Free analytical Tutorials using step by step approach with examples and matched exercises are presented here. Detailed solutions to the examples are also included. Several tutorials have been designed so that they can be used with the applets tutorials in this site.
Applications, Graphs, Domain and Range of Functions
Applications of Functions. Several problems and exercises to illustrate possible applications of functions.
Questions on one to one Functions. Several questions with detailed solutions as well as exercises with answers on how to prove that a given function is a one to one function.
Slopes of Perpendicular Lines Questions. A detailed tutorial on proof that the slope of two parallel lines are equal and also questions with detailed solution.
Slopes of Perpendicular Lines Questions. A detailed tutorial on the proof of the fact that two perpendicular lines have slopes such that one is the negative of the reciprocal of the other and also questions with detailed solutions.
Exponential and Logarithmic Functions and Equations
Introduction to Polynomials. Definition of degree, leading coefficient, monomial, binomial, trinomial and constant, linear, quadratic and cubic polynomial.
Percent Maths Problems Several word problems on percentage with detailed solutions are presented.
Percent Maths Questions Several questions on percentages, with detailed solutions are presented.
Convert Percentages, Fractions and Decimals Tutorial on how to convert percentages, fractions and decimals. Questions with detailed solutions as well as exercises with answers are presented.
Vectors
Vector Addition and Scalar Multiplication. A tutorial on how to find components of a vector , add two vectors, multiply a vector by a scalar. Examples, solutions, exercises and answers are included.
Matrix Addition and Multiplication. A tutorial on how to add, multiply by a scalar and multiply matrices with examples, solutions, exercises and answers.
The Inverse of a Square Matrix. A tutorial on how to find the inverse of any square matrix. The proof of a formula that gives the inverse of an invertible 2 x 2 matrix is also included.
Complex Numbers
Complex Numbers - Basic Operations. A tutorial on how to find the conjugate of a complex number and add, subtract, multiply, divide complex numbers supported by online calculators.
Cramer's Rule to Solve Systems of Equations. A tutorial on proving Cramer's rule for a 2 by 2 systems of linear equations. Presentation of the rule for a 3 by 3 systems of equations. An example on using Cramer's rule is presented.