What is the best way to study for a math test?

#1 Practice Daily

Learning is a process, not an event. Rome was not built in one day, and you will not learn all you need to know for a test in one day. You need to prepare by practicing every day. How do you practice every day? First, you should work on your homework every day. Second, read the section below on flashcards.

#2 Don’t Skip Something You Don’t Understand

In math, one topic is built on another, and the math you are learning in this class will be used in the next class. You cannot afford to skip anything or not learn one topic. If you miss a problem on the homework, a quiz, or a test, you need to learn that topic. 

One idea is to create a page at the beginning of your notebook and keep a list there of problems you have missed. That way, you have a place to start when you’re studying for a test. These are the topics you need to relearn.

You can also add the topics you miss on homework, quizzes, and tests to your flashcards. See below.

#3 Use Flashcards

When you sit down to take a test, you have to be able to pull the information on how to solve each problem out of your head. To prepare for the test, you need to practice pulling information out of your head without assistance or hints. Flashcards are the best way to practice this.

A lot of people think that you can’t use flashcards to study math, but you can. Start creating flashcards from the beginning of the class, or start right now. 

On each flashcard, write one of each type of math problem from your homework. In your homework you do multiple problems of the same type. Just choose one of each type of problem to add to your flashcards, then work the problem out on the back of the card. 

To study using your flashcards, look at the first card. Then in your head think of the steps you need to take to solve the problem. You are practicing pulling out of your head how to solve the problem, which is exactly what you need to do on a test. Don’t worry about getting the right answer, as long as you know the steps you need to take to solve that problem. 

Example 1

Front of Card: Solve for x. y=3x + 7

Think: I need to get x by itself on one side of the equation. X is being multiplied by 3 and then 7 is being added to it. I need to subtract 7 from both sides of the equation. Then I need to divide both sides by 3. 

Turn the card over and check your work.

Example 2

Front of Card: Factor  $9x^2-16$

Think: Hm, 9 and $x^2$ and 16 are perfect squares, and they are being subtracted. That means this is a difference of squares. I just need to write ( ____ - ____)(____ + ____) and put the square root of 9 and $x^2$ in the first place of each parentheses and the square root of 16 in the second space of each parentheses. 

Turn the card over and check your work.

Example 3

Front of Card: The initial position of a particle is 0. If its velocity is described by v(t) = 4t + 5, what is its position at the time when the velocity is equal to 45?

Think: The position s(t) is equal to ∫v(t) dt and ∫ 4t + 5 dt is 2t2 + 5t + C. Now, since we know that the initial position of the particle (at t = 0) is 0, we know C is 0. So, we will use s(t) = 2t2 + 5t. To find the time t when at which the velocity is 45, set v(t) equal to 45 and solve it.

Turn the card over and check your work.

Don’t let yourself cheat and look at the back of the card if you struggle a little. Let your brain work. If your brain has to struggle to come up with the answer, that’s good. That means you’re learning. Only turn the card over for help if you absolutely cannot come up with the answer.

As you go through your flashcards, place the ones you answered right away in one pile, and the ones you struggled on, even if you got them right, in another pile. The ones you struggle with, you need to practice regularly. The ones you answer easily you can set aside, they should be shuffled into the pile you’re working on every once in a while, like maybe once a week. The goal is to be able to answer every card right away, without hesitation. 

It is helpful to go through your flashcards for 10-15 minutes every day. If you find you’re struggling with a lot of the questions, you should increase the frequency of your studying. Maybe study for 20 minutes in the morning and 20 minutes in the evening. The time between study is important. It gives your brain time to process that information and put it into your long term memory. 

If you do this, you will find that you don’t even need to “study” the night before your math tests because you already know all the material!

“It’s the night before the test and it’s too late to study for 10 minutes every day!” 

That’s okay. You can also use flashcards to study the night before a test too. You will have to put in the time making and studying your flashcards, but this is the best way to study for a math test. And don’t let someone else make the cards for you. Making the cards is part of your learning.

#4 Things NOT To Do

Reread your Textbook

This will give you the illusion of fluency, and you will fool yourself into thinking you understand the material, but you don’t.

Rewatch Lectures

Again, this gives you the illusion of fluency. You can follow what the instructor is doing, but that doesn’t mean you can do it yourself or that you will remember what to do when presented with a similar problem.

Look Through Your Homework

This also gives you the illusion of fluency. 

Redo your Homework

Redoing your homework is very time consuming, and it won’t help you focus on the problems you struggle with.