4MA0 Foundation June 2016 Paper 2 Q22
22
Diagram NOT accurately drawn
(a) Work out the perimeter of the triangle. (4)
(b) The length of AB is 13.5 cm correct to 3 significant figures.
Write down the lower bound of the length of AB. (1)
Write down the lower bound of the length of AB. (1)
| Scheme | Marks |
|---|---|
| \(13.5^2 + 60^2\) or 182.25 + 3600 or 3782.25 | M1 |
| \(\sqrt{\text{“3782.25”}}\) or awrt 61.5 | M1 |
| \(13.5 + 60 + \sqrt{\text{“3782.25”}}\) or 13.5 + 60 + 61.5 | M1 |
| 135 | A1 |
| (4) |
Notes
M1: For squaring and adding
M1: (Dep) for square root
M1: Dep
A1: Cao
NB: A0 if 61.5 is rounded from an inexact value (eg 61.505…)
Alternative method – using Trigonometry
| Scheme | Marks |
|---|---|
| Eg \(A = 77.3(196\ldots)\) and \(\sin \text{“77.3”} = \dfrac{60}{AC}\) | M1 |
| \((AC =)\ \dfrac{60}{\sin \text{“77.3”}}\) or awrt 61.5 | M1 |
| \(13.5 + 60 + \dfrac{60}{\sin \text{“77.3”}}\) or 13.5 + 60 + 61.5 | M1 |
| 135 | A1 |
Notes
M1: For finding a correct angle AND a correct trig statement
M1: (Dep) For an expression for \(AC\)
M1: Dep
A1: cao
NB: A0 if 61.5 is rounded from an inexact value (eg 61.505…)
| Scheme | Marks |
|---|---|
| 13.45 | B1 |
| (1) |