Higher January 2022 Paper 1R Q3
3 The shaded shape is made using three identical right-angled triangles and a square.
Diagram NOT accurately drawn
Work out the perimeter of the shaded shape.
(4)
| Scheme | Marks |
|---|---|
| \(12.8^2 + x^2 = 16^2\) oe or \(163.84 + x^2 = 256\) or \((x^2 =)\ 16^2 - 12.8^2\ (= 92.16)\) or \((x^2 =)\ 256 - 163.84\ (= 92.16)\) | M1 |
\((x =)\ \sqrt{16^2 - 12.8^2}\ (= \sqrt{92.16})\ (= 9.6)\) or \((x =)\ \sqrt{256 - 163.84}\ (= \sqrt{92.16})\ (= 9.6)\) | M1 |
| (12.8 – “9.6”) + “9.6” + “9.6” + 16 + 16 + 16 oe | M1 |
| 70.4 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for applying Pythagoras theorem correctly
Allow \(\cos^{-1}\left(\dfrac{12.8}{16}\right)(= 36.9\ldots)\) and \(\dfrac{x}{\sin(36.9\ldots)} = \dfrac{16}{(\sin 90)}\)
M1: for square rooting
Allow \(x = \dfrac{16}{(\sin 90)} \times \sin(36.9\ldots)\)
M1: (dep on M1) for a complete method to find the perimeter
A1: oe e.g. \(\dfrac{352}{5}\)