CIE May 2023 9709 Pure Maths Paper 11 (9709/11/m/j/23)

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This page covers Questions and Worked Solutions for CIE Pure Maths Paper 1 May/June 2023, 9709/11.

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CIE May/June 2023 9709 Pure Maths Paper 11 (pdf)

  1. Solve the equation 4 sin 1 + tan 1 = 0 for 0° < 1 < 180°.
  2. (a) Find the first three terms in the expansion, in ascending powers of x, of 2 + 3x4.
  3. The diagram shows graphs with equations y = f(x) and y = g(x). Describe fully a sequence of two transformations which transforms the graph of y = f(x) to y = g(x).
  4. The diagram shows a sector ABC of a circle with centre A and radius 8 cm. The area of the sector is 16/3π cm2. The point D lies on the arc BC. Find the perimeter of the segment BCD.
  5. The line with equation y = kx − k, where k is a positive constant, is a tangent to the curve with equation y = −1/2x. Find, in either order, the value of k and the coordinates of the point where the tangent meets the curve
  6. The first three terms of an arithmetic progression are p2/6, 2p − 6 and p.
    (a) Given that the common difference of the progression is not zero, find the value of p

  1. A curve has equation y = 2 + 3 sin 1/2 x for 0 ≤ x ≤ 4π.
    (a) State greatest and least values of y
  2. The functions f and g are defined as follows, where a and b are constants.
  3. Water is poured into a tank at a constant rate of 500 cm3 per second. The depth of water in the tank, t seconds after filling starts, is h cm. When the depth of water in the tank is hcm, the volume, V cm3, of water in the tank is given by the formula
  4. The diagram shows part of the curve with equation
  5. The equation of a curve is such that dy/dx = 6x2 − 30x + 6a, where a is a positive constant. The curve has a stationary point at (a, −15)
  6. The diagram shows a circle P with centre (0, 2) and radius 10 and the tangent to the circle at the point A with coordinates (6, 10). It also shows a second circle Q with centre at the point where this tangent meets the y-axis and with radius 5/2 &radical;5

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