Higher June 2018 Paper 2 Q22
22
Diagram NOT accurately drawn
\(A\), \(D\), \(B\) and \(E\) are points on a circle, centre \(O\).
\(AFBC\), \(OEC\) and \(OFD\) are straight lines.
\(AF\) = 7 cm, \(FB\) = 4 cm, \(BC\) = 5 cm, \(FD\) = 2 cm and \(CE\) = \(x\) cm.
Work out the value of \(x\).
Show your working clearly.
(6)
| Scheme | Marks |
|---|---|
| 7 × 4 = 2(2\(r\) – 2) or 7 × 4 = 2(\(d\) – 2) | M1 |
| \(r\) = 8 or \(d\) = 16 | A1 |
| 5 × (5 + 4 + 7) = \(x\) × (2 × “8” + \(x\)) | M1 |
| \(x^2 + 16x - 80\) (= 0) | A1 |
\((x - 4)(x + 20)\) (= 0) \(\dfrac{-16 \pm \sqrt{16^2 - 4 \times 1 \times (-80)}}{2 \times 1}\) or \(\dfrac{-16 \pm \sqrt{576}}{2}\) | M1 |
| Working required Answer: 4 | A1 |
| (6) | |
| (6 marks) |
Notes
M1: Or a correct equation in \(r\)
eg 5.5² − 1.5² = 4\(r\) − 4
M1: Accept 5 × 16 = \(x\)(2\(r\) + \(x\))
M1: Correct factors or evidence of correct use of quadratic formula.
A1: dep on first 2 method marks
Incorrect working giving the radius as 16 cm gains M0A0