Edexcel GCSE
Mathematics (Linear) – 1MA0
ALGEBRA:
SOLVING EQUATIONS
Materials required for examination Items included with question papers Ruler graduated in centimetres and Nil
millimetres, protractor, compasses, pen, HB pencil, eraser.
Tracing paper may be used.
Instructions
Use black ink or ball-point pen.
Fill in the boxes at the top of this page with your name, centre number and candidate number.
Answer all questions.
Answer the questions in the spaces provided – there may be more space than you need.
Calculators may be used.
Information
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.
1. (a) Solve 2y = 8
y = …………...
(1) (b) Solve t – 4 = 7
t = …………...
(1) (c) Solve
4 x = 3
x = …………...
(1) (3 marks)
2. (a) Solve 3 y = 6
y = ………
(1)
(b) Solve 7y = 54
y = ………
(1) (c) Solve 2t – 5 = 9
t = …………...
(2) (4 marks)
3. (a) Solve 4w = 20
w = ………
(1)
(b) Solve x − 6 = 3
x = ………
(1) (c) Solve
3 y = 7
y = ………
(1) (3 marks)
4. (a) Solve 3x = 12
x = ...
(1)
(b) Solve y – 7 = 5
y = ...
(1)
(c) Solve 2t + 8 = 3
t = ...
(2)
(d) Solve 5 2y
= 4
y = ...
(2) (3 marks)
5. (a) Solve 6g = 18
g = ...
(1) (b) Solve y + 5 = 12
y = ...
(1) (c) Solve
4 x = 3
x = ...
(1) (d) Solve 5h + 7 = 17
h = ...
(2) (5 marks)
6. (a) Solve b – 7 = 12
b = ...
(1) (b) Solve 5e = 40
e = ...
(1) (c) Solve 4m + 6 = 15
m = ...
(2) (d) Solve 5w – 6 = 10
w = ...
(2) (6 marks)
7. (a) Solve 4x + 1 = 9
x = ...
(2)
(b) Solve 2x – 5 = 4
x = ………
(2) (c) Solve 2y – 1 = 12
y = ...
(2) (6 marks)
8. (a) Solve 4x + 1 = 19
x = ...
(2)
(b) Solve 4x + 3 = 19
x = ………
(2)
(c) Solve 2q + 7 = 1
q = ...
(2) (6 marks)
9. (a) Solve x + x + x = 15
x = ...
(2)
(b) Solve 6x – 7 = 38
x = ………
(2) (c) Solve 7x + 18 = 74
x = ...
(2) (6 marks)
10. (a) Solve 2y + 3 = 8
y = ...
(2)
(b) Solve 5(t – 3) = 25
t = ………
(2)
(c) Solve 4(5y – 2) = 48
y = ...
(2) (6 marks)
11. Solve 13x + 1 = 11x + 9
x = ...
(3 marks)
12. Solve 5t – 4 = 3t + 6
t = ...
(3 marks)
13. Solve 4y + 3 = 2y + 8
(3 marks)
14. Solve 5y + 1 = 3y + 13
y = ...
(3 marks)
15. Solve 3y + 10 = 5y + 3
y = ...
(3 marks)
16. Solve 2y + 17 = 6y + 5
y = ...
(3 marks)
Name:
Exam Style Questions
Equipment needed: Calculator, pen
Guidance
1. Read each question carefully before you begin answering it.
2. Check your answers seem right.
3. Always show your workings
Video Tutorial
Answers and Video Solutions
© Corbettmaths 2022
Substitution
Video 20
www.corbettmaths.com/contents
1. Find the value of if
...
(1) 2. Find the value of when and
...
(2) 3. Find the value of when and
...
(2) 4. Circle the expression that has the greatest value when
(1)
5c + 2 c = 6
4a − b a = 9 b = 8
12h + 9t h = 11 t = 3
y = 10
2y 31 − y y + 9 y
2
© Corbettmaths 2022
5. If and , find the value of (a)
...
(1) (b)
...
(1) (c)
...
(1) (d)
...
(2)
6.
Find P if W = 3 and L = 9
...
(2)
x = 6 y = − 2 x
25x + y
x + y
2y + 20 x
P = 2W + 2L
© Corbettmaths 2022
7. You are given that , and
Find the value of (a)
...
(2) (b)
...
(1)
8. The cost of hiring a hot tub is found using the formula Hire cost = £50 plus an extra £45 per day
(a) Work out the hire cost for hiring the hot tub for 21 days.
...
(2)
Alex hires the hot tub for a number of days and the cost is £545 (b) How many days did Alex hire the hot tub?
...
(2)
m = 0.5 p = 0.75 c = 2.2
3c + m
m + p + c
© Corbettmaths 2022
9. This formula can be used to convert between Celsuis (C) and Fahrenheit (F).
(a) Convert into Fahrenheit
...
(2) (b) Convert into Celsius
...
(2)
10. Given that , and
Work out the value of
...
(3)
F = 1.8C + 32 2
∘C
50
∘F
a = 4 b = 9 c = − 5
ab + 24 2c
© Corbettmaths 2022
11. (a) Find the value of when and
...
(2) (b) Find the value of when and
...
(2)
12.
Find W if P = 30 and L = 11
...
(2) 13.
Work out the value of
...
(2)
5(a + c) a = 4 c = 9
7x + 2y x = 2 y = − 9
P = 2W + 2L
y = w − 2a
2w = 400 a = 5
y
© Corbettmaths 2022
14. The cost in pounds, C, of hiring a car is given by
where d is the number of days the car is hired.
(a) Find C if d = 4
...
(2)
(b) Find d if C = 245
...
(2)
15.
(a) Work out the value of W when and
...
(2) (b) Work out the value of x when and
...
(2)
C = 25d + 45
W = 2x + 5y
x = 8 y = − 3
W = 59 y = 7
© Corbettmaths 2022
16. The amount of medicine, s ml, to give to a puppy, up to 18 months old, can be worked out using the formula.
s is the amount of medicine, in ml.
a is the dose for an adult dog, in ml.
m is the age of the puppy, in months.
A puppy is 3 months old.
An adult dog’s dose is 45ml.
Work out the amount of medicine the puppy should be given.
...ml (3) 17.
Find m if , and
...
(2)
s = am 18
m = abc
a = 3 b = − 8 c = 2
© Corbettmaths 2022
18. Heidi is a plumber.
She uses this formula to work out the cost to charge her customers.
C is the total cost of the job, in pounds.
h is the number of hours worked.
p is the cost of any parts used, in pounds.
d is the distance travelled, in miles.
Heidi’s last job took 3 hours and the cost of the parts used was £17.50 The total cost of the job was £156
Work out how far Heidi travelled in miles.
...miles (3)
19.
Work out the value of
...
(2)
C = 40h + p + 0.5d
x + 3 = 10
5x − 3 4
© Corbettmaths 2022
20.
(a) Work out v when , and
...
(2) (b) Work out when , and
...
(2) (c) Work out when , and
...
(2)
21.
(a) Work out the value of
...
(2) (b) Work out the value of
...
(1)
v = u + at
u = 23 a = 4 t = 3
u v = 30 a = 2 t = 8
t v = 40 u = 12 a = 4
2 x − y = 17
6x − 3y
y − 2x
© Corbettmaths 2022
22.
Explain what happens to the value of y when the value of x doubles.
……….………..
……….………..
(2)
23.
Explain what happens to the value of y when the value of x doubles.
……….………..
……….………..
(2)
24. Calculate the value of when and
...
(2)
y = 7x
2y = 800 x
3x
y− y
xx = 3 y = 6
© Corbettmaths 2022
25.
m and n are negative integers.
Write down a pair of possible values for m and n.
m = ... and n = ...
(2)
26.
Find y if
...
(2)
80 = 2mn
y = (x − 5)(x + 1) x = − 3
© Corbettmaths 2022
27.
Work out the value of when
...
(3)
w = x 2y
4w + 3y = 30
x y = 4
© Corbettmaths 2022