College Math Refresher

Whether you have a Ph.D. in civil engineering or a bachelor’s degree in music, chances are you’ll have to use math at some point in your adult life. From taxes and cooking to design projects and computer programming, math is — and will remain — an essential skill set. This refresher guide was designed to help you revitalize your rusty math skills for today’s world, and can even introduce you to a few new concepts along the way.

Five Mathematical Areas to Familiarize Yourself With

Throughout the history of science and philosophy, the concept of reason has been picked apart by the world’s greatest minds. Of all the many investigations made into the concept, mathematics remains one of the best tools we can use to get closer to fully understanding the “laws” which govern reality. Below is a brief overview of several mathematical areas, with brief descriptions and test questions you can use to study.


This area of mathematics is usually studied by middle school students as an introduction to algebra. In some senses, it’s the backbone of everyday math. Therefore, refreshing yourself on the core concepts can be quite easy if you have some background with arithmetic, multiplication and division in the form of basic algebraic equations.

Test Your Knowledge!

Solve for “x”:

  1. 2 + x = 4
  2. (15 – 5) – x = 10

There are a few steps we need to follow in order to “solve for x.” The key is to isolate the “x” before the equal sign. For the first question, simply subtract 2 from both sides of the equal sign. Subtracting 2 from 2 equals 0, and 2 from 4 equals 2 (you cannot subtract a number from x). Now your equation should look like 0 + x = 2, which is essentially x = 2. Now try the second question and see how you do!


Typically, students study some form of calculus as a junior or senior in high school, or in the first years of college. It certainly is not the easiest area of mathematics! The invention of calculus is often credited to 17th century thinkers Isaac Newton and Wilhelm Gottfried Leibniz and is defined as the mathematical study of change. Change, as we all know, can be quite complicated, and the study of calculus definitely follows suit.

Because calculus equations can get rather complicated and unwieldy, there will not be any practice questions for you to take in this article. If you’re looking to spark your memory, this basic calculus refresher created by Dr. Ismor Fischer at the University of Wisconsin is a great resource to keep handy.


Like calculus, this area of mathematics is something many people tend to just get or struggle their whole lives trying to grasp. It requires a keen sense of spatial intuition, in addition to a robust knowledge of algebra and trigonometry. Invented by the ancient Greek mathematician Euclid, geometry is the study of shapes and sizes, as well as distinguishing the various properties of space.

Test Your Knowledge!

  1. What is the supplementary angle to 24?
  2. Find the area of a circle with a radius of 7.

For the first question, you should know that supplementary angles must add up to a total of 180. So solving this question is rather easy, just subtract 24 from 180 and voila! Question number two requires the memorization of a formula (geometry requires that you memorize many different formulas). The formula you need in order to find the area of a circle is: Area = Pi (3.14) x Radius squared.


Trigonometry is quite similar to geometry, except it’s all about triangles. You’d never realize how important triangles are to our world until you study a bit of trigonometry. In addition to naturally proceeding geometry during a student’s course of study in mathematics, it also tends to precede the study of calculus. Many of the functions and equations learned in trigonometry are often heavily used in careers that rely upon applied mathematics, such as engineering.

Test Your Knowledge!

  1. Find the Sine of angle A with and adjacent side of 8, an opposite side of 9 and a hypotenuse of 10.

If the question above seems like a bunch of gibberish, don’t worry; you’re not alone. Without going into too much detail, the Sine is really just a ratio of two sides of a right triangle: the opposite side of angle A and the triangle’s hypotenuse (the diagonal side). So, the equation would be: Sin A = opposite / hypotenuse (adjacent side doesn’t matter for this formula). See if you can do it!

Applied Math

As the name would imply, the various systems of applied math are considered to be the more practical areas of mathematics. Examples of applied math include statistics, computer science and economics. Typically, areas within applied mathematics fall under the auspices of the liberal sciences, and do not often require the same degree of mathematical knowledge needed by students of the hard sciences.

Test Your Knowledge!

  1. (Probability) If you roll a die once, what is the probability that it will show an even number?
  2. (Economics) Last month, shoppers bought 200 boxes of cereal out of 250 total boxes from the grocery store. This month, 300 shoppers wanted to buy cereal, but only 250 new boxes of cereal arrived. Did the supply or demand increase for cereal this month? Was the demand met?

The first question is pretty easy compared to other probability scenarios. On a normal,

6-sided die, there are 6 possible outcomes: 3 possible even numbers and 3 possible odd numbers. Therefore, there is a 50% (1/2) chance the die will show an even number. The second question is also relatively simple. Since 300 shoppers (100 more than the previous month) wanted to buy cereal, the demand obviously increased. Moreover, 50 boxes were carried over from the previous month, making the total number of boxes available for this month 300. Therefore, the supply also increased and the demand was met.

Resources for Refreshing Your Math Skills

Below is a list of some of the greatest resources you can use to continue your refreshing your knowledge of mathematics:

  • The Ultimate Math Refresher for the GRE, GMAT, and SAT: This comprehensive study guide is an excellent resource for refreshing your skills in several mathematical areas, such as arithmetic, algebra and geometry. Not only does the book go over these areas in depth, it can help you prepare for the math component of several college and graduate school entrance exams.
  • Oxford University Mathematics OpenCourseWare: This site, hosted by Oxford University, offers several massively open online courses (MOOCs) across many areas of mathematics that any sort of student can study for free. While many of these courses probably shouldn’t be taken by beginners, the courses available, such as Introduction to Pure Mathematics, offer great refresher materials for college or grad school students.
  • S.O.S. Math: Helpful to both beginning and advanced math enthusiasts, this site is a boon for many of us who need to brush up on our math skills across several popular areas of mathematics. In addition to several areas of math outlined earlier in this guide, S.O.S. Math also provides helpful information about books and other math-related sites you can learn from.
  • King of Math: This game app for iOS devices provides people with a fun way to refresh their skills across several areas of mathematics. The game starts you off as a farmer who must level up by answering several fast-paced math exercises across areas such as statistics, arithmetic and geometry.

Math Makes the World Go Round

Resources we use to refresh our skills across various areas of mathematics are not only helpful when promoting our ability to think quantitatively, but could prepare you for a real world situation where such knowledge might come in handy. Even though your current major or profession may not require a strong knowledge of math to get by, taking some time to refresh yourself on many of the topics outlined above could end up helping you in more ways than you think.

Answers to Questions Above:

  • Pre-Algebra: 2; 0
  • Geometry: 156; 156.86
  • Trigonometry: 0.9
  • Applied Math: (See Guide)