Edexcel 2019 AS Maths Paper 1, 8MA0/01

Edexcel May/June 2019 AS Maths Paper 1 (Question Paper)
Edexcel May/June 2019 AS Maths Paper 1 (Mark Scheme)

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1. The line l1 has equation 2x + 4y – 3 = 0
   The line l2 has equation y = mx + 7, where m is a constant.
   Given that l1 and l2 are perpendicular,
   (a) find the value of m.
   The lines l1 and l2 meet at the point P.
   (b) Find the x coordinate of P.
2. Find, using algebra, all real solutions to the equation
3. (a) Given that k is a constant, find
4. A tree was planted in the ground.
   Its height, H metres, was measured t years after planting.
   Exactly 3 years after planting, the height of the tree was 2.35 metres.
   Exactly 6 years after planting, the height of the tree was 3.28 metres.
   Using a linear model,
   (a) find an equation linking H with t.
   The height of the tree was approximately 140 cm when it was planted.
   (b) Explain whether or not this fact supports the use of the linear model in part (a).
5. A curve has equation

6. Figure 1 shows a sketch of a triangle ABC with AB = 3x cm, AC = 2x cm and angle CAB = 60°
   Given that the area of triangle ABC is 18√3 cm²
   (a) show that x = 2√3
   (b) Hence find the exact length of BC, giving your answer as a simplified surd.
7. The curve C has equation
8. (a) Find the first 3 terms, in ascending powers of x, of the binomial expansion of
9. A company started mining tin in Riverdale on 1st January 2019.
   A model to find the total mass of tin that will be mined by the company in Riverdale is given by the equation
   T = 1200 – 3(n – 20)²
   where T tonnes is the total mass of tin mined in the n years after the start of mining.
   Using this model,
   (a) calculate the mass of tin that will be mined up to 1st January 2020,
   (b) deduce the maximum total mass of tin that could be mined,
   (c) calculate the mass of tin that will be mined in 2023.
   (d) State, giving reasons, the limitation on the values of n.
10. A circle C has equation x² + y² – 4x + 8y – 8 = 0
    (a) Find
    (i) the coordinates of the centre of C,
    (ii) the exact radius of C.
    The straight line with equation x = k, where k is a constant, is a tangent to C.
    (b) Find the possible values for k.
11. f(x) = 2x³ – 13x² + 8x + 48
    (a) Prove that (x – 4) is a factor of f(x).
    (b) Hence, using algebra, show that the equation f(x) = 0 has only two distinct roots.
12. (a) Show that
13. Figure 3 shows a sketch of part of the curve with equation
    y = 2x³ – 17x² + 40x
    The curve has a minimum turning point at x = k.
    The region R, shown shaded in Figure 3, is bounded by the curve, the x-axis and the line with equation x = k.
14. The value of a car, £V, can be modelled by the equation

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