CIE March 2022 9709 Pure Maths Paper 3

CIE March 2022 9709 Pure Maths Paper 3 (pdf)

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1. Solve the inequality |2x + 3| > 3|x + 2|.
2. On a sketch of an Argand diagram, shade the region whose points represent complex numbers z satisfying the inequalities
3. The variables x and y satisfy the equation xⁿy² = C, where n and C are constants. The graph of ln y against ln x is a straight line passing through the points [0.31, 1.21] and [1.06, 0.91], as shown in the diagram. Find the value of n and find the value of C correct to 2 decimal place
4. The parametric equations of a curve are
5. The angles α and β lie between 0° and 180° and are such that

6. Find the complex numbers w which satisfy the equation
7. (a) By sketching a suitable pair of graphs, show that the equation (b) Verify by calculation that this root lies between 1 and 2.
8. (a) Find the quotient and remainder when
9. The variables x and y satisfy the differential equation
10. The diagram shows the curve y = sin 2x cos²x for 0 ≤ x ≤ 1/2 π, and its maximum point M.
    (a) Using the substitution u = sin x, find the exact area of the region bounded by the curve and the x-axis.
    (b) Find the exact x-coordinate of M
11. The points A and B have position vectors
12. The diagram shows the curve

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