Algebra | - Functions (its types, definitions, inverse theorems & functions, range, domain, & inverse
- Mathematical induction (mathematical induction & theorem principles, mathematical induction applications, divisibility problems
- Matrices (its types, multiplication of matrices & scalar multiple of a matrix, matrix transport, determinants & its properties, inverse & adjoint of a matrix, inconsistency & consistency of system of simultaneous equations, matrix rank, simultaneous linear equation solutions)
- Complex numbers (CN as an ordered pair of real numbers, fundamental operations, complex number representation in a+ib form, amplitude & modulus of complex numbers, illustrations, polar & geometrical representation of complex numbers in Argand plane, diagram of Argand
- Theorem by De Moivre (rational & integral indices, unity’s nth root, geometrical interpretations, illustrations
- Quadratic expressions (equation in 1 variable, quadratic expressions sign, signs change, minimum & maximum value, quadratic inequations
- Equations theory (roots & coefficients relation in an equation, equation solving at the time two or more roots are connected by certain relation, real coefficient equation, complex roots occurrence in conjugate pairs & its consequences, equations transformation definitions & certain theorems)
- Permutations & combinations (counting’s fundamental principle, circular & linear permutations, N dissimilar things take r at a time permutations, circular permutations, permutation with constraint repetitors, combinations definitions & theorems)
- Binomial theorem (positive integral index binomial theorem, rational index binomial theorem, use binomial theorem for approximation)
- Partial functions
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Trigonometry | - Trigonometric ratios till transformation (variation, trigonometric functions transformation periodicity & graphs, compound angles trigonometric ratios, multiple & sub-multiple angles trigonometric ratios, transformations)
- Trigonometric equations (trigonometric equations general solutions, simple trigonometric equations, solutions)
- Inverse trigonometric functions (graph & properties of inverse trigonometric functions, reduce a trigonometric function into a bijective function)
- Hyperbolic functions (its definition, graphs, inverse hyperbolic function definition & graph, hyperbolic functions addition formulae
- Properties of triangle (sides & angles of triangle relationship, cosine, sine, tangent, & projectile rules, areas of triangle & half angle formulae, excircles & incircle of a triangle
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Vector algebra | - Addition of vectors (a vector-like triad of real number, vector classification, vectors addition, scalar multiplication, angle in between two nonzeros, vectors linear combination, vector component in three dimensions, line and plane vector equations with their cartesian equivalent forms)
- Product of vectors (dot/scalar product of 2 vectors, geometrical interpretations, orthogonal projections, dot product properties, dot product expression in i,j,k system, angle between 2 vectors, vectors methods geometrical, plane in normal form vector equation, angle in between 2 planes, two vectors & properties vector product, vectors product in j,k, i system, areas of vectors, scalar triple product, plane’s vector equation, vector triple products)
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Measures of dispersion & probability | - Measures of dispersion (range, mean deviation, standard &variance deviation of grouped & ungrouped data, analysis of frequency distribution, and coefficient of variation with equal means but multiple variances)
- Probability (random events & experiments, probability classical definition, addition theorem/axiomatic approach of probability, dependent & independent events, conditional probability, theorem by Baye, and multiplication theorem)
- Probability distribution & random variables (random variables, theoretical discrete distribution, Poisson and binomial distribution)
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Coordinate geometry | - Locus (its definition, illustrations, finding equal equations of locus, problem with it)
- Transformation of axes (rules, illustrations, and derivations, rotation of axes, derivations, illustrations)
- The straight line (fundamental results revision, straight line, normal form, straight line, illustrations, symmetric form, reduction in various forms, tow straight lines intersection, straight lines family, concurrent lines & its conditions, angle in between 2 lines, perpendicular length from a point to line, two parallel line distance, triangle properties)
- Pair of straight lines (pair of lines equations passing through the origin, the angle between pair of lines, perpendicular & coincident lines condition, angles bisectors, the bisector of angles pairs, lines pair, general equation second degree, parallel lines condition & distance between them, pair of lines point of intersection, homogenizing a second-degree equation with the first-degree equation in x & y)
- Circle (equation of a circle, equation of the circle with line segment as equation & diameter of the circle via 3 non-collinear points, circle’s parametric equation, point’s position in a plane of a circle, point definition of a tangent power, straight line position in the plane of a circle, condition applicable for a line to be tangent, chord joining circle’s two points, tangent equation on a point of a circle, two circles relative position, the center of similitude, pair of the tangent equation from an external point)
- System of circles (angle in between 2 intersecting circles, orthogonality condition, two circles radical axis, two circles common tangent & common chord, line and circle intersection)
- Parabola (conic sections, parabola, parabola equation in standard form, parabola forms, tangent & normal equations at a point on parabola, straight lines conditions to be tangent)
- Ellipse (ellipse equation in standard form, tangent & normal equation at a point on the ellipse, conditions for a straight line to become tangent)
- Hyperbola (hyperbola equation in standard form, tangent & normal equations at a point on hyperbola, conditions for straight line to become tangent)
- Three-dimensional coordinates (coordinates, section formulae, triangle & tetrahedron centroid)
- Direction cosines/rations
- Plane (plane’s cartesian equation, illustrations)
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Calculus | - Limits & continuity (neighborhoods & integral, limits, standard limits, continuity)
- Differentiation (function’s derivative, elementary properties, trigonometric/inverse trigonometric/hyperbolic/inverse hyperbolic function, differentiation methods, derivatives, second order derivatives)
- Applications of derivatives (approximations & errors, derivative geometrical interpretation, tangent & normal equations to a curve, tangent length, condition for orthogonality of curve and angle between 2 curves, derivative as a rate of change, Lagrange’s mean value theorem& Rolle’s theorem, increasing/decreasing functions, minima/maxima)
- Integration ( integration as a reverse process for differentiation, standard form, integral properties, substitution methods, algebraic/logarithmic/exponential/inverse trigonometric functions integration, integration by parts, exponential/inverse/logarithmic functions integration, partial fraction method, reduction formula)
- Definite integrals (definite integral as the limit of a sum, definite integral interpretation as an area, integral calculus fundamental theorem, definite integral to areas application, reduction formula)
- Differential equations (differential equations formation, order & degree of an ordinary differential equation, solving differential equation with different methods)
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