Number 10

3 marks · Normal

The expressions and . (a) Simplify as far as possible. [1] (b) Write down in the form , where is an integer. [2]

(a)

Simplify as far as possible.

[1 mark]

(b)

Write in the form , where is an integer.

[2 marks]

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(a) 8\sqrt{5}

(b) 10\sqrt{5}

Common mistakes: Leaving unsimplified; Incorrectly combining surds with different radicands

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Marking points

M1 (a) · 1 mark · Attempts to simplify .

M2 (b) · 1 mark · Attempts to add . (follow-through)

A1 (b) · 1 mark · Writes the final answer in the correct form. (follow-through)

Worked solution

(a) .

(b) .