4400 Higher June 2006 Paper 3 Q16

16 Part of the graph of \(y = x^2 - 2x - 4\) is shown on the grid.

(a) Write down the coordinates of the minimum point of the curve. (1)

(b) Use the graph to find estimates of the solutions to the equation \(x^2 - 2x - 4 = 0\)
Give your answers correct to 1 decimal place. (2)

(c) Draw a suitable straight line on the grid to find estimates of the solutions of the equation \(x^2 - 3x - 6 = 0\) (3)

(d) For \(y = x^2 - 2x - 4\)

(i) find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\),

(ii) find the gradient of the curve at the point where \(x = 6\) (4)

Scheme	Marks
1, −5	B1
	(1)

Mark scheme (b)

Scheme	Marks
Points of intersection of curve and \(x\)-axis indicated	M1
3.2 \(\quad\) −1.2	A1
	(2)

M1: May be implied by one correct solution

A1: for both values seen
Allow ± 0.1
Condone coordinates
Allow solutions to > 1dp unless there is clear evidence that the formula has been used