Introduction to Differentiation
Limits, derivatives as rates of change, differentiating polynomials using the power rule, tangents and normals, stationary points, and increasing and decreasing functions.
Active lessons
7
Status
Active
Lesson flow
Learn -> Guided Practice -> Independent Practice -> Mastery Quiz
Diagnostic
Take the topic test
A timed, ~60-minute test drawn at random across all 7 subtopics of this unit. You get a marked result, a predicted band, and a clear list of which subtopics to re-practise.
Unit pathway
Lesson pathway
7 of 7 active
Lesson 1
The Derivative as Rate of Change
Understand average rate of change, instantaneous rate of change, tangent gradients, derivative notation, signs, and units.
Lesson 2
Differentiating Polynomial Terms
Learn how to differentiate polynomial terms using the power rule, with a focus on coefficients, powers, constants, and common mark-losing mistakes.
Lesson 3
Differentiating Polynomial Functions
Learn how to differentiate full polynomial functions term-by-term using correct derivative notation and simplification.
Lesson 4
Tangents and Normals
Use derivatives to find gradients and equations of tangents and normals to curves.
Lesson 5
Stationary Points
Find stationary points by solving where the derivative is equal to zero.
Lesson 6
Increasing and Decreasing Functions
Use the sign of the derivative to determine where a function is increasing or decreasing.
Lesson 7
First Derivative Test
Classify stationary points by testing the sign of the first derivative on either side.