Some of the questions on the Praxis Core exam’s mathematics section are not multiple choice. You’ll be asked to type the answer in a box for this type of question. These are called constructed response questions.

You’ll encounter only a handful of constructed response questions, but you should be familiar with how they work and what’s expected in your answers. Because you won’t have the benefit of being able to look at any answer choices, you need to be aware of the requirements for submitting answers in the correct forms.

Tips for preparing responses and answering questions

The first thing to make sure of before you submit a constructed response is that the answer you typed is the answer you actually got. Leaving out a decimal, a digit, π, or something else essential to a correct answer will result in a wrong answer. Figuring out a correct answer is not the final step. Submitting the correct answer is the only thing that counts.

Also, make sure you’re very clear on the instructions. A question might ask something like what measure of an angle is represented by (2x + 3)°, in which case you would have to figure out the value of a variable to determine the answer.

For such a question, make sure your answer is the measure of the angle and not the value of the variable. That is one example of when paying close attention to the question is necessary.

You also need to be careful about subtle parts of instructions. A question may ask for an exact answer, an answer rounded to the nearest hundredth, or an answer in terms of π. If you’re asked to answer in terms of π, your answer should have π in it.

That means you do not want to use 3.14 in your calculation. 3.14 is not π; it is a rounded approximation of it. Neglecting to follow the instructions exactly can cause an answer to be incorrect.

Some constructed response questions ask for more than one answer. If you’re given such a question, make sure you give all the required answers. People are so used to answering each question with one answer submission on a test that they can easily overlook the need for more than one answer to a constructed response question on the Praxis exam. Again, you need to follow instructions very closely.

Understanding the importance of avoiding careless errors

Careless errors are one of the major obstacles that stand between people and high levels of math success. The problem seems to apply especially to algebra students. To avoid careless errors, you must be cautious in all aspects of working through the math problem. Several methods can be used to defeat this menace:

  • Work every step of a problem on scratch paper. Even if you feel like you can make a calculation correctly in your head, you should work it out completely so you have a visual account of what you are doing. This greatly helps you avoid going in a wrong direction.

  • Always be on the lookout for errors. Try to catch them before they would otherwise happen. Think about how careful surgeons are when they perform surgery. One false move can be tragic. Missing a problem on the Praxis Core exam isn’t quite as tragic, but it is unfortunate. Be careful and aware of potential mistakes, just like a surgeon.

  • Talk problems out in your head as you work them. This process adds one more level of attention in addition to thinking about the problems and seeing them worked out on paper.

  • Go back over problems if you have time. If you finish the test before your time runs out, don’t pass up the opportunity to review your answers and possibly push up your score. Every minute you can spend reviewing your answers is valuable.

  • Be especially careful when working with negative numbers. They are the number one area for careless errors. If you see a negative sign, think of it as a wet floor sign telling you to be extra cautious.

  • Don’t assume that not noticing a careless error means you didn’t make one. Careless errors are sneaky. Most of them aren’t caught in the act, but the damage they cause is almost always revealed.

Some proper ways of representing answers

The instructions for constructed response questions tell you how you’re required to answer them if more than one possibility would otherwise exist. If an answer includes a unit of measurement, you need to submit it. If you’re asked to answer something in terms of some kind of unit, variable, or other representation, including it in your answer is a must.


What is the volume of a sphere that has a radius of 9 centimeters? Give your answer in terms of π.

The correct answer is 972π cm3. The volume of a sphere is 4/3πr3.


The unit used for the radius is centimeters, so the unit used for volume must be cubed centimeters (cm3). The answer to the problem has to involve a number times π and also cm3. The proper answer is therefore 972π cm3, not just 972π or the result of multiplying 972 by 3.14. You should force your constructed responses to pass a major inspection that you conduct.

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