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

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This page covers Questions and Worked Solutions for CIE Pure Maths Paper 1 May/June 2023, 9709/12.

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

  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

  1. By first expanding (cos θ + sin θ)2, find the three solutions of the equation
    (cos θ + sin θ)2 = 1
  2. The diagram shows the graph of y = f(x) where the function f is defined b
  3. 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.
  4. 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
  5. The equation of a curve is

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