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This page covers Questions and Worked Solutions for CIE Pure Maths Paper 13 October/November 2020, 9709/13.

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CIE Oct 2020 9709 Pure Maths Paper 13 (pdf)

- (a) Express x
^{2}+ 6x + 5 in the form (x + a)^{2}+ b, where a and b are constant

(b) The curve with equation y = x^{2}is transformed to the curve with equation y = x^{2}+ 6x + 5.

Describe fully the transformation(s) involve - The function f is defined by

(a) Find

(b) The equation of a curve is such - Solve the equation
- A curve has equation y = 3x
^{2}− 4x + 4 and a straight line has equation y = mx + m − 1, where m is a constant.

Find the set of values of m for which the curve and the line have two distinct points of intersection. - In the expansion of (a + bx)
^{7}, where a and b are non-zero constants, the coefficients of x, x^{2}and x^{4}are the first, second and third terms respectively of a geometric progression.

Find the value of a/b - The function f is defined by

(a) Find an expression for f^{−1}(x)

(b) Show that

(c) State the range of

- The first and second terms of an arithmetic progression are

(a) Show that the common difference is

(b) Find the exact value of the 13th term when θ = 1/6 π - The equation of a curve is

(a) Find

(b) Find the coordinates of the stationary point and determine the nature of the stationary point - In the diagram, arc AB is part of a circle with centre O and radius 8 cm. Arc BC is part of a circle with centre A and radius 12 cm, where AOC is a straight line.

(a) Find angle BAO in radians

(b) Find the area of the shaded region

(c) Find the perimeter of the shaded region. - A curve has equation

(a) It is given that when x = 1/4, the gradient of the curve is 3.

Find the value of k.

(b) It is given instead that

Find the value of k. - A circle with centre C has equation (x − 8)
^{2}+ (y − 4)^{2}= 100.

(a) Show that the point T(−6, 6) is outside the circle.

Two tangents from T to the circle are drawn.

(b) Show that the angle between one of the tangents and CT is exactly 45°

The two tangents touch the circle at A and B.

(c) Find the equation of the line AB, giving your answer in the form y = mx + c.

(d) Find the x-coordinates of A and B.

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