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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
Would you like to study the entire math course in 24 hours? Master all important concepts and learn how to solve problems. Super review your upcoming exams with our cheat sheets. Get started with out rapid courses now!
Introductory Statistics
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