4MA0 Higher January 2017 Paper 3R Q10
10 Here is an isosceles triangle.
Diagram NOT accurately drawn
Work out the area of the triangle.
Give your answer correct to 3 significant figures.
(4)
| Scheme | Marks |
|---|---|
| \(18^2 - (14 \div 2)^2\) (=275) | M1 |
| \(\sqrt{18^2 - (14 \div 2)^2}\) or \(\sqrt{275}\) or \(5\sqrt{11}\) or 16.5… or 16.6 | M1 |
| 0.5 × 14 × “16.5…” or \(35\sqrt{11}\) | M1 |
| 116 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: or M1 for \(\cos x = \dfrac{7}{18}\) or \(\sin y = \dfrac{7}{18}\)
or \(\cos z = \dfrac{18^2 + 18^2 - 14^2}{2 \times 18 \times 18}\)
M1: or M1 for \(x = \cos^{-1}\left(\dfrac{7}{18}\right)\) or \(x\) = 67.1…
or \(y = \sin^{-1}\left(\dfrac{7}{18}\right)\) or \(y\) = 22.8…
or \(z = \cos^{-1}\left(\dfrac{18^2 + 18^2 - 14^2}{2 \times 18 \times 18}\right)\) or \(z\) = 45.77...
M1: or M1 for 0.5×14×18×sin(“67.1…”) or
0.5×18×18×sin(2ד22.8…”) or
0.5×18×18×sin(“45.77...”)
A1: 116 – 116.1
NB Allow use of Hero’s formula
Alternative scheme
| Scheme | Marks |
|---|---|
| 25(25 – 18)(25 – 18)(25 – 14)(= 13475) oe | M2 |
| \(\sqrt{13475}\) oe | M1 |
| 116 | A1 |