For AQA
General Certificate of Secondary Education
Mathematics
Paper 1A
Higher Tier
H
Non-calculator
For this paper you must have:
• mathematical instruments.
You must not use a calculator.
Time allowed
•
1 hour 30 minutes
Instructions, Information and Advice
•
•
•
•
Do not write on the question paper – use blank paper and the answer sheets provided.
The maximum mark for this paper is 70.
The quality of your written communication is specifically assessed in questions 3, 6 and 11.
These questions are indicated with an asterisk (*)
In all calculations, show clearly how you work out your answer.
Formulae: Higher Tier
Volume of prism = area of cross-section × length
Volume of sphere =
4 3
πr
3
Area of trapezium =
Volume of cone =
1
(a + b)h
2
1 2
πr h
3
Surface area of sphere = 4πr2
Curved surface area of cone = πr l
In any triangle ABC
1
Area of triangle =
ab sin C
2
a
b
c
Sine rule
=
=
sin A
sin B
sin C
The Quadratic Equation
Cosine rule a2 = b2 + c2 – 2cb cos A
x=
The solutions of ax2 + bx + c = 0,
where a ≠ 0, are given by
−b±  b 2−4ac 
2a
Written by Shaun Armstrong
Only to be copied for use in the purchaser's school or college
2012 AHA Paper 1 short Page 1
© Churchill Maths Limited
Answer all questions.
1
SIDE
FRONT
The diagram shows a prism.
The cross-section of the prism is a regular hexagon.
(a)
Sketch the front elevation of the prism from the direction shown.
(2 marks)
(b)
Sketch the side elevation of the prism from the direction shown.
(1 mark)
2
(a)
Simplify
2p – q + 3p + 4q
(2 marks)
(b)
Simplify
m9 ÷ m2
(1 mark)
(c)
Factorise fully
9xy2 – 6y3
(2 marks)
*3
Holly is carrying out a survey about healthy eating.
This is one of the questions.
How many pieces of fruit did you eat yesterday?
Tick one box
1 to 2
(a)
3 to 4
4 or more
Write down two criticisms of the response section for this question.
(2 marks)
Holly carries out her survey by asking her questions of several groups of people.
After asking each question, she goes round the group and records each person's
answer.
(b)
Give one reason why this is not a good survey method.
(1 mark)
2012 AHA Paper 1 short Page 2
© Churchill Maths Limited
4
(a)
xº
Not drawn
accurately
32º
The shape in the diagram above is made up of six identical isosceles triangles.
Work out the value of x.
(3 marks)
(b)
5
Use a ruler and pair of compasses to construct the bisector of the angle on the
answer sheets.
Leave in your constuction lines.
(2 marks)
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 marks)
The total charge (£C) for a job taking t hours is shown on the graph on the answer
sheets for each plumber.
The total that Badri charges is given by the formula C = 30t
(b)
Write down a formula for the total that Martin charges.
(2 marks)
(c)
Write down the value of t at the point where the two graphs intersect.
(1 mark)
(d)
*6
Explain how your answer to part (c) is useful to someone choosing between
Martin and Badri to do a plumbing job.
(1 mark)
3
Lanika needs a sheet of card that is at least 10 mm thick.
At home, she finds some card but she doesn't know how thick it is.
Lanika finds that there are 45 sheets of card with a total thickness is 14 mm.
Is the card thick enough for Lanika to use?
Show how you decide.
(3 marks)
2012 AHA Paper 1 short Page 3
© Churchill Maths Limited
7
In a game, two players take it in turns to roll two ordinary dice.
The dice are fair and numbered from 1 to 6.
If, on one turn, the number on one of the dice is twice the number on the other dice, the
player receives a bonanza card.
In one game, each player had 42 turns before the game ended.
Work out an estimate for the number of bonanza cards each player received in the
game.
(4 marks)
8
The graph on the answer sheets shows the price of printing A4 colour leaflets.
(a)
What is the price for 1000 leaflets?
(1 mark)
(b)
A company spends £380 on leaflets.
How many leaflets do they have printed?
(1 mark)
(c)
Rhona is thinking of ordering 1500 leaflets.
Angela says that for an extra 50%, Rhona could get 3 times as many leaflets.
Is Angela correct?
You must show how you decided.
(3 marks)
9
(a)
Write 63 as a product of its prime factors.
(2 marks)
Hisham and Marlon are comparing how far they step when walking.
Hisham's step is 63 cm in length, from the heel of one foot to the heel of the other foot.
63 cm
Hisham and Marlon start walking with their left heels exactly in line.
After walking 6.3 metres, one of Hisham's heels is exactly in line with one of Marlon's
heels.
(b)
The length of Marlon's step is an exact number of centimetres between
40 and 80.
Find all the possible lengths of Marlon's step.
(5 marks)
2012 AHA Paper 1 short Page 4
© Churchill Maths Limited
10
(a)
Find the value of
−
(i)
4
(ii)
(b)
1
2
(1 mark)
 
1
27
−
2
3
(2 marks)
Show that
 27 −  2 ≡ 3 – k 6

3
where k is a fraction to be found.
(3 marks)
11
Residents who live on Stratton Avenue complain of cars driving too fast on their road.
In a study, the speed of 100 cars is recorded and the results are shown in the
cumulative frequency diagram on the answer sheets.
The speed limit on Stratton Avenue is 30 miles per hour.
(a)
What percentage of the cars in the study were breaking the speed limit?
(1 mark)
(b)
Use the graph to estimate the median speed of the cars in the study.
(1 mark)
(c)
Use the graph to estimate the interquartile range of the speed of the cars in the
study.
(2 marks)
Following the study, speed cameras are put up on Stratton Avenue.
A second study records the speed of 100 cars one month later.
The results are summarised in the table on the next page.
*(d)
Speed (v miles per hour)
Frequency
0 < v ≤ 10
4
10 < v ≤ 20
15
20 < v ≤ 30
35
30 < v ≤ 40
28
40 < v ≤ 50
16
50 < v ≤ 60
2
Use the data and the grid on the answer sheets to find out if the speed cameras
have had an effect.
Comment on your findings.
(5 marks)
2012 AHA Paper 1 short Page 5
© Churchill Maths Limited
y
12
(0, 5)
y = f(x)
(8, 0)
x
The graph of y = f(x) intersects the x-axis at (8, 0) and the y-axis at (0, 5).
(a)
Write down the coordinates of the point where each of these graphs intersects
the y-axis.
(i)
y = f(x) + 1
(1 mark)
(ii)
y = 2f(x)
(1 mark)
(iii)
y = f(3x)
(1 mark)
(b)
Write down the coordinates of the point where each of these graphs intersects
the x-axis.
(i)
y = f(x + 6)
(1 mark)
(ii)
y = f(2x)
(1 mark)
(iii)
y = f(–x)
(1 mark)
13
Not drawn
accurately
An ornament is in the shape of a tetrahedron.
Each face is an equilateral triangle of side 4 cm.
(a)
4 cm
Show that the surface area of the ornament is 16  3 cm2.
(5 marks)
A larger version of the ornament is similar in shape and has sides of length 12 cm.
(b)
Find the exact surface area of the larger ornament.
(3 marks)
END
2012 AHA Paper 1 short Page 6
© Churchill Maths Limited