# P1 Tutorials

## Prior Knowledge

## Algebra Basics

- Expanding a single bracket
- Expanding two or more brackets
- Squaring a bracket
- Terms in expressions and equations
- Identity or equation - what is the difference?
- Linear equations with a positive x-term
- Linear equations with a negative x-term
- Linear equations with two x-terms
- Linear equations with brackets
- Fractional linear equations

## Polynomials

## Indices

- Introduction to indices (exponents)
- Multiplication rules for indices
- Division rule for indices
- Negative indices
- Fractions raised to a negative index
- Rational (fractional) indices
- Simplifying terms with negative powers
- Expressing terms in the form ax
^{n} - Equations in which the power has to be found
- Summary of indices
- Exam Questions - Indices

## Algebra and Functions 1

## Completing the Square

## Quadratics

## Quadratic Equations

## Quadratic Equations – Roots and Discriminant

## Quadratic Graphs

## Inequalities

## Algebra and Functions 2

## Coordinate Geometry

## Lines

## Trigonometry

## Trigonometric Ratios

## Trigonometric Graphs and Transformations

## Applications of Trigonometry

## Trigonometric Equations

## Vectors

## Vectors

## Scalar Product (Dot Product)

## Sequences and Series

## Arithmetic Progressions

## Geometric Series

## Differentiation

## Differentiation – Introduction

## Tangents and Normals

## The Chain Rule

## Connected Rates of Change

## Stationary Points

## Increasing and Decreasing functions

## Integration

## Integration – Introduction

## Equations of Curves

## Integration – Common Functions

## Definite Integration

## Applications of Integration – Area bound by a curve

## Applications of Integration – Volumes of revolution

- Volume of revolution about the x-axis
- Exam Questions - Volume of revolution about the x-axis
- Volume of revolution about the x-axis generated between curves
- Volume of Revolution about the y-axis
- Exam Questions - Volume of Revolution about the y-axis
- Volume of Revolution about the y-axis generated between curves