Fractions: WJEC GCSE Intermediate June 2023 Unit 1 Q9

Intermediate June 2023 Unit 1 Q9

(a) Express 48 as a percentage of 400. [2]

(b) Share £45 in the ratio 8 : 1. [2]

£ ………… and £ …………

(c) Express \(1 - \dfrac{1}{2^3}\) as a single fraction in the form \(\dfrac{a}{b}\), where \(a\) and \(b\) are integers. [2]

Mark scheme (a)

Scheme	Marks	Comments
\(\dfrac{48}{400}\) (× 100) or equivalent	M1	M1 for sight of 0·12.
= 12(%)	A1	Note: other complete valid methods to look out for include: 48 ÷ 4 10% + 1% + 1% (= 40 + 4 + 4) (48 out of 400 =) 12 out of 100 = 12(%)

Mark scheme (b)

Scheme	Marks	Comments
Use of \(\dfrac{45}{9}\) or equivalent	M1	Sight of an appropriate 5 (or 40) implies M1.
(£)40 AND (£)5	A1	Accept in either order.

Mark scheme (c)

Scheme	Marks	Comments
( 1 − ) \(\dfrac{1}{8}\)	B1	Award B1 for sight of \(\dfrac{1}{8}\) or 0·125 or 1 ÷ 8.
= \(\dfrac{7}{8}\)	B1	FT from \(1 - \dfrac{m}{n}\) where \(\dfrac{m}{n}\) clearly shown as ‘their \(\dfrac{1}{8}\)’ provided it is written as a fraction and not \(\dfrac{1}{2}\) Mark final answer. A final answer of 0·875 is awarded B1B0.

Scheme	Marks	Comments
\(\dfrac{8 - 1}{8}\) or \(\dfrac{2^3 - 1}{2^3}\)	B1	For consistent correct use of \(2^3 = 8\)
= \(\dfrac{7}{8}\)	B1	FT for ‘their consistent value of \(2^3\)’ e.g. \(\dfrac{6 - 1}{6} = \dfrac{5}{6}\) gains B0B1. Mark final answer. A final answer of 0·875 is awarded B1B0.