Foundation November 2022 Paper 2 Q16

AQACurrent spec5 marksPie Charts

16 Some people were asked for the main way they listen to music.

A pie chart is drawn to represent their answers.

Not drawn accurately

(a) Work out the size of angle \(x\). [2 marks]

(b) 135 people said Computer.

How many people said Phone? [3 marks]

Mark scheme (a)

Answer	Mark	Comments
\(360 - 162 - 40 - 90\) or 68 or \(x + x + 162 + 40 + 90 = 360\)	M1	oe eg \(360 - 292\) or \(2x + 292 = 360\)
34	A1

\(68 \div 2\)	M1
68 may be embedded for M1 eg \(68 + 162 + 40 + 90 = 360\) eg \(162 + 40 + 90 + 30 + 38 = 360\) (because 30 and 38 total 68) eg \(162 + 40 + 90 + 34 + 34 = 360\) (34 needs to be selected to score A1)	M1 M1 M1
34 seen followed by answer 68	M1A0

Mark scheme (b)

Answer	Mark	Comments
\(\dfrac{135}{90}\) or 1.5 or \(\dfrac{90}{135}\) or 0.66(…) or 0.67 or any correct method that would lead to answer 243 eg \(\dfrac{162}{90} \times 135\) or \(135 \div \dfrac{90}{162}\) or \(\dfrac{162}{360} \times 135 \times 4\) or \(0.45 \times 540\) or \(135 \times 4 \div \dfrac{360}{162}\) or \(162 + 162 \div 2\) or \(135 + 108\)	M2	oe M1 linking a correct angle with number of people eg \(90 \to 135\) or \(\dfrac{1}{4} \to 135\) or \(180 \to 270\) or \(72 \to 108\) or \(135 \times 360 \div 90\) or \(135 \times 4\) or 540 or \(\dfrac{162}{90}\) or 1.8 or \(\dfrac{90}{162}\) or 0.55(…) or 0.56 or \(\dfrac{162}{360}\) or 0.45 or 45% or \(\dfrac{360}{162}\) or 2.22(…)
243	A1

Up to M2 may be awarded for correct work with no answer, or incorrect answer, even if this is seen amongst multiple attempts
M1 may be seen as eg \(90 = 135\)
If shown on pie chart, just writing 135 in Computer sector is insufficient for M1 unless 90 or \(\dfrac{1}{4}\) also shown
Allow embedded fraction, even in an incorrect calculation for at least M1 eg \(\dfrac{90}{162} \times 135\) eg \(\dfrac{90}{135} \times 162\)	M1 M2
Build-up must be correct or full method must be shown
243 from an incorrect method eg \(135 + 40 + 68\)	M0A0