CIE March 2022 9709 Pure Maths Paper 2

CIE March 2022 9709 Pure Maths Paper 2 (pdf)

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1. Solve the equation |5x − 2| = |4x + 9|.
2. A curve has equation y = 7 + 4 ln(2x + 5). Find the equation of the tangent to the curve at the point (−2, 7), giving your answer in the form y = mx + c.
3. The variables x and y satisfy the equation y = 3^2aa^x, where a is a constant. The graph of ln y against x is a straight line with gradient 0.239. (a) Find the value of a correct to 3 significant figures. (b) Hence find the value of x when y = 36. Give your answer correct to 3 significant figures.
4. (a) Show that sin 2θ cot θ − cos 2θ = 1.
5. (a) Given that y = tan²x

6. The polynomial p(x) is defined by
   p(x) = 4x³ + 16x² + 9x - 15,
   (a) Find the quotient when p(x) is divided (2x + 3), and show that the remainder is -6.
7. A curve has equation e^2xy − e^y = 100. (b) Show that the curve has no stationary points. It is required to find the x-coordinate of P, the point on the curve at which the tangent is parallel to the y-axis. (c) Show that the x-coordinate of P satisfies the equation

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