1Permutation and CombinationCounting principles, permutations (including with repetition and circular), combinations and their properties.Board exam — marks not publishedView topicsHide topics
Basic principle of counting
Permutations
Combinations
3 topics
2Binomial TheoremThe binomial theorem for a positive integer and any index, the general and middle terms, binomial coefficients, approximation, Euler's number e and the series of eˣ, aˣ and log(1 + x).Board exam — marks not publishedView topicsHide topics
Binomial theorem for a positive integer
General term, middle term and binomial coefficients
Binomial theorem for any index and approximation
Exponential and logarithmic series
4 topics
3Complex NumbersPolar form, De Moivre's theorem and its applications (powers and roots), cube roots of unity, Euler's formula.Board exam — marks not publishedView topicsHide topics
Polar form of a complex number
De Moivre's theorem and applications
Cube roots of unity
Euler's formula
4 topics
4Sequence, Series and Mathematical InductionSums of natural numbers, their squares and cubes, and proof by the principle of mathematical induction.Board exam — marks not publishedView topicsHide topics
Sum of natural numbers, squares and cubes
Principle of mathematical induction
2 topics
5Systems of Linear Equations by MatricesSolving systems of up to three linear equations by Cramer's rule, the matrix (inverse) method and row-equivalent (augmented) matrices.Board exam — marks not publishedView topicsHide topics
Cramer's rule
Matrix inverse method
Row-equivalent (augmented) matrix method
3 topics
6Properties and Solution of TrianglesSine, cosine, tangent and projection laws, half-angle formulae and area, and solving triangles in simple cases.Board exam — marks not publishedView topicsHide topics
Sine law
Cosine law
Tangent law
Projection laws
Half-angle formulae
Solution of triangles
6 topics
7Conic SectionsTangency to a circle, tangents and normals to circles and parabolas, standard equations of the parabola, ellipse and hyperbola, eccentricity, foci and latus rectum.Board exam — marks not publishedView topicsHide topics
Condition of tangency and tangent/normal to a circle
Standard equation of a parabola
Tangent and normal to a parabola
Standard equation of an ellipse
Standard equation of a hyperbola
5 topics
8Product of VectorsScalar and vector products, projection, angle between vectors, geometric meaning, properties and applications (area, work, proofs in geometry and trigonometry).Board exam — marks not publishedView topicsHide topics
Scalar (dot) product and projection
Vector (cross) product
Geometric interpretation and properties
Applications of products of vectors
4 topics
9Correlation and RegressionKarl Pearson's correlation coefficient, Spearman's rank correlation and the two regression equations, with prediction.Board exam — marks not publishedView topicsHide topics
Karl Pearson's correlation coefficient
Rank correlation
Regression equations and prediction
3 topics
10ProbabilityDependent and independent events, conditional probability and the multiplication law.Board exam — marks not publishedView topicsHide topics
Dependent and independent events
Conditional probability
2 topics
11Derivatives and their ApplicationsDerivatives of hyperbolic and inverse hyperbolic functions, L'Hospital's rule, differentials, tangents and normals, and the derivative as a rate of change.Board exam — marks not publishedView topicsHide topics
Derivatives of hyperbolic and inverse hyperbolic functions
L'Hospital's rule
Differentials
Tangent and normal
Derivative as rate of measure
5 topics
12Anti-derivativesStandard integrals, integrals reducible to standard forms (substitution, trigonometric forms) and integrals of rational functions (partial fractions).Board exam — marks not publishedView topicsHide topics
Standard integrals
Integrals reducible to standard forms
Integrals of rational functions
3 topics
13Differential EquationsOrder and degree; first-order first-degree equations — variables separable, homogeneous, linear (integrating factor) and exact.Board exam — marks not publishedView topicsHide topics
Order and degree
Variables separable
Homogeneous equations
Linear equations and integrating factor
Exact equations
5 topics
14Computational Methods or MechanicsThe paper's alternatives: computational methods (Gauss elimination, Gauss-Seidel, the simplex method for linear programming) OR mechanics (parallelogram and triangle laws, Lami's theorem, coplanar forces, Newton's laws, projectiles, rectilinear motion).Board exam — marks not publishedView topicsHide topics
Gauss elimination method
Gauss-Seidel method
Simplex method
Resultant and equilibrium of forces (Lami's theorem)
