Edexcel Jan 2020 IAL Pure Maths WMA11/01

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

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1. Find, in simplest form,
2. Given y = 3^x, express each of the following in terms of y. Write each expression in its simplest form.
3. Figure 1 shows part of the curve with equation y = x² + 3x – 2. The point P(3,16) lies on the curve.
   (a)Find the gradient of the tangent to the curve at P.
   The point Q with x coordinate 3 + h also lies on the curve.
   (b)Find, in terms of h, the gradient of the line PQ. Write your answer in simplest form.
   (c)Explain briefly the relationship between the answer to (b) and the answer to (a).
4. Figure 2 shows the plan view of a house ABCD and a lawn APCDA.
   ABCD is a rectangle with AB = 16m.
   APCOA is a sector of a circle centre O with radius 12m.
   The point O lies on the line DC, as shown in Figure 2.
5. (a) Show that the size of angle AOD is 1.231 radians to 3 decimal places
   The lawn APCDA is shown shaded in Figure 2.
   (b)Find the area of the lawn, in m², to one decimal place.
   (c)Find the perimeter of the lawn, in metres, to one decimal place.

6. The line l1 has equation 3x – 4y + 20 = 0The line l2 cuts the x-axis at R(8,0) and is parallel to l1
   (a)Find the equation of l2, writing your answer in the form ax + by + c = 0, where a, b and c are integers to be found.
   The line l1 cuts the x-axis at P and the y-axis at Q.Given that PQRS is a parallelogram, find
   (b)the area of PQRS,
   (c)the coordinates of S.
7. Figure 3 shows part of the curve C₁ with equation y = 3 sinx, where x is measured in degrees.
   The point P and the point Q lie on C₁ and are shown in Figure 3.
   (a)State
   (i)the coordinates of P,
   (ii)the coordinates of Q.
   A different curve C₂ has equation y = 3 sinx + k, where k is a constant.The curve C₂ has a maximum y value of 10
   The point R is the minimum point on C₂ with the smallest positive x coordinate.
   (b)State the coordinates of R.
   
8. The straight line l has equation y = k(2x – 1), where k is a constant.
   The curve C has equation y = x² + 2x + 11
   Find the set of values of k for which l does not cross or touch C.
   
9. A curve has equation
   Find the x coordinate of the point on the curve at which dy/dx = 0
   
10. The curve C₁ has equation y = f (x), where f(x) = (4x – 3)(x – 5)²
    (a)Sketch C₁ showing the coordinates of any point where the curve touches or crosses the coordinate axes.
    (b)Hence or otherwise
    (i)find the values of x for which f(1/4 x) = 0
    (ii)find the value of the constant p such that the curve with equation y = f(x) + p passes through the origin.
    A second curve C₂ has equation y = g(x), where g(x) = f (x + 1)
    (c)(i)Find, in simplest form, g(x).
    You may leave your answer in a factorised form.
    (ii)Hence, or otherwise, find the y intercept of curve C₂
    
11. A curve has equation y = f (x), where
    The point P(4,–50) lies on the curve.
    Given that fʹ(x) = –4 at P,
    (a)find the equation of the normal at P, writing your answer in the form y = mx + c, where m and c are constants,
    (b)find f(x).

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