Numerical methods in contextEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

State the change of sign test for a root.
Why must you mention that f is continuous?
What is an iterative formula?
At the limit of a convergent iteration, what equation does \alpha satisfy?
How do you rearrange x^3-4x-7=0 to x=\sqrt[3]{4x+7}?
How do you prove a root is 2.30 to 2 d.p.?
When does x{n+1}=g(xn) converge near \alpha?
What is a cobweb pattern?
What is a staircase pattern?
Why check the domain after finding a root in a context question?
What three things make a full 'show a root lies in an interval' answer?
Which angle mode is used for \theta-\sin\theta=0.6?

Exam questions on Numerical methods in context

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).