Edexcel May June 2021 IAL Pure Maths WMA11/01

Edexcel May June 2021 IAL Pure Maths WMA11/01 question paper

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1. The curve C has equation
   (a) Find dy/dx, giving your answer in simplest form.
   The point P(4, 3) lies on C.
   (b) Find the equation of the normal to C at the point P. Write your answer in the form
   ax + by + c = 0, where a, b and c are integers to be found.
2. f(x) = ax³ + (6a + 8)x² – a²x
   where a is a positive constant.
   Given f(–1) = 32
   (a) (i) show that the only possible value for a is 3
   (ii) Using a = 3 solve the equation
   f(x) = 0
3. Figure 1 shows the plan view of a flower bed.
   The flowerbed is in the shape of a triangle ABC with

• AB = p metres
• AC = q metres
• BC = 2√2 metres
• angle BAC = 60°
  (a) Show that

4. Find
   writing each term in simplest form
5. The share value of two companies, company A and company B, has been monitored over a 15-year period.
   The share value P_A of company A, in millions of pounds, is modelled by the equation
   P_A = 53 – 0.4(t – 8)²
   t ≥ 0
   where t is the number of years after monitoring began.
   The share value P_B of company B, in millions of pounds, is modelled by the equation
   P_B = –1.6t + 44.2 t ≥ 0
   where t is the number of years after monitoring began.
   Figure 2 shows a graph of both models.
   Use the equations of one or both models to answer parts (a) to (d).
   (a) Find the difference between the share value of company A and the share value of company B at the point monitoring began.
   (b) State the maximum share value of company A during the 15-year period.
   (c) Find, using algebra and showing your working, the times during this 15-year period when the share value of company A was greater than the share value of company B.
   (d) Explain why the model for company A should not be used to predict its share value when t = 20

6. The curve C has equation y = f(x), x > 0
   Given that

• C passes through the point P(8, 2)
• fʹ(x) = 32/3x2 + 3 -
  (a) find the equation of the tangent to C at P. Write your answer in the form y = mx + c, where m and c are constants to be found.
  (b) Find, in simplest form, f(x).

7. The line l₁
   has equation 4y + 3x = 48
   The line l₁ cuts the y-axis at the point C, as shown in Figure 3.
   (a) State the y coordinate of C.
   The point D(8, 6) lies on l₁
   The line l₂ passes through D and is perpendicular to l₁
   The line l₂ cuts the y-axis at the point E as shown in Figure 3.
   (b) Show that the y coordinate of E is −14/3
   A sector BCE of a circle with centre C is also shown in Figure 3.
   Given that angle BCE is 1.8 radians,
   (c) find the length of arc BE.
   The region CBED, shown shaded in Figure 3, consists of the sector BCE joined to the triangle CDE.
   (d) Calculate the exact area of the region CBED.
8. The curve C₁ has equation
   y = 3x² + 6x + 9
   (a) Write 3x² + 6x + 9 in the form
   a(x + b)2 + c
   where a, b and c are constants to be found.
   The point P is the minimum point of C₁
   (b) Deduce the coordinates of P
9. Figure 4 shows a sketch of the curve with equation
   y = tanx –2π ≤ x ≤ 2π
   The line l, shown in Figure 4, is an asymptote to y = tanx
   (a) State an equation for l.
   A copy of Figure 4, labelled Diagram 1, is shown on the next page

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