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This page covers Questions and Worked Solutions for Edexcel Jan 2021 IAL Pure Maths, WMA13/01.

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Edexcel Jan 2021 IAL Pure Maths WMA13/01 question paper

Edexcel Jan 2021 IAL Pure Maths WMA13/01 mark scheme

- Find

giving your answer in simplest form. - Figure 1 shows a sketch of the curve with equation y = f(x), where x ∈ R and f(x) is
a polynomial.

The curve passes through the origin and touches the x-axis at the point (3, 0)

There is a maximum turning point at (1, 2) and a minimum turning point at (3, 0)

On separate diagrams, sketch the curve with equation

(i) y = 3f(2x)

(ii) y = f(−x) − 1

On each sketch, show clearly the coordinates of

- the point where the curve crosses the y-axis
- any maximum or minimum turning points

- (a) Show that

where a, b, c and d are integers to be found.

(b) Hence find f^{−1}(x)

(c) Find the domain of f^{−1} - Figure 2 shows a sketch of the graph with equation y = f(x), where
f(x) = |3x + a| + a

and where a is a positive constant.

The graph has a vertex at the point P, as shown in Figure 2.

(a) Find, in terms of a, the coordinates of P.

(b) Sketch the graph with equation y = g(x), where

g(x) = |x + 5a|

On your sketch, show the coordinates, in terms of a, of each point where the graph cuts or meets the coordinate axes.

The graph with equation y = g(x) intersects the graph with equation y = f(x) at two points.

(c) Find, in terms of a, the coordinates of the two points - The temperature, θ °C, inside an oven, t minutes after the oven is switched on, is given by

θ = A – 180e^{–kt}

where A and k are positive constants.

Given that the temperature inside the oven is initially 18°C,

(a) find the value of A.

The temperature inside the oven, 5 minutes after the oven is switched on, is 90°C.

(b) Show that k = plnq where p and q are rational numbers to be found.

Hence find

(c) the temperature inside the oven 9 minutes after the oven is switched on, giving your answer to 3 significant figures,

(d) the rate of increase of the temperature inside the oven 9 minutes after the oven is switched on. Give your answer in °C min^{–1}to 3 significant figures.

- f(x) = x cos(x/3), x > 0

(a) Find fʹ(x)

(b) Show that the equation fʹ(x) = 0 can be written as - (a) Prove that
- The percentage, P, of the population of a small country who have access to the internet, is
modelled by the equation

P = ab^{t}

where a and b are constants and t is the number of years after the start of 2005

Using the data for the years between the start of 2005 and the start of 2010, a graph is plotted of log_{10}P against t.

The points are found to lie approximately on a straight line with gradient 0.09 and intercept 0.68 on the log_{10}P axis.

(a) Find, according to the model, the value of a and the value of b, giving your answers to 2 decimal places.

(b) In the context of the model, give a practical interpretation of the constant a.

(c) Use the model to estimate the percentage of the population who had access to the internet at the start of 2015 - Find
- The curve C has equation

x = 3 sec^{2}2y, x > 3, 0 < y < π/4

(a) Find dy/dx in terms of y.

(b) Hence show that

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