Higher November 2021 Paper 3 Q10
10 The diagram shows two right-angled triangles \(ACB\) and \(DEB\).
\(AD = 9\) cm
\(DE = 2\) cm
\(DB = 6\) cm
Calculate the length of \(CB\).
Give your answer correct to 2 decimal places. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 14.14 | P1 | works out scale factor eg \((9 + 6) \div 6\ (= 2.5)\) OR for start of process to find angle \(DBE\) eg \(\sin B = \dfrac{2}{6}\) oe |
| P1 | uses Pythagoras eg \(6^2 - 2^2\ (= 32)\) or \(\sqrt{32}\ (= 5.6...)\) OR calculates \(AC\) eg \(2 \times \text{``}2.5\text{''}\ (= 5)\) OR for complete process to find angle \(DBE\) eg \(\sin^{-1}\left(\dfrac{2}{6}\right)\ (= 19.4...)\) | |
| P1 | complete process to find \(CB\) eg \(\text{``}2.5\text{''} \times \text{``}\sqrt{32}\text{''}\ (= 10\sqrt{2})\) or \(\sqrt{(9 + 6)^2 - \text{``}5\text{''}^2}\ (= 10\sqrt{2})\) OR uses trigonometry, eg \(15 \times \cos \text{``}19.4...\text{''}\) | |
| A1 | 14.1 to 14.15 |
Additional guidance
Note method can be carried out in either order
May be seen on diagram
If the answer is given within the range but then rounded incorrectly award full marks.