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Praxis Core Math: Algebra Practice Questions

Algebra dominates Praxis Core Math. Even questions related to geometry, statistics, and numbers/quantity may have an algebraic component. So it’s good to know exactly what to expect when it comes to Praxis Core algebra.

There are three types of algebra questions on the Praxis Core math exam. The most complex algebra question type is the story problem. In Core Math algebra story problems, you’ll need to read about a situation involving numbers, come up with an algebra equation that works, and calculate the answer.

The other two categories of algebra questions are somewhat simpler. You can expect to see problems related to equivalent expressions and solving algebraic equations for a single variable. In both cases, the equation that you start with is provided, and you must carry out the correct algebraic steps to arrive at the correct answer.

Below is a practice set of Praxis Core Math algebra problems that can help you prepare for the exam. An answer key appears at the very bottom of this post. Once you finish the problems, check the answer key and see how you did.

Practice algebraic story problem

PraxisCoreMathAlgebraGraphic

The pictograph above shows the number of new textbooks a local public school must purchase for their fifth grade classes before the next school year begins. Math books cost $25 each, English books cost $15 each, and the total cost of the textbooks is $5700. If each history book costs c dollars, what is the value of c?

    A) 35
    B) 30
    C) 25
    D) 20
    E) 15

 

Practice equivalent expressions problem

Which of the following expressions is equivalent to 19-3x for all values of x?

    A) 3 – 2(8 –x)

    B) 22 – (3 – 3x)

    C) 4 + 3(5 –x)

    D) 3(2 –x) -13

    E) 19(1 –x) – 16x

 

Practice algebra equation problem

If 14(2x + 1) = 7(x + 9) + 1, what is the value of x? Give your answer as a fraction.

fraction-answer

(Note: This question is in one of the Praxis Core’s alternative question formats  for Math.)

 

Answer Key:

    1) B
    2) C
    3) 50/21

 

Notes about the answers:

Story problem:The correct starting equation uses the three variables Math, English, and History. These variables can be expressed respectively as M, E, and H. The equation you start with will multiply the number of each type of book (20 times the number of icons on the chart) with its unit price, to equal a total of $5700. From there, you plug in the numbers you have to solve for unknown variable d, the cost of an individual history textbook. The steps look like this:

    1) 20*25*M+ 20*15*E+ 20*d*= 5700

    2) 20*25*3 + 20*15*2 + 20*d*6 = 5700

    3) 1500 + 600 + 120d= 5700

    4) 2100 +120= 5700

    5) 2100 + 120d– 2100 = 5700 – 2100

    6) 120d= 3600

    7) (120d)/120 = 3600/120

    8) d= 3600/120

    9) d= 30

Equivalent expressions problem: To solve this, use the commutative property of multiplication to “factor out” everything in the parentheses in each answer choice. From there, rewrite each answer choice in its simplest form. You’ll see that only answer C becomes 19-3x after being factored out and simplified.

Algebra equation problem: Starting with the given equation, the steps are as follows:

    1) 14(2x+ 1) = 7(x+ 9) + 1

    2) 28x+ 14 = 7x+ 63 +1

    3) 28x+ 14 = 7x+ 64

    4) 28x+ 14 – 14 = 7x+ 64 – 14

    5) 28x= 7x+ 50

    6) 28x– 7x= 7x+ 50 – 7x

    7) 21x= 50

    8) 21x/21 = 50/21

    9) = 50/21

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9 Responses to Praxis Core Math: Algebra Practice Questions

  1. Pamela T Phillips June 25, 2016 at 2:30 PM #

    #3 on the Algebra should be 50/21

    • Sheri July 3, 2016 at 7:11 PM #

      I also got 50/21

      • David Recine
        David Recine July 5, 2016 at 12:09 PM #

        50/21 is correct. I made a mistake in my original post. (Embarrassing, but it happens.) Thanks to everyone who brought this to my attention. 🙂

  2. Ted July 5, 2016 at 8:10 AM #

    Pamela (above) is correct. Here are the steps:

    1) 14(2x + 1) = 7(x + 9) + 1
    2) 28x + 14 = 7x + 63 +1
    3) 28x + 14 = 7x + 64
    4) 28x + 14 – 14 = 7x + 64 – 14
    5) 28x = 7x + 50
    6) 28x – 7x = 7x + 50 – 7x
    7.) 21X = 50
    8) x – 50/21

    • David Recine
      David Recine July 5, 2016 at 11:59 AM #

      Ted– You’re absolutely correct– not quite sure how I made that mistake in my original post. But apologies from me, and thanks to you bringing it to my attention.

      I’ve corrected the steps for the algebra equation problem, thanks to your feedback. I added one extra step between your steps 7 and 8, just to make the whole process as clear as possible. And I also fixed some troublesome formatting issues that were making this post hard to read. 😉

  3. Nancy May 28, 2018 at 12:50 PM #

    It seems to me that the question about which answer is equivalent to 19-3x should also include answer B. 22-(3-3x)=19-3x

    • Magoosh Test Prep Expert
      Magoosh Test Prep Expert June 2, 2018 at 12:35 PM #

      Hi Nancy,

      Answer choice (B) is incorrect because we have to distribute the negative negative (minus) sign. If we simplify this expression, it becomes:
      22-(3-3x)
      22-3 + 3x
      19+3x
      When there is a parenthesis after a subtraction sign, I like to imagine that there is a “1” in front of the parenthesis. In this case, we have to distribute -1 to each term in the parenthesis, which changes the sign of the 3x term. So, (B) is not a correct answer here!

  4. Michelle Hubbard August 24, 2018 at 9:19 AM #

    I keep taking core skills math and missing it by 4 points. It’s becoming very discouraging. I keep studying and practices. I dont know what else to do.

    • Magoosh Test Prep Expert
      Magoosh Test Prep Expert August 24, 2018 at 10:37 AM #

      Hi Michelle,

      I’m sorry this is happening to you! “Plateauing” at a certain score is a frustrating but not uncommon problem for Praxis preppers. When you start to plateau, the best thing to do is to really analyze your past, present, and ongoing practice. What types of questions are you missing, and why? Try to identify a pattern of mistakes. For example, are certain math operations especially challenging for you on the exam? Are there certain passage types in Reading that you are stronger on or weaker on? In Fore Writing, what question types are the hardest for you, and for that matter, what are your Core Writing strengths?

      To do this kind of analysis, you need to tap into as many practice question sets as you can. Go through (or review) resources such as the questions in the official Core Math Study Companion, the official Core Math practice tests, this blog’s archive of Praxis practice questions, and Magoosh Praxis Premium.

      Then, as I said, really analyze which questions you’ve missed, and why you missed those questions. To do that, consider keeping a detailed error log, as described and shown in Magoosh’s error logging tutorial. (The example error logs there are for GRE and GMAT, but the techniques are equally applicable to Praxis.) Once you review your error logs, a pattern of weaknesses that you can really focus on should become apparent.


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