Study plan: Kirill Evstafev
1. Algebra
● Sequences, including sigma notation
● Exponents, including fraction
exponents
● Logarithms, including change of base
● Binomial expansion, including
combinations and permutations
● Proof by induction
● Complex numbers, including Cartesian
and Polar forms, Euler’s and De
Moivre’s Theorems, and roots of
complex numbers
● Systems of linear equations
2. Functions
● Basic functions, including linear and
quadratic
● Features of functions, including
asymptotes
● Other functions, including rational,
general exponential functions,
logarithmic functions
● Function classifications, including odd
and even, one-to-one, many-to-one
● Inverses
● Composite functions
● Function transformations, including
stretching, reflecting, shifting,
absolutes and reciprocals
● Polynomial division, including the
factor and remainder theorem and the
fundamental theorem of algebra
● Sums and products of roots of
functions
3. Vectors
● How vectors work
● Working with vectors, including
addition, subtraction and scalar
multiplication
● Unit vectors
● Position vectors vs. direction vectors,
including equations of lines in vector
form
● Dot, or scalar, product
● Cross, or vector, product, including
geometric interpretation
● Planes, including equations and
intersections with lines and other
planes
● Normal vectors
● Angles between lines and planes
4. Trigonometry and circular functions
● Units
● Circle formulae
● Right-angle triangles
● Non-right angle triangles
● Bearings
● Standard angles and the unit circle
● Graphs of trigonometric functions,
including transformations
● Trigonometric identities, including
double and half angle formulae
● Inverse and reciprocal trigonometric
functions
5. Differentiation
● Definition of the derivative
● Power rule
● Product and quotient rules
● Chain rule
● Standard derivatives
● Implicit differentiation
● The tangent and normal equation
● Turning points
● Sketching graphs
● Applications of differentiation,
including kinematics and optimisation
● Related rates
6. Integration
● Indefinite integration
● Integration by substitution
● Integration by parts
● Use of trigonometric identities
● Definite integration vs. area
● Volumes of revolution
7. Probability
● Venn diagrams, including mutual
exclusivity, intersections, compliments
and conditional probability
● Tree diagrams
● Tables of outcomes
● Probability distributions, including the
binomial, Normal, and Poisson
Bayes Theorem
8. Statistics
● Descriptive, or summary, statistics
● Graphs to represent data, including
cumulative frequency , box and
whisker plots and histograms
● Use of a GDC
● Bivariate analysis, including regression
lines, PMCC and scatter plots