Edexcel Oct 2020 IAL Pure Maths WMA11/01

Edexcel Oct 2020 IAL Pure Maths WMA11/01 (pdf)

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1. Given that
   find the values of the constants a, b and c.
2. f(x) = 3 + 12x – 2x²
   (a) Express f(x) in the form
   a – b(x + c)²
   where a, b and c are integers to be found.
   The curve with equation y = f(x) – 7 crosses the x‑axis at the points P and Q and crosses the y-axis at the point R.
   (b) Find the area of the triangle PQR, giving your answer in the form m√n where m and n are integers to be found.
3. Figure 1 shows the design for a badge.
   The design consists of two congruent triangles, AOC and BOC, joined to a sector AOB of a circle centre O.

• Angle AOB = α
• AO = OB = 3 cm
• OC = 5 cm
  Given that the area of sector AOB is 7.2cm²
  (a) show that α = 1.6 radians.

4. Use algebra to solve the simultaneous equations
   y – 3x = 4
   x² + y² + 6x – 4y = 4
   You must show all stages of your working.
5. Figure 2 shows a sketch of the curve with equation y = f(x).
   The curve passes through the points (–5, 0) and (0, –3) and touches the x‑axis at the point (2, 0).
   On separate diagrams sketch the curve with equation
   (a) y = f(x + 2)
   (b) y = f(–x)
   On each diagram, show clearly the coordinates of all the points where the curve cuts or touches the coordinate axes.

6. The point A has coordinates (–4, 11) and the point B has coordinates (8, 2).
   (a) Find the gradient of the line AB, giving your answer as a fully simplified fraction. The point M is the midpoint of AB. The line l passes through M and is perpendicular to AB.
   (b) Find an equation for l, giving your answer in the form px + qy + r = 0 where p, q and r are integers to be found.
   The point C lies on l such that the area of triangle ABC is 37.5 square units.
   (c) Find the two possible pairs of coordinates of point C
7. The curve C has equation
8. The curve C has equation
   y = (x – 2)(x – 4)²
   (a) Show that
9. A curve with equation y = f(x) passes through the point (9, 10). Given that

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