IGCSE Maths Specification

Edexcel A 4MA1

Section 3.4: Calculus

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#3.4A

understand the concept of a variable rate of change

#3.4B

differentiate integer powers of \(x\)

#3.4C

determine gradients, rates of change, stationary points, turning points (maxima and minima) by differentiation and relate these to graphs

Find the coordinates of the maximum and minimum points

#3.4D

distinguish between maxima and minima by considering the general shape of the graph only

#3.4E

apply calculus to linear kinematics and to other simple practical problems

The displacement, \(s\) metres, of a particle from a fixed point \(O\) after \(t\) seconds is given by:
\(s = 24t^2 - t^3, 0 \leq t \leq 20\)
Find expressions for the velocity and the acceleration.