CIE May 2023 9709 Pure Maths Paper 12 (9709/12/m/j/23)

CIE May/June 2023 9709 Pure Maths Paper 12 (pdf)

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1. The equation of a curve is such that dy/dx = 4/(x − 3)³ for x > 3. The curve passes through the point (4, 5). Find the equation of the curve.
2. The coefficient of x⁴ in the expansion of (x + a)⁶ is p and the coefficient of x² in the expansion of (ax + 3)⁴ is q. It is given that p + q = 276.
   Find the possible values of the constant
3. (a) Express 4x² − 24x + p in the form a(x + b)² + c, where a and b are integers and c is to be given in terms of the constant p.
4. Solve the equation 8x⁶ + 215x³ − 27 = 0.
5. The diagram shows the curve with equation
6. The diagram shows a sector OAB of a circle with centre O. Angle AOB = θ radians and OP = AP = x.
   (a) Show that the arc length AB is 2xθ cos θ

7. By first expanding (cos θ + sin θ)², find the three solutions of the equation
   (cos θ + sin θ)² = 1
8. The diagram shows the graph of y = f(x) where the function f is defined b
9. The second term of a geometric progression is 16 and the sum to infinity is 100.
   (a) Find the two possible values of the first term.
10. The equation of a circle is (x − a)² + (y − 3)² = 20. The line y = 1/2 x + 6 is a tangent to the circle at the point P.
    (a) Show that one possible value of a is 4 and find the other possible valu
11. The equation of a curve is

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