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Edexcel GCSE
Mathematics A
Paper 2 (Calculator)
Higher Tier
Friday 14 June 2013 Morning
Time: 1 hour 45 minutes
Paper Reference
1MA0/2H
You must have: Ruler graduated in centimetres and millimetres,
protractor, pair of compasses, pen, HB pencil, eraser, calculator.
Tracing paper may be used.
Total Marks
Instructions
black ink or ball-point pen.
t Use
in the boxes at the top of this page with your name,
t Fill
centre number and candidate number.
all questions.
t Answer
the questions in the spaces provided
t Answer
there may be more space than you need.
may be used.
t IfCalculators
your calculator does not have a button, take the value of to be
t 3.142
unless the question instructs otherwise.
Information
The total mark for this paper is 100
t The
for each question are shown in brackets
t usemarks
this as a guide as to how much time to spend on each question.
Questions labelled with an asterisk (*) are ones where the quality of your
t written
communication will be assessed.
Advice
each question carefully before you start to answer it.
t Read
an eye on the time.
t Keep
Try
to
every question.
t Checkanswer
t your answers if you have time at the end.
P43600A
2013 Pearson Education Ltd.
6/5/5/
*P43600A0128*
Turn over
GCSE Mathematics 1MA0
Formulae: Higher Tier
You must not write on this formulae page.
Anything you write on this formulae page will gain NO credit.
Volume of prism = area of cross section length
Area of trapezium =
1
(a + b)h
2
a
cross
section
h
b
lengt
Volume of sphere =
4 3
3
Volume of cone =
Surface area of sphere = 4 2
1 2
h
3
Curved surface area of cone =
r
l
h
r
In any triangle ABC
The Quadratic Equation
The solutions of ax2 + bx + c = 0
where 0, are given by
C
b
A
Sine Rule
x=
B
b (b 2 4ac)
2a
a
b
c
=
=
sin A sin B sin C
Cosine Rule a2 = b2 + c 2 2bc cos A
Area of triangle =
1
ab sin C
2
*P43600A0228*
Answer ALL questions.
Write your answers in the spaces provided.
You must write down all stages in your working.
1
Here is a cuboid.
Diagram NOT
accurately drawn
1.5 cm
1.5 cm
6 cm
The cuboid is 6 cm by 1.5 cm by 1.5 cm.
Work out the total surface area of the cuboid.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . .
cm2
(Total for Question 1 is 3 marks)
*P43600A0328*
Turn over
*2 Here is a list of ingredients for making 18 mince pies.
Ingredients for 18 mince pies
225 g of butter
350 g of flour
100 g of sugar
280 g of mincemeat
1 egg
Elaine wants to make 45 mince pies.
Elaine has
1 kg of butter
1 kg of flour
500 g of sugar
600 g of mincemeat
6 eggs
Does Elaine have enough of each ingredient to make 45 mince pies?
You must show clearly how you got your answer.
(Total for Question 2 is 4 marks)
*P43600A0428*
The scatter graph shows some information about 10 cars, of the same type and make.
The graph shows the age (years) and the value () of each car.
10000
8000
6000
value ()
4000
2000
2
3
age (years)
The table shows the age and the value of two other cars of the same type and make.
age (years)
value ()
3.5
8200
5000
(a) On the scatter graph, plot the information from the table.
(1)
(b) Describe the relationship between the age and the value of the cars.
. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
A car of the same type and make is 2
1
years old.
2
(c) Estimate the value of the car.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 3 is 4 marks)
*P43600A0528*
Turn over
Rhiana plays a game.
The probability that she will lose the game is 0.32
The probability that she will draw the game is 0.05
Rhiana is going to play the game 200 times.
Work out an estimate for the number of times Rhiana will win the game.
..............................................
(Total for Question 4 is 3 marks)
*P43600A0628*
Mason is doing a survey to find out how many magazines people buy.
He uses this question on his questionnaire.
How many magazines do you buy?
0 to 4
4 to 8
8 to 12
(a) Write down two things wrong with this question.
1
. . . . . . ............................................................................................ . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . ............................... ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . ............................................................................................ . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . ............................... ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(b) Write a better question for Mason to use on his questionnaire to find out how many
magazines people buy.
(2)
Mason asks his friends at school to do his questionnaire.
This may not be a good sample to use.
(c) Give one reason why.
. . . . . . . . . . . ........................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . ........................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . ........................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 5 is 5 marks)
*P43600A0728*
Turn over
Tame Valley is a company that makes yoghurt.
A machine fills trays of 20 pots with yoghurt.
In one hour, the machine fills a total of 15000 pots.
Work out how many seconds the machine takes to fill each tray of 20 pots.
.................................................................
(Total for Question 6 is 4 marks)
*P43600A0828*
seconds
Colin, Dave and Emma share some money.
3
Colin gets
of the money.
10
Emma and Dave share the rest of the money in the ratio 3 : 2
What is Daves share of the money?
.................................................................
(Total for Question 7 is 4 marks)
*P43600A0928*
Turn over
The diagram shows the plan of a playground.
80 m
Diagram NOT
accurately drawn
30 m
60 m
50 m
40 m
Bill is going to cover the playground with tarmac.
It costs 2.56 to cover each square metre with tarmac.
Work out the total cost of the tarmac Bill needs.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 8 is 4 marks)
10
*P43600A01028*
9
C
R
B
Diagram NOT
accurately drawn
35q
A
x
Q
P
ABC, PQR and AQD are straight lines.
ABC is parallel to PQR.
Angle BAQ = 35q
Angle BQA = 90q
Work out the size of the angle marked x.
Give reasons for each stage of your working.
x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .
(Total for Question 9 is 4 marks)
*P43600A01128*
11
Turn over
10 The equation
x3 + 2x = 110
has a solution between 4 and 5
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show ALL your working.
x = ..............................................
(Total for Question 10 is 4 marks)
12
*P43600A01228*
11 XYZ is a right-angled triangle.
X
Diagram NOT
accurately drawn
1.35 m
Y
3.25 m
Calculate the length of XZ.
Give your answer correct to 3 significant figures.
..............................................
(Total for Question 11 is 3 marks)
*P43600A01328*
13
Turn over
12 (a) Solve 3(x 2) = x + 7
x = ..............................................
(3)
(b) Solve
2 y
=1
5
y = ..............................................
(2)
(Total for Question 12 is 5 marks)
14
*P43600A01428*
13
y
B (7, 5)
Diagram NOT
accurately drawn
A (1, 2)
A is the point (1, 2)
B is the point (7, 5)
(a) Find the coordinates of the midpoint of AB.
(................................ , ............. . . . . . . . . . . . . . . . . . . . )
(2)
P is the point (4, 4)
Q is the point (1, 5)
(b) Find the gradient of PQ.
..............................................
(2)
(Total for Question 13 is 4 marks)
*P43600A01528*
15
Turn over
*14 Viv wants to invest 2000 for 2 years in the same bank.
The International Bank
The Friendly Bank
Compound Interest
Compound Interest
4% for the first year
1% for each extra year
5% for the first year
0.5% for each extra year
At the end of 2 years, Viv wants to have as much money as possible.
Which bank should she invest her 2000 in?
(Total for Question 14 is 4 marks)
16
*P43600A01628*
15 (a) Complete the table of values for y = x2 2x
x
(2)
(b) On the grid, draw the graph of y = x2 2x for values of x from 2 to 4
y
10
8
6
4
2
2
2
4
(2)
(c) Solve x2 2x 2 = 1
.................................................................
(2)
(Total for Question 15 is 6 marks)
*P43600A01728*
17
Turn over
*16
Diagram NOT
accurately drawn
S
O
x
32q
P
T
S and T are points on the circumference of a circle, centre O.
PT is a tangent to the circle.
SOP is a straight line.
Angle OPT = 32q
Work out the size of the angle marked x.
Give reasons for your answer.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .
(Total for Question 16 is 5 marks)
18
*P43600A01828*
17 Some girls did a sponsored swim to raise money for charity.
The table shows information about the amounts of money () the girls raised.
Least amount of money ()
10
Greatest amount of money ()
45
Median
25
Lower quartile
16
Upper quartile
42
(a) On the grid, draw a box plot for the information in the table.
10
20
30
40
Amount of money ()
50
60
(2)
Some boys also did the sponsored swim.
The box plot shows information about the amounts of money () the boys raised.
10
20
30
40
Amount of money ()
50
60
(b) Compare the amounts of money the girls raised with the amounts of money the boys
raised.
. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 17 is 4 marks)
*P43600A01928*
19
Turn over
18 Make p the subject of the formula
y = 3p2 4
.................................................................
(Total for Question 18 is 3 marks)
19 (a) Factorise
6 + 9x
.................................................................
(1)
(b) Factorise
y2 16
.................................................................
(1)
(c) Factorise
2p2 p 10
.................................................................
(2)
(Total for Question 19 is 4 marks)
20
*P43600A02028*
*20 The diagram shows a ladder leaning against a vertical wall.
Diagram NOT
accurately drawn
6m
y
2.25 m
The ladder stands on horizontal ground.
The length of the ladder is 6 m.
The bottom of the ladder is 2.25 m from the bottom of the wall.
A ladder is safe to use when the angle marked y is about 75q.
Is the ladder safe to use?
You must show all your working.
(Total for Question 20 is 3 marks)
*P43600A02128*
21
Turn over
21 In Holborn School there are
460 students in Key Stage 3
320 students in Key Stage 4
165 students in Key Stage 5
Nimer is carrying out a survey.
He needs a sample of 100 students stratified by Key Stage.
Work out the number of students from Key Stage 3 there should be in the sample.
.................................................................
(Total for Question 21 is 2 marks)
22 h is inversely proportional to the square of .
When = 5, h = 3.4
Find the value of h when = 8
h = .................................................................
(Total for Question 22 is 3 marks)
22
*P43600A02228*
23 Dan does an experiment to find the value of .
He measures the circumference and the diameter of a circle.
He measures the circumference, C, as 170 mm to the nearest millimetre.
He measures the diameter, d, as 54 mm to the nearest millimetre.
Dan uses =
C
d
Calculate the upper bound and the lower bound for Dans value of .
upper bound = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
lower bound = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 23 is 4 marks)
*P43600A02328*
23
Turn over
24 ABC is a triangle.
A
6 cm
Diagram NOT
accurately drawn
7 cm
60q
C
(a) Work out the area of triangle ABC.
Give your answer correct to 3 significant figures.
.................................................................
cm2
(2)
(b) Work out the length of the side AB.
Give your answer correct to 3 significant figures.
.................................................................
(3)
(Total for Question 24 is 5 marks)
24
*P43600A02428*
cm
25 Solve the simultaneous equations
x2 + y2 = 9
x+y =2
Give your answers correct to 2 decimal places.
x = .............................................. y = ..............................................
or x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . y = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 25 is 6 marks)
TOTAL FOR PAPER IS 100 MARKS
*P43600A02528*
25
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26
*P43600A02628*
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*P43600A02728*
27
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28
*P43600A02828*
