Graphs 6

3 marks · Easy

The equation models the volume, in cubic centimetres, of a container where is the length in centimetres.

(a)

Calculate the volume when .

[1 mark]

(b)

Find the value of for which between and .

[2 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.

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(a) -4 cm^3

(b) x = 0 or x = 3 · must show States both x = 0 and x = 3, in range

Common mistakes: Solving V = x^3 + 3x^2; Making sign errors

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Substitutes x = 2 correctly into the formula.

M2 (b) · 1 mark · Sets V = 0 and attempts to solve x^3 - 3x^2 = 0.

A1 (b) · 1 mark · Gives both solutions x = 0 and x = 3 (within the given range).

Worked solution

a) Substitute :

b) Set :

Factorising:

So, or .