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
