Standard Level
From Ibstudy
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
