Higher November 2023 Paper 3 Q24
24 The diagram shows a triangular prism with a horizontal rectangular base \(ABCD\).
\(M\) is the midpoint of \(AD\).
The vertex \(T\) of the prism is vertically above \(M\).
\(P\) is the point on \(AB\) such that \(AP : PB = 5 : 2\)
Calculate the size of the angle between \(TP\) and the base \(ABCD\) of the prism.
Give your answer correct to 1 decimal place. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 12.2 | P1 | for process to find \(AP\), eg \(\tfrac{5}{7} \times 14.7\ (= 10.5)\) or for showing the required angle on a diagram eg with an arc |
| P1 | for process to find \(MP\), eg \(\sqrt{\text{``}10.5\text{''}^2 + 1.9^2}\) oe \((= 10.6\ldots)\) or for a process to find \(TP\), eg \(\sqrt{\text{``}10.5\text{''}^2 + 1.9^2 + 2.3^2}\) oe \((= 10.9\ldots)\) | |
| P1 | for using appropriate trigonometry ratio to find angle \(TPM\), eg \(\tan TPM = \dfrac{2.3}{\text{``}10.6\ldots\text{''}}\) or \(\sin TPM = \dfrac{2.3}{\text{``}10.9\ldots\text{''}}\) or \(\cos TPM = \dfrac{\text{``}10.6\ldots\text{''}}{\text{``}10.9\ldots\text{''}}\) | |
| A1 | for answer in the range 12.1 to 12.2 |
Additional guidance
Check diagram for working
If an answer is shown in the range in working and then incorrectly rounded award full marks.