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

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

• Show Step-by-Step Solutions

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

7. A curve has equation y = 2 + 3 sin 1/2 x for 0 ≤ x ≤ 4π.
   (a) State greatest and least values of y
8. The functions f and g are defined as follows, where a and b are constants.
9. 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
10. The diagram shows part of the curve with equation
11. 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)
12. 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

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.