Edexcel May June 2021 IAL Pure Maths WMA12/01

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

  1. 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.
  2. Figure 1 shows a sketch of the curve with equation y = 4x
    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 = 2x
    (ii) y = 4x – 6
    Label clearly the coordinates of any points of intersection with the coordinate axes.
    The curve with equation y = 2x
    meets the curve with equation y = 4x – 6 at the point P.
    (b) Using algebra, find the exact coordinates of P.
  3. (i) Prove that for all single digit prime numbers, p,
    p3 + p is a multiple of 10
    (ii) Show, using algebra, that for
    (n + 1)3 – n3
    is not a multiple of 3
  4. (a) Find, in ascending powers of x, up to and including the term in x3, the binomial expansion of fully simplifying each coefficient.
    (b) Use the answer to part (a) to find an approximation for 2.012513
    Give your answer to 3 decimal places.
    Without calculating 2.012513
    (c) state, with a reason, whether the answer to part (b) is an overestimate or an underestimate.
  5. Figure 2 shows a sketch of part of the graph of the curves C1 and C2
    The curves intersect when x = 2.5 and when x = 4
    A table of values for some points on the curve C1 is shown below, with y values given to 3 decimal places as appropriate.

  1. A circle has equation x2 – 6x + y2 + 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.
  2. (a) Given that
    3 log3(2x – 1) = 2 + log3(14x – 25)
    show that
    2x3 – 3x2 – 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
    3log3(2x – 1) = 2 + log3(14x – 25)
  3. (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
    3sin3 x = 5sin x – 7sinx cos x
    can be written in the form
    sinx (a cos2 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
    3sin3 x = 5sin x – 7sinx cos x
  4. 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 250000cm3

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