Unit 6
4 marks · Easy(a) The population P of a type of insects is inversely proportional to the average daily temperature T. When T = 15°C, P = 600.
(b) Let set A = {T | P ≥ 200, T > 0}.
Find P when T = 30°C.
List all integer values of T, greater than 0 and less than or equal to 45, for which P ≥ 200.
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) P = 300
(b) T = 1 to 45, except T > 45 excluded. Largest integer satisfying 600/T ≥ 200 is 3, so T = 1,2,3 only.
Common mistakes: inverting ratio or missing valid T
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Marking points
M1 (a) · 1 mark · States or uses correct inverse proportion formula.
A1 (a) · 1 mark · Finds P for T = 30°C (P=300).
M1 (b) · 1 mark · Sets up correct inequality for P ≥ 200.
A1 (b) · 1 mark · Finds all integer T for which P ≥ 200 holds, i.e., T = 1, 2, 3.
Worked solution
(a) P = k/T. When T = 15, P = 600, so k = 600 × 15 = 9000. When T = 30, P = 9000/30 = 300.
(b) 600/T ≥ 200 ⇒ T ≤ 3, and since T > 0 and integer ≤ 45, T = 1, 2, 3.