Exam-Style Questions on Surds

Problems on Surds adapted from questions set in previous Mathematics exams.

1.

GCSE Higher

(a) Without using a calculator, show that $$\sqrt{28}=2\sqrt7$$

The point $$X$$ is shown on the unit grid below. The point $$Y$$ is $$\sqrt17$$ units from $$X$$ and lies on the intersection of two grid lines. Mark one possible position for $$Y$$.

2.

GCSE Higher

(a) Express $$\sqrt{5} + \sqrt{20}$$ in the form $$a \sqrt{5}$$ where $$a$$ is an integer.

(a) Express $$( \frac{1}{ \sqrt{5} } ) ^ 9$$ in the form $$\frac{ \sqrt{b}}{c}$$ where $$b$$ and $$c$$ are integers.

3.

GCSE Higher

(a) Write this list of numbers in order, smallest first.

$$\sqrt{47}, \frac{22}{3}, 3.5^2, 8.64$$

(b) Write $$(1 + \sqrt5)^2$$ in the form $$a + b\sqrt5$$ .

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The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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