GCSEMathsAQAExam Questions2. AlgebraAlgebra Toolkit

Algebra Toolkit (AQA GCSE Maths)

Exam Questions

2 hours43 questions
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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
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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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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
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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
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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
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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
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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
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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
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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
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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 = .........................................................

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14
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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
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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
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Complete the statement.

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

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1
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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
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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
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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
Sme Calculator1 mark

Find the other solution.
 

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

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