4400 Higher June 2008 Paper 3 Q21

EdexcelHigherOld spec8 marksDrawing & Using Graphs

21 The diagram shows part of the graph of \(y = \mathrm{f}(x)\).

Graph of the curve y = f(x) for x from -2 to 4.5 and y from -10 to 30

(a) Calculate an estimate for the gradient of the curve at the point where \(x = 3\) (3)

(b) Find an estimate for the solution of the equation \(\mathrm{f}(x) = 0\) (1)

The equation \(\mathrm{f}(x) = mx + c\) where \(m\) and \(c\) are numbers, has three solutions.
Two of the solutions are \(x = -1\) and \(x = 1\)

(c)

(i) Find the value of \(c\).

(ii) Find the third solution of the equation \(\mathrm{f}(x) = mx + c\).

(4)

Mark scheme (a)

Scheme	Marks
tan drawn at (3, 6.5)	M1
\(\dfrac{\text{vertical difference}}{\text{horizontal difference}}\)	M1
2.5 − 6.5 inc	A1
	(3)

Notes

M1: tan or tan produced passes between points (2, \(0 \leqslant y \leqslant 4\)) and (4, \(9 \leqslant y \leqslant 12\))

M1: finds their \(\dfrac{\text{vertical difference}}{\text{horizontal difference}}\) for two points on tan

or finds their \(\dfrac{\text{vertical difference}}{\text{horizontal difference}}\) for two points on curve, where one of the points has an \(x\)-coordinate between 2.5 and 3 inc and the other point has an \(x\)-coordinate between 3 and 3.5 inc

A1: dep on both M marks

Scheme	Marks
\(-1.7\)	B1
	(1)

Scheme	Marks
(i) line joining (\(-1\), 11) & (1, 13)	M1
12	A1
(ii) produces line to cut curve again	M1
4	A1
	(4)
	(8 marks)