Sample from
Churchill Maths
Name
Class
For Edexcel GCSE
Mathematics
Unit 2 : Number, Algebra, Geometry 1
(Non-Calculator)
Higher Tier
Paper A
Time : 1 hour 15 minutes
Total Marks
You must have:
Ruler, protractor, compasses, pen, pencil, eraser.
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 60.
The marks for each question are shown in brackets.
Calculators must not be used.
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 Unit 2 Page 1
© Churchill Maths Limited
Turn over ►
Sample from
Churchill Maths
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 Unit 2 Page 2
© Churchill Maths Limited
−b± b2−4 ac 
2a
Sample from
Churchill Maths
Answer ALL questions.
Write your answers in the spaces provided.
You must write down all stages in your working.
1
In 1985 petrol cost £1.95 per gallon.
In 2005 petrol cost 80p per litre.
Harry says that the price of petrol more than doubled from 1985 to 2005.
Is Harry correct?
Explain your answer.
………………………………
(Total for Question 1 is 3 marks)
2
(a)
Simplify
2p – q + 3p + 4q
(2)
………………………………
(b)
Simplify
m9 ÷ m2
(1)
………………………………
(c)
Factorise fully
9xy2 – 6y3
(2)
………………………………
(Total for Question 2 is 5 marks)
2012 EHA Unit 2 Page 3
© Churchill Maths Limited
Turn over ►
Sample from
Churchill Maths
3
(a)
Complete this table of values for y = 3x – 1
x
–1
y
–4
0
1
2
(2)
(b)
On the grid, draw the line y = 3x – 1
y
5
4
3
2
1
–1 O
–1
1
2
x
–2
–3
–4
(2)
(c)
Here are the equations of three more lines.
y = 2x – 1
y = 2 – 3x
y = 3x  3
Tick the box under each equation of a line that is parallel to the line y = 3x – 1
(1)
(Total for Question 3 is 5 marks)
2012 EHA Unit 2 Page 4
© Churchill Maths Limited
Sample from
Churchill Maths
4
Diagram NOT
accurately drawn
P
O
R
Q
P and Q are points on a circle, centre O.
The tangents to the circle at P and Q intersect at the point R.
Angle PRQ = 53º.
Work out the size of angle POQ.
…………………………… º
(Total for Question 4 is 2 marks)
2012 EHA Unit 2 Page 5
© Churchill Maths Limited
Turn over ►
Sample from
Churchill Maths
5
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 Unit 2 Page 6
© Churchill Maths Limited
Sample from
Churchill Maths
(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 5 is 5 marks)
*6
Lanika needs a sheet of card that is at least
3
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.
………………………………
(Total for Question 6 is 3 marks)
2012 EHA Unit 2 Page 7
© Churchill Maths Limited
Turn over ►
Sample from
Churchill Maths
7
(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 7 is 6 marks)
2012 EHA Unit 2 Page 8
© Churchill Maths Limited
Sample from
Churchill Maths
8
(a)
Write 63 as a product of its prime factors
(2)
………………………………
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)
Marlon's step is between 40 cm and 80 cm in length.
Find all the possible lengths of Marlon's step.
(6)
………………………………
(Total for Question 8 is 8 marks)
2012 EHA Unit 2 Page 9
© Churchill Maths Limited
Turn over ►
Sample from
Churchill Maths
9
y
F
G
(5, 6, 0)
I
H
(5, 6, 4)
D
E
O
A
(0, 0, 8)
C
B
z
x
Diagram NOT
accurately drawn
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 9 is 6 marks)
2012 EHA Unit 2 Page 10
© Churchill Maths Limited
Sample from
Churchill Maths
10
Find the value of
(a)
4
−
1
2
(1)
………………………………
(b)
 
1
27
−
2
3
(2)
………………………………
(Total for Question 10 is 3 marks)
11
(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 11 is 6 marks)
2012 EHA Unit 2 Page 11
© Churchill Maths Limited
Turn over ►
Sample from
Churchill Maths
12
Vicky is making a path using paving stones.
It is made up of octagonal and square stones.
The octagonal stones are made from a square by removing the four corners.
The dimensions are shown below.
The size of the square stones is such that they tesselate with the octagonal stones.
10 cm
Diagram NOT
accurately drawn
10 cm
30 cm
30 cm
(a)
Work out the area of this section of path.
Diagram NOT
accurately drawn
(5)
…………………………… cm2
2012 EHA Unit 2 Page 12
© Churchill Maths Limited
Sample from
Churchill Maths
Vicky decides that the width of the path is to be three octagonal stones.
She is not sure how long the path will be but there will be no square stones on the
edges.
(b)
Find an expression, in terms of n for the number of square stones in the path when
it has n octagonal stones.
Show how you find your answer.
(3)
………………………………
(Total for Question 12 is 8 marks)
TOTAL FOR PAPER IS 60 MARKS
2012 EHA Unit 2 Page 13
© Churchill Maths Limited
Turn over ►