Syllabus
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Topic catalog(35)
Topic 1
Topic 1: Number and algebra
6 subtopicsThis topic covers fundamental numerical concepts, sequences, series, logarithms, complex numbers, methods of proof, and systems of equations.
- Sequences and SeriesAnalyze arithmetic and geometric sequences and series, including the use of formulae for terms and sums, sigma notation, and infinite geometric series.
- Exponents and LogarithmsApply the laws of exponents and logarithms to simplify expressions and solve exponential equations, including operations with scientific notation.
- The Binomial TheoremUse the binomial theorem for positive integer exponents and its extension to fractional and negative exponents, including permutations and combinations as counting principles.
- Methods of ProofUnderstand and apply different methods of mathematical proof, including simple deductive proof, proof by induction, and proof by contradiction.
- Complex NumbersWork with complex numbers in Cartesian, polar, and Euler forms, including operations, De Moivre's theorem, and finding powers and roots.
- Advanced AlgebraUtilize techniques such as partial fraction decomposition and solve systems of linear equations in up to three variables.
Topic 2
Topic 2: Functions
6 subtopicsThis topic explores the concept of a function, its properties, graphical representations, and analysis of various function types including polynomial, rational, and exponential functions.
- Fundamentals of FunctionsUnderstand the core concepts of functions, including domain, range, inverse functions, composite functions, and graphical representation.
- Linear, Quadratic and Polynomial FunctionsAnalyze and solve problems involving linear, quadratic, and higher-order polynomial functions, including finding roots, vertices, and applying the factor and remainder theorems.
- Exponential and Logarithmic FunctionsInvestigate the properties and graphs of exponential and logarithmic functions and their use in modeling real-world phenomena.
- Rational FunctionsAnalyze rational functions, including identifying vertical, horizontal, and oblique asymptotes, and sketching their graphs.
- Graph Transformations and AnalysisApply transformations to graphs of functions and analyze key features such as intercepts, turning points, and asymptotes, including transformations involving the modulus function.
- Solving Equations and InequalitiesSolve various types of equations and inequalities involving functions, both analytically and graphically.
Topic 3
Topic 3: Geometry and trigonometry
6 subtopicsThis topic develops an understanding of two and three-dimensional geometry, trigonometry, circular functions, and the use of vectors to model movement and position.
- 3D Geometry and TrigonometryApply trigonometric principles, including the sine and cosine rules, to solve problems in both two and three dimensions, including finding distances, angles, and volumes.
- Circular Functions and IdentitiesUnderstand the unit circle, radian measure, and trigonometric identities, including Pythagorean, compound angle, and double angle identities.
- Trigonometric Equations and GraphsAnalyze and graph trigonometric functions, including their transformations, and solve trigonometric equations in a finite interval.
- Introduction to VectorsRepresent vectors in two and three dimensions, and perform vector algebra including addition, subtraction, and scalar multiplication.
- Scalar (Dot) and Vector (Cross) ProductsCalculate and interpret the scalar and vector products of two vectors to find the angle between them, determine perpendicularity, and find areas.
- Vector Equations of Lines and PlanesUse vectors to represent lines and planes in 3D space, and solve problems involving intersections, angles, and distances.
Topic 4
Topic 4: Statistics and probability
6 subtopicsThis topic covers the collection, analysis, and interpretation of data, as well as the theory and application of probability to model uncertainty and risk.
- Descriptive StatisticsOrganize, represent, and analyze data using measures of central tendency, dispersion, and graphical methods like histograms and box-and-whisker plots.
- Correlation and RegressionAnalyze bivariate data using scatter diagrams, calculate Pearson's correlation coefficient, and determine the equation of the regression line for prediction.
- Probability TheoryApply fundamental concepts of probability, including conditional probability, independent events, and the use of Venn and tree diagrams to solve problems.
- Random VariablesAnalyze discrete and continuous random variables, their probability distributions, and calculate expected value, variance, and standard deviation.
- Standard DistributionsModel real-world situations using the binomial and normal distributions to calculate probabilities.
- Bayes' TheoremApply Bayes' theorem to solve problems involving conditional probability with a maximum of three events.
Topic 5
Topic 5: Calculus
6 subtopicsThis topic introduces the concepts of differential and integral calculus, exploring limits, derivatives, integrals, and their applications in optimization, kinematics, and differential equations.
- Differential CalculusUnderstand the concept of a limit and derivative from first principles, and apply rules of differentiation including the chain, product, and quotient rules.
- Applications of DifferentiationUse derivatives to analyze function behavior, find tangents and normals, solve optimization problems, and model rates of change and kinematics.
- Integral CalculusUnderstand integration as anti-differentiation and apply techniques such as substitution, integration by parts, and partial fractions to find indefinite and definite integrals.
- Applications of IntegrationUse definite integrals to calculate areas between curves and volumes of revolution, and apply integration to solve kinematic problems.
- First-Order Differential EquationsSolve first-order differential equations using methods such as separation of variables, homogeneous equations, and the integrating factor.
- Series and ApproximationsUse L'Hôpital's rule to evaluate limits of indeterminate forms and find and use Maclaurin series expansions for standard functions.
Past papers(2)
Topic analytics
Hot topics (9)
Top third by occurrences — likely to come up again.
- Solving Equations and Inequalities10×
- Complex Numbers8×
- Applications of Differentiation7×
- Trigonometric Equations and Graphs6×
- Integral Calculus5×
- Linear, Quadratic and Polynomial Functions5×
- Scalar (Dot) and Vector (Cross) Products5×
- Sequences and Series5×
- Standard Distributions5×
Medium topics (9)
Middle of the pack.
- Advanced Algebra4×
- Correlation and Regression4×
- Rational Functions4×
- Applications of Integration3×
- Circular Functions and Identities3×
- Differential Calculus3×
- Exponents and Logarithms3×
- Fundamentals of Functions3×
- Graph Transformations and Analysis3×
Cold topics (8)
Bottom third — overdue. Worth a closer look.
- Series and Approximations3×
- 3D Geometry and Trigonometry2×
- Descriptive Statistics2×
- Methods of Proof2×
- Probability Theory2×
- Random Variables2×
- First-Order Differential Equations1×
- The Binomial Theorem1×
Not yet seen (4)
From the syllabus but absent from every uploaded paper.
- Bayes' Theorem0×
- Exponential and Logarithmic Functions0×
- Introduction to Vectors0×
- Vector Equations of Lines and Planes0×