AQA GCSE Maths

Topic Questions

GCSEMathsAQATopic Questions2. AlgebraAlgebra Toolkit

Algebra Toolkit

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1
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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.

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2
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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

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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

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

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

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6
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y space equals space 10 over x

If the value of x doubles, what happens to the value of y?
Circle your answer.

divided by 2 cross times 2 divided by 5 cross times 5

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7
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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.

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8
Sme Calculator1 mark

Circle 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

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9
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Use the formula s space equals space u t space plus space 1 half a t squared.

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

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

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10
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Simplify 3 a space plus space 7 b space minus space 4 a space plus space b.

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11
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Simplify.

3 a minus 5 b minus a plus 2 b

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12
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Simplify 5 c minus d minus 3 d minus 2 c.

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13
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Find the value of 7 x space plus space 3 y when x equals 12 and y equals negative 6.

 

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14
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Complete the statement.

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

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1
Sme Calculator2 marks

y space equals space p space minus space 2 q x squared p space equals space minus 10 q space equals space 3 x space equals space minus 5

      Work out the value of y.

   

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2
Sme Calculator3 marks

a over b equals 3 c

b over c equals 2

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

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3
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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.

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4
Sme Calculator4 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= .....................

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5
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Amy has x beads.

Billy has three more beads than Amy.

Carly has four times as many beads as Billy.

Circle 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

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6
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.

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7
Sme Calculator3 marks

table attributes columnalign right center left columnspacing 0px end attributes row d equals cell 2 f end cell 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

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8
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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...............................................

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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 = ....................................................

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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 = ....................................................

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10b
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Find the other solution.
 

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

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1a
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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.

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1b
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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

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2
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A space equals space 4 b c space space space A space equals 100 space space space b space equals space 2

  Work out the value of  c.

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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.

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4
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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.

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5a
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h space equals space 3 t squared

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

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5b
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h space equals space 3 t squared

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

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5c
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Make a the subject of the formula

v equals space u plus a t

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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]

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7
Sme Calculator1 mark

Simplify  16 a squared space divided by space a space plus space 3 a space cross times space 2

Circle your answer.

22 a 8 a 38 a 2 a

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8
Sme Calculator1 mark

Circle 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

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9
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Circle the expression that is equivalent to  2 a space plus space 5 a space cross times space 4 a space – space a

a space plus space 20 a squared 21 a squared 28 a squared space – space a 2 a space plus space 15 a squared

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10
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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

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11
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...................................................

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12
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 .........................................

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13a
Sme Calculator2 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 = .........................................................

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13b
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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 = ..........................................................

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13c
Sme Calculator2 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 = .........................................................

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14
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.

begin mathsize 16px style s equals u t plus 1 half a t squared end style

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15
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Simplify.

2 p minus q minus 3 q minus 5 p

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16
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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 ................................................

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17
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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 ............................................

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18
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 ...............................................

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19
Sme Calculator1 mark

Complete the statement.

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

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