CIE March 2021 9709 Pure Maths Paper 1

CIE March 2021 9709 Pure Maths Paper 1 (pdf)

• Show Step-by-Step Solutions

1. (a) Find the first three terms in the expansion, in ascending powers of x, of (1 + x)⁵
   (b) Find the first three terms in the expansion, in ascending powers of x, of (1 − 2x)⁶
   (c) Hence find the coefficient of x² in the expansion of (1 + x)⁵5(1 − 2x)⁶
2. By using a suitable substitution, solve the equation
3. Solve the equation
4. A line has equation y = 3x + k and a curve has equation y = x² + kx + 6, where k is a constant.
   Find the set of values of k for which the line and curve have two distinct points of intersection.
5. In the diagram, the graph of y = f(x) is shown with solid lines. The graph shown with broken lines is a transformation of y = f(x).
   (a) Describe fully the two single transformations of y = f(x) that have been combined to give the resulting transformation.
   (b) State in terms of y, f and x, the equation of the graph shown with broken lines.

6. A curve is such that and A(1,-3) lies on the curve. A point is moving along the curve and at A the y-coordinate of the point is increasing at 3 units per second.
   (a) Find the rate of increase at A of the x-coordinate of the point.
   (b) Find the equation of the curve.
7. Functions f and g are defined as follows:
   (a) Express f(x) in the form (x + a)² + b and state the range of f.
   (b) Find an expression for f⁻¹(x)
   (c) Solve the equation gf(x) = 13.
8. The points A(7, 1), B(7, 9) and C(1, 9) are on the circumference of a circle.
   (a) Find an equation of the circle.
   (b) Find an equation of the tangent to the circle at B.
9. The first term of a progression is cos θ, where 0 < θ < 1/2 π
   (a) For the case where the progression is geometric, the sum to infinity is 1/cosθ
   (i) Show that the second term is cos θ sin²θ
   (ii) Find the sum of the first 12 terms when θ = 1/3 π, giving your answer correct to 4 significant figures.
   (b) For the case where the progression is arithmetic, the first two terms are again cos θ and cos θ sin²θ respectively.
   Find the 85th term when θ = 1/3 π
10. The diagram shows a sector ABC which is part of a circle of radius α. The points D and E lie on AB and AC respectively and are such that AD = AE = kα, where k < 1. The line DE divides the sector into two regions which are equal in area.
    (a) For the case where angle BAC = 1/6 π radians, find k correct to 4 significant figures.
    (b) For the general case in which angle BAC = θ radians, where 0 < θ < 1/2 π, it is given that θ/sin θ > 1.
    Find the set of possible values of k.
11. The diagram shows the curve with equation y = 9(x^-1/2 - 4x^-3/2). The curve crosses the x-axis at the point A.
    (a) Find the x-coordinate of A.
    (b) Find the equation of the tangent to the curve at A
    (c) Find the x-coordinate of the maximum point of the curve.
    (d) Find the area of the region bounded by the curve, the x-axis and the line x = 9.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.