Rounding, significant figures, decimal places

Converting numbers to and from scientific notation (a×10k)

The concept (and basic properties) of limits and derivatives

Power rule, chain rule, product rule, quotient rule, derivatives of ex, ax, loga​(x), trigonometric, and inverse trigonometric functions

Definitions of tangent and normal, finding tangent and normal lines to a function

Increasing and decreasing intervals, stationary points (maxima and minima), and optimisation

Definition of the second derivative, concavity, inflexion points

Taking the nth derivative, inductive proofs with the nth derivative

Concept of an integral, areas with definite integrals, and basic anti-derivative solving skills

Antiderivatives of polynomials, trigonometric, inverse trigonometric, exponential, and logarithmic functions

The reverse chain rule, integration by substitution, integration by parts, additional strategies

Computations involving distance, displacement, velocity, and acceleration

Exponents, properties of exponents, and solving exponential equations

Definition and evaluation of logarithms, properties of logs, e and the natural log, change of base rule

Nth roots, fractional and rational exponents, conjugates

Graphing exponential functions, Exponential growth and decay, logarithmic inverse functions

Introduction to the definition, properties, and general term of an arithmetic sequence

Introduction to definition, identification, and general term of geometric sequences

Definition of series, formula for arithmetic series

Summation notation, properties of sums

Definition and general term of geometric series, finite and infinite series, convergence

Working with sequences on a calculator, computations and applications of a calculator

Compound growth, depreciation, interest, inflation, real value

Regressions of y on x, regressions of x on y, the correlation coefficient r, the rank correlation coefficient rs​, extrapolation and interpolation of data

Theoretical and experimental probability, complementary events, expected number of outcomes, sample space

Venn diagrams, intersection and union of events, conditional probability, independent events

Tree diagrams, selection with/without replacement, dependence

Bayes' theorem with 2 and 3 events, sum of conditional probabilities

Distance between two points, midpoint of two points, and finding gradient using two points

Gradient-intercept form, point-gradient form, vertical lines, horizontal lines, standard form of a line

Parallel and perpendicular lines, intersection of 2 straight lines, solving a two-variable system of equations

Vertex, standard, and factored form, axis of symmetry, concavity, quadratic formula

Evaluating the discriminant, sum and product of roots, quadratic inequalities, quadratics of other forms