Higher November 2020 Paper 2 Q23
23 Right-angled triangle \(ABC\) is the cross section of a prism.
\(AB = 5\) cm \(BC = 12\) cm
\(M\) is the midpoint of \(CF\).
\(AM = 16\) cm
Work out the volume of the prism. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(5^2 + 12^2\) or 169 or \(\sqrt{5^2 + 12^2}\) or 13 | M1 | oe |
| \(\sqrt{16^2 - \text{their } 169}\) or \(\sqrt{16^2 - \text{their } 13^2}\) or \(\sqrt{87}\) or [9.3, 9.33] | M1dep | oe eg \(\sqrt{16^2 - 5^2 - 12^2}\) may be implied eg [18.6, 18.7] |
| \(0.5 \times 5 \times 12 \times 2 \times\) their [9.3, 9.33] | M1dep | oe |
| [558, 559.8] or \(60\sqrt{87}\) | A1 | accept 560 with full method seen SC3 [1116, 1119.6] or \(120\sqrt{87}\) |
| Alternative method 2 | ||
| \(16^2 - 5^2\) or 231 or \(\sqrt{16^2 - 5^2}\) or 15.19(8…) or 15.199 or 15.2 | M1 | oe |
| \(\sqrt{\text{their } 231 - 12^2}\) or \(\sqrt{\text{their } 15.2^2 - 12^2}\) or \(\sqrt{87}\) or [9.3, 9.33] | M1dep | oe eg \(\sqrt{16^2 - 5^2 - 12^2}\) may be implied eg [18.6, 18.7] |
| \(0.5 \times 5 \times 12 \times 2 \times\) their [9.3, 9.33] | M1dep | oe |
| [558, 559.8] or \(60\sqrt{87}\) | A1 | accept 560 with full method seen SC3 [1116, 1119.6] or \(120\sqrt{87}\) |
Additional guidance
| Lengths may be seen on the diagram | |
| 1st and 2nd M marks can be awarded even if not subsequently used | |
| \(5^2 + 12^2 + 16^2\) | M1M0M0A0 |