Calculus

AS: Use of Mathematics
Calculus

This book covers the optional unit Modelling with calculus.

The mathematical content of this book includes:

• gradients of straight lines and curves and their interpretation as rates of change;

• using small increments to find gradients of chords and tangents and the notation associated with differentiation;

• differentiation of polynomials, trigonometric and exponential functions;

• differentiation of functions of functions and products;

• second derivatives, notation and interpretation;

• using differentiation to analyse and make sense of mathematical models;

• numerical methods to find areas under graphs;

• definite and indefinite integration of polynomials, trigonometric and exponential functions;

• using integration to make sense of mathematical models;

• the solution of first order differential equations including the use of direction-field diagrams.

Click here (126 KB) to download the Resource sheets as flagged on activity boxes in the book.