11–12Mathematics Advanced 11–12 Syllabus

Recognise speed as a rate of change of distance with respect to time

Use the definition for average rate of change to determine the average speed of an object from a given distance–time graph

Describe the difference between the average speed of an object and its instantaneous speed

Relate the instantaneous speed of an object to the gradient of the tangent at that point on its distance–time graph

Estimate the instantaneous speed of an object from its distance–time graph

Recognise when modelling with a linear function that its gradient is the rate of change and determine the rate of change for linear functions in practical situations

Recognise when modelling with a non-linear function that the rate of change is not constant and is represented by the gradient of the tangent to the curve at each point on the curve

Estimate the instantaneous rate of change of a non-linear function at a given point from a given graph of a practical situation

Examine the gradient of a curve at a point on the curve using graphing applications

Define differentiation as the process of finding the derivative of a function

Find derivatives of constant and linear functions

Use the rules for differentiation to find equations of tangents and normals to a curve at points on the curve

Find points on a curve where the tangent or normal has a given gradient

Identify and apply the product, quotient or chain rule, or a combination of the rules, as appropriate to differentiate a given function

Define and distinguish between displacement and distance and between velocity and speed

Use graphs of functions and their derivatives, without the use of algebraic techniques, to describe and interpret physical phenomena

Solve problems by determining the velocity of a particle moving in a straight line, given its displacement from a point as a function of time