4MA0 Higher January 2012 Paper 4 Q17

EdexcelHigherOld spec12 marksDrawing & Using Graphs Functions

17 \[\mathrm{f}(x) = \sqrt{x - 6}\]

(a) Find \(\mathrm{f}(10)\) (1)

(b) State which values of \(x\) must be excluded from a domain of f (2)

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

Graph of y = g(x) for x from -2 to 4.5, y from -10 to 30

(d) Find \(\mathrm{fg}(0)\) (2)

(e) One of the solutions of \(\mathrm{g}(x) = k\), where \(k\) is a number, is \(x = 1\)
Find the other solutions.
Give your answers correct to 1 decimal place. (3)

(f) Find an estimate for the gradient of the curve at the point where \(x = 3.5\)
Show your working clearly. (3)

Mark scheme (a)

Scheme	Marks
2	B1
	(1)

Notes

B1: cao

Apart from Questions 3, 13(b) and 17(f) (where the mark scheme states otherwise), the correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method.

Scheme	Marks
\(x \lt 6\)	B2
	(2)

Scheme	Marks
7	B1
	(1)

Scheme	Marks
\(\mathrm{g}(0) = 15\)	M1
3	A1
	(2)

Mark scheme (e)

Scheme	Marks
\(k = 12\)	M1
−0.7 or −0.8 3.8	A2
	(3)

Notes

M1: May be stated or indicated on diagram. May be implied by one correct solution.

A2: A1 for solution rounding to −0.7 or −0.8
A1 for solution rounding to 3.8

Mark scheme (f)

Scheme	Marks
tan drawn at \(x = 3.5\)	M1
\(\dfrac{\text{vertical difference}}{\text{horizontal difference}}\)	M1
6.5 – 11 inc	A1
	(3)
	(Total 12 marks)

Notes

M1: tan or tan produced passes between points (3, \(3 \leqslant y \leqslant 6\)) and (4, \(11 \leqslant y \leqslant 14\))

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 3 and 3.5 inc and the other point has an \(x\)-coordinate between 3.5 and 4 inc

A1: dep on both M marks