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Mathematics - Analysis and Approaches
10 sections available · 65 chapters available
Free Mathematics - Analysis and Approaches study notes for IB Diploma Programme (DP) - SL & HL students. Each chapter breaks down a key concept with examples and practice prompts you can turn into AI drills in the thinka app.
Syllabus component
Number and algebra
Standard form and laws of exponents
Arithmetic sequences and series
Geometric sequences, series and infinite sums
Financial applications: compound interest and depreciation
Logarithms and exponential equations
Deductive proof, equality and identity
The binomial theorem and Pascal's triangle
Number and algebra (HL)
Counting principles and the extended binomial theorem (HL)
Partial fractions (HL)
Complex numbers in Cartesian form and the complex plane (HL)
Polar and Euler form; De Moivre's theorem (HL)
Proof by induction, contradiction and counterexample (HL)
Systems of linear equations (HL)
Functions
Straight lines, gradients and intercepts
Functions, domain, range, composite and inverse functions
Graphs and their key features
Quadratic functions, equations and the discriminant
Reciprocal and rational functions; asymptotes
Exponential and logarithmic functions
Solving equations and real-life modelling
Transformations of graphs
Functions (HL)
Polynomial functions; factor and remainder theorems (HL)
Rational functions with quadratic numerator or denominator (HL)
Odd, even and self-inverse functions; domain restriction (HL)
Inequalities of the form g(x) >= f(x) (HL)
Modulus, reciprocal and composite graphs; modulus equations (HL)
Geometry and trigonometry
Three-dimensional geometry: distance, volume, surface area and angles
Right-angled trigonometry, sine rule and cosine rule
Radian measure, arc length and sector area
The unit circle and exact trigonometric values
Trigonometric identities and double angle formulae
Circular functions and their graphs
Trigonometric equations
Reciprocal, inverse and compound angle trigonometry (HL)
Vectors, lines and planes (HL)
Vectors and vector algebra (HL)
Scalar product and angles between vectors (HL)
Vector equations of lines (HL)
Parallel, intersecting and skew lines (HL)
Vector product and its applications (HL)
Equations of planes (HL)
Intersections and angles involving planes (HL)
Statistics and probability
Sampling, data types, bias and outliers
Presenting data: histograms, cumulative frequency and box plots
Measures of central tendency and dispersion
Correlation and regression lines
Probability, sample spaces and combined events
Discrete random variables and the binomial distribution
The normal distribution and standardization
Bayes' theorem and continuous random variables (HL)
Calculus
Limits, the derivative and increasing or decreasing functions
Differentiating polynomials
Tangents and normals
Chain, product and quotient rules
The second derivative and graphs of f, f' and f''
Optimization and points of inflexion
Kinematics: displacement, velocity and acceleration
Integration, definite integrals and areas
Calculus (HL)
Continuity, differentiability and differentiation from first principles (HL)
Limits and l'Hopital's rule (HL)
Implicit differentiation and related rates (HL)
Further derivatives and integrals (HL)
Integration by substitution and by parts (HL)
Areas and volumes of revolution (HL)
Differential equations, Euler's method and integrating factors (HL)
Maclaurin series (HL)
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