Higher June 2021 Paper 1 Q15
15 \(P\), \(Q\) and \(R\) are points on a circle, centre \(O\).
\(TRV\) is the tangent to the circle at \(R\).
Diagram NOT accurately drawn
Reflex angle \(POR = 238°\)
Angle \(QRV = 60°\)
Calculate the size of angle \(OPQ\).
Give a reason for each stage of your working.
(4)
| Scheme | Marks |
|---|---|
\(ORQ = 90 - 60\ (= 30)\) or \(OQR = 30\) or \(PQR = 0.5 \times (360 - 238)\ (= 61)\) or \(QPR = 60\) or \(OPR = \dfrac{180 - (360 - 238)}{2}\ (= 29)\) | M1 |
| Working not required, so correct answer scores M1A1 (unless from obvious incorrect working) Answer: 31 | A1 |
| NB: degrees symbol not essential for reasons We will allow the symbol Δ for ‘triangle’ ∠ for angle Σ for sum Answer: full reasons for method used | B2 |
| (4) | |
| (4 marks) |
Notes
M1: The correct working or the correct angle for ORQ or OQR or PQR or QPR or OPR. Must be clearly stated as the correct angle or shown on the diagram in correct position. (eg just seeing 30 in working without a label is not sufficient for the award of this mark)
A1: if not on answer line, may be seen on diagram or clearly labelled
B2: (dep on a fully correct method that should lead to the answer) for fully correct reasons for method used (underlined words must be seen) eg
Angle between tangent and radius is 90°
Angles around a point total 360°
Angle at centre is twice angle at circumference/edge
Total of angles in triangle is 180° / triangle 180°
Base angles in an isosceles triangle (or 2 sides equal, so 2 angles equal)
Angles in a quadrilateral total 360° or quadrilateral 360° / Accept “4-sided shape” or “quad”
Alternate segment theorem
(B1 dep on M1 for at least one reason for method used)