2D Area & Perimeter: Eduqas GCSE Higher November 2022 Paper 2 Q5

Higher November 2022 Paper 2 Q5

EduqasHigherCurrent spec7 marks2D Area & Perimeter Circles & Sectors Units & Time

(a) Circle the correct conversion of 7 m³ to cm³. [1]

0·000 07 0·07 700 70 000 7 000 000

(b) The diagram shows a shape made from a trapezium and a circle.

Trapezium with parallel sides 79 cm (top) and 62 cm (bottom), shaded, with a white circle of diameter 30 cm touching both parallel sides

Diagram not drawn to scale

The parallel sides of the trapezium are tangents to the circle.
The diameter of the circle is 30 cm.

The ratio of the white area to the shaded area is as follows.

white area : shaded area
1 : \(k\)

Find the value of \(k\).
Show all your working and give your answer correct to 1 significant figure. [6]

Scheme	Marks	Comments
7 000 000 indicated	B1

Mark scheme (b)

Scheme	Marks	Comments
\(\dfrac{1}{2}\times(79+62)\times 30\) oe	B1	(= 2115)
\(\pi(30\div 2)^2\)	B1	(= 706.858...)
\((\tfrac12 \times (79 + 62) \times 30 - \pi \times 15^2) \div (\pi \times 15^2)\) OR \(\tfrac12 \times (79 + 62) \times 30 \div (\pi \times 15^2) - 1\)	M2	dep on at least B1 awarded; FT ‘their area of circle’ or ‘their area of trapezium’ for M2 or M1 (= (2115 − 225π) ÷ 225π) Award M1 for one of the following: \(\tfrac12 \times (79 + 62) \times 30 - \pi \times 15^2\) (= 1408.1..) \(\tfrac12 \times (79 + 62) \times 30 \div (\pi \times 15^2)\) (= 2.99..) (706.9 : 2115) = 1 : 2.9(9..) or 1 : 3
(\(k\) = ) 1.9(921...) si	A1	CAO
(\(k\) = ) 2	B1	FT ‘their 1.99...’ rounded to 1 sig fig, providing at least M1 previously awarded and a ratio obtained (not for rounding an area). An answer of (\(k\) = ) 2 implies the previous A1 if no incorrect working seen e.g. 706.9 : 1408 = 1 : 2 Note: unsupported answers of 1:2 or k = 2 are awarded zero marks
	(7)

Corrected by Westie's Workshop

The board's mark scheme printed “unsupported answers of 1:2 or k = 2 or are awarded zero marks”. Changed to “unsupported answers of 1:2 or k = 2 are awarded zero marks” because the second “or” has nothing after it, so it is a printing slip. Which answers get zero marks is unchanged.

Original: see the board's mark scheme PDF (link above).