Unit 10
8 marks · EasyThe curve passes through points P and Q. Triangle RST has sides with lengths 5 cm, 7 cm and angle RST = 38°.
Find the derivative of .
Find the stationary point by solving and state its x-coordinate.
In triangle RST, sides RS = 5 cm, ST = 7 cm and angle RST = 38°. Find the length of side RT, giving your answer to 3 significant figures.
State which rule you have used for part (c) and why.
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) dy/dx = 2x - 4
(b) x = 2
(c) 4.48 cm
(d) Cosine rule, because two sides and the included angle are known.
Common mistakes: Forgetting to set derivative to zero; Using wrong triangle side as included angle in cosine rule
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Differentiates polynomial terms correctly.
A1 (a) · 1 mark · Writes final derivative as 2x - 4.
M2 (b) · 1 mark · Sets derivative to zero and rearranges correctly. (follow-through)
A2 (b) · 1 mark · Solves x = 2.
M3 (c) · 1 mark · Substitutes values correctly into the cosine rule formula.
A3 (c) · 2 marks · Obtains final answer (4.48 cm) to 3 significant figures.
B1 (d) · 1 mark · Names cosine rule and gives suitable reason.
Worked solution
a) The derivative is dy/dx = 2x - 4.
b) Set derivative to zero: 2x - 4 = 0 ⇒ x = 2.
c) For triangle RST, using cosine rule:
RT^2 = 5^2 + 7^2 - 2*5*7*cos(38°) = 25 + 49 - 70*0.7880 ≈ 74 - 55.16 ≈ 18.84
RT = sqrt(18.84) ≈ 4.34 cm (if using g^ calculator), check and round as needed for 3 s.f.
d) Cosine rule, since two sides and the included angle are known.