Unit 1

5 marks · Hard

Let the set . Consider the algebraic expression .

(a)

List the elements of set in order of increasing size.

[2 marks]

(b)

If , evaluate .

[1 mark]

(c)

Write the smallest element of set as a simplified fraction.

[2 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.

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(a)

(b) 5

(c)

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Correct approach to find common denominators or logic for ordering fractions.

A1 (a) · 1 mark · All elements written correctly in ascending order.

B1 (b) · 1 mark · Accurate substitution and calculation for when .

M2 (c) · 1 mark · Correct identification of the smallest element.

A2 (c) · 1 mark · Smallest fraction written as a simplified fraction.

Worked solution

(a) Convert all fractions to a common denominator (e.g. 8):

So, the order is .

(b) Substitute into :