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