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GCSEMathsEdexcelHigherExam Questions2. AlgebraIntroduction to Algebra

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

Exam code: 1MA1

2 hours39 questions
Easy
Medium
Hard
1
Sme Calculator2 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
Sme Calculator2 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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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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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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Simplify   a b space minus space 5 g space plus 5 a b space minus 2 g

How did you do?

61 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

71 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
Sme Calculator2 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?

92 marks

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

How did you do?

102 marks

Simplify 3 a minus 5 b minus a plus 2 b

How did you do?

112 marks

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

How did you do?

12
Sme Calculator2 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?

131 mark

Complete the statement.

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

How did you do?

1a
Sme Calculator2 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
Sme Calculator2 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
Sme Calculator2 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
Sme Calculator3 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
Sme Calculator2 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
Sme Calculator2 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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h space equals space 3 t squared

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

How did you do?

5c2 marks

Make a the subject of the formula

v equals space u plus a t

How did you do?

6
Sme Calculator3 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
Sme Calculator2 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
Sme Calculator2 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?

92 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?

10a2 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?

10b2 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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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
Sme Calculator2 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
Sme Calculator2 marks

Simplify 2 p minus q minus 3 q minus 5 p

How did you do?

13
Sme Calculator2 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
Sme Calculator2 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
Sme Calculator2 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
Sme Calculator1 mark

Complete the statement.

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

How did you do?

1
Sme Calculator2 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?

23 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
Sme Calculator3 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?

43 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?

54 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
Sme Calculator1 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
Sme Calculator2 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
Sme Calculator2 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
Sme Calculator4 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
Sme Calculator2 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
Sme Calculator1 mark

Find the other solution.  

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

How did you do?