4MA0 Higher June 2012 Paper 4 Q16
16
Diagram NOT accurately drawn
\(A\), \(B\), \(C\) and \(D\) are four points on a circle.
\(ABX\) and \(DCX\) are straight lines.
\(AB\) = 7 cm, \(BX\) = 5 cm and \(CX\) = 6 cm.
Angle \(BXC = 28^\circ\)
(a) Calculate the length of \(AC\).
Give your answer correct to 3 significant figures. (3)
Give your answer correct to 3 significant figures. (3)
(b) Calculate the length of \(DC\). (3)
| Scheme | Marks |
|---|---|
| (“\(AC^2\)”=) \(6^2 + (7+5)^2 - 2 \times 6 \times (7+5)\cos 28\) | M1 |
| (“\(AC^2\)”=)52.855... | A1 |
| 7.27 | A1 |
| (3) |
Notes
A1: A1 awrt to 52.8 or 52.9
A1: A1 awrt to 7.27
Apart from questions 5, 7, 13c, 16b, 20, 21 and 22 (where the mark scheme states otherwise) the correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method.
| Scheme | Marks |
|---|---|
| 6 × “DX” = 12 × 5 | M1 |
| “DX” = (12 × 5 ÷ 6) (=10) “DC” = “10” − 6 | M1 |
| 4 | A1 |
| (3) | |
| (Total 6 marks) |
Notes
M1: M1 for an attempt to use intersecting chord theorem (external or internal case e.g 7 × 5 = 6 × “x”)
M1: must see a correct justification for the value 10 seen
A1: Ans dependent on at least M1