Name
Class
For Edexcel GCSE
Mathematics
Paper 2A (Calculator)
Higher Tier
Time : 1 hour 45 minutes
Total Marks
You must have:
Ruler, protractor, compasses, pen, pencil, eraser, calculator.
Instructions and Information
•
•
•
•
•
•
Write your name in the box at the top of the page.
Answer all the questions in the spaces provided.
The total mark for this paper is 100.
The marks for each question are shown in brackets.
Calculators may be used.
If your calculator does not have a  button, take the value of
 to be 3.142 unless the question instructs otherwise.
• Questions labelled with an asterisk (*) are ones where the
quality of your written communication will be assessed.
Advice
•
•
•
•
Read each question carefully before you start to answer it.
Keep an eye on the time.
Try to answer every question.
Check your answers if you have time at the end.
Written by Shaun Armstrong
Only to be copied for use in the purchaser's school or college
2012 EHA Paper 2 Page 1
© Churchill Maths Limited
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GCSE Mathematics
Formulae: Higher Tier
You must not write on this formulae page.
Volume of prism = area of cross section × length
Area of trapezium =
1
2
(a + b)h
a
h
cross
section
th
leng
b
4
1
Volume of sphere = 3 πr3
Surface area of sphere = 4πr2
Volume of cone = 3 πr2h
Curved surface area of cone = πrl
r
l
h
r
In any triangle ABC
The Quadratic Equation
The solutions of ax2 + bx + c = 0
where a ≠ 0, are given by
C
a
b
A
Sine Rule
c
x=
B
a
b
c
=
=
sin A
sin B
sin C
Cosine Rule a2 = b2 + c2 – 2bc cos A
Area of triangle =
1
2
ab sin C
2012 EHA Paper 2 Page 2
© Churchill Maths Limited
−b± b2−4 ac 
2a
Answer ALL questions.
Write your answers in the spaces provided.
You must write down all stages in your working.
1
Eight 5p coins weigh 26 g.
Work out the weight of three 5p coins.
…………………………… g
(Total for Question 1 is 2 marks)
2
(a)
A bag of potatoes weighs 2 kg.
Approximately how much does the bag weigh in pounds?
(1)
………………………… pounds
(b)
Which of these distances is the largest?
8 centimetres
3 inches
82 millimetres
Explain your answer.
(2)
………………………………
(Total for Question 2 is 3 marks)
2012 EHA Paper 2 Page 3
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3
Martin and Badri are plumbers.
Martin charges a £25 call-out fee and £20 per hour of work.
Badri doesn't charge a call out fee but charges £30 per hour of work.
(a)
Calculate how much less Badri charges for a 1 hour job.
(2)
£ ……………………………
The total charge (£C) for a job taking t hours is shown on the graph below for each
plumber.
Badri
Martin
100
Total cost
(£C)
80
60
40
20
O
1
2
3
4
Time at job (t hours)
The total that Martin charges is given by the formula C = 25  20t
(b)
Write down a formula for the total that Badri charges.
(1)
………………………………
2012 EHA Paper 2 Page 4
© Churchill Maths Limited
(c)
Write down the value of t at the point where the two graphs intersect.
(1)
t = ……………………………
(d)
Explain how your answer to part (c) is useful to someone choosing between
Martin and Badri to do a plumbing job.
(1)
……………………………………………………………………………………………
……………………………………………………………………………………………
(Total for Question 3 is 5 marks)
*4
Fran wants to save up £75 before she goes on holiday on the 19th June.
She starts saving 50p a day on the 1st April.
On 16th April she increases the amount she saves each day to 80p.
On 12th May Fran increases the amount again to £1.20
On 18th June, after adding £1.20 for the day, she counts her savings.
Has Fran reached her target?
Show how you decide.
………………………………
(Total for Question 4 is 4 marks)
2012 EHA Paper 2 Page 5
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5
Dhakwan has an empty metal barrel.
The barrel is in the shape of a cylinder.
The height of the barrel is 1.2 m.
The diameter of the base of the barrel is 80 cm.
1.2 m
Dhakwan fills the barrel with water from a tap.
The tap fills the barrel at the rate of 1 litre per second.
Find how long it takes to fill the barrel.
Give your answer to the nearest minute.
80 cm
………………………… minutes
(Total for Question 5 is 5 marks)
2012 EHA Paper 2 Page 6
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6
On the grid, draw the graph of y = x2 + 3
y
12
11
10
9
8
7
6
5
4
3
2
1
–4
–3
–2
–1 O
1
2
3
4
x
(Total for Question 6 is 4 marks)
2012 EHA Paper 2 Page 7
© Churchill Maths Limited
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7
Samaira asked 10 families in different towns to record the maximum temperature each
day in January.
She then worked out the mean of these maximum temperatures.
Samaira also asked the families how much they spent on gas in January.
The scatter graph shows her results.
40
Cost of
Gas Used
(£)
35
30
25
20
0
(a)
2
4
6
8
Mean Maximum Temperature (ºC)
10
What type of correlation does this scatter graph show?
(1)
………………………………
(b)
Draw a line of best fit on the scatter graph.
(1)
(c)
The mean maximum temperature in January in Ullapool was 0.4ºC.
Explain why it might not be sensible to use your line of best fit to estimate the
cost of the gas used by a family living in Ullapool.
(1)
……………………………………………………………………………………………
……………………………………………………………………………………………
2012 EHA Paper 2 Page 8
© Churchill Maths Limited
The table below summarises the maximum temperature for each day in January where
Samaira lives.
* (d)
Maximum
Temperature (ºC)
Number
of days
3
3
4
6
5
10
6
7
7
4
8
1
Estimate the cost of gas used by Samaira's family in January.
(4)
£ ……………………………
(Total for Question 7 is 7 marks)
2012 EHA Paper 2 Page 9
© Churchill Maths Limited
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8
(a)
Diagram NOT
accurately drawn
xº
32º
The shape in the diagram above is made up of six identical isosceles triangles.
Work out the value of x.
(3)
x = ……………………………
(b)
Diagram NOT
accurately drawn
yº
The diagram shows four sides of a regular polygon.
A dotted line is drawn between two of the vertices of the polygon.
Find, in terms of y, an expression for the number of sides of the polygon.
(3)
………………………………
(Total for Question 8 is 6 marks)
2012 EHA Paper 2 Page 10
© Churchill Maths Limited
9
A film was shown seven times over one weekend at a cinema with 120 seats.
The number of tickets sold for five of the showings were
69
106
51
89
72
The median number of tickets sold was 78.
The mean number of tickets sold was 81.
Work out how many tickets were sold at the other two showings of the film.
………………………………
and ………………………………
(Total for Question 9 is 3 marks)
10
(a)
Convert 0. 6̇ to a fraction.
(1)
………………………………
(b)
Write the reciprocal of 50 as a decimal.
(1)
………………………………
(c)
Work out the difference between
1
80
and 8 × 10 –3.
(2)
………………………………
(Total for Question 10 is 4 marks)
2012 EHA Paper 2 Page 11
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11
Hafid is playing darts.
He needs a score of 19 followed by a score of 20 to win a game of round-the-clock.
The probability that he will score 19 with his first dart is 0.3
The probability that he will score 20 with his second dart is 0.4
(a)
What is the probability that he does not score 19 with his first dart?
(1)
………………………………
(b)
What is the probability that he gets a score of 19 followed by a score of 20?
(2)
………………………………
(Total for Question 11 is 3 marks)
12
A new company had sales of £25 000 in total in its first two years.
The ratio of sales in its first year to its second year was 2 : 3
The company's profit was £600 in the first year and £1200 in the second year.
Find the ratio of the company's profit as a percentage of sales in its first year to its
second year.
Give your answer in its simplest form.
………………………………
(Total for Question 12 is 5 marks)
2012 EHA Paper 2 Page 12
© Churchill Maths Limited
13
(a)
Solve
(i)
4p – 7 = 37
(2)
………………………………
(ii)
3(1 – 2y) = 15 – 4y
(3)
………………………………
* (b)
Anna orders 2 cups of coffee and 4 cups of tea.
She is charged £11.
When Anna looks at her receipt she sees that she's been charged for 4 cups of
coffee and 2 cups of tea.
The cost should have been £10 so she is refunded £1.
Work out the cost of a cup of coffee and the cost of a cup of tea.
(5)
Coffee £ …………………
Tea £ …………………
(Total for Question 13 is 10 marks)
2012 EHA Paper 2 Page 13
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14
y
F
G
(5, 6, 0)
I
H
(5, 6, 4)
D
E
O
A
(0, 0, 8)
C
Diagram NOT
accurately drawn
B
z
x
The diagram shows a prism on a 3-dimensional grid.
The point D is the midpoint of BG.
(a)
Find the coordinates of the points
(i)
I,
(1)
( …… , …… , …… )
(ii)
D.
(2)
( …… , …… , …… )
1 unit on the grid represents 1 cm.
(b)
Work out the volume of the prism.
(3)
…………………………… cm3
(Total for Question 14 is 6 marks)
2012 EHA Paper 2 Page 14
© Churchill Maths Limited
15
(a)
Express
4
2
+
x−3
x−1
as a single fraction in its simplest form.
(3)
………………………………
(b)
Simplify fully
4x  6
2
4x −9
(3)
………………………………
(Total for Question 15 is 6 marks)
16
Nena wants to find out how much a taxi to the airport will cost.
The distance to the airport is 35 miles to the nearest 5 miles.
The cost will be £1.60 per mile to the nearest 10p.
What is the most that the taxi to the airport will cost?
£ ……………………………
(Total for Question 16 is 3 marks)
2012 EHA Paper 2 Page 15
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17
Just Clothes takes orders for its products on its website and from a catalogue.
The manager of the company wants to do a survey of 100 customers who have ordered
products in the last month.
The table gives some information about all 840 customers over the last month.
Website
Catalogue
Male
144
65
Female
348
283
The manager decides to use a sample stratified by gender and source of order.
* (a)
Write down two advantages of using a stratified sample.
(2)
First advantage ………………………………………………………………………….
……………………………………………………………………………………………
Second advantage ……………………………………………………………………….
……………………………………………………………………………………………
(b)
How many women who ordered from the catalogue should be in the sample.
(2)
………………………………
(Total for Question 17 is 4 marks)
2012 EHA Paper 2 Page 16
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18
Roger invested £2000 in a savings account.
The account paid 5% compound interest per year.
(a)
Work out how much was in the account after 3 years.
(3)
£ ……………………………
Lisa invested £400 in a different savings account.
The account paid x % compound interest per year.
(b)
Circle the expression below which gives the amount, in pounds, in the account
after 3 years.
(1)

x
1
100

 
3
x
100
× 400

3
× 400
100 − x
100

3
× 400
(Total for Question 18 is 4 marks)
19
(a)
Factorise fully
8pq – 16q3
(2)
………………………………
(b)
Find the positive solution to the equation
5x2 – 3x – 1 = 0
Give your answer correct to 3 significant figures.
(3)
………………………………
(Total for Question 19 is 5 marks)
2012 EHA Paper 2 Page 17
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20
Here are 10 letters printed on plastic tiles.
A
A
B
C
C
D
D
D
E
F
The tiles are put into a bag and two are picked out at random.
Work out the probability that the tiles picked out have the same letter on them.
Give your answer in its simplest form.
(Total for Question 20 is 4 marks)
2012 EHA Paper 2 Page 18
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21
A
Diagram NOT
accurately drawn
Q
N
100 km
A plane leaves an airport, A, and flies for 100 km on a bearing of 140º.
The plane then turns and flies on a bearing of 045º until it is due East of A.
The plane then flies directly back to A.
Work out the total distance travelled by the plane.
…………………………… km
(Total for Question 21 is 7 marks)
TOTAL FOR PAPER IS 100 MARKS
2012 EHA Paper 2 Page 19
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