CIE May 2022 9709 Pure Maths Paper 13

CIE May/June 2022 9709 Pure Maths Paper 13 (pdf)

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1. The coefficient of x³ in the expansion of …
2. The diagram shows part of the curve with equation y = p sin(qθ) + r, where p, q and r are constants.
   (a) State the value of p
3. An arithmetic progression has first term 4 and common difference d. The sum of the first n terms of the progression is 5863.
4. (a) The curve with equation y = x² + 2x − 5 is translated by
5. (a) Solve the equation
6. The function f is defined by f(x) = 2x² − 16x + 23 for x < 3.
   (a) Express f(x) in the form 2(x + a)² + b.

7. The diagram shows the circle with equation (x − 2)2 + (y + 4)2 = 20 and with centre C. The point B has coordinates (0, 2) and the line segment BC intersects the circle at P.
   (a) Find the equation BC.
8. The diagram shows the curve with equation y = x^1/2 + 4x−^1/2. The line y = 5 intersects the curve at the points A(1, 5) and B(16, 5).
   (a) Find the equation of the tangent to the curve at the point A.
9. The diagram shows triangle ABC with AB = BC = 6 cm and angle ABC = 1.8 radians. The arc CD is part of a circle with centre A and ABD is a straight line.
   (a) Find the perimeter of the shaded region.
   (b) Find the area of the shaded region.
10. The function f is defined by f(x) = (4x + 2)^-2 for x > −1/2
11. The point P lies on the line with equation y = mx + c, where m and c are positive constants. A curve has equation y = −m/x. There is a single point P on the curve such that the straight line is a tangent to the curve at P.
    (a) Find the coordinates of P, giving the y-coordinate in terms of m

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