Higher November 2021 Paper 2 Q14
14
\(A\), \(B\), \(C\) and \(D\) are four points on a circle.
\(SBT\) is a tangent to the circle.
Angle \(ABD = 20^\circ\)
the size of angle \(BAD\) : the size of angle \(BCD = 3 : 1\)
Find the size of angle \(SBA\).
Give a reason for each stage of your working. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 25 with reasons | M1 | for method to find angle \(BCD\) eg \(180 \div (3 + 1)\ (= 45)\) or \(BAD = 180 \div (3 + 1) \times 3\ (= 135)\) |
| M1 | for method to find angle \(BDA\) eg \(180 - 20 - (180 - \text{``}45\text{''})\ (= 25)\) or method to find angle \(SBD\) eg \(SBD = BCD\ (= 45)\) | |
| C2 | for finding \(SBA\ (= 25)\) and both reasons given, eg Opposite angles of a cyclic quadrilateral add up to 180 for angle \(SBD = 45\) because alternate segment theorem | |
| (C1 | (dep M1) for one reason given Opposite angles of a cyclic quadrilateral add up to 180 for angle \(SBD = 45\) because alternate segment theorem) |
Additional guidance
Could be shown on the diagram or in working
Do not award if it ambiguous as to which angle is being found
Underlined words need to be shown; reasons need to be linked to their method