This is part of a collection of videos showing step-by-step solutions for CIE A-Level Mathematics past papers.

This page covers Questions and Worked Solutions for CIE Pure Maths Paper 1 February/March 2020, 9709/12.

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CIE Mar 2020 9709 Pure Maths Paper 12 (pdf)

- The function f is defined by f(x)

Determine whether f is an increasing function, a decreasing function or neither. - The graph of y = f(x) is transformed to the graph Describe fully the two single transformations which have been combined to give the resulting transformation
- The diagram shows part of the curve with equation y = x
^{2}+ 1. The shaded region enclosed by the curve, the y-axis and the line y = 5 is rotated through 360° about the y-axis.

Find the volume obtained - A curve has equation y = x
^{2}− 2x − 3. A point is moving along the curve in such a way that at P the y-coordinate is increasing at 4 units per second and the x-coordinate is increasing at 6 units per second.

Find the x-coordinate of P - Solve the equation
- The coefficient of 1/x in the expansion of

(a) Find the possible values of the constant a

(b) Hence find the coefficient of 1/x^{7}in the expansion

- The diagram shows a sector AOB which is part of a circle with centre O and radius 6 cm and with
angle AOB = 0.8 radians. The point C on OB is such that AC is perpendicular to OB. The arc CD is
part of a circle with centre O, where D lies on OA.

Find the area of the shaded region. - A woman’s basic salary for her first year with a particular company is $30 000 and at the end of the year she also gets a bonus of $600.

(a) For her first year, express her bonus as a percentage of her basic salary.

At the end of each complete year, the woman’s basic salary will increase by 3% and her bonus will increase by $100.

(b) Express the bonus she will be paid at the end of her 24th year as a percentage of the basic salary paid during that year - (a) Express 2x
^{2}+ 12x + 11 in the form 2(x + a)^{2}+ b, where a and b are constants

The function f is defined by f(x) = 2x^{2}+ 12x + 11 for x ≤ −4.

(b) Find an expression for f^{-1}(x) and state the domain of f^{-1}

The function g is defined by g(x) = 2x − 3 for x ≤ k.

(c) For the case where k = −1, solve the equation fg(x) = 193

(d) State the largest value of k possible for the composition fg to be defined - The gradient of a curve at the point (x, y) is given by
x. The curve has a stationary
point at (a, 14), where a is a positive constant.

(a) Find the value of a.

(b) Determine the nature of the stationary point.

(c) Find the equation of the curve - (a) Solve the equation 3 tan
^{2}x − 5 tan x − 2 = 0 for 0° ≤ x ≤ 180°.

(b) Find the set of values of k for which the equation 3 tan^{2}x − 5 tan x + k = 0 has no solutions

(c) For the equation 3 tan^{2}x − 5 tan x + k = 0, state the value of k for which there are three solutions in the interval 0° ≤ x ≤ 180°, and find these solutions - A diameter of a circle C
_{1}has end-points at (−3, −5) and (7, 3).

(a) Find an equation of the circle C_{1}

The circle C_{1}s translated by to give circle C_{2}, as shown in the diagram.

(b) Find an equation of the circle C_{2}

The two circles intersect at points R and S.

(c) Show that the equation of the line RS is y = −2x + 13

(d) Hence show that the x-coordinates of R and S satisfy the equation 5x^{2}− 60x + 159 = 0

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