Circles & Sectors: WJEC GCSE Numeracy Higher November 2023 Unit 2 Q1

Numeracy Higher November 2023 Unit 2 Q1

WJECHigherCurrent spec4 marksCircles & Sectors Units & Time

1. Treviso is a company that designs and builds bicycles.
Each wheel on Treviso’s new bike has a diameter of 29 inches.

Remember: 1 foot = 12 inches

Ollie tests Treviso’s new bike over a distance of 1000 feet.
How many times will a wheel rotate during the test? [4]

Mark scheme

Scheme	Marks	Comments
(Number of revolutions is) \(\dfrac{1000}{\pi \times 29 \div 12}\) or \(\dfrac{1000 \times 12}{\pi \times 29}\) or equivalent	M3	Complete method May be seen in stages M2 for any one of the following, or equivalents: π × 29 ÷ 12 \(\dfrac{1000}{\pi \times 29}\) \(\dfrac{\pi \times 29}{1000 \times 12}\) \(\dfrac{1000}{\pi \times (29 \div 2) \div 12}\) \(\dfrac{1000}{\pi \times (2 \times 29) \div 12}\) M1 for any one of the following, that may be embedded in other working: 29 ÷ 12 (= 2.4(1666…)) 1000 × 12 (= 12000) π × 29 (= 91.06 to 91.118) \(\dfrac{1000}{\pi \times n \div 12}\) where n ≠ 0, e.g. 1000 × 12 ÷ (π × 29\(^2\)) \(\dfrac{1000}{29 \div 12}\) (= 413.79…) 1000 x 12 ÷ 29 (= 413.79…)
Answer in the inclusive range 131 to 132 (revolutions)	A1	CAO

Scheme

Marks

Comments

(Number of revolutions is) \(\dfrac{1000}{\pi \times 29 \div 12}\)
or \(\dfrac{1000 \times 12}{\pi \times 29}\)
or equivalent

Complete method
May be seen in stages

M2 for any one of the following, or equivalents:

π × 29 ÷ 12
\(\dfrac{1000}{\pi \times 29}\)
\(\dfrac{\pi \times 29}{1000 \times 12}\)
\(\dfrac{1000}{\pi \times (29 \div 2) \div 12}\)
\(\dfrac{1000}{\pi \times (2 \times 29) \div 12}\)

M1 for any one of the following, that may be embedded in other working:

29 ÷ 12 (= 2.4(1666…))
1000 × 12 (= 12000)
π × 29 (= 91.06 to 91.118)
\(\dfrac{1000}{\pi \times n \div 12}\) where n ≠ 0, e.g. 1000 × 12 ÷ (π × 29\(^2\))
\(\dfrac{1000}{29 \div 12}\) (= 413.79…)
1000 x 12 ÷ 29 (= 413.79…)

Answer in the inclusive range 131 to 132 (revolutions)

CAO