)
(c) Find all possible integer values of y that satisfy the inequality:
3- y
-2 <3
2
.................................................................................…read more

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