GCSEMathsEdexcelHigherExam Questions2. AlgebraIntroduction to Algebra

Introduction to Algebra (Edexcel GCSE Maths: Higher): Exam Questions

Exam code: 1MA1

2 hours40 questions
Easy
Medium
Hard
1
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2 marks
q1-easy-2-1-algebra-toolkit-edexcel-gcse-maths

You can work out the amount of medicine, c ml, to give to a child by using the formula

c space equals space fraction numerator m a over denominator 150 end fraction

m is the age of the child, in months.
a is an adult dose, in ml.

A child is 30 months old.
An adult's dose is 40 ml.

Work out the amount of medicine you can give to the child.

How did you do?

2
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2 marks

f space equals space 3 g space plus space 7 h

Work out the value of f when g space equals space long dash 5 and space h space equals space 2

How did you do?

3
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2 marks

Simplify         4 y space plus space 2 x space long dash space 3 space plus space 3 x space plus space 8

How did you do?

4
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2 marks

Simplify       6 g long dash space 5 h minus space 4 g space plus space 2 h

How did you do?

5
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2 marks

Simplify   a b space minus space 5 g space plus 5 a b space minus 2 g

How did you do?

6
1 mark

Choose the expression that is equivalent to 3 a space – space a space cross times space 4 a space plus space 2 a

  • 8 a squared plus space 2 a

  • 12 a squared

  • 5 a minus space 4 a squared

  • 3 a minus space 6 a squared

Choose your answer

7
1 mark

Sofia is trying to simplify  fraction numerator 6 c plus 10 over denominator 2 end fraction

Her method is

  • divide 6 c by 2

  • then add 10

Evaluate her method.

How did you do?

8
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2 marks

Use the formula s space equals space u t space plus space 1 half a t squared.

Calculate s when u equals 5, t equals 10 and a equals 3.

s = ..............

How did you do?

9
2 marks

Simplify 3 a space plus space 7 b space minus space 4 a space plus space b.

How did you do?

10
2 marks

Simplify 3 a minus 5 b minus a plus 2 b

How did you do?

11
2 marks

Simplify 5 c minus d minus 3 d minus 2 c.

How did you do?

12
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2 marks

Find the value of 7 x space plus space 3 y when x equals 12 and y equals negative 6.

How did you do?

13
1 mark

Complete the statement.

When w equals ............... , 10 w equals 70.

How did you do?

1a
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2 marks

The body mass index, B , for a person of mass m kg and height h metres is given by the formula

B equals m over h squared

Usman has a mass of 50 kg.
He has a height of 1.57 m.

Work out Usman's body mass index.
Give your answer correct to one decimal place.

How did you do?

1b
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2 marks

Tom's height is 1.80m.
He wants his body mass index to be 21

Work out the mass that will give Tom a body mass index of 21.

How did you do?

2
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2 marks

A space equals space 4 b c

  • A equals 100

  • b equals 2

Work out the value of  c.

How did you do?

3
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3 marks

You can change temperatures from °F to °C by using the formula

C space equals space fraction numerator 5 open parentheses F minus 32 close parentheses over denominator 9 end fraction

F is the temperature in °F.
C is the temperature in °C.

The minimum temperature in an elderly person's home should be 20 °C.

Mrs Smith is an elderly person.
The temperature in Mrs Smith's home is 77 °F.

Decide whether or not the temperature in Mrs Smith's home is lower than the minimum temperature should be.

How did you do?

4
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2 marks

x space equals space 0.7

Work out the value of  fraction numerator open parentheses x plus 1 close parentheses squared over denominator 2 x end fraction

Write down all the figures on your calculator display.

How did you do?

5a
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2 marks

h space equals space 3 t squared

Work out the value of h when t space equals space 5

How did you do?

5b
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2 marks

h space equals space 3 t squared

Work out the value of t when h space equals space 108

How did you do?

5c
2 marks

Make a the subject of the formula

v equals space u plus a t

How did you do?

6
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3 marks

h space equals space 5 t squared space plus space 2

i) Work out the value of h when t space equals space minus 2

[1]

ii) Work out a value of t when h equals space 47 space

[2]

How did you do?

7
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2 marks

w space equals space 5 y squared space – space y cubed

Work out the value of w when y space equals space – 2

w space equals space...................................................

How did you do?

8
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2 marks

G space equals space c squared space – space 4 c

Find the value of G when c space equals space – 5

G space equals .........................................

How did you do?

9
2 marks

Given that a space cross times space 60 space equals space b  work out the value of fraction numerator 4 b over denominator a end fraction

How did you do?

10a
2 marks

Martina has answered some questions on algebra. In each question, she has made an error.

Describe her error and give the correct answer to each problem.

Question 1       Simplify. 2a × a × a

         Martina’s answer 4a

Martina’s error is .......................................................................................................................

Correct answer = .........................................................

How did you do?

10b
2 marks

Question 2   Simplify.  x to the power of 10 over x squared

Martina’s answer x to the power of 5

Martina’s error is .......................................................................................................................

Correct answer = ........................................................

How did you do?

10c
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2 marks

Question 3      s equals u t plus 1 half a t squared  

Find s when u space equals space 0, t space equals space 5 and a space equals space 6.

Martina’s solution  s equals 0 cross times 5 plus 1 half cross times 6 cross times 5 squared

   s equals 0 plus 15 squared

   s equals 225

Martina’s error is............................................................

Correct answer = ........................................................

How did you do?

11
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2 marks

Find the value of s when u space equals space 12 comma a space equals space 10 and t space equals space 4.

s equals u t plus 1 half a t squared

How did you do?

12
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2 marks

Simplify 2 p minus q minus 3 q minus 5 p

How did you do?

13
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2 marks

space y equals m x plus c  

Find the value of space y when m equals negative 3, x equals negative 2 and c equals negative 8.  

space y equals ...............................................

How did you do?

14
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2 marks

y space equals space m x space plus space c.

Find the value of y when m space equals space minus 2, x space equals space minus 7 and c space equals space minus 3.

y space equals ..............................................

How did you do?

15
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2 marks

s equals u t plus 1 half a t squared

Find the value of s when u equals 5.2 comma space space t equals 7 and a equals 1.6.

s equals ..............................................

How did you do?

16
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1 mark

Complete the statement.

When 5 x equals 15, 12 x equals....................

How did you do?

17
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3 marks

Let a equals negative 1 and b equals negative 3.

Compare each pair of expressions by writing the correct symbol <, > or = between them.

a over 5

b over 3

2 a

b squared

a open parentheses b minus 1 close parentheses

negative 4 a

How did you do?

1
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2 marks

y space equals space p space minus space 2 q x squared

  • p equals negative 10

  • q equals 3

  • x equals negative 5

Work out the value of y.

How did you do?

2
3 marks

table row d equals cell 2 f end cell end table and table row cell fraction numerator e minus f over denominator d minus e end fraction end cell equals cell 1 fourth end cell end table

Work out the ratio e space colon space f

How did you do?

3
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3 marks

a over b equals 3 c and b over c equals 2

Work out the value of a when c space equals space 8

How did you do?

4
3 marks

a spaceand b are positive values.

Show that  fraction numerator 7 a plus 2 b minus 3 a over denominator 8 a plus 6 b plus 2 a minus b end fraction always simplifies to the same value.

How did you do?

5
4 marks

Work out the values of a and b in the identity

5 left parenthesis 7 x space plus space 8 right parenthesis space plus space 3 left parenthesis 2 x space plus space b right parenthesis space identical to space a x space plus space 13

a = .....................        b= .....................

How did you do?

6
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1 mark

Amy has x beads.

Billy has three more beads than Amy.

Carly has four times as many beads as Billy.

Choose the expression for the number of beads that Carly has.

  • 4 x space plus space 3

  • 3 x space plus space 4

  • 4 left parenthesis x space plus space 3 right parenthesis

  • x space plus space 12

Choose your answer

7
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2 marks

Kelly is trying to work out the two values of w for which 3 w space minus space w cubed space equals space 2
Her values are 1 and -1

Are her values correct?
You must show your working.

How did you do?

8
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2 marks

space y equals x to the power of 4 minus 4 x cubed space

Find the value of y when x equals negative 1.

y equals................................................

How did you do?

9
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4 marks

s equals u t plus 1 half a t squared

Find s when t equals 26.5 comma space u equals 104.3 comma space a equals negative 2.2 space. 
Give your answer in standard form, correct to 4 significant figures.  

s = ..................................................

How did you do?

10a
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2 marks

One solution of the equation a x squared plus a equals 150 is x equals 7.

Find the value of a.  

a = .................................................

How did you do?

10b
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1 mark

Find the other solution.  

x = ..................................................

How did you do?