 In this section there are wide range of Math Formula Sheets, thousands of mathematics problems, examples and questions with solutions and detailed explanations are included to help you explore and gain deep understanding of math, pre-algebra, algebra, pre-calculus, calculus, functions, quadratic equations, logarithms, exponents, trigonometry and geometry etc.

## Basic Math Algebra, Pre-Algebra

Arithmetic, Roots and Powers, Factorization, Natural numbers, Integers, Rational expressions, Rules of evaluation of expressions, variable manipulation, Surds and Indices, Basic algebra formulas.
Topics of Pre-Calculus
1. The formal rules of algebra
2. Rational and irrational numbers, what is a rational number? Which numbers have rational square roots? The decimal representation of irrationals. What is a real number?
3. Functions, what is a function? The domain and the range. Functional notation. The argument. A function of a function.
4. Introduction to graphs, The graph of a function. Coordinate pairs of a function. The height of the curve at x.
5. Basic graphs, The constant function. The identity function. The absolute value function. The parabola. The square root function. The cubic function. The reciprocal function.
6. The vocabulary of polynomial functions Variables versus constants. Definition of a polynomial in x. The degree of a term and of a polynomial. The leading coefficient. The general form of a polynomial.
7. The roots, or zeros, of a polynomial. A polynomial equation. The roots of a polynomial. The x- and y-intercepts of a graph. The relationship between the roots and the x-intercepts.
8. The slope of a straight line. Definition of the slope. Positive and negative slope. A straight line has only one slope. “Same slope” and “parallel.” Perpendicular lines. The slope and one point specify a straight line.
9. Linear functions: The equation of a straight line. The equation of the first degree. The graph of a first-degree equation: a straight line. The slope-intercept form, and its proof.
10. Quadratics: Polynomials of the second degree. Quadratic equation: Solution by factoring. A double root. Quadratic inequalities. The sum and product of the roots.
11. Completing the square. Solving a quadratic equation by completing the square. The quadratic formula.
12. Synthetic division by x – a. The remainder theorem.
13. Roots of polynomials of degree greater than 2. The factor theorem. The fundamental theorem of algebra. The integer root theorem. Conjugate pairs.
14. Multiple roots. Point of inflection. Concave upward, concave downward.
15. Reflections of a graph. Reflection about the x-axis. Reflection about the y-axis. Reflection through the origin.
16. Symmetry of a graph. Symmetry with respect to the y-axis. Symmetry with respect to the origin. Test for symmetry. Odd and even functions.
17. Translations of a graph. Definition of a translation. The equation of a circle. The vertex of a parabola. Vertical stretches and shrinks.
18. Rational functions. Singularities. The reciprocal function. Horizontal and vertical asymptotes.
19. Inverse functions. Definition of inverses. Constructing the inverse. The graph of an inverse function.
20. Logarithms. The system of common logarithms. The system of natural logarithms. The three laws of logarithms. Change of base.
21. Logarithmic and exponential functions. Inverse relations. Exponential and logarithmic equations. Creating one logarithm from a sum.
22. Sigma notation for sums
23. Factorials
24. Permutations and Combinations. The Fundamental Principle of Counting. Factorial representations.
25. The binomial theorem. Pascal’s triangle. Multiplication of sums. A proof of the binomial theorem.
26. Mathematical induction

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