Edexcel Oct 2020 IAL Pure Maths WMA13/01 (pdf)
- Solve, for 0 ≤ x < 360°, the equation
2cos2x = 7cosx
giving your solutions to one decimal place.
- 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 = abt
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
- Figure 1 shows a sketch of a curve with equation y = f(x) where
- 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.
- (a) Show that
- Figure 3 shows a sketch of curve C1
with equation y = 5ex−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.
- (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
- (i) The curve C has equation y = g(x) where
- (a) Given that
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