Unit 10
8 marks · EasyA curve has equation .
Differentiate the equation to find .
Find the coordinates of the stationary point of the curve.
A triangle has sides 12 cm, 8 cm and 7 cm, opposite angles respectively. Use the cosine rule to find the size of angle .
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a)
(b) Stationary point at
(c) Angle (3 s.f.) degrees
Common mistakes: sign error in differentiation; substitute wrong values in cosine rule; forgetting to solve derivative = 0 for x
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Attempts to differentiate each term.
A1 (a) · 1 mark · Correct derivative:
M2 (b) · 1 mark · Equates derivative to 0 to find x. (follow-through)
M3 (b) · 1 mark · Finds corresponding y value. (follow-through)
A2 (b) · 1 mark · Correct stationary point: (follow-through)
M4 (c) · 1 mark · Sets up the cosine rule correctly.
M5 (c) · 1 mark · Carries out calculation for . (follow-through)
A3 (c) · 1 mark · Correct value for (accept answers in range 129–131°). (follow-through)
Worked solution
a) Differentiate each term: so .
b) Stationary points occur when
So stationary point is .
c) Label triangle as: a = 12 cm (opposite A), b = 8 cm, c = 7 cm.