Numerical methods in contextEdexcel A-Level Maths: Mind map

Exam questions on Numerical methods in context

1. A manufacturer finds that the break-even selling price, £$x$, of a product satisfies $f(x)=x^3-4x-7=0$.
   Show that $x^3-4x-7=0$ can be rearranged to give $x=\sqrt{4+\frac{7}{x}}$.2 marks
2. A scientist models the concentration of drug A as $5e^{-0.4t}$ mg per litre and of drug B as $t$ mg per litre, where $t$ is the time in hours since the start. The concentrations are equal when $t$ is a root of $f(t)=t-5e^{-0.4t}=0$.
   Show that the root of $f(t)=0$ lies between $t=2.1$ and $t=2.2$.2 marks
3. A decorative pond is in the shape of a segment of a circle of radius $10$ m. The chord of the segment subtends an angle of $\theta$ radians at the centre of the circle, and the area of the pond is $30$ m$^2$.
   Show that $\theta-\sin\theta=0.6$.3 marks