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This page covers Questions and Worked Solutions for Edexcel May June 2021 IAL Pure Maths, WMA12/01.

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Edexcel May June 2021 IAL Pure Maths WMA12/01 (pdf)

- Adina is saving money to buy a new computer. She saves £5 in week 1, £5.25 in week 2,
£5.50 in week 3 and so on until she has enough money, in total, to buy the computer.

She decides to model her savings using either an arithmetic series or a geometric series.

Using the information given,

(a) (i) state with a reason whether an arithmetic series or a geometric series should be used,

(ii) write down an expression, in terms of n, for the amount, in pounds (£), saved in week n.

Given that the computer Adina wants to buy costs £350

(b) find the number of weeks it will take for Adina to save enough money to buy the computer. - Figure 1 shows a sketch of the curve with equation y = 4
^{x}

A copy of Figure 1, labelled Diagram 1, is shown on the next page.

(a) On Diagram 1, sketch the curve with equation

(i) y = 2^{x}

(ii) y = 4^{x}– 6

Label clearly the coordinates of any points of intersection with the coordinate axes.

The curve with equation y = 2^{x}

meets the curve with equation y = 4^{x}– 6 at the point P.

(b) Using algebra, find the exact coordinates of P. - (i) Prove that for all single digit prime numbers, p,

p^{3}+ p is a multiple of 10

(ii) Show, using algebra, that for

(n + 1)^{3}– n^{3}

is not a multiple of 3 - (a) Find, in ascending powers of x, up to and including the term in x
^{3}, the binomial expansion of fully simplifying each coefficient.

(b) Use the answer to part (a) to find an approximation for 2.01251^{3}

Give your answer to 3 decimal places.

Without calculating 2.01251^{3}

(c) state, with a reason, whether the answer to part (b) is an overestimate or an underestimate. - Figure 2 shows a sketch of part of the graph of the curves C
_{1}and C_{2}

The curves intersect when x = 2.5 and when x = 4

A table of values for some points on the curve C_{1}is shown below, with y values given to 3 decimal places as appropriate.

- A circle has equation x
^{2}– 6x + y^{2}+ 8y + k = 0

where k is a positive constant.

Given that the x-axis is a tangent to this circle,

(a) find the value of k.

The circle meets the coordinate axes at the points R, S and T.

(b) Find the exact area of the triangle RST. - (a) Given that

3 log_{3}(2x – 1) = 2 + log_{3}(14x – 25)

show that

2x^{3}– 3x^{2}– 30x + 56 = 0

(b) Show that –4 is a root of this cubic equation.

(c) Hence, using algebra and showing each step of your working, solve

3log_{3}(2x – 1) = 2 + log_{3}(14x – 25) - (i) Solve, for 0 < θ < 360°, the equation

3sin (θ + 30°) = 7 cos(θ + 30°)

giving your answers to one decimal place.

(ii) (a) Show that the equation

3sin^{3}x = 5sin x – 7sinx cos x

can be written in the form

sinx (a cos^{2}x + b cos x + c) = 0

where a, b and c are constants to be found.

(b) Hence solve for 2/π < x < 2/π

the equation

3sin^{3}x = 5sin x – 7sinx cos x - Figure 3 shows a sketch of a square based, open top box.

The height of the box is h cm, and the base edges each have length l cm.

Given that the volume of the box is 250000cm^{3}

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