| Date | May Specimen | Marks available | 4 | Reference code | SPM.1.sl.TZ0.6 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Calculate | Question number | 6 | Adapted from | N/A |
Question
The diagram shows a rectangular based right pyramid VABCD in which \({\text{AD}} = 20{\text{ cm}}\), \({\text{DC}} = 15{\text{ cm}}\) and the height of the pyramid, \({\text{VN}} = 30{\text{ cm}}\).
Calculate
(i) the length of AC;
(ii) the length of VC.
Calculate the angle between VC and the base ABCD.
Markscheme
(i) \(\sqrt {{{15}^2} + {{20}^2}} \) (M1)
Note: Award (M1) for correct substitution in Pythagoras Formula.
\({\text{AC}} = 25{\text{ (cm)}}\) (A1) (C2)
(ii) \(\sqrt {{{12.5}^2} + {{30}^2}} \) (M1)
Note: Award (M1) for correct substitution in Pythagoras Formula.
\({\text{VC}} = 32.5{\text{ (cm)}}\) (A1)(ft) (C2)
Note: Follow through from their AC found in part (a).
\(\sin {\text{VCN}} = \frac{{30}}{{32.5}}\) OR \(\tan {\text{VCN}} = \frac{{30}}{{12.5}}\) OR \(\cos {\text{VCN}} = \frac{{12.5}}{{32.5}}\) (M1)
\({ = 67.4^ \circ }\) (\(67.3801 \ldots \)) (A1)(ft) (C2)
Note: Accept alternative methods. Follow through from part (a) and/or part (b).
