Standard Level

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=Mathematics Standard Level=
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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

Revision as of 23:12, 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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