Foundation June 2022 Paper 2 Q11

AQACurrent spec4 marksFractions

11 Nihal has savings of £168

He uses \(\dfrac{5}{7}\) of his savings to buy sports equipment.

(a) Assume that he will use \(\dfrac{1}{3}\) of the rest of the money to buy a shirt.

How much of his savings, in £, will he have left? [3 marks]

(b) In fact, he uses more than \(\dfrac{1}{3}\) of the rest of the money to buy a shirt.

What does this tell you about how much of his savings he has left?

Tick one box. [1 mark]

Mark scheme (a)

Answer	Mark	Comments
Alternative method 1
\(\dfrac{5}{7} \times 168\) or 120	M1	oe eg \(168 \div 7 \times 5\) implied by 48 allow 0.71(4…) or 71(.4…)% for \(\dfrac{5}{7}\)
\(\dfrac{1}{3} \times (168 -\) their 120) or \(\dfrac{1}{3} \times 48\) or 16 or \(\left(1 - \dfrac{1}{3}\right)\) \(\times\ (168 -\) their 120) or \(\left(1 - \dfrac{1}{3}\right)\) \(\times\) 48	M1	oe must subtract their 120 from 168 with \(10 \lt\) their \(120 \lt 150\) allow 0.33(3…) or 33(.3…)% for \(\dfrac{1}{3}\) allow 0.66(6…) or 0.67 or 66(.6…)% or 67% for \(\left(1 - \dfrac{1}{3}\right)\) 16 is M1M1
32(.00p)	A1	SC2 80 SC1 40
Alternative method 2
\(\left(1 - \dfrac{5}{7}\right)\) \(\times\) 168 or 48	M1	oe eg \(168 \div 7 \times 2\) allow 0.28(6…) or 0.29 or 28(.6…)% or 29% for \(\left(1 - \dfrac{5}{7}\right)\)
\(\dfrac{1}{3} \times\) their 48 or 16 or \(\left(1 - \dfrac{1}{3}\right)\) \(\times\) their 48	M1	oe \(18 \lt\) their \(48 \lt 100\) allow 0.33(3…) or 33(.3…)% for \(\dfrac{1}{3}\) allow 0.66(6…) or 0.67 or 66(.6…)% or 67% for \(\left(1 - \dfrac{1}{3}\right)\) 16 is M1M1
32(.00p)	A1	SC2 80 SC1 40

Up to M2 may be awarded for correct work with no, or incorrect answer, even if this is seen amongst multiple attempts
\(\dfrac{5}{7} \times 168 = 120\), \(120 \div 3 = 40\), Answer 40	M1M0A0 (or SC1)
\(\dfrac{5}{7} \times 168 = 120\), \(120 \div 3 = 40\), Answer 80	SC2
Alt 1 Allow 0.71(4…) or 71(.4…)% for \(\dfrac{5}{7}\) and 0.33(3…) or 33(.3…)% for \(\dfrac{1}{3}\)
eg \(0.71 \times 168 = 119.28\)	M1
\(0.33 \times (168 - 119.28) = 16.08\), Answer 32.64	M1A0
Do not allow \(\dfrac{5}{7} = 0.7\) or \(\dfrac{2}{7} = 0.3\) or \(\dfrac{1}{3} = 0.3\) or \(\dfrac{2}{3} = 0.7\)
eg \(0.7 \times 168 = 117.6\)	M0
\(0.3 \times (168 - 117.6) = 15.12\), Answer 35.28	M0A0
Second mark of Alt 1 is independent
eg \(0.7 \times 168 = 117.6\) (unacceptable to use 0.7 for \(\dfrac{5}{7}\))	M0
\((168 - 117.6) \div 3 = 16.8\)	M1A0
Second mark of Alt 2 is independent
eg \(0.3 \times 168 = 50.4\) (unacceptable to use 0.3 for \(\dfrac{2}{7}\))	M0
\(0.33 \times 50.4 = 16.63\)	M1A0
Calculation shown as eg \(71\% \times 168\)	M1