Edexcel Jan 2021 IAL Pure Maths WMA13/01 question paper
Edexcel Jan 2021 IAL Pure Maths WMA13/01 mark scheme
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
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
(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.
(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 = abt
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 log10 P against t.
The points are found to lie approximately on a straight line with gradient 0.09 and intercept
0.68 on the log10 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
- The curve C has equation
x = 3 sec2 2y, x > 3, 0 < y < π/4
(a) Find dy/dx in terms of y.
(b) Hence show that
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