# Edexcel 2020 IAL Pure Maths WMA13/01 Specimen

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

1. The point P(7, –2) lies on the curve with equation y = f(x). State the coordinates of the image of P under the transformation represented by the curve with equation (a) y = f(x + 4) + 1 (b) y = f(–2x) + 7
2. (a) Using the identity for cos(A ± B), prove that cos2A ≡ 1 – 2sin2A (b) Hence find, using calculus, the exact value of
3. Guinea pigs and rabbits were introduced onto an island at the same time. The number of guinea pigs, G, t months after they were introduced onto the island is modelled by the equation G = a + 60e–0.05t where a is a positive constant. The number of rabbits, R, t months after they were introduced onto the island is modelled by the equation R = 100 + 80e0.05t Given that there were twice as many guinea pigs as rabbits introduced onto the island, (a) find the value of a.
4. Solve, for 0 ≤ θ < 2π, the equation 3sin 2θ + 5 cos 2θ = 4 giving each answer to 2 significant figures.
5. A function f is defined by

1. Figure 1 shows a sketch of the curve with equation y = │sin x│+ 1, 0 ≤ x ≤ 2π The point P(a,b) lies on the curve and is shown on Figure 1. Given that the gradient of the curve at P is − 1/2 (a) find the exact value of a and the exact value of b. A straight line with positive gradient passes through P. Given that the straight line intersects the curve at exactly three distinct points, (b) find the range in values of the gradient of the line
2. A curve has equation
3. Liam monitored the population of a small country over a 10-year period. The population, P, measured in thousands of people, is modelled by the equation P = ab–t where a and b are constants and t is the number of years since monitoring began. (a) Show that this equation can be expressed in the form
4. A curve has equation
5. Figure 3 shows a sketch of the curve with equation

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