In my opinion, multiple choice math tests are the most difficult type of test you can take. Instead of the usual partial credit, everything becomes all or nothing! Miss a negative sign somewhere? You may end up with no credit.

As a student, the best thing you can do is understand how these tests are written. Both poorly written and well written tests follow typical patterns that, if you know about, will give you a much better chance than guessing on the questions you are unsure of.

The Distractors

The incorrect answer choices in multiple choice tests are called distractors. In a well written test, these are found by purposely doing the most common errors that students do and then making that an answer choice. The idea is that a student who knows what they are doing will not make these mistakes.

How can you use this to your advantage? Know the common mistakes for the type of problem you are doing and try to use this to eliminate answers. I’ll show you an example:

Muliply (-3)(3).

(A) -9

(B) -6

(C)  6

(D)  9

Let’s pretend you are completely stuck on this problem because you forgot how to multiply. What’s a common mistake here? Well, usually people mess up the sign when they are dealing with negative numbers right? If you know that the sign MUST be negative, you can eliminate answer choices (C) and (D) and increase your chance of guessing right!

This works on any level of math test but does require you to know what you are doing at least a little bit. So, pay attention to what your instructor points out as the “obvious” mistakes or what your common mistakes are to help you when you get stuck! I have used this method to write these types of questions even for calculus exams and know that others do as well. Do students always forget to distribute? (answer: yes)… figure out the answer you would get without distributing and eliminate it!

Note: Unfortunately in a poorly written test, the answer choices may just be made up making this method useless! Luckily, it is often true that a poorly written multiple choice tests makes the correct answer obvious since several of the answers will not be realistic.

Over the next few weeks, I will add more tips specifically about this type of test. If you have your own tips, please share them!

Many students view calculus nervously – worried that somehow it will be tougher than any math class they have taken yet. In reality, the basic material in calculus is not that difficult, and many things that helped you understand math before will still help you at this level. The list below has been made from years of observing what successful students do differently in calculus courses. Whether you are in calculus now or taking it next semester you are likely to find some good ideas below:

1.      Check your algebra skills

To be able to DO calculus you need to really understand algebra – really really understand it.  Details that may have been possible to overlook now matter bigtime! Can you take a really large fraction with algebraic expressions in the numerator and denominator and simplfy it? Do you remember how to multiply polynomials? Actually just about everything you learned in algebra will come up at some point. If you are already taking calculus or will be soon, it would be helpful to pick up an algebra book for when you get stuck. Something like Schaum’s outline which gives the step by step instructions without any of the extras (plus its only $13!). There are also plenty of free resources such as purple math and our very own algebra review articles. (If you don’t have time for all that, our algebra bootcamp may help)

2.    Get up to speed on your graphing calculator

If you haven’t used a graphing calculator much yet, you will find it amazing how much actually seeing the functions help you understand what is going on. If you are working on a problem and really stuck, sometimes taking a look at the graph helps you find your mistakes. If at all possible get comfortable with the calculator BEFOREHAND! It is a lot more difficult to learn a new calculator along with a lot of new math ideas.

3.   Don’t just memorize – learn WHY

Algebra is very step by step and in some ways you can solve problems without ever really thinking about what you are doing. If you learn the steps you can get an answer. You could probably do the same with calculus but just as in algebra there is a major problem with this style of learning: If you run into any trouble at all you will be done! If you don’t understand why then how will you work your way out of a jam? With the more open ended problems this can be a real issue. So, when you read examples or try problems, pay attention to why each step is done. Once you see this you may start finding shortcuts and realizing that you really don’t have to memorize as much as you thought.

4.    Pay attention to notation

It may seem silly, but the little details of the correct notation are important. This is the language of calculus and if you are using it incorrectly, how can you expect to truly understand anything? If someone had problems with reading comprehension as far as recognizing questions and then you noticed he was using question marks incorrectly in his own writing, wouldn’t you think that was part of the issue? When you forget a “dx” or to get rid of the integral symbol after you have taken the integral you are making it impossible to go back and truly read your work. How will you review what you did? Will you be able to follow it?

5.   Actually learn the formulas

Ok earlier, I said “don’t just memorize”. This is true. BUT – you will have to memorize some things. There is simply no way around this whatsoever, so just make it happen. You MUST memorize the rules for differentiation and integration for instance. The best way to achieve this is by working problem after problem after problem until they are second nature. You know how if I ask you name, you dont have to write it first or even think? You just KNOW. That’s how it should be with the formulas/rules in calculus.

In ten years of off and on teaching I have heard this many more times than I can count. I have to admit that since I have always taught at the college level I used to be surprised when I heard this. Part of me USED to think “haven’t you grown out of this yet?” . Recently I realized that I am being asked this because no one has given students a truthful answer. Unless you plan on going into a technical field (or just love math)

YOU VERY WELL MAY NEVER SOLVE AN EQUATION AGAIN IN YOUR LIFE

…or simplify an algebraic expression, or reduce a matrix, or…. Etc. You get the idea.

You will probably not do this anymore than you will repeatedly lift a heavy object in a specific manner for a set number of repetitions. Strangely however, no one ever asks “when will I ever use this” while weightlifting.

Basic math is certainly used every day by the average person. Fractions, decimals, addition and subtraction find their way into many tasks. Math truly is the language of science and defines how the world works. But just like you don’t need to know programming to use a computer – you don’t necessarily need to know algebra and calculus to operate in the day to day world.

However, just like being strong and in shape is an asset in day to day life, so is problem solving. By learning methods and concepts from mathematics you are not only learning the language of how the world works but you are simply learning how to THINK LOGICALLY AND SOLVE PROBLEMS.

You are learning how to get information out of a seemingly complex situation, use a process, find answers, and make decisions. You are learning how to put complex ideas together and take things that appear unrelated and use them at the same time. I could go on and on.

If you don’t think you use any type of problem solving skills in your day to day life then let’s have a 5 minute conversation. I will point out all the times in your day where you used these skills. (how did you decide the best way to avoid that traffic jam this morning?)

Then there is the bonus. If you DO decide “you know what I am interested in physics” (or computer science, or engineering, or any science) SURPRISE not only have you learned how to think logically but you already know how to read the language of these fields: Mathematics.

So when will you use it? EVERY DAY OF YOUR LIFE…..See ya’ll at the gym!