4MA0 Higher June 2015 Paper 4R Q17
17 \(J\), \(K\), \(L\) and \(M\) are points on the circumference of a circle.
\(GJH\) is the tangent to the circle at \(J\).
\(MK\) and \(JL\) intersect at the point \(P\).
\(GML\) is a straight line.
Angle \(HJK = 62^\circ\), angle \(JKM = 21^\circ\) and angle \(JGL = 78^\circ\)
Diagram NOT accurately drawn
(a) Write down the size of angle \(MLJ\). (1)
(b) Write down the size of angle \(JLK\). (1)
(c) Work out the size of angle \(KPL\). (3)
| Scheme | Marks |
|---|---|
| 21 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| 62 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(\angle KJL = 37^\circ\) or \(\angle PJM = 60^\circ\) or \(\angle LKM = 60^\circ\) or \(\angle LMP = 37^\circ\) or \(\angle MPJ = 58^\circ\) or \(MPL = 122^\circ\) or \(JPK = 122^\circ\) | M2 |
| 58 | A1 |
| (3) |
Notes
M2: If not M2 then M1 for: \(\angle GJL = 81^\circ\) or \(\angle GMJ = 81^\circ\) or \(JKL = 81^\circ\) or \(JML = 99^\circ\)
Angles may be marked on the diagram or labelled in the working.