Standard Level

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===Algebra===
===Algebra===
o Linear equations
o Linear equations
 +
o Linear inequalities
o Linear inequalities
 +
o Straight-line graphs
o Straight-line graphs
 +
o Simultaneous linear equations
o Simultaneous linear equations
 +
o Factorisation
o Factorisation
 +
o Quadratic equations
o Quadratic equations
 +
o Completing the square
o Completing the square
 +
o Quadratic formula
o Quadratic formula
 +
o Disguised quadratic equations
o Disguised quadratic equations
 +
o Sketching the graph of a quadratic function
o Sketching the graph of a quadratic function
 +
o Algebraic fractions
o Algebraic fractions
 +
===Circular functions and trigonometry===
===Circular functions and trigonometry===
o Triangles
o Triangles
 +
o Radian measure
o Radian measure
 +
o The functions of sin, cos and tan
o The functions of sin, cos and tan
 +
o Sine and Cosine rules
o Sine and Cosine rules
===Functions and equations===
===Functions and equations===
o Transforming the graph of a function
o Transforming the graph of a function
 +
o Mappings
o Mappings
 +
o Composite Functions
o Composite Functions
 +
o Inverse Functions
o Inverse Functions
===Differentiation 1===
===Differentiation 1===
o Gradient of a curve
o Gradient of a curve
 +
o The derivative of y = ax^n
o The derivative of y = ax^n
 +
o Sum of difference of two functions
o Sum of difference of two functions
 +
o The second derivative
o The second derivative
 +
o Tangents and normals to a curve
o Tangents and normals to a curve
 +
o Gradient as a rate of change
o Gradient as a rate of change
 +
o Maximum, minimum and point of inflexion
o Maximum, minimum and point of inflexion
 +
o Practical applications of maxima and minima
o Practical applications of maxima and minima
===Intergration===
===Intergration===
o Anti-differentiation
o Anti-differentiation
 +
o Variable acceleration
o Variable acceleration
 +
o Area under a curve
o Area under a curve
 +
o Volume of revolution about the x-axis
o Volume of revolution about the x-axis
===Sequences and series===
===Sequences and series===
o Sequences
o Sequences
 +
o Series and sigma notation
o Series and sigma notation
 +
o Arithmetic sequences
o Arithmetic sequences
 +
o Geometric sequences
o Geometric sequences
 +
o Infinite geometric sequences
o Infinite geometric sequences
 +
o Binominal expansions
o Binominal expansions
===Differentiation 2===
===Differentiation 2===
o Funtion of a function
o Funtion of a function
 +
o The product and quotient rules
o The product and quotient rules
 +
o Applications of differentiation
o Applications of differentiation
===Further Trigonometry===
===Further Trigonometry===
o The functions sin x, cos x, tan x
o The functions sin x, cos x, tan x
 +
o Trigonometric equations
o Trigonometric equations
 +
o Double angles
o Double angles
===Calculus with Trigonometry===
===Calculus with Trigonometry===
o Sin x and cos x
o Sin x and cos x
 +
o Differentiating tan x
o Differentiating tan x
 +
o Applications
o Applications
===Exponents and Logarithms===
===Exponents and Logarithms===
o Negative and fractional exponents
o Negative and fractional exponents
 +
o Surds
o Surds
 +
o Logarithms
o Logarithms
 +
o The exponential function
o The exponential function
===Calculus with Exponents and Logarithms===
===Calculus with Exponents and Logarithms===
o The function  y = a^x
o The function  y = a^x
 +
o Natural logarithms
o Natural logarithms
 +
o Applications
o Applications
===Matrices===
===Matrices===
o Introduction to matrices
o Introduction to matrices
 +
o Matrix multiplication
o Matrix multiplication
 +
o 2x2 matrices
o 2x2 matrices
 +
o 3x3 matrices
o 3x3 matrices
===Vectors===
===Vectors===
o Introduction
o Introduction
 +
o Addition and subtraction of vectors
o Addition and subtraction of vectors
 +
o Position vectors
o Position vectors
 +
o The scalar product
o The scalar product
 +
o Vector equation of a line
o Vector equation of a line
 +
o Applications of vectors
o Applications of vectors
===Probability===
===Probability===
o Combined events
o Combined events
 +
o Conditional probability
o Conditional probability
===Statistics===
===Statistics===
o Population and samples
o Population and samples
 +
o Diagrammatic representation of data
o Diagrammatic representation of data
 +
o Mode, Median and mean
o Mode, Median and mean
 +
o Measures of dispersion
o Measures of dispersion
 +
o Cumulative frequency
o Cumulative frequency
 +
o Histograms
o Histograms
 +
o Random Variables
o Random Variables
 +
o The binomial distribution
o The binomial distribution
 +
o The normal distribution
o The normal distribution

Revision as of 23:14, 10 June 2008

Contents

Mathematics Standard Level

This is a far more managable course than it's Higher Level brother.

The SL course consists of:

Algebra

o Linear equations

o Linear inequalities

o Straight-line graphs

o Simultaneous linear equations

o Factorisation

o Quadratic equations

o Completing the square

o Quadratic formula

o Disguised quadratic equations

o Sketching the graph of a quadratic function

o Algebraic fractions


Circular functions and trigonometry

o Triangles

o Radian measure

o The functions of sin, cos and tan

o Sine and Cosine rules

Functions and equations

o Transforming the graph of a function

o Mappings

o Composite Functions

o Inverse Functions

Differentiation 1

o Gradient of a curve

o The derivative of y = ax^n

o Sum of difference of two functions

o The second derivative

o Tangents and normals to a curve

o Gradient as a rate of change

o Maximum, minimum and point of inflexion

o Practical applications of maxima and minima

Intergration

o Anti-differentiation

o Variable acceleration

o Area under a curve

o Volume of revolution about the x-axis

Sequences and series

o Sequences

o Series and sigma notation

o Arithmetic sequences

o Geometric sequences

o Infinite geometric sequences

o Binominal expansions

Differentiation 2

o Funtion of a function

o The product and quotient rules

o Applications of differentiation

Further Trigonometry

o The functions sin x, cos x, tan x

o Trigonometric equations

o Double angles

Calculus with Trigonometry

o Sin x and cos x

o Differentiating tan x

o Applications

Exponents and Logarithms

o Negative and fractional exponents

o Surds

o Logarithms

o The exponential function

Calculus with Exponents and Logarithms

o The function y = a^x

o Natural logarithms

o Applications

Matrices

o Introduction to matrices

o Matrix multiplication

o 2x2 matrices

o 3x3 matrices

Vectors

o Introduction

o Addition and subtraction of vectors

o Position vectors

o The scalar product

o Vector equation of a line

o Applications of vectors

Probability

o Combined events

o Conditional probability

Statistics

o Population and samples

o Diagrammatic representation of data

o Mode, Median and mean

o Measures of dispersion

o Cumulative frequency

o Histograms

o Random Variables

o The binomial distribution

o The normal distribution

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