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Mathematics branch of mathematics that uses basic operations to solve expressions Linear equations:
A linear equation is an equation involving only the sum or product of constants and the first power of a variable.
where m is the slope and b is the y intercept is the general form of an equation in slope intercept form.
The formula of a slope= where and are two points in ordered pair form.
The general form of point slope form is:
where m is the slope, and is the two points in ordered pair form.
The quadratic formula equals:
where a, b and c are constants of a quadratic equation is of the form
Factoring is a process of dividing out a factor from a mathematical expression.
Common factors technique is of the form ax+bx=x(a+b).
Difference of squares: .
Difference of cubes: .
Rationalizing is the process of removing an irrational expression from the numerator of a fraction. Order and Inequalities: Number line: An axis or ray usually horizontal on which real numbers are represented and ordered from left to right. Absolute value: For a real number a, it is a if a is greater than or equal to zero or –a if a is less than zero. It is denoted. Conic sections:
The general equation of a circle:
. Where r is the radius of the circle and is the center of the circle
The general equation of an ellipse:
Natural logarithm: A log taken to base “e”, is approximately 2.7. Natural Log Function: . Exponential function: .
Rapid Study Kit for "Title":
Core Concept Tutorial
Problem Solving Drill
Review Cheat Sheet
"Title" Tutorial Summary :
This tutorial deals with the algebraic concepts needed to have a strong knowledge foundation for a Calculus course. Linear and quadratic equations are needed to be introduced in this Calculus course because they will be referred to in some Calculus topics.
Specific properties of the basic algebraic concepts needed for a Calculus course are discussed in this tutorial. Important equations such as logarithmic and exponential equations are mentioned in this tutorial so a deeper understanding of them is developed which will be needed for some differentiation and integration ideals.
Specific Tutorial Features:
Linear equations and inequalities are introduced in this tutorial with the help of examples.
The graphical representation of inequalities are covered in this tutorial along with their use with linear equations.
Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
Definition slides introduce terms as they are needed.
Visual representation of concepts
Animated examples—worked out step by step
A concise summary is given at the conclusion of the tutorial.
"Title" Topic List:
The basic rules of Algebra Algebraic linear equations The graphical representation of a linear equation and its definition An equation and it slope intercept form Linear equation and its slope Equations that have polynomials Quadratic equations and its solutions Higher polynomial equations Polynomial equations and their factoring Common polynomial factoring techniques Rationalizing of polynomial equations Order and Inequalities Number line and its graphical representation used in example problems How to solve simple linear inequalities? Absolute value How to solve absolute value inequalities? Inequalities that have polynomials How to solve polynomial inequalities? Conic Sections Ellipses The properties of ellipses Circles The properties of circles Exponentials and logarithms Exponentials and logarithmic functions and their definitions Graphs and applications of exponentials and logarithmic equations