4MA0 Higher January 2016 Paper 3 Q17
17

Diagram NOT accurately drawn
\(L\), \(M\) and \(P\) are points on a circle, centre \(O\)
Angle \(LMP\) = 48°
(a)
(i) Write down the size of angle \(LOP\)
(ii) Give a reason for your answer.
(2)
Diagram NOT accurately drawn
\(Q\), \(R\), \(S\) and \(T\) are points on a circle.
\(ATB\) is the tangent to the circle at \(T\)
Angle \(STR\) = 26°
Angle \(RQT\) = 73°
(b) Work out the size of angle \(STA\)
Give a reason for each stage in your working. (3)
Give a reason for each stage in your working. (3)
| Scheme | Marks |
|---|---|
| (i) Answer: 96 | B1 |
| (ii) Answer: Angle at the centre is twice angle at the circumference | B1 |
| (2) |
Notes
B1: (indep)
| Scheme | Marks |
|---|---|
| 73 − 26 | M1 |
| 47 | A1 |
| B1 | |
| (3) |
Notes
M1: for a complete method
B1: (dep on M1) Alternate segment theorem
Alternative Scheme
| Scheme | Marks |
|---|---|
| Angle \(RST\) = 180 − 73 (=107) and Angle \(SRT\) = 180 − 26 − "107" | M1 |
| 47 | A1 |
| B1 |
Notes
B1: (dep on M1) Alternate segment theorem