Edexcel Oct 2019 IAL Pure Maths WMA11/01

Edexcel Oct 2019 IAL Pure Maths WMA11/01 (pdf)

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1. Figure 1 shows a sector AOB of a circle with centre O and radius r cm.
   The angle AOB is 1.25 radians.
   Given that the area of the sector AOB is 15 cm²
   (a) find the exact value of r,
   (b) find the exact length of the perimeter of the sector. Write your answer in simplest form
2. A tree was planted in the ground.
   Exactly 2 years after it was planted, the height of the tree was 1.85 m.
   Exactly 7 years after it was planted, the height of the tree was 3.45 m.
   Given that the height, H metres, of the tree, t years after it was planted in the ground, can be modelled by the equation
   H = at + b
   where a and b are constants,
   (a) find the value of a and the value of b.
   (b) State, according to the model, the height of the tree when it was planted.
3. Figure 2 shows a sketch of the curve C with equation y = x² – 5x + 13
   The point M is the minimum point of C.
   The straight line l passes through the origin O and intersects C at the points M and N as shown.
   Find, showing your working
4. A parallelogram ABCD has area 40 cm²
   Given that AB has length 10 cm, BC has length 6 cm and angle DAB is obtuse, find
   (a) the size of angle DAB, in degrees, to 2 decimal places,
   (b) the length of diagonal BD, in cm, to one decimal place
   
5. A curve has equation

6. The curve C has equation
   
7. Figure 4 shows part of the curve with equation y = 2x² + 5
   The point P(2,13) lies on the curve.
   (a) Find the gradient of the tangent to the curve at P.
8. Solve, using algebra, the equation
9. Figure 5 shows a sketch of part of the curve C with equation
10. Figure 6 shows a sketch of part of the curve with equation y = f(x), where
    f(x) = (2x + 5)(x – 3)²
11. A curve has equation y = f(x).

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