Surds
Number
- Higher
- Non-calculator
- 8 questions
- 29 marks
These are original practice questions, not a past paper. This site is independent and not affiliated with AQA or Pearson.
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Simplify $\sqrt{48}$.
2 marks
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Simplify $\sqrt{75}$.
2 marks
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Simplify $\sqrt{50} + \sqrt{18}$.
3 marks
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Expand and simplify $(\sqrt{3} + 2)(\sqrt{3} - 1)$.
3 marks
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Rationalise the denominator of $\dfrac{6}{\sqrt{3}}$.
4 marks
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Rationalise the denominator of $\dfrac{8}{\sqrt{5} - 1}$.
4 marks
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Show that $(\sqrt{12} + \sqrt{3})^{2} = 27$.
5 marks
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Simplify $\sqrt{32} \times \sqrt{2}$. Then show that $(\sqrt{18} - \sqrt{8})(\sqrt{18} + \sqrt{8}) = 10$.
6 marks
Mark scheme
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Answer. $4\sqrt{3}$
- $\sqrt{48} = \sqrt{16 \times 3}$
- $4\sqrt{3}$
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Answer. $5\sqrt{3}$
- $\sqrt{75} = \sqrt{25 \times 3}$
- $5\sqrt{3}$
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Answer. $8\sqrt{2}$
- $\sqrt{50} = 5\sqrt{2}$ and $\sqrt{18} = 3\sqrt{2}$.
- $8\sqrt{2}$
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Answer. $1 + \sqrt{3}$
- $3 - \sqrt{3} + 2\sqrt{3} - 2$
- $1 + \sqrt{3}$
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Answer. $2\sqrt{3}$
- $\dfrac{6\sqrt{3}}{3}$
- $2\sqrt{3}$
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Answer. $2\sqrt{5} + 2$
- Multiply by $\sqrt{5} + 1$.
- $\dfrac{8(\sqrt{5} + 1)}{4} = 2(\sqrt{5} + 1)$.
- $2\sqrt{5} + 2$
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Answer. $27$
- $\sqrt{12} = 2\sqrt{3}$, so $\sqrt{12} + \sqrt{3} = 3\sqrt{3}$.
- $(3\sqrt{3})^{2} = 9 \times 3 = 27$.
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Answer. $8$, and the product is $10$
- $\sqrt{32} \times \sqrt{2} = \sqrt{64} = 8$.
- The second part is a difference of squares: $18 - 8$.
- $18 - 8 = 10$.