CIE March 2022 9709 Pure Maths Paper 1

CIE March 2022 9709 Pure Maths Paper 1 (pdf)

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1. A curve with equation y = f(x) is such that …
2. A curve has equation y = x² + 2cx + 4 and a straight line has equation y = 4x + c, where c is a constant.
   Find the set of values of c for which the curve and line intersect at two distinct points.
3. Find the term independent of x in each of the following expansions.
4. The first term of a geometric progression and the first term of an arithmetic progression are both equal to a.
   The third term of the geometric progression is equal to the second term of the arithmetic progression.
   The fifth term of the geometric progression is equal to the sixth term of the arithmetic progression.
   Given that the terms are all positive and not all equal, find the sum of the first twenty terms of the arithmetic progression in terms of a.
5. (a) Express 2x² − 8x + 14 in the form 2[(x − a)² + b]
   (b) Describe fully a sequence of transformations that maps the graph of y = f(x) onto the graph of y = g(x), making clear the order in which the transformations are applied.

6. The circle with equation (x + 1)² + (y − 2)² = 85 and the straight line with equation y = 3x − 20 are shown in the diagram. The line intersects the circle at A and B, and the centre of the circle is at C.
   (a) Find, by calculation, the coordinates of A and B
   (b) Find an equation of the circle which has its centre at C and for which the line with equation y = 3x − 20 is a tangent to the circle.
7. (a) Show that
8. The diagram shows the circle with equation
9. Functions f, g and h are defined as follows:
10. The diagram shows a circle with centre A of radius 5 cm and a circle with centre B of radius 8 cm. The circles touch at the point C so that ACB is a straight line. The tangent at the point D on the smaller circle intersects the larger circle at E and passes through B.
    (a) Find the perimeter of the shaded region.
11. It is given that a curve has equation

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