GCSEMathsEdexcelHigherExam Questions2. AlgebraAlgebraic Fractions

Algebraic Fractions (Edexcel GCSE Maths: Higher)

Exam Questions

3 hours45 questions
Medium
Hard
Very Hard
1
Sme Calculator3 marks

Write as a single fraction in its simplest form

fraction numerator 2 over denominator y plus 3 end fraction space minus space fraction numerator 1 over denominator y minus 6 end fraction

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2
Sme Calculator3 marks

Write     fraction numerator 5 over denominator x minus 3 end fraction minus fraction numerator 4 over denominator x plus 3 end fraction  as a single fraction in its simplest form.

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3
Sme Calculator3 marks

Simplify        fraction numerator x plus 1 over denominator 2 end fraction space plus space fraction numerator x plus 3 over denominator 3 end fraction

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4
Sme Calculator2 marks

Simplify   fraction numerator 4 open parentheses x plus 5 close parentheses over denominator x squared space plus 2 x minus 15 end fraction

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5
Sme Calculator1 mark

Simplify       fraction numerator 3 open parentheses x plus 1 close parentheses over denominator open parentheses x plus 1 close parentheses squared end fraction

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6
Sme Calculator3 marks

Express

3 over x plus fraction numerator x plus 2 over denominator 2 x end fraction plus 1 fourth

as a single fraction in its simplest form.

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7
Sme Calculator3 marks

Express fraction numerator 4 over denominator x minus 2 end fraction minus fraction numerator 3 over denominator x plus 1 end fraction as a single fraction.

Give your answer in its simplest form.

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8
Sme Calculator3 marks

Write fraction numerator 2 x plus 1 over denominator 4 end fraction plus fraction numerator x minus 2 over denominator 3 end fraction as a single fraction in its simplest form.

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9
Sme Calculator2 marks

Write as a single fraction  fraction numerator 2 over denominator 3 x end fraction plus fraction numerator 4 over denominator 5 x end fraction minus fraction numerator 9 over denominator 10 x end fraction

Give your answer in its simplest form.

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10
Sme Calculator3 marks

Simplify fully fraction numerator 10 x squared space plus space 23 x space plus 12 over denominator 4 x squared space minus space 9 end fraction

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11
Sme Calculator1 mark

Simplify  3 over x plus 4 over x
Circle your answer.

7 over x

fraction numerator 7 over denominator 2 x end fraction

12 over x

12 over x squared

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12
Sme Calculator2 marks

Simplify  fraction numerator 25 a over denominator 8 end fraction cross times fraction numerator 2 a over denominator 5 end fraction

Give your answer as a single fraction in its simplest form.

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13
Sme Calculator3 marks

Show that, for x not equal to space 0

   fraction numerator x plus 4 over denominator 3 x end fraction space minus space fraction numerator 5 over denominator 2 x end fraction

can be written in the form  fraction numerator a x space plus space b over denominator c x end fraction where a, b and c are integers.

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14
Sme Calculator1 mark

Circle the expression that is equivalent to fraction numerator 3 x squared over denominator 6 x squared space plus space 3 end fraction

fraction numerator x squared over denominator 2 x squared plus space 3 end fraction

fraction numerator x squared over denominator 6 x squared plus space 1 end fraction

fraction numerator x squared over denominator 2 x squared plus space 1 end fraction

1 half plus space x squared

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15
Sme Calculator3 marks

Write as a single fraction in its simplest form.

fraction numerator 3 over denominator x minus 1 end fraction plus fraction numerator 4 over denominator x plus 2 end fraction

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16
Sme Calculator2 marks

Express as a single fraction.

fraction numerator m plus 1 over denominator n plus 1 end fraction minus m over n

Simplify your answer.

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1
Sme Calculator3 marks

Simplify fully     fraction numerator 2 x squared space minus 5 x space plus space 3 over denominator x squared space plus space 5 x space minus 6 end fraction 

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2
Sme Calculator3 marks

Write as a single fraction in its simplest form   fraction numerator 5 over denominator 2 space minus x end fraction space minus space 4 over x

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3
Sme Calculator3 marks

Simplify  fraction numerator x squared space minus space 16 over denominator 2 x squared space minus space 5 x space minus 12 end fraction

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4
Sme Calculator3 marks

Simplify fully  fraction numerator 3 x squared minus 8 x space minus 3 over denominator 2 x squared space minus space 6 x end fraction

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5
Sme Calculator3 marks

Show that  fraction numerator 2 x squared space minus space 3 x space minus space 5 over denominator x squared space plus space 6 x space plus 5 end fraction  can be written in the form  fraction numerator a x space plus space b over denominator c x plus space d end fraction where a comma space b comma space c and d are integers.

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6a
Sme Calculator3 marks

Simplify fully    fraction numerator x squared space plus space 3 x space minus space 4 over denominator 2 x squared space minus space 5 x space plus 3 end fraction

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6b
Sme Calculator3 marks

Write fraction numerator 4 over denominator x plus 2 end fraction space plus space fraction numerator 3 over denominator x minus 2 end fraction  as a single fraction in its simplest form.

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7
Sme Calculator2 marks

Show that  fraction numerator a over denominator b plus 1 end fraction minus a over open parentheses b plus 1 close parentheses squared can be written as  fraction numerator a b over denominator open parentheses b plus 1 close parentheses squared end fraction

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8
Sme Calculator3 marks

Simplify      fraction numerator x squared space minus 9 over denominator 2 x squared space plus space 5 x minus 3 end fraction

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9
Sme Calculator3 marks

Solve fraction numerator 4 space minus space 3 x over denominator 5 end fraction space minus space fraction numerator 3 x space minus 5 over denominator 2 end fraction space equals space minus 3

Show clear algebraic working.

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

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10
Sme Calculator5 marks

Solve the equation

fraction numerator 5 over denominator x plus 2 end fraction plus fraction numerator 3 over denominator x squared plus 2 x end fraction equals 2

Show clear algebraic working.

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11
Sme Calculator3 marks

Simplify fully fraction numerator x to the power of 5 space minus space 4 x cubed over denominator 3 x space minus space 6 end fraction

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12
Sme Calculator3 marks

Show that, for x space not equal to space – 1

   fraction numerator 8 x squared minus space 8 over denominator 4 x plus space 4 end fraction simplifies to the form a x space plus space b       
where a and b are integers.

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13
Sme Calculator4 marks

Show that fraction numerator x plus 9 over denominator x squared minus 1 end fraction plus fraction numerator 4 over denominator x plus 1 end fraction can be written in the form fraction numerator a over denominator x minus 1 end fraction where a is an integer.

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14
Sme Calculator6 marks

Show that fraction numerator 5 x over denominator x plus 5 end fraction plus fraction numerator 25 over denominator x minus 7 end fraction minus fraction numerator 300 over denominator open parentheses x plus 5 close parentheses open parentheses x minus 7 close parentheses end fraction simplifies to an integer.

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1
Sme Calculator4 marks

2 minus space fraction numerator x plus 2 over denominator x minus 3 end fraction minus fraction numerator x minus 6 over denominator x plus 3 end fraction  can be written as a single fraction in the form fraction numerator a x space plus space b over denominator x squared space minus 9 end fraction

where a spaceand b are integers.

Work out the value of a and the value of b.

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2
Sme Calculator3 marks

Show that fraction numerator 1 over denominator 6 x squared space plus space 7 x space minus 5 end fraction divided by fraction numerator 1 over denominator 4 x squared space minus 1 end fraction simplifies to fraction numerator a x space plus space b over denominator c x space plus space d end fraction where a comma space b comma space c and d are integers.

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3a
Sme Calculator2 marks

Simplify fully       fraction numerator 3 minus space x over denominator 3 x squared space minus space 5 x space minus 12 end fraction

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3b
Sme Calculator3 marks

Write fraction numerator x over denominator x minus 1 end fraction minus fraction numerator x over denominator x plus 1 end fraction as a single fraction in its simplest form.

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4
Sme Calculator4 marks

Write

      4 space minus space open square brackets open parentheses x plus 3 close parentheses divided by fraction numerator x squared space plus space 5 x space plus 6 over denominator x minus 2 end fraction close square brackets

as a single fraction in its simplest form.
You must show your working.

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5
Sme Calculator4 marks

Show that  fraction numerator 3 x plus 6 over denominator x squared minus 3 x minus 10 end fraction divided by fraction numerator x plus 5 over denominator x cubed minus 25 x end fraction simplifies to straight a x where straight a is an integer.

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6
Sme Calculator4 marks

Show that 6 plus space open square brackets open parentheses x plus 5 close parentheses space divided by space fraction numerator x to the power of 2 space end exponent plus space 3 x space minus 10 over denominator x minus 1 end fraction close square brackets  simplifies to fraction numerator a x space minus b over denominator c x minus d end fraction  where a comma space b comma space c and d are integers.

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7
Sme Calculator4 marks

Write fraction numerator 25 x squared minus 64 over denominator 5 x squared minus 13 x minus 6 end fraction cross times fraction numerator x squared minus 8 x plus 15 over denominator 5 x plus 8 end fraction minus open parentheses x minus 7 close parentheses

as a single fraction in its simplest form.
Show clear algebraic working.

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8
Sme Calculator4 marks

Given that  x equals fraction numerator 5 over denominator 9 y plus 5 end fraction and that y equals fraction numerator 5 over denominator 5 a minus 2 end fraction

find an expression for x in terms of a.
Give your expression as a single fraction in its simplest form.

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9
Sme Calculator3 marks

Express  fraction numerator 1 over denominator 9 x squared minus 25 end fraction minus fraction numerator 1 over denominator 6 x plus 10 end fraction as a single fraction in its simplest form.

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10
Sme Calculator2 marks

Simplify  fraction numerator 2 to the power of n space end exponent minus space 1 over denominator 4 to the power of n space minus space 1 end fraction

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11
Sme Calculator5 marks

The flight of a plane was in two stages.

The table shows information about the flight.

 

Distance (miles)

Speed (mph)

Time (hours)

1st stage

731

x

731 over x

2nd stage

287

x minus 24

fraction numerator 287 over denominator x minus 24 end fraction

In total, the flight lasted 2 hours.
Work out the value of x.

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12
Sme Calculator5 marks

Solve  fraction numerator 5 over denominator 4 x plus 1 end fraction equals fraction numerator 2 x over denominator x squared plus 3 end fraction

Give your solutions to 3 significant figures.
You must show your working.

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13
Sme Calculator4 marks

Solve  fraction numerator x over denominator x space plus space 4 end fraction space plus space fraction numerator 7 over denominator x minus 2 end fraction space equals space 1

You must show your working.

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

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14
Sme Calculator6 marks

Solve x over 4 minus space fraction numerator 2 x over denominator x plus 2 end fraction space equals space 1

Give your solutions to 2 decimal places.
You must show your working.

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15
Sme Calculator6 marks

Solve this equation, giving your answers correct to 1 decimal place.

fraction numerator 5 over denominator x space plus space 2 end fraction space plus space fraction numerator 3 over denominator x space minus space 3 end fraction space equals space 2

x = ........... or x = ...........

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