Edexcel GCSE
Higher Tier
Student Paper 1
Time: 1 hour
You must have:
Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser. Tracing paper may be used.
Instructions



Use black ink or ball-point pen.
Answer all questions.
Answer the questions in the spaces provided
– there may be more space than you need.


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.
Information



The total mark for this paper is 62.
The marks for each question are shown in brackets
– use 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
written communication will be assessed
– you should take particular care on these questions with your spelling,
punctuation and grammar, as well as the clarity of expression.
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.
GCSE Mathematics
Formulae: Higher Tier
Volume of prism = area of cross section × length
Volume of sphere
4
3
πr3
Volume of cone
1
3
πr2h
Surface area of sphere = 4πr2
Curved surface area of cone = πrl
In any triangle ABC
The Quadratic Equation
The solutions of ax2+ bx + c = 0
where a ≠ 0, are given by
x=
Sine Rule
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
2
 b  (b 2  4ac)
2a
1.
Solve the simultaneous equations
2x + 2y = 8
4y = 2x + 10
x = ……………………………………..
y = ……………………………………..
(Total for this Question 1 is 4 marks)
(Grade B)
___________________________________________________________________________
2.
(a) If the second of three consecutive whole numbers is n, write the first and third number in
terms of n.
............................................................
(2)
(b) Prove that if you add the squares of three numbers that are consecutive and subtract 2
from the result you will always get a multiple of 3.
You may use your answers from part (a) in your answer.
(5)
(Total for Question 2 is 7 marks)
(Grade A*)
___________________________________________________________________________
3
3.
Vinnie has a Fiat 500.
The value of the car (V) in pounds (£) is directly proportional to the car’s age (A) in years.
The initial cost of the car was: £17,500
After 35 years, the car’s value has increased by 45%
(a) Find the formula of V in terms of A after 35 years.
..................................................
(2)
(b) Calculate the value of the car after 65 years.
.................................................
(1)
(Total for Question 3 is 3 marks)
(Grade A)
___________________________________________________________________________
4
4.
A
E is the midpoint of AB
D is the midpoint of CA
Find CE in terms of a and b.
a
D
E
B
C
b
(Total for Question 4 is 5 marks)
(Grade ?)
___________________________________________________________________________
5.
Express 0.07 as a fraction.
You must use algebra.
(Total for Question 5 is 2 marks)
(Grade A)
___________________________________________________________________________
5
6.
x
O
A
21º
B
O is the centre of the circle.
Angle BAO is 21º.
(a) What is angle AOB? Give reasons for your answer.
...............................................................................................................................................
...............................................................................................................................................
(3)
(b) What is angle x? Give reasons for your answer
...............................................................................................................................................
...............................................................................................................................................
(2)
(Total for Question 6 is 5 marks)
(Grade B)
___________________________________________________________________________
6
7.
(a) Work out 49
1
2
................................
(1)
(b) Divide your answer by 14,000. Then put this into Standard Form.
................................
(3)
(Total for Question 7 is 4 marks)
(Grade C)
___________________________________________________________________________
8.
Work out the values of
(a) 49

1
2
................................
(1)
(b) 30
................................
(1)
(c)
3
8
................................
(1)
(d)
3

9
27
................................
(3)
(e) 64
2
3
................................
(2)
(Total for Question 8 is 8 marks)
(Grade B/A)
___________________________________________________________________________
7
9.
Solve 7x2 + 5x – 2 = 0
Give your answer to 3 significant figures.
................................
(Total for Question 9 is 6 marks)
(Grade B/A)
___________________________________________________________________________
10.
Suzy Sue wrote down the cost of 27 CDs in HMV. Here are the prices she found.
09
05
31
14
27
03
45
53
12
40
15
32
17
24
50
01
34
22
03
42
11
36
10
29
18
(a) In the space below, draw a stem and leaf diagram to show these costs and include a key .
(3)
(b) Find the medium price
£................................
(1)
(c) Find the interquartile range
................................
(2)
(Total for Question 10 is 6 marks)
(Grade B/A)
___________________________________________________________________________
8
11.
There are 3 bottles of Hair dye One Brown, one Red and one Purple.
Kimberley doesn’t know what colour to dye her hair; her very good friend Hillary decides to
mix the bottles and put them into different boxes.
Hillary picks one box, while being blindfolded, and then Kimberley also picks a box.
What is the probability she will end up with bright hair and in isolation ?
(Anything mixed with brown will not be a bright colour)
(Total for Question 11 is 3 marks)
(Grade A/A*)
___________________________________________________________________________
9
12.
(a) Express 124 as a product of its prime factors.
................................
(2)
(b) Find the highest common factor (HCF) of 124 and 80.
................................
(1)
(c) Find the lowest common multiple (LCM) of 124 and 80
................................
(1)
(Total for Question 12 is 4 marks)
(Grade C)
___________________________________________________________________________
10
13.
This is a door wedge.
Angle DAE = 27°.
Angle DEA = 90°.
The line BA = 30 cm.
The line AE = 30 cm.
Calculate the angle CAF. Give your answer to 3 significant figures.
(Total for Question 13 is 6 marks)
(Grade A)
___________________________________________________________________________
11
Mark Schemes
1.
2x + 2y = 8
2x – 4y = –10
6y = 18
y=3
2x + 2(3) = 8
x=1
M1 for coefficients of x or y the same followed by correct operation (condone one arithmetic
error)
A1 cao for first solution
M1 (dep on M1) for correct substitution of found value into one of the equations or
appropriate method after starting again (condone one arithmetic error)
A1 cao for second solution
OR
M1 for full method to rearrange and substitute to eliminate x or y, (condone one arithmetical
error)
A1 cao for first solution
M1 (dep on M1) for correct substitution of found value into one of the equations or
appropriate method after starting again (condone one arithmetic error)
A1 cao for second solution
___________________________________________________________________________
2.
(a)
n – 1, n, n + 1
1 mark for : (n – 1)² + n² + (n + 1)²
1 mark for: (n – 1)(n – 1) + n² + (n + 1)(n + 1)
And also expanding brackets: n² – n – n + 1 + n² + n² + n + n + 1
1 mark for: 3n²+2
1 mark for: Subtracting 2 from the result to get 3n²
1 mark for: Explanation saying that it is a multiple of 3,. e.g. 3(n2)
___________________________________________________________________________
3.
V ∝ A (M1 for identifying relationship between the two variables)
V = kA
V after 35 years = (45/100)  17,500 = 7,875 + 17,500 = £25,375
25,375 = k(35)
(25,375/35) = k
725 = k
V = 725(A)
(M2 for using the equation, re-arranging it and expressing it in terms of V)
V = 725(75) = £ 47,125
(M1 for correctly substituting values into the equation)
___________________________________________________________________________
12
4.
AB = AC + CB
AB = –a + b
AE = 12 (–a + b)
(M1)
(M1)
(M1)
CE = CA + AE
= a + 12 (–a + b)
(M1)
1
1
=a– 2a+ 2b
= 12 a + 12 b
(A1)
___________________________________________________________________________
5.
Working:
x = 0.07070707…
100x = 7.070707…
99x = 7
M1for 0.07070707…
A1 for 7/99
___________________________________________________________________________
6.
M1 for Isosceles Triangle from point O
M1 for 180 – (21 + 21)
A1 for answer AOB = 138º
M1 for angle at circumference is half the angle at the centre
A1 for angle x = 69º
___________________________________________________________________________
7.
Use of √ (1 mark);
= 7 (1 mark)
7 ÷ 14,000
(1 mark)
= 0.0005
(1 mark)
4
= 5  10⁻
(1 mark)
___________________________________________________________________________
8.
(a)
1
7
(1)
(b)
1
(1)
(c)
2
(1)
(d)
1
(3)
(e) 16
(2)
___________________________________________________________________________
13
9.
(M1) for use of
(M2) for
(A3) for x = 0.286 and x = 1.00
10.
(a)
0
1
2
3
4
5
1
0
2
1
0
0
3
1
4
2
2
3
3
2
7
4
5
(lose mark if not rounded correctly)
5 9
4 5 7 8
9
6
Key: 2│7 = 27
M2 for fully correct diagram
[M1 for ordered leaves with one error or omission or a complete unordered diagram]
M1 for a correct key
(b)
22
A1 cao
(c)
23
M1 for 34 or 11
Or clear attempt to find UQ & LQ from a list of values or in stem and leaf diagram
A1 cao
11.
1/3 she will be put into isolation.
2/3 will not be put into isolation
12.
No mark scheme given.
14
13.
ANSWER: 19.8° (3 significant figures)
Working Out – with diagrams
1.
2.
3.
15