GCSEFurther MathsAQAExam Questions2. Algebra & FunctionsAlgebraic Fractions

Algebraic Fractions (AQA GCSE Further Maths)

Exam Questions

52 mins14 questions
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Hard
Very Hard
1
Sme Calculator2 marks

Simplify fraction numerator x plus 2 over denominator 9 end fraction cross times fraction numerator 3 over denominator 4 open parentheses x plus 2 close parentheses end fraction.

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2
Sme Calculator2 marks

Write fraction numerator 5 over denominator 6 a end fraction plus a over 4 as a single fraction. Give your answer in its simplest form.

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3
Sme Calculator3 marks

Write  fraction numerator 7 over denominator 9 x end fraction plus fraction numerator 2 over denominator 3 x squared end fraction  as a single fraction in its simplest form.

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4
Sme Calculator2 marks

Write 5 minus 2 over y as a single fraction.

Give your answer in its simplest form.

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5a
Sme Calculator2 marks

Work out     fraction numerator a b over denominator c d end fraction divided by fraction numerator b c over denominator a d end fraction

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

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5b
Sme Calculator2 marks

Work out      fraction numerator 7 over denominator 2 x squared end fraction plus fraction numerator 4 over denominator 3 x end fraction

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

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1
Sme Calculator3 marks

Simplify fully fraction numerator 15 x squared y space minus space 5 x y squared over denominator 12 x space minus 4 y end fraction

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2
Sme Calculator4 marks

Simplify fully    fraction numerator x minus x cubed over denominator 2 x plus 2 x squared end fraction

You must show your working.

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3a
Sme Calculator1 mark

Circle the expression that is equivalent to    1 over a plus 1 over b

fraction numerator 2 over denominator a plus b end fraction

fraction numerator a b over denominator b plus a end fraction

fraction numerator 2 over denominator a b end fraction

fraction numerator b plus a over denominator a b end fraction

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3b
Sme Calculator3 marks

Simplify fully   fraction numerator 6 c to the power of 4 minus c cubed over denominator 36 c squared minus 1 end fraction.

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4
Sme Calculator2 marks

Simplify   fraction numerator x squared minus 7 x plus 10 over denominator x squared minus 2 x minus 15 end fraction

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5
Sme Calculator6 marks

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

Do not use trial and improvement. Write your solutions to 3 significant figures.

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6
Sme Calculator4 marks

Show that  fraction numerator x to the power of 4 over denominator x plus 4 end fraction cross times fraction numerator x plus 2 over denominator x end fraction divided by fraction numerator x squared over denominator 3 x plus 12 end fraction

simplifies to the form a x squared space plus space b x where a and b are integers.

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1
Sme Calculator5 marks

Simplify    fraction numerator 8 x cubed minus 50 x over denominator 2 x open parentheses 6 x squared minus x minus 35 close parentheses end fraction

Give your answer in the form   fraction numerator a x plus b over denominator c x plus d end fraction   where a comma space b comma space c and d are integers.

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2
Sme Calculator6 marks

Write

fraction numerator 9 over denominator 2 x squared minus x minus 1 end fraction minus fraction numerator 12 over denominator 4 x squared minus 1 end fraction

as a single algebraic fraction.

Give your answer fully simplified.

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3
Sme Calculator5 marks

straight f open parentheses x close parentheses equals fraction numerator x over denominator 2 x plus 1 end fraction  for positive values of x.

Work out   straight f open parentheses x plus 1 close parentheses minus straight f open parentheses x close parentheses

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

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