# BBC bitesize GCSE calculator (higher)

maths exam, GCSE (higher) calculator

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GCSE BITESIZE examinations
General Certificate of Secondary Education
Specimen paper
MATHEMATICS
HIGHER TIER
Paper 2 Calculator
Time allowed: 1 hour 45 minutes
Answer all questions in the space provided.
Mark allocations are shown in brackets.
The maximum mark for this paper is 110.
Show clearly how you work out your answer.
In addition to this paper, you will require:
- calculator
- ruler graduated in centimetres and millimetres
- protractor
- compasses
- pen
- HB pencil
- eraser
- tracing paper (optional)
1

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### Page 2

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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

### Page 3

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Answer all questions in the spaces provided.
3.46 3 + 2.3 2 + 1
1. Calculate the value of + 3.6
2.7
Give your answer correct to 3 significant figures.
Answer:................................................................ ........... (3 marks)
2. Sam uses 140g of flour to make 12 cakes.
How much flour will Sam need to make 21 cakes?
Answer:................................................................ ......g (2 marks)
3. (a) Write the following in standard form:
(i) 156,700,000 = ...............................................
(ii) 0.000341 = .................................................. ..…read more

### Page 4

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Rearrange the following, making c the subject:
3c + b
=c+a
2
...................................................................................... (3 marks)
5. A ship sets off on a bearing of 072° from port a nd travels 3.4km in a straight
line. How far north of the ship's starting position is its final position? Give your
answer to 2 decimal places.
Port
.................................................................................km (3 marks)
6. Complete the following:
(a) 4m = ...............................................km (1 mark)
(b) 30 litres = ...............................................ml (1 mark)
(c) 8cm2 = ...............................................…read more

### Page 5

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A plasma screen television is being sold by two companies:
Plasma-4-U is charging £1599 including VAT.
Commercial Displays Limited is charging £1526 + VAT.
What is the difference in price to the customer (including VAT)?
[VAT is charged at 17.5%]
Answer: £................................................................ ...... (3 marks)
8. Simplify:
(a) (3 x 2 y 3 ) 3
Answer:................................................................ ....... (2 marks)
x 2 + 4x
(b) 2
x + 3x - 4

### Page 6

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The two box plots give data about the journey time from Birmingham to
Manchester of trains run by two different companies. Give a reason, supported
by the two different statistics, to suggest why one of the companies is better.
Journey time from London to Manchester
..........................................................................................(4 marks)
10. The dimensions of this rectangle are given correct to the nearest mm.
Calculate the greatest and least values for the area of the rectangle.
Greatest = ......................................... cm2 (2 marks)
Least = .........................................…read more

### Page 7

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The equation x 3 - x 2 = 40 has a solution between x = 3 and x = 4 .
Use trial and improvement to find the value of x , giving your answer correct to 1
decimal place. Show all your working.
Answer:................................................................ ........... (4 marks)
12. A bag contains 7 coloured marbles. 3 of them are red, and the remainder are
blue. Two marbles are removed from the bag, one at a time, replacing the first
marble before the second is drawn.…read more

### Page 8

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Find the midpoint and the length to 2 decimal places of the line AB, given that
A = (­2, 1) and B = (5, 3).
Midpoint............................................................................ (2 marks)
Length.............................................................................. (2 marks)
14. A javelin throw can be modelled as a triangle for training purposes. A trainer
suggests that if the thrower can get the javelin to fly 80m to its highest point,
then half as far coming down, a long throw will result.…read more

### Page 9

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Fill in the following table for the function: y = x 2 - 3 x - 3 (3 marks)
x -2 -1 0 1 2 3 4 5
y
(b) Plot the graph (2 marks)
(c) Find approximate solutions to x² - 3x - 3 = 0
.............................................................................. (3 marks)
(d) Find approximate solutions to x² - 3x - 3 = 3

### Page 10

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The table shows the probabilities of different weather, and the probability that
an ice-cream stall will make a profit on any given day.
(a) Given that all of the possibilities are shown, complete the table.
Ice-cream Weather
stall
Profit 0.78 Sunny 0.32
Break even 0.07 Dull
Loss Raining 0.18
(2 marks)
(b) Would it be reasonable to calculate the probability that on a given day it
was sunny and the ice-cream stall made a profit as 0.78 × 0.32? Justify