4400 Higher June 2007 Paper 3 Q14
14
(a) Make \(r\) the subject of the formula \(A = \pi r^2\), where \(r\) is positive. (2)
The area of a circle is 14 cm2, correct to 2 significant figures.
(b)
(i) Work out the lower bound for the radius of the circle.
Write down all the figures on your calculator display.
Write down all the figures on your calculator display.
(ii) Give the radius of the circle to an appropriate degree of accuracy.
You must show working to explain how you obtained your answer. (4)
You must show working to explain how you obtained your answer. (4)
| Scheme | Marks |
|---|---|
| \(r^2 = \dfrac{A}{\pi}\) | M1 |
| \(\sqrt{\dfrac{A}{\pi}}\) | A1 |
| (2) |
Notes
M1: for \(r^2 = \dfrac{A}{\pi}\) or \(r^2 = A \div \pi\)
A1: Ignore ±
| Scheme | Marks |
|---|---|
(i) \(\sqrt{\dfrac{13.5}{\pi}}\) | M1 |
| 2.07296... | A1 |
(ii) \(\sqrt{\dfrac{14.5}{\pi}}\) or 2.14836... | M1 |
| 2.1 | A1 |
| (4) | |
| (6 marks) |
Notes
M1: for 13.5 seen
A1: for answer which rounds to 2.073
M1: for \(\sqrt{\dfrac{14.5}{\pi}}\) or value which rounds to 2.148 or 2.149 cao
A1: dep on previous 3 marks in (b)