Algebra 5

4 marks · Hard

Rearrange the formula to make the subject, expressing your answer in terms of . Show the necessary algebraic steps.

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h = \frac{-7 \pm \sqrt{49 + 8A}}{4}

Also accept: h = \frac{-7 + \sqrt{49 + 8A}}{4};\ h = \frac{-7 - \sqrt{49 + 8A}}{4}

Common mistakes: Incorrect order of rearrangement; Omitting +/− in square root

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Marking points

M1 · 1 mark · Equates equation to quadratic form: 2h^2 + 7h - A = 0

M2 · 1 mark · Identifies a=2, b=7, c=-A for quadratic formula; attempts substitution (follow-through)

A1 · 1 mark · Correct substitution giving h = ( -7 ± √(49 + 8A) ) / 4 (or equivalent in correct form) (follow-through)

A1b · 1 mark · Shows both + and - roots; expresses answer in terms of A (follow-through)

Worked solution

Starting from:

This is a quadratic in . Use the quadratic formula: