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
- The diagram shows part of the curve with equation y = x2 + 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 = x2 − 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/x7in 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 2x2 + 12x + 11 in the form 2(x + a)2 + b, where a and b are constants
The function f is defined by f(x) = 2x2 + 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 tan2x − 5 tan x − 2 = 0 for 0° ≤ x ≤ 180°.
(b) Find the set of values of k for which the equation 3 tan2x − 5 tan x + k = 0 has no solutions
(c) For the equation 3 tan2x − 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 C1
has end-points at (−3, −5) and (7, 3).
(a) Find an equation of the circle C1
The circle C1 s translated by to give circle C2, as shown in the diagram.
(b) Find an equation of the circle C2
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 5x2 − 60x + 159 = 0
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