Unit 10

8 marks · Easy

The distance, metres, travelled by a moving object after seconds is given by .

(a)

Find an expression for the velocity of the object at time .

[2 marks]

(b)

Calculate the velocity when seconds.

[1 mark]

(c)

A triangle has sides of lengths 10 cm and 15 cm, and the angle between them is . Work out the area of the triangle, giving your answer to 3 significant figures.

[5 marks]

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.

Show answer

(a) Velocity

(b) Velocity at is m/s

Common mistakes: wrong sign in differentiation; incorrect use of sine area formula (wrong angle or sides); missing degree/radian error

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Differentiates correctly with respect to .

A1 (a) · 1 mark · Correct expression for velocity: .

M2 (b) · 1 mark · Substitutes into velocity expression. (follow-through)

M3 (c) · 1 mark · Identifies correct sides and angle for sine area formula.

M4 (c) · 1 mark · Writes area formula: .

M5 (c) · 1 mark · Substitutes values correctly, checks calculator in degrees. (follow-through)

A2 (c) · 2 marks · Correct area to 3 s.f. (accept 69.2–69.7 cm^2). (follow-through)

Worked solution

a) Differentiate :

b) Velocity at : m/s

c) Area of triangle with sides 10 cm, 15 cm and included angle 68°: