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 Math Study Lounge These study sheets are for quick review on the subjects. Refer to our rapid courses for comprehensive review.     - Getting Started with Algebra     - Geometry Basics     - How to Solve Math Problems     - Trigonometry Quick Review     - Statistics At-A-Glance     - Calculus Preview
Home » Getting Started with Algebra

Key Terms

• Data sets: A logically meaningful grouping or collection of similar or related data.
• Relation: The way that two data sets relate to each other.
• Algebra: A branch of mathematics that substitutes letters for numbers.
• Variables: A symbol that is usually defined to denote any member of a set of objects.
• Algebra equations: A scale, what is done on one side of the scale with a number is also done to the other side of the scale.
• Functions: A relation, such that each element of a set is associated with a unique element of another set.
• VANG: acronym (initials) representing the four mode through which a concept should be explored and mastered in mathematics.
Objective of algebra
• Describe the relation between natural events by functions and graphs.
• Graphs and equivalent to algebra functions once a coordinante system is selected.
Using algebra functions

Using Graphs

The content of this course

• Equations and inequalities: (Core #2 and Core #6). Equations containing single variable will be discussed in core #2 together with single variable inequalities based on the concept of absolute values. Equation systems containing multi-variables will be discussed in core #6.
• Functions and their graphs: (Basic concepts: core #3; and some particular catergories of functions are presented in: core #4, core #5, and core #7). Based on different graph features, polynomial and rational functions, exponential and logarithmic functions, and conics are three main catergories of functions to be addressed.
• Discrete function problem: (Series and Probability: Core #8) The data set is composed of discrete numbers in an ordered manner and is called series. We will use counting principle to define a unique function on this data set. The value of this function is the times a number occurs in the data set.

Concept map

Prerequisite knowledge

• number systems (integers, fractions, decimals, ratios signed numbers, and proportions, percents, measurement );
• basic computational skills (i.e. adding, subtracting and multiplying polynomials, factoring polynomials, solving linear equations)
Similarity between algebra and other math
• Material is rigidly structured;
• What you have learned in the past is built upon;
• What you learn at the beginning will be used later
Difference between algebra and other math
• Algebra is more an abstract system built to describe natural events by mathematical operations
• Algebra is oriented more toward analysis and less toward basic mathematical skills
Future courses based on algebra
• Geometry;
• Trigonometry;
• Statistics;
• calculus;
Algebra tips
• Remember the key features of basic catergories of functions and their graphs;
• Write the functions of given relations correctly and check whether they are right by retriving the verbal expression of the functions. (Remember VANG);
• If you have troubles in algebra functions, think about their graphs; if you have problems in analyzing graphs, think about their functions. Remember functions and graphs are equivalent;
• You will be better at many “fundamental algebra” skills because of the frequency of their use – be patient and value them;
Algebra is best practiced with others who are at close to your ability level.  Find 2 – 5 people who are reliable and study weekly with them;
• Algebra was created to analyze natural evens accurately.  You will find analyzing skills improving, but must be persistent, especially at first;
• Algebra is abstract.  Understand variables and focus on the key features of the basic functions and solve more practice problems!
• The fact that you are committed to working through our tutorials is a credit to your desire and dedication.  This course was designed with the same desire and dedication, along with research-based, time tested methods.  YOU CAN DO IT – WE WILL HELP
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