EXN.1.SL.TZ0.2

pestleMathematicsAISLPaper 1EXN· sl-2-5-modelling-functionssource ↗

A factory produces engraved gold disks. The cost $C$ of the disks is directly proportional to the cube of the radius $r$ of the disk.

A disk with a radius of $0.8$ cm costs $375$ US dollars (USD).

Find an equation which links $C$ and $r$ .

[3]

Find, to the nearest USD, the cost of disk that has a radius of $1.1$ cm.

[2]

Markscheme / solution

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

$C = k r^{3}$ (M1)

$375 = k \times 0 . 8^{3} \Rightarrow k = 732 (732.421 \dots)$ (M1)

$C = 732 r^{3}$ A1

[3 marks]

$C = 732.42 \dots \times 1 . 1^{3}$ (M1)

$C = $ 975 (974.853 \dots)$ A1

Note: accept $$ 974$ from use of $C = 732 r^{3}$ .

[2 marks]

Examiners’ report

[N/A]