The Ultimate Basic Math Reviewer

Last Updated on 10/10/2021 by FilipiKnow

Everything around you involves mathematics.

From mundane daily tasks to monumental breakthroughs, there’s always math involved. Whatever career you will pursue in the future, chances are you will need to have at least a basic understanding of mathematical concepts.

For these reasons, studying math becomes a significant human activity. 

Mathematics is the study of quantities, structure, space, and analysis.

We are studying Mathematics not just to learn these formulas, equations, expressions, or complex terminologies. We are also learning to develop our analytical, logical, decision-making, and critical thinking skills.

In this reviewer, we will discuss the basics of different subfields of mathematics – arithmetic, algebra, geometry, trigonometry, statistics, calculus, and logic.

This basic math reviewer will serve as your key to understand mathematics and discover its practical uses.

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1. Arithmetic and Number Sense.

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Image by Alicja from Pixabay

Our journey of learning mathematics starts with numbers. We are all familiar with numbers since we use them to count objects. However, there are more things to learn about numbers aside from counting them. These things are what we’re going to talk about in this chapter.



2. Algebra.

We can represent a number or a quantity using any symbols or letters. Algebra deals with the use of representations for numbers and how we can use them to solve equations, derive formulas, simplify expressions, and so on. In this chapter, I’ll discuss how symbols or letters can be used to represent quantities, solve equations and inequalities, graph in a coordinate system, analyze functions, and simplify algebraic expressions.


  • Algebraic Expressions
  • Laws of Exponents
  • Polynomials
  • Special Products and Factoring
  • Linear Equations
  • Quadratic Equations
  • Rational Expressions
  • Radical Expressions
  • Inequalities
  • Functions
  • Cartesian Coordinate System
  • Using Algebra to Solve Word Problems

3. Geometry.

Johannes Kepler said that geometry is the “archetype of the beauty of the world”. Most of the fascinating things are products of geometry. For instance, the Egyptian Pyramids’ proportions are based on geometric concepts. In this chapter, we will explore the properties of geometric figures that we are all familiar with – triangles, quadrilaterals, circles, and angles.


  • Introduction to Geometry: Undefined Terms, Definitions, Postulates, and Theorems
  • All about Angles
  • Perimeter and Area of Plane Figures
  • Volume of Solid Figures
  • Circles
  • Right Triangles

4. Trigonometry.

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Image by PIRO4D from Pixabay

Have you ever wondered how a satellite system works or how the distance of a boat from a lighthouse can be calculated? Both of these things can be explained by trigonometry.

Trigonometry deals with the relationships between the angles and sides of a triangle. In this chapter, we are going to discuss the six trigonometric functions and the Unit Circle.


  • Six Trigonometric Functions
  • Unit Circle

5. Statistics.

basic math reviewer 5
Image by Lorenzo Cafaro from Pixabay

The modern world relies on data–from surveys, polls, quality testing, and medicine to the stock market, weather forecasts, research studies, and so on. We are able to harness information from a set of data through statistics. 

Statistics deals with collecting, organizing, and interpreting data. We will explore in this chapter the basics of statistics and how we can use it to solve real-life problems.


  • Measures of Central Tendency
  • Probability
  • Factorials

6. Calculus.

basic math reviewer 6
Image by athree23 from Pixabay

The discovery of calculus is one of the most significant breakthroughs not only in mathematics but also in other fields such as engineering, physics, economics, computer science, actuarial science, and so on. We wouldn’t have been able to build this modern society were it not for calculus. Basically, calculus deals with how things change. In this chapter, you are going to learn the basics of calculus including the concept of limits and basic differentiation.


  • Limits and Continuity
  • Basic Differentiation
  • Basic Integration

7. Logic.

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Image by klimkin from Pixabay

All creatures that can swim are fish. John can swim. Therefore, John is a fish.

Can you explain why the statement above is wrong?

Logic deals with proper reasoning. In this chapter, you will learn the basics of propositional logic and apply it to determine whether a given statement is true or not.


  • Propositional Logic
  • Truth Tables and Logical Equivalences

Jewel Kyle Fabula

Jewel Kyle Fabula is a Bachelor of Science in Economics student of the University of the Philippines Diliman. His passion for learning mathematics developed as he competed in some mathematics competitions during his Junior High School years. He loves cats, playing video games, and listening to music.

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