IGCSEMathsCambridge (CIE)ExtendedExam QuestionsAlgebra & SequencesAlgebraic Fractions

Algebraic Fractions (Cambridge (CIE) IGCSE Maths: Extended): Exam Questions

Exam code: 0580 & 0980

2 hours40 questions

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Algebraic Fractions

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Hard
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1
2 marks

Simplify fraction numerator p over denominator 2 q end fraction cross times fraction numerator 4 p q over denominator t end fraction.

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2
3 marks

Write as a single fraction in its simplest form.

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

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3
3 marks

Simplify fraction numerator a b minus b squared over denominator a squared minus b squared end fraction.

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4
3 marks

Write as a single fraction in its simplest form.

1 over x minus fraction numerator 1 over denominator x plus 1 end fraction

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5
2 marks

Simplify.

fraction numerator 3 plus x over denominator 9 minus x squared end fraction

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6
3 marks

Write as a single fraction in its simplest form.

fraction numerator 1 over denominator y minus 1 end fraction minus 1 over y

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7
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3 marks

Write as a single fraction in its simplest form.

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

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1
3 marks

Write as a single fraction in its simplest form.

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

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2
4 marks

Simplify.

fraction numerator x to the power of 2 space end exponent minus space 5 x over denominator 2 x squared space minus space 50 end fraction

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3
3 marks

Write as a single fraction in its simplest form.

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

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4
4 marks

Write as a single fraction in its simplest form.

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

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5
3 marks

Write as a single fraction in its simplest form. 

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

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6
3 marks

Simplify fraction numerator x cubed plus 5 x squared over denominator x squared minus 25 end fraction, giving your answer as a single fraction.

How did you do?

7
3 marks

Write as a single fraction in its simplest form.

fraction numerator 5 over denominator x minus 2 end fraction minus fraction numerator x minus 5 over denominator 2 end fraction

How did you do?

8
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3 marks

fraction numerator 3 over denominator m plus 4 end fraction minus 4 over m equals 6

Show that this equation can be written as  6 m squared plus 25 m plus 16 equals 0 .

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9
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3 marks

Solve fraction numerator 7 over denominator x plus 1 end fraction plus fraction numerator 4 over denominator x plus 4 end fraction equals 3

How did you do?

10a
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3 marks

Show that the equation fraction numerator 7 over denominator x plus 1 end fraction plus fraction numerator 4 over denominator x plus 4 end fraction equals 3 simplifies to 3 x squared plus 4 x minus 20 equals 0

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10b
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3 marks

Hence, or otherwise, solve fraction numerator 7 over denominator x plus 1 end fraction plus fraction numerator 4 over denominator x plus 4 end fraction equals 3

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1
4 marks

Simplify.

fraction numerator u x space minus space 2 u space minus space x space plus space 2 over denominator u to the power of 2 space end exponent minus space 1 end fraction

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2
3 marks

straight f open parentheses x close parentheses equals 3 x plus 2  and  straight g open parentheses x close parentheses equals x squared plus 1.

 

Find space fraction numerator straight g open parentheses x close parentheses over denominator straight f open parentheses x close parentheses end fraction plus x.
Give your answer as a single fraction, in terms of x, in its simplest form.

How did you do?

3a
2 marks

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

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3b
3 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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