## Chapter 1: Number & Algebra

Sequence and Series

- 1.2 Arithmetic sequence and series
- 1.3 Geometric sequence and series
- 1.4 Compound interest, Annual Depreciation & Inflation
- 1.8 sum of infinite geometric sequence

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Exponents and Logarithms

- 1.5 Laws of exponents , Intro to logs with base 10 and base e
- 1.7 Laws of logs / logs and exponents equations

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Binomial Theorem

- 1.9 Binomial Theorem
- 1.10.2 Binomial theorem of fractional and negative indices(NOT for AA SL)

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Permutation and Combination

- 1.10.1 Counting priciples, permutations and combinations(Not for AA SL)

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Matrices
46

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System of linear equations

- 1.16 Systems of linear equations(NOT for AA SL)

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Complex Numbers

- 1.12 Complex number introduction(NOT for AA SL)
- 1.13 Complex number polar form(NOT for AA SL)
- 1.14 De Moivre’s theorem & powers and roots of complex numbers(NOT for AA SL)

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Proofs

- 1.6 Simple deductive proofs
- 1.15.1 Proof by mathematical induction(NOT for AA SL)
- 1.15.2 Proof by contradiction(NOT for AA SL)
- 1.15.2 Proof by Counter example(NOT for AA SL)

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## Chapter 2: Functions

Functions and Roots

- 2.1 Coordinate Geometry of straight lines
- 2.2 Concept of function & inverse of a function
- 2.5 Composite function
- 2.8 Reciprocal & Rational functions, Vertical & horizontal asymptotes
- 2.9 Exponential & logarithmic functions & their graphs
- 2.10 solving equations both graphically & analytically
- 2.12 Polynomial functions, factor and remainder theorem, sum & products of roots(NOT for AA SL)
- 2.13 rational functions, oblique asymptotes(NOT for AA SL)
- 2.14 Even and odd functions(NOT for AA SL)
- 2.15 solving inequality both graphically and analytically.(NOT for AA SL)

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Graphs

- 2.3 Graph of functions
- 2.4 Key features of graph
- 2.11 Transformation of graphs
- 2.16 Graph of modulus functions and solutions(NOT for AA SL)

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Quadratics

- 2.6 Quadratic function
- 2.7 solving quadratic equations and inequalities, discriminant 45

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## Chapter 3: Geometry & Trigonometry

Trigonometry

- 3.1 Co-ordinate geometry basics & surface area, volume of 3D objects.
- 3.2 Non-right angled triangle trigonometry , sine rule, cosine rule & area of triangle
- 3.3 Angle of elevation & depression, Bearings
- 3.6 Trig Identities
- 3.7 Trig functions and its transformations, real life examples (height of tide and Ferris wheel)
- 3.8 Solving Trigonometric equations
- 3.9 Reciprocal trig ratios & Inverse Trig functions(NOT for AA SL)
- 3.10 Compound angle and double angle identities for tan(NOT for AA SL)
- 3.11 Symmetric properties of trignometric functions(NOT for AA SL)

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Radian Measure

- 3.4 Radian measure, length of arc, area of sector
- 3.5 Unit circle concept

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Vectors

- 3.12 Introduction to vectors(NOT for AA SL)
- 3.13 Scalar product of vectors (DOT product)(NOT for AA SL)
- 3.14 Vector equation of line(NOT for AA SL)
- 3.15 Point of intersection of lines, skew lines(NOT for AA SL)
- 3.16 Vector product of vectors (CROSS product)(NOT for AA SL)
- 3.17 Vector equation of a plane(NOT for AA SL)
- 3.18 Intersection of line and plane(NOT for AA SL)

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## Chapter 4: Statistics & Probability

Statistics

- 4.1 Sampling techniques
- 4.2 Presentation of data, Histograms, box and whisker diagrams
- 4.3 Measure of central tendency, measure of dispersion
- 4.4 Co-relation and regression
- 4.10 regression line x on y

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Probability

- 4.5 Probability basics
- 4.6 Venn diagram, tree diagram, sample space , conditional probability
- 4.7 Discrete random variable
- 4.8 Binomial distribution
- 4.9 Normal distribution
- 4.11 Conditional probability
- 4.12 standardization of normal variables
- 4.13 Bays theorem(NOT for AA SL)
- 4.14 Mean, mode, median, variance, standard deviation of Continuous Random Variables(NOT for AA SL)

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## Chapter 5: Calculus

Differentiation

- 5.1 Introduction to limit
- 5.2 Increasing decreasing functions
- 5.3 derivative of a function
- 5.4 Equations of tangents and normals
- 5.6 Rules of differentiation
- 5.7 Graphical interpretation of differentiation
- 5.8 Maximum, minimum, point of inflection
- 5.12 Continuity and differentiability of a function(NOT for AA SL)
- 5.12.1 First principle of differentiation(NOT for AA SL)
- 5.12.2 Higher derivatives(NOT for AA SL)
- 5.13 L’Hospital’s rule(NOT for AA SL)
- 5.14 Implicit differentiation(NOT for AA SL)
- 5.19 Maclaurin series(NOT for AA SL)

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Integration

- 5.5 Integration
- 5.10 Indefinite integrals
- 5.11 Definite integrals, area under the curve
- 5.15 Methods of integrations part1: partial fraction etc.(NOT for AA SL)
- 5.16 Methods of integrations part2: Integration by parts and when substitution is given(NOT for AA SL)
- 5.17.1 Area of the region enclosed by curve and y-axis by integration(NOT for AA SL)
- 5.17.2 Volume of revolution(NOT for AA SL)

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Kinematics

- 5.9 Kinematics

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Differential Equations

- 5.18.1 Differential Equations- Euler's method(NOT for AA SL)
- 5.18.2 Differential Equations- Variables separable(NOT for AA SL)
- 5.18.3 Differential Equations- Homogeneous(NOT for AA SL)
- 5.18.4 Differential Equations- Linear DE, using Integrating factor(NOT for AA SL)

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