Edexcel May June 2021 IAL Pure Maths WMA12/01

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

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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 = 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.
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.

6. 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.
7. (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)
8. (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
9. 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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