SM015

1.0   NUMBER SYSTEM

        1.1  Real Numbers

        1.2  Complex Numbers

        1.3  Indices, Surds and Logarithms

2.0   EQUATIONS, INEQUALITIES AND ABSOLUTE VALUES

        2.1  Equations

        2.2  Inequalities

        2.3  Absolute Values

3.0   SEQUENCES AND SERIES

        3.1  Sequences and series

        3.2  Binomial Expansion

4.0   MATRICES AND SYSTEMS OF LINEAR EQUATIONS

        4.1  Matrices

        4.2  Determinant of Matrices

        4.3  Inverse of a Matrix

        4.4  System of Linear Equations with Three Variables

5.0   FUNCTIONS AND GRAPHS

        5.1  Functions

        5.2  Composite Functions

        5.3  Inverse Functions

        5.4  Exponential and Logarithmic Function

6.0   POLYNOMIALS

        6.1  Remainder Theorem, Factor Theorem and Zeros of polynomials.

        6.2  Partial Fractions

7.0  TRIGONOMETRIC FUNCTIONS

       7.1  Trigonometric Ratios and Identities

       7.2  Compound Angles

       7.3  Solutions of Trigonometric Equations

8.0   LIMITS AND CONTINUITY

        8.1  Limits

        8.2  Asymptotes

        8.3  Continuity

9.0   DIFFERENTIATION

        9.1  Derivative of a Function

        9.2  Rules of Differentiation

        9.3  Differentiation of Exponential, Logarithmic and Trigonometric Functions

        9.4  Implicit Differentiations

        9.5  Parametric Differentiation

10.0  APPLICATIONS OF DIFFERENTIATION

        10.1  Extremum Problems

        10.2  Rate of Change

 

SM025

1.0   INTEGRATION

        1.1  Integration of Functions

        1.2  Integration of Trigonometric

        1.3  Techniques of Integration Functions

        1.4  Definite Integrals

2.0    FIRST ORDER DIFFERENTIAL EQUATIONS

        2.1  Separable Variables

        2.2  First Order Linear Differential Equations

        2.3  Applications

3.0   NUMERICAL METHODS

        3.1  Solutions of Non-Linear Equations

        3.2  Newton-Raphson Method

        3.3  Trapezoidal Rule

4.0   CONICS

        4.1  Circles

        4.2  Ellipses

        4.3  Parabolas

5.0    VECTORS

         5.1  Vectors in 3 Dimensions

         5.2  Scalar Product

         5.3  Vector Product

         5.4  Applications of Vectors in Geometry

6.0     DATA DESCRIPTION

          6.1  Introduction to Data

          6.2  Measures of Location

          6.3  Measures of Dispersion

7.0     PERMUTATIONS AND COMBINATIONS

          7.1  Permutations

          7.2  Combinations

8.0      PROBABILITY

          8.1  Probability

9.0      RANDOM VARIABLES

           9.1  Introduction to Random Variables

           9.2  Discrete Random Variables

           9.3  Continuous Random Variables

10.0     SPECIAL PROBABILITY   DISTRIBUTIONS          

            10.1  Binomial Distribution

            10.2  Poisson Distribution

            10.3  Normal Distribution

            10.4  Distribution Approximation

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