4MA0 Foundation January 2015 Paper 2R Q18
18 The wheel of the Singapore Flyer is a circle with a diameter of 150 metres.
(a) Calculate the circumference of the wheel.
Give your answer correct to the nearest metre. (2)
Give your answer correct to the nearest metre. (2)
The wheel takes 30 minutes to rotate once.
(b) Work out the average speed of a point on the circumference of the wheel as it rotates once.
Give your answer in metres per second correct to 3 significant figures. (3)
Give your answer in metres per second correct to 3 significant figures. (3)
The diagram shows a giant wheel above horizontal ground.
Diagram NOT accurately drawn
The wheel is a circle of diameter \(D\) metres.
The lowest point of the wheel is \(h\) metres above the ground.
The centre of the wheel is \(x\) metres above the ground.
(c) Express \(h\) in terms of \(D\) and \(x\) (2)
| Scheme | Marks |
|---|---|
| \(\pi \times 150\) oe | M1 |
| 471 | A1 |
| (2) |
Notes
A1: awrt 471
| Scheme | Marks |
|---|---|
| 30 × 60 (=1800) or “471” ÷ 30 (=15.7) | M1 |
| “471” ÷ ”1800” or “15.7” ÷ 60 | M1 |
| 0.262 | A1 |
| (3) |
Notes
M1: dep
A1: for 0.26 – 0.262 or ft from (a)
| Scheme | Marks |
|---|---|
Radius = \(x - h\) or \(\dfrac{D}{2} = x - h\) oe | M1 |
| \(h = x - \dfrac{D}{2}\) oe | A1 |
| (2) | |
| (7 marks) |
Notes
A1: or \(h = \dfrac{2x - D}{2}\)