Unit 7

5 marks · Normal

This question tests understanding of recurring decimals and solving quadratic equations.

(a)

Write the recurring decimal as a fraction in its simplest form.

[2 marks]

(b)

Let be the fraction you found in part (a). Solve the quadratic equation for .

[3 marks]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

(a) 47/99 · must show Correct recurring decimal conversion to fraction

(b) x=1 or x=2 · must show Both roots of the quadratic equation

Common mistakes: Incorrect fraction for a recurring decimal; Factoring errors in quadratic

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Let , multiply both sides by 100 and subtract equations.

A1 (a) · 1 mark · Correct fraction in simplest form:

M2 (b) · 1 mark · Set up and attempt to solve with correct values of . Factorises or uses quadratic formula. (follow-through)

A2 (b) · 2 marks · Both correct values: and , follow through from their part (a) if value is substituted appropriately. (follow-through)

Worked solution

Let

Subtract the first from the second:

The quadratic equation is .

Factorise: .

So or .