Higher November 2019 Paper 4 Q18
18 The diagram shows a right-angled triangular prism ABCDEF.
Length AD = 11 cm, length CD = 10 cm and length CF = 6 cm.
(a) Calculate the volume of the prism. [2]
(b) Use trigonometry to show that angle FDC = 31°, correct to the nearest degree. [2]
(c) Calculate the exact length of AF. [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 330 | 2 | M1 for \(\frac{1}{2} \times 10 \times 6 \times 11\) | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| tan […] = \(\frac{6}{10}\) oe | 1 | accept any correct method, equivalents include tan-1(0.6) | |
| 30.9[…] | 1 | ||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\sqrt{257}\) cao | 4 | M3 for \(\sqrt{11^2 + 10^2 + 6^2}\) or better or M2 for 112 + 102 + 62 or M1 for 112 + 102 or 102 + 62 or [FD =] \(\frac{10}{\cos 31}\) or \(\frac{6}{\sin 31}\) | implied by 16.0[3…] implied by 257 implied by [FD =] \(\sqrt{136}\) or 11.6 to 11.7 or [AC =] \(\sqrt{221}\) or 14.8 to 14.9 |