Higher June 2018 Paper 1R Q16
16
Diagram NOT accurately drawn
The points \(B\), \(C\), \(Y\) and \(X\) lie on a circle.
\(AXY\) and \(ABC\) are straight lines.
\(AX\) = 12 cm \(XY\) = \(x\) cm \(AB\) = \(x\) cm \(BC\) = 4 cm
(a) Show that \(x^2 - 8x - 144 = 0\) (3)
(b) Find the length of \(AC\).
Show your working clearly.
Give your answer correct to 3 significant figures. (4)
Show your working clearly.
Give your answer correct to 3 significant figures. (4)
| Scheme | Marks |
|---|---|
| \(x(x + 4) = 12(12 + x)\) | M1 |
| \(x^2 + 4x = 144 + 12x\) | M1 |
| Shown | A1 |
| (3) |
Notes
M1: for at least one correct expression
A1: for completion
| Scheme | Marks |
|---|---|
\(x = \dfrac{--8 \pm \sqrt{(-8)^2 - 4 \times 1 \times (-144)}}{2}\) or \(\dfrac{8 \pm \sqrt{8^2 - 4 \times 1 \times (-144)}}{2}\) or \(\dfrac{8 \pm \sqrt{-8^2 - 4 \times 1 \times (-144)}}{2}\) | M1 |
\(\dfrac{8 \pm \sqrt{640}}{2}\) or \(\dfrac{--8 \pm \sqrt{(-8)^2 - -576}}{2 \times 1}\) or \(\dfrac{8 \pm 8\sqrt{10}}{2}\) NB denominator must be 2×1 or 2 and there must be evidence for correct order of operations in the numerator Allow + instead of ± in the formula | M1 |
| A1 | |
| 20.6 | B1 |
| (4) | |
| (7 marks) |
Notes
M1: M1 for correctly substituting into the quadratic formula
condone one sign error in substitution; allow partial correct evaluation
M1: If the first M1 is awarded and an answer of 16.6.... or \(4 + 4\sqrt{10}\) seen award this M mark
A1: (dep on M1) 16.6….
B1: (dep on M1) 20.6 - 20.65 ft