Free Praxis Middle School Mathematics 5164 practice test: are you ready?

5 sample Praxis Middle School Mathematics 5164 questions, explained

From the practice tests in our guide. Try them before you open the answer.

1. 1. Which statement about the decimal 0.101001000100001... is true?

   • A. It is irrational because any decimal that is not terminating is irrational.
   • B. It is rational because its digits display a clear pattern.
   • C. It is irrational because no fixed block of digits repeats forever, even though the run lengths of zeros are structured.
   • D. It is rational because all decimals generated by a rule have repeating decimal expansions.
   Show the answer

   Correct: C (It is irrational because no fixed block of digits repeats forever, even though the run lengths of zeros are structured.).

   A rational decimal must either terminate or eventually repeat one fixed block. This decimal does neither, so it is irrational. The visible growth in the zero runs is not a repeating block, so a rational classification is unsupported.

   Topic: Numbers and Operations I, Real Numbers, Integer Arithmetic, and Exponents

2. 2. A student converts 29/4 by dividing and writes the mixed number 7 1/7. Which error explains the incorrect denominator?

   • A. The student added the quotient and the remainder.
   • B. The student used the denominator as the whole-number part.
   • C. The student placed the remainder over the quotient instead of over the original denominator.
   • D. The student used the dividend as the denominator.
   Show the answer

   Correct: C (The student placed the remainder over the quotient instead of over the original denominator.).

   The fractional part must keep the original denominator, 4, so the correct conversion is 7 1/4. Because 7 is both the quotient and the written denominator, the student incorrectly used the quotient as the denominator.

   Topic: Numbers and Operations II, Fractions, Mixed Numbers, and Decimals

3. 3. At a school, 30 students are in the band and 45 are not in the band. What is the ratio of band students to non-band students in simplest form?

   • A. 3:2
   • B. 2:3
   • C. 30:45
   • D. 45:30
   Show the answer

   Correct: B (2:3).

   Band students are named first, so the ratio begins as 30:45. Dividing 30 and 45 by their common factor 15 gives 2:3. Option A is the ratio of non-band students to band students, not the ratio asked for.

   Topic: Numbers and Operations III, Ratios, Unit Rates, Proportions, and Percents

4. 4. A plumber charges a $60 service call fee plus $45 for each hour of work. Which expression gives the total charge for h hours of work?

   • A. 60h + 45
   • B. 60 + 45h
   • C. 105h
   • D. 45 + 60h
   Show the answer

   Correct: B (60 + 45h).

   The $60 service call fee is a constant term, and the $45 per-hour rate is the coefficient multiplied by h, so the correct expression is 60 + 45h. Choice A reverses the fixed fee and the hourly rate.

   Topic: Algebra I, Expressions, Linear Equations, and Inequalities

5. 5. Which pair of equations describes a system with no solution because the lines are parallel and distinct?

   • A. y = 2x + 5 and y = -2x + 5
   • B. y = 2x + 5 and y = 2x + 1
   • C. y = 2x + 5 and y = 3x + 5
   • D. y = 2x + 5 and y = 2x + 5
   Show the answer

   Correct: B (y = 2x + 5 and y = 2x + 1).

   The two equations have the same slope, 2, so the lines are parallel. Their y-intercepts, 5 and 1, are different, so the lines are distinct and the system has no solution. Choice D gives the same line, and choices A and C give lines with different slopes that intersect exactly once.

   Topic: Algebra II, Systems of Linear Equations and Their Applications

Frequently asked questions

Is this Praxis Middle School Mathematics 5164 practice test free?

Yes. It is free, it needs no account, and you see your result immediately.

How is the readiness verdict calculated?

80% or more correct = ready, 65-79% = almost, below 65% = not yet. It is a conservative bar for practice, not the official passing score of the exam.

Where do the questions come from?

From the practice tests in our Praxis Middle School Mathematics 5164 study guide, mixed across every topic of the exam: 25 questions per attempt. The sample questions on this page are not repeated in the test.