Algebraic Fractions | AQA GCSE Further Maths Topic Questions 2020

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1

3 marks

Simplify fully $\frac{15 x^{2} y - 5 x y^{2}}{12 x - 4 y}$

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2a

2 marks

Work out $\frac{a b}{c d} \div \frac{b c}{a d}$

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

[2]

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2b

2 marks

Work out $\frac{7}{2 x^{2}} + \frac{4}{3 x}$

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

[2]

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3

5 marks

Simplify $\frac{8 x^{3} - 50 x}{2 x (6 x^{2} - x - 35)}$

Give your answer in the form $\frac{a x + b}{c x + d}$ where $a, b, c$ and $d$ are integers.

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4a

1 mark

Circle the expression that is equivalent to $\frac{1}{a} + \frac{1}{b}$

\frac{2}{a + b}

\frac{a b}{b + a}

\frac{2}{a b}

\frac{b + a}{a b}

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4b

3 marks

Simplify fully $\frac{6 c^{4} - c^{3}}{36 c^{2} - 1}$

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5

2 marks

Write $\frac{5}{6 a} + \frac{a}{4}$ as a single fraction.
Give your answer in its simplest form.

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6

4 marks

Simplify fully $\frac{x - x^{3}}{2 x + 2 x^{2}}$

You must show your working.

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7

3 marks

Write $\frac{7}{9 x} + \frac{2}{3 x^{2}}$ as a single fraction in its simplest form.

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8

4 marks

Show that $\frac{x^{4}}{x + 4} \times \frac{x + 2}{x} \div \frac{x^{2}}{3 x + 12}$

simplifies to the form $a x^{2} + b x$ where $a$ and $b$ are integers.

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9

2 marks

Simplify $\frac{x^{2} - 7 x + 10}{x^{2} - 2 x - 15}$

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10

6 marks

Solve $\frac{3}{x - 2} + \frac{2}{x - 1} = 5$

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

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11

5 marks

$f (x) = \frac{x}{2 x + 1}$ for positive values of $x$ .

Work out $f (x + 1) - f (x)$

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

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Algebraic Fractions (AQA GCSE Further Maths)

Topic Questions