1MA0 Higher June 2013 Paper 2 Q16
*16
Diagram NOT accurately drawn
\(S\) and \(T\) are points on the circumference of a circle, centre \(O\).
\(PT\) is a tangent to the circle.
\(SOP\) is a straight line.
Angle \(OPT = 32^\circ\)
Work out the size of the angle marked \(x\).
Give reasons for your answer. (5)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| Angle \(POT = 180 - 90 - 32 = 58\) (angle between radius and tangent = 90° and sum of angles in a triangle = 180°) Angle \(OST\) = angle \(OTS = 58 \div 2\) (ext angle of a triangle equal to sum of int opp angles and base angles of an isos triangle are equal) or (angle at centre = 2x angle at circumference) OR Angle \(SOT = 90 + 32 = 122\) (ext angle of a triangle equal to sum of int opp angles) \((180 - 122) \div 2\) (base angles of an isos triangle are equal) | 29 | 5 | B1 for angle \(OTP = 90^\circ\), quoted or shown on the diagram M1 for a method that leads to \(180 - (90 + 32)\) or 58 shown at \(TOP\) M1 for completing the method leading to “58”÷2 or 29 shown at \(TSP\) A1 cao C1 for “angle between radius and tangent = 90°” and one other correct reason given from theory used NB: C0 if inappropriate rules listed OR B1 for angle \(OTP = 90^\circ\), quoted or shown on the diagram M1 for a method that leads to 122 shown at \(SOT\) M1 for \((180 - \text{``}122\text{''}) \div 2\) or 29 shown at \(TSP\) A1 cao C1 for “angle between radius and tangent = 90°” and one other correct reason given from theory used NB: C0 if inappropriate rules listed |