# CXC general proficiency math exam: Mathematics May/June 2008- Question 9

Section 2

9. (a) Simplify

(i)X² x X³ ÷ X^{4} (1 mark)

(ii)a^{3/2}b^{5/2} x (square root of) ab³. (2 marks)

(b) If ƒ(x) = 2x - 3, find the value of

(i) ƒ(2) (1 mark)

(ii) ƒ^{-1}(0) (2 marks)

(iii) ƒ^{-1} ƒ(2) (2 marks)

(c) The temperature, K. of a liquid t minutes after heating is given in the table below.

t (time in minutes)- 0 - 10 - 20 - 30 - 40 - 50 - 60

K (Temp. in ËšC)- 84 - 61 - 40 - 29 - 27 - 26 - 25

(i) Using a scale of 2cm to represent 10 seconds on the horizontal axis and scale of 2cm to represent 10 degrees on a vertical axis, construct a temperature-time graph to show how the liquid cools in the 60 minute interval.

Draw a smooth curve through all the plotted points. (4 marks)

(ii) Use your graph to estimate

a) the temperature of the liquid after 15 minutes

b) the rate of cooling of the liquid at t = 30 minutes. (3 marks)

Total 15 marks

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