Angles (Including Parallel Lines): WJEC GCSE Numeracy Intermediate November 2023 Unit 2 Q5

Numeracy Intermediate November 2023 Unit 2 Q5

WJECIntermediateCurrent spec13 marksAngles (Including Parallel Lines)Circles & Sectors Compound Measures

5. Treviso is a company that designs and builds bicycles.

(a)

Treviso has designed this new bike frame.
The missing angles need to be calculated.

Bike frame made of straight lines. Two lines marked with single arrows are parallel; the middle strut and the right-hand post are marked with double arrows and are parallel. Angle 54° at the bottom between the strut and the diagonal; angle 48° at the top right between the top bar and the diagonal; angles a and c at the top of the strut, and b at the top right between the diagonal and the post

Diagram not drawn to scale

Find the size of each of the angles \(a\), \(b\) and \(c\). [3]

\(a\) = …………… ° \(b\) = …………… ° \(c\) = …………… °

(b)

Each wheel on Treviso’s new bike has a diameter of 29 inches.

(i)

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]

(ii)

Remember: 12 inches ≈ 30 cm

What is the diameter of each wheel in millimetres? [3]

Diameter is …………… mm

(c) Ollie uses the new bike in a 48 km race.
He completes the race in a time of 1 hour 30 minutes.
Calculate his average speed for the race.
Give your answer in km / h. [3]

Average speed is …………… km / h

Scheme	Marks	Comments
		Answer spaces take precedence, if blank check the diagram
a = 54°	B1
b = 54°	B1	FT ‘their a’
c = 78°	B1	FT 132 – ‘their a’ or 132 – ‘their b’

Mark scheme (b)

Scheme	Marks	Comments
(i) (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 × 29²) \(\dfrac{1000}{29 \div 12}\) (= 413.79…) 1000 x 12 ÷ 29 (= 413.79…)
Answer in the inclusive range 131 to 132 (revolutions)	A1	CAO
(ii) (10 ×) 29 × 30 ÷ 12 or equivalent or for an answer of 72.5	M2	Allow embedded with an incorrect change of units Allow (10 ×) 2.4(16…) × 30 M1 for any one of the following: 30 ÷ 12 (= 2.5) 29 ÷ 12 (= 2.4166…) sight of 2.4, 2.41, 2.416(6…) or 2.42 sight of (1 inch =) 2.5 (cm)
725 (mm)	A1	Answer space takes precedence Allow answers in the range 720 (mm) to 726 (mm) from premature approximation, not from incorrect working

Mark scheme (c)

Scheme	Marks	Comments
(Average speed in km/h =) \(\dfrac{48}{1.5}\) or equivalent	M2	M1 for sight of \(\dfrac{48}{1.3}\) or \(\dfrac{48}{90}\) or for answers of 36.9(…) or 37 or 0.53(33...)
32 (km/h)	A1	CAO. Answer space takes precedence