Exponential and trigonometric graphs

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Calculator · 2 marks
(a) A model gives the mass of a culture at times 0, 1, 2, 3 and 4 hours as 80, 120, 180, 270 and 405 grams respectively. The plotted points are joined by straight segments. Use this graph model to estimate when the mass reaches 300 grams. Give your answer to 1 decimal place. (2)
Question 2Non-calculator · 4 marks
A population model is $P=40(1.5)^t$ , where t is years after the initial measurement.
(a) Find the modelled population after 3 years. (2)
(b) Find t when the model gives P = 202.5. (2)
Question 3Non-calculator · 5 marks
$\sin 40^{\circ} = 0.643$ , correct to 3 decimal places.
(a) Find another angle between $0^{\circ}$ and $360^{\circ}$ whose sine is $0.643$ . (1)
(b) Find the angle between $180^{\circ}$ and $270^{\circ}$ whose sine is $-0.643$ . (2)
(c) Find the angle $x$ between $0^{\circ}$ and $90^{\circ}$ with $\cos x = 0.643$ . (2)

Answers and marks

(a) $3.2$ hours

(a) $135$

M1 Repeated percentage growth uses the multiplier raised to the number of years.
A1 Correct answer: $135$

(b) $4$

(a) $140^{\circ}$

(b) $220^{\circ}$

M1 Using $180^{\circ} + 40^{\circ}$ or the rotational symmetry about $(180, 0)$ .
A1 The correct answer, $220^{\circ}$ .

(c) $50^{\circ}$

P1 Using $\cos x = \sin(90^{\circ} - x)$ (the cosine graph is the sine graph shifted by $90^{\circ}$ ).
A1 The correct answer, $50^{\circ}$ .

Exponential and trigonometric graphs

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