CIE May 2022 9709 Pure Maths Paper 11

CIE May/June 2022 9709 Pure Maths Paper 11 (pdf)

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1. (a) Express x² − 8x + 11 in the form (x + p)² + q where p and q are constants
2. The thirteenth term of an arithmetic progression is 12 and the sum of the first 30 terms is −15.
   Find the sum of the first 50 terms of the progression.
3. The coefficient of x⁴ in the expansion of
4. (a) Prove the identity
5. The diagram shows a sector ABC of a circle with centre A and radius r. The line BD is perpendicular to AC. Angle CAB is θ radians
6. The function f is defined as follows:

7. The diagram shows the curve with equation y = (3x − 2)^1/2 and the line y = 1/2 x + 1. The curve and the line intersect at points A and
8. (a) The curve y = sin x is transformed to the curve y = 4 sin(1/2 x − 307deg;).
   Describe fully a sequence of transformations that have been combined, making clear the order in which the transformations are applied
9. The equation of a circle is x² + y² + 6x − 2y − 26 = 0.
   (a) Find the coordinates of the centre of the circle and the radius. Hence find the coordinates of the lowest point on the circle.
   (b) Find the set of values of the constant k for which the line with equation y = kx − 5 intersects the circle at two distinct points.
10. The equation of a curve is such that

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