(a) Complete the table of values for \(y = x^3 - 12x + 2\)
\(x\)
−3
−2
−1
0
1
2
3
4
\(y\)
11
−7
18
(2)
(b) On the grid, draw the graph of \(y = x^3 - 12x + 2\) for values of \(x\) from −3 to 4(2)
(c) For the curve with equation \(y = x^3 - 12x + 2\)
(i) find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\)
(ii) find the gradient of the curve at the point where \(x = 5\)
(4)
Mark scheme (a)
Scheme
Marks
18 13 2 −9 −14
B2
(2)
Notes
B2: for all correct B1 for 3 or 4 correct
Mark scheme (b)
Scheme
Marks
Points
B1
Curve
B1
(2)
Notes
B1: ± ½ sq ft from (a) if at least B1 in (a)
B1: ft if B1 awarded for points or if there is not more than one point incorrectly plotted and at least B1 scored in (a) Award for single curve (not line segments) which does not miss more than one plotted point by more than ½ square
Mark scheme (c)
Scheme
Marks
(i) Answer: \(3x^2 - 12\)
B2
(ii) \(3 \times 5^2 - 12\)
M1
63
A1
(4)
(8 marks)
Notes
B2: B2 for \(3x^2 - 12\) B1 for two of three terms differentiated correctly
M1: for substn \(x = 5\) in their (c)(i) if at least B1 scored in (c)(i)
