CIE Oct 2020 9709 Pure Maths Paper 1 (pdf)
- Find the set of values of m for which the line with equation y = mx − 3 and the curve with equation y = 2x2 + 5 do not meet.
- The equation of a curve is such that. It is given that the curve passes through the
point (2, 7). Find the equation of the curve.
- Air is being pumped into a balloon in the shape of a sphere so that its volume is increasing at a constant rate of 50 cm3s−1.
Find the rate at which the radius of the balloon is increasing when the radius is 10 cm.
- In the diagram, the lower curve has equation y = cos θ. The upper curve shows the result of applying a combination of transformations to y = cos θ.
Find, in terms of a cosine function, the equation of the upper curve.
- In the expansion of , the coefficients of x6 and x3 are equal.
(a) Find the value of the non-zero constant a.
(b) Find the coefficient of x6 in the expansion of
- The equation of a curve is . Find the coordinates of the point on the curve at which the gradient is 4/3.
7 (a) Show that
(b) Hence solve the equation
- A geometric progression has first term a, common ratio r and sum to infinity S. A second geometric progression has first term a, common ratio R and sum to infinity 2S.
(a) Show that r = 2R − 1.
It is now given that the 3rd term of the first progression is equal to the 2nd term of the second
(b) Express S in terms of a.
- The diagram shows a circle with centre A passing through the point B. A second circle has centre B and passes through A. The tangent at B to the first circle intersects the second circle at C and D.
The coordinates of A are (−1, 4) and the coordinates of B are (3, 2).
(a) Find the equation of the tangent CBD.
(b) Find an equation of the circle with centre B
(c) Find, by calculation, the x-coordinates of C and D.
- The diagram shows a sector CAB which is part of a circle with centre C. A circle with centre O and radius r lies within the sector and touches it at D, E and F, where COD is a straight line and angle ACD is θ radians.
(a) Find CD in terms of r and sin θ
It is now given that r = 4 and θ = 1/6 π
(b) Find the perimeter of sector CAB in terms of π
(c) Find the area of the shaded region in terms of π and √3
- The functions f and g are defined by
f(x) = x2 + 3 for x > 0,
g(x) = 2x + 1 for x > −1/2.
(a) Find an expression for fg(x).
(b) Find an expression for (fg)-1(x) and state the domain of (fg)-1.
(c) Solve the equation fg(x) − 3 = gf(x).
- The diagram shows a curve with equation y = 4x1/2 − 2x for x ≥ 0, and a straight line with equation y = 3 − x. The curve crosses the x-axis at A(4, 0) and crosses the straight line at B and C.
(a) Find, by calculation, the x-coordinates of B and C.
(b) Show that B is a stationary point on the curve.
(c) Find the area of the shaded region
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