# Edexcel Jan 2020 IAL Pure Maths WMA13/01

This is part of a collection of videos showing step-by-step solutions for Edexcel A-Level Mathematics past papers.
This page covers Questions and Worked Solutions for Edexcel Jan 2020 IAL Pure Maths, WMA13/01.

Related Pages
More A Levels Past Papers

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

1. A population of a rare species of toad is being studied.
The number of toads, N, in the population, t years after the start of the study, is modelled by the equation
According to this model,
(a) calculate the number of toads in the population at the start of the study,
(b) find the value of t when there are 420 toads in the population, giving your answer to 2 decimal places.
(c) Explain why, according to this model, the number of toads in the population can never reach 500
2. The function f and the function g are defined by
3. Figure 1 shows a linear relationship between log10 y and log10 x
The line passes through the points (0, 4) and (6, 0) as shown.
(a) Find an equation linking log10 y with log10 x
4. (a) Find f′(x) in the form
5. (a) Use the substitution t = tanx to show that the equation
12tan 2x + 5cot x sec2 x = 0
can be written in the form
5t4 – 24t2 – 5 = 0
(b) Hence solve, for 0 ≤ x < 360°, the equation
12tan 2x + 5 cot x sec2 x = 0

1. Figure 2 shows part of the graph with equation y = f(x), where
f(x) = 2|2x – 5| + 3, x ≥ 0
The vertex of the graph is at point P as shown.
(a) State the coordinates of P.
(b) Solve the equation f(x) = 3x – 2
Given that the equation
f(x) = kx + 2
where k is a constant, has exactly two roots,
(c) find the range of values of k.
2. Figure 3 shows a sketch of part of the curve with equation
y = 2 cos 3x – 3x + 4, x > 0
where x is measured in radians.
The curve crosses the x‑axis at the point P, as shown in Figure 3.
Given that the x coordinate of P is α,
(a) show that α lies between 0.8 and 0.9
3. (i) Find, using algebraic integration, the exact value of
4. f(θ) = 5cos θ – 4sinθ, θ ∈ R
(a) Express f(θ) in the form Rcos(θ + α), where R and α are constants, 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.
The curve with equation y = cos θ is transformed onto the curve with equation y = f(θ) by a sequence of two transformations.
Given that the first transformation is a stretch and the second a translation,
(b) (i) describe fully the transformation that is a stretch,
(ii) describe fully the transformation that is a translation

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 