Edexcel Oct 2020 IAL Pure Maths WMA13/01

Edexcel Oct 2020 IAL Pure Maths WMA13/01 (pdf)

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1. Solve, for 0 ≤ x < 360°, the equation 2cos2x = 7cosx giving your solutions to one decimal place.
2. A scientist monitored the growth of bacteria on a dish over a 30-day period. The area, N mm², of the dish covered by bacteria, t days after monitoring began, is modelled by the equation log10N = 0.0646 t + 1.478, 0 ≤ t ≤ 30 (a) Show that this equation may be written in the form N = ab^t where a and b are constants to be found. Give the value of a to the nearest integer and give the value of b to 3 significant figures. (b) Use the model to find the area of the dish covered by bacteria 30 days after monitoring began. Give your answer, in mm², to 2 significant figures
3. Figure 1 shows a sketch of a curve with equation y = f(x) where
4. Figure 2 shows a sketch of part of the graph with equation y = f(x) where f(x) = 21 − 2| 2 − x | x ≥ 0 (a) Find ff(6) (b) Solve the equation f(x) = 5x Given that the equation f(x) = k , where k is a constant, has exactly two roots, (c) state the set of possible values of k.
5. (a) Show that

6. Figure 3 shows a sketch of curve C1 with equation y = 5e^x−1 + 3 and curve C2 with equation y = 10 − x² The point P lies on C1 and has y coordinate 18 (a) Find the x coordinate of P, writing your answer in the form lnk, where k is a constant to be found.
7. (a) Express cosx + 4sinx in the form Rcos(x − α) where R > 0 and 0 < α < π/2 Give the exact value of R and give the value of α, in radians, to 3 decimal places. A scientist is studying the behaviour of seabirds in a colony. She models the height above sea level, H metres, of one of the birds in the colony by the equation
8. (i) The curve C has equation y = g(x) where
9. (a) Given that

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