Topic 1: Number and algebra
- standard notation
- sequences
- arithmetic sequences and series
- geometric sequences and series
- financial applications
-
- laws of exponents powers page
- logarithms logarithms page
- simple deductive proof
-
- laws of exponents (rational exponents)
- laws of logarithms
- change of base
- solving exponential equations
- sum of infinite convergent sequences
-
- binomial theorem
- Pascal’s triangle - binomial coeeficient
- (HL)
- counting principles counting principles
- binomial - fractional and negative indices
- partial fractions (HL)
- complex numbers (HL) complex numbers page
- modulus-argument form (HL)
- (HL)
- complex conjugates
- de Moivre’s theorem
- powers and roots of complex numbers
- (HL)
- proof by mathematical induction
- proof by contradiction
- use of a counter example
- solutions of systems of equations (HL)
Topic 2: Functions
- Equation of a line
- domain and range, inverse function
- graph of a function
- key features of graphs, intersections
- Composite functions, identity function
- quadratic function
- quadratic equation
- reciprocal function
- exponential function - logarithmic function
- solving equations
- transformation of graphs
- polynomial functions (HL)
- rational functions (HL)
- odd & even (HL)
- inequalities (HL)
- modulus (HL)
Topic 3: Geometry and trigonometry
- distance between two points
- use of sine, cosine and tangent ratios
- applications of trigonometry, Pythagoras’ theorem
- sine rule
- cosine rule
- Pythagoras’ theorem
- radian measures
- trigonometry in terms of the unit circle
- trig identities
- trigonometric functions
- trigonometric equations
- reciprocal trigonometric functions (HL)
- compound angle identities (HL)
- relationship between trigonometric functions (HL)
- vectors (HL)
- scalar product (HL)
- vector equation of a line (HL) page on lines
- coincident, parallel, intersecting skew lines (HL)
- vector product (HL)
- vector equation of a plane, Cartesian equation of a plane (HL) page
- intersections of line and plane, 2 planes, 3 planes, angles (HL) distance
Topic 4: Probability and statistics
- Concepts of population, sample, random sample, discrete and continuous data, etc.
- presentation of data
- measures of central tendency sd and variance
- linear correlation
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- concepts of trial,
- outcome,
- equally likely outcome,
- relative frequency
- sample space (U)
- event
- complementary events
- expected number of occurences
- Venn diagrams, tree diagrams, sample space diagrams and tables of outcomes
- discrete random variables
- binomial distribution
- normal distribution
- equation of regression
- formulas for conditional probability and independent events, testing for independence
- standardisation of of normal variables, inverse normal calculations
- Bayes’ theorem (HL)
- Variance of a discrete random variable, etc.
Topic 5: Calculus
- limits and rate of change differentiation
- increasing and decreasing functions
- power rule for differentiation
- tangents and normals at a given point
- introduction to integration archimedes
- derivative of
$x^n, \sin x, \cos x, \mathrm{e}^x$
and$\ln x$
. - the second derivative
- local maximum and minimum points curve sketching
- kinematic problems
- indefinite integral of
$x^n, \sin x, \cos x, \frac{1}{x}$
and$\mathrm{e}^x$
improper integrals - definite integrals, area of a region
- informal understanding of continuity (HL)
- l’Hopitâl’s rule (HL)
- implicit differentiation (HL)
- derivatives of all six trig functions and inverses (HL)
- integration by substitution, integration by parts, repeated (HL)
- area enclosed by a curve and the y-axis, solids of revolution (HL)
- First order differential equations (HL)
- Maclaurin series (HL)