P2 Tutorials
Algebra and Functions
Algebraic Long Division
Factor and Remainder Theorems
Logarithmic and Exponential Functions
Exponential Functions and Logarithms
- Exponential functions: what they are and their graphs
- What do we mean by a log?
- Rules of logs
- Logarithms - Change of Base
- Simplifying and expanding
- Converting between Logarithmic and Power (Exponential) equations
- Modelling exponential growth and decay
- Exponential and log equations
- Simultaneous equations
- Solving inequalities
- Exam Questions - Logarithms
The Exponential Function ex and Natural Log Functions
Modelling Curves of the form y=kxn and y=kax
Trigonometry
Sec θ, Cosec θ and Cot θ
Identities & Equations – Pythagorean Type
Identities – Addition type
Identities & Equations – Double angle type
Identities – Half angle type
Identities – Triple angle type
Identities & Equations – Harmonic Formulae
Exam Questions – Mixed trigonometry
Differentiation
Standard Differentials
The Chain Rule
The Product and Quotient Rules
More Standard Differentials
The Reciprocal Function of dx/dy
Parametric Functions
Integration
Integration – Common Functions
- Integration:(ax+b)n types
- Exam Questions - Integration:(ax+b)n types
- Integrating exponential functions ex, eax and e(ax+b)
- Exam Questions - Integrating exponential functions ex, eax and e(ax+b)
- Integrating reciprocal functions 1/x and 1/(ax+b)
- Exam Questions - Integrating reciprocal functions 1/x and 1/(ax+b)
- Integrals of the form : f '(x)/f(x)
- Integrals of the form : f'(x)ef(x)