4MA0 Higher January 2017 Paper 4 Q19

EdexcelHigherOld spec7 marksDrawing & Using Graphs

19 Here is the graph of \(\;y = \mathrm{h}(x)\)

Graph of the cubic curve y = h(x) for x from about -3.3 to 2.6, crossing the x-axis at -3, 0 and 2, with a maximum near (-1.8, 8.2) and a minimum near (1.1, -4)

(a) Use the graph to find an estimate for the gradient of the curve \(\;y = \mathrm{h}(x)\;\) at \(\;(-1, 6)\) (3)

(b) By drawing a suitable straight line on the grid, find an estimate for the solution of the equation \(\;\mathrm{h}(x) = 7 - 2x\)
Give your answer correct to 1 decimal place. (2)

The equation \(\;\mathrm{h}(x) = k\;\) has 3 different solutions for \(\;a \lt k \lt b\)

Mark scheme (a)

Scheme	Marks
tangent at (−1, 6)	M1
\(\dfrac{\text{difference in } y \text{ values}}{\text{difference in } x \text{ values}}\)	M1
−5	A1
	(3)

Notes

M1: For a drawing a tangent

M1: Dep on first M1 awarded

For \(\dfrac{\text{difference in } y \text{ values}}{\text{difference in } x \text{ values}}\) for any two points on a tangent (ignore negative gradient) or

For gradient in the range 4 to 6 inclusive

A1: Accept answer in the range -6 to -4 inclusive
dep on M1

Scheme	Marks
graph \(y = -2x + 7\)	M1
2.2	A1
	(2)

Scheme	Marks
	M1
−4, 8.2	A1
	(2)
	(7 marks)