Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The diagram depicts a circle with centre $O$ and radius $10$ cm. The chord $AB$ splits the circle into two parts whose areas are in the ratio $1 : 4$, and the task is to determine the length of $AB$. The angle $AOB$ is $\theta$ radians.
(i)[3]
Show that $\theta = \dfrac{2}{5}\pi + \sin \theta$.
(ii)[5]
With all working shown, apply an iterative formula based on the equation in part (i), using an initial value of $2.1$, to determine $\theta$ correct to $2$ decimal places. Hence calculate the length of $AB$ in centimetres correct to $1$ decimal place.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write or imply an area expression” …