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Date May 2022 Marks available 5 Reference code 22M.1.AHL.TZ1.16
Level Additional Higher Level Paper Paper 1 Time zone Time zone 1
Command term Find Question number 16 Adapted from N/A

Question

The wind chill index W is a measure of the temperature, in °C, felt when taking into account the effect of the wind.

When Frieda arrives at the top of a hill, the relationship between the wind chill index and the speed of the wind v in kilometres per hour (km h-1) is given by the equation

W=19.34-7.405v0.16

Find an expression for dWdv.

[2]
a.

When Frieda arrives at the top of a hill, the speed of the wind is 10 kilometres per hour and increasing at a rate of 5km h-1minute-1.

Find the rate of change of W at this time.

[5]
b.

Markscheme

use of power rule             (M1)

dWdv=-1.1848v-0.84   OR   -1.18v-0.84            A1

 

[2 marks]

a.

dvdt=5             (A1)

dWdt=dvdt×dWdv             (M1)

dWdt=-5×1.1848v-0.84

when v=10

dWdt=-5×1.1848×10-0.84             (M1)

-0.856  -0.856278°C min-1             A2

 

Note: Accept a negative answer communicated in words, “decreasing at a rate of…”.
Accept a final answer of -0.852809°C min-1 from use of -1.18.
Accept 51.4 (or 51.2)°C hour-1.

 

[5 marks]

b.

Examiners report

There was some success in using the power rule to differentiate the function in part (a). Many failed to recognize that part (b) was a related rates of change problem. There was also confusion about the term “rate of change” and with the units used in this question.

a.
[N/A]
b.

Syllabus sections

Topic 5—Calculus » AHL 5.9—Differentiating standard functions and derivative rules
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