• 60 questions

Praxis 5162 Practice Test

Unofficial Algebra I practice questions in the three content categories of the ETS Study Companion.

Solve a = (b + c)h/2 for b.

Pick an answer, then press Check answer. Then you see Correct or Not quite, with the reason. Keys: A to D pick, Enter checks.

Print covers the next 60 questions. Share this set copies a link to the same questions in the same order.

Exam mode: 60 questions, 150 minutes.

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Unofficial practice questions, not affiliated with ETS (Educational Testing Service). Bank checked October 6, 2026.

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All 60 questions

Principles of algebra 23

  • A gym charges a $25 joining fee and $15 a month. Which equation gives the number of months m that $205 pays for? ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), C. creating equations and inequalities that describe relationships
  • A print order must satisfy x + y ≤ 500 and 0.4x + 0.1y ≤ 80, where x is the number of color flyers and y the number of black flyers. Which order (x, y) is a viable option? ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), C. creating equations and inequalities that describe relationships
  • A student solves 3x + 5 = 20 and writes 3x = 15 on the next line. Which property justifies that step? ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), D. justifying the reasoning used to solve equations
  • A table gives the dollars left on a transit card after x rides: (0, 50), (2, 44) and (4, 38). What does the slope mean? ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), H. intercepts of a line and slope as a rate of change
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Principles of algebra, continued

  • A tank holds 20 gallons after 2 minutes and 11 gallons after 5 minutes. What is the slope of the line through (2, 20) and (5, 11)? ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), H. intercepts of a line and slope as a rate of change
  • Completing the square rewrites x² − 10x + 7 = 0 as (x − 5)² = q. What is q? ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), E. techniques for solving equations and inequalities
  • In the expression 7x² − 4x + 9, what is the coefficient of the linear term? ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), A. writing algebraic expressions in equivalent forms
  • Multiply (2x − 5)(3x + 4). ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), B. arithmetic operations on polynomials
  • Simplify (5x² − 3x + 2) − (2x² + 4x − 7). ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), B. arithmetic operations on polynomials
  • Solve 7 − 3x > 19. ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), E. techniques for solving equations and inequalities
  • Solve a = (b + c)h/2 for b. ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), C. creating equations and inequalities that describe relationships
  • Solve ax − 3 = b for x, where a ≠ 0. ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), E. techniques for solving equations and inequalities
  • Solve the system 2x + 3y = 12 and x − y = 1. Give the answer as (x, y). ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), F. techniques for solving systems of equations and inequalities
  • Solve x² + 6x + 2 = 0. ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), E. techniques for solving equations and inequalities
  • To eliminate x, a student multiplies one equation of a system by 3 and keeps the other. Why does the new system have the same solutions? ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), F. techniques for solving systems of equations and inequalities
  • What is the average rate of change of f(x) = x² + 2x from x = 1 to x = 4? ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), G. rate of change of nonlinear functions
  • What is the x-intercept of the line 3x − 4y = 24? ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), H. intercepts of a line and slope as a rate of change
  • What kind of solutions does 2x² − 4x + 5 = 0 have? ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), E. techniques for solving equations and inequalities
  • Where do the graphs of y = x² − 3 and y = 2x intersect? ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), F. techniques for solving systems of equations and inequalities
  • Which expression is equivalent to 3^(2t + 1)? ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), A. writing algebraic expressions in equivalent forms
  • Which expression is equivalent to 4x² − 36? ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), A. writing algebraic expressions in equivalent forms
  • Which form of x² − 8x + 21 shows the minimum value of the expression directly? ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), A. writing algebraic expressions in equivalent forms
  • Which point is in the solution set of y > 2x − 1? ETS, Praxis Algebra I (5162) Study Companion: I. Principles of Algebra (38% of the test), F. techniques for solving systems of equations and inequalities

Functions 18

  • A linear function has f(2) = 9 and f(6) = 21. What is f(x)? ETS, Praxis Algebra I (5162) Study Companion: II. Functions (30% of the test), E. linear, quadratic and exponential models
  • A sequence starts at a(1) = 3, and each later term is 2 times the term before it. Which explicit formula matches it? ETS, Praxis Algebra I (5162) Study Companion: II. Functions (30% of the test), C. modeling relationships between quantities with functions
  • A tank holds 300 gallons and drains 12 gallons each minute. Which function gives the gallons left after t minutes? ETS, Praxis Algebra I (5162) Study Companion: II. Functions (30% of the test), C. modeling relationships between quantities with functions
  • A town of 8,000 people grows 5% a year. Which function gives its population after t years? ETS, Praxis Algebra I (5162) Study Companion: II. Functions (30% of the test), E. linear, quadratic and exponential models
  • An arithmetic sequence has first term 7 and common difference 4. Which explicit formula gives the nth term? ETS, Praxis Algebra I (5162) Study Companion: II. Functions (30% of the test), C. modeling relationships between quantities with functions
  • For x = 0, 1, 2, 3 a table gives y = 4, 12, 36, 108. Which type of function fits the table? ETS, Praxis Algebra I (5162) Study Companion: II. Functions (30% of the test), E. linear, quadratic and exponential models
  • The height in meters of a ball t seconds after it is thrown is h(t) = −5t² + 20t + 1. After how many seconds is it highest? ETS, Praxis Algebra I (5162) Study Companion: II. Functions (30% of the test), B. analyzing function behavior in different representations
  • If f(x) = 3x² − 2x + 1, what is f(−2)? ETS, Praxis Algebra I (5162) Study Companion: II. Functions (30% of the test), A. the function concept and function notation
  • If f(x) = x + 2 and g(x) = x − 3, what is the domain of the quotient f/g, (x + 2)/(x − 3)? ETS, Praxis Algebra I (5162) Study Companion: II. Functions (30% of the test), D. building new functions from existing functions
  • In A(t) = 1500(1.04)^t, the balance in dollars after t years, what does 1.04 show? ETS, Praxis Algebra I (5162) Study Companion: II. Functions (30% of the test), E. linear, quadratic and exponential models
  • The sequence 5, 8, 11, 14, … is treated as a function a(n) with a(1) = 5. What is its domain? ETS, Praxis Algebra I (5162) Study Companion: II. Functions (30% of the test), A. the function concept and function notation
  • What is the domain of f(x) = √(x − 5)? ETS, Praxis Algebra I (5162) Study Companion: II. Functions (30% of the test), A. the function concept and function notation
  • What is the inverse of f(x) = (2x − 5)/3? ETS, Praxis Algebra I (5162) Study Companion: II. Functions (30% of the test), D. building new functions from existing functions
  • Which function is even? ETS, Praxis Algebra I (5162) Study Companion: II. Functions (30% of the test), B. analyzing function behavior in different representations
  • Which function of t shows exponential decay? ETS, Praxis Algebra I (5162) Study Companion: II. Functions (30% of the test), B. analyzing function behavior in different representations
  • Which set of ordered pairs is not a function? ETS, Praxis Algebra I (5162) Study Companion: II. Functions (30% of the test), A. the function concept and function notation
  • With f(x) = x², the graph of g(x) = f(x − 4) + 2 = (x − 4)² + 2 is the graph of f moved how? ETS, Praxis Algebra I (5162) Study Companion: II. Functions (30% of the test), D. building new functions from existing functions
  • Writing f(x) = x² − 2x − 15 in factored form shows its zeros. What are they? ETS, Praxis Algebra I (5162) Study Companion: II. Functions (30% of the test), B. analyzing function behavior in different representations

Number, quantity, probability and statistics 19

  • A bag holds 5 red and 3 blue marbles. Two are drawn without replacement. What is the probability that the two marbles are different colors? ETS, Praxis Algebra I (5162) Study Companion: III. Number and Quantity; Probability and Statistics (32% of the test), G. probabilities of simple and compound events
  • A bus seats 48 students and 130 students are going on a trip. Dividing gives about 2.71. How many buses must be ordered? ETS, Praxis Algebra I (5162) Study Companion: III. Number and Quantity; Probability and Statistics (32% of the test), C. reasoning quantitatively and using units
  • A car travels 60 miles per hour. How many feet per second is that? One mile is 5,280 feet. ETS, Praxis Algebra I (5162) Study Companion: III. Number and Quantity; Probability and Statistics (32% of the test), C. reasoning quantitatively and using units
  • A fair coin is flipped and a fair six-sided die is rolled. What is the probability of heads and a number greater than 4? ETS, Praxis Algebra I (5162) Study Companion: III. Number and Quantity; Probability and Statistics (32% of the test), G. probabilities of simple and compound events
  • A faucet drips 15 milliliters a minute. How many liters does it drip in 4 hours? ETS, Praxis Algebra I (5162) Study Companion: III. Number and Quantity; Probability and Statistics (32% of the test), C. reasoning quantitatively and using units
  • A nonzero rational number times an irrational number is which of these? ETS, Praxis Algebra I (5162) Study Companion: III. Number and Quantity; Probability and Statistics (32% of the test), B. properties of rational and irrational numbers
  • A regression line for hours studied x and test score y is ŷ = 6.5x + 52. What score does it predict for 4 hours? ETS, Praxis Algebra I (5162) Study Companion: III. Number and Quantity; Probability and Statistics (32% of the test), F. creating and interpreting linear regression models
  • A regression line is ŷ = 3x + 10, and one observed data point is (5, 22). What is the residual at that point? ETS, Praxis Algebra I (5162) Study Companion: III. Number and Quantity; Probability and Statistics (32% of the test), F. creating and interpreting linear regression models
  • A two-way table shows that 40 of 100 ninth graders and 30 of 50 tenth graders walk to school. Of the students who walk, what fraction are tenth graders? ETS, Praxis Algebra I (5162) Study Companion: III. Number and Quantity; Probability and Statistics (32% of the test), E. summarizing and interpreting data on two variables
  • Among schoolchildren, shoe size and reading score have a correlation coefficient of 0.8. What can be concluded? ETS, Praxis Algebra I (5162) Study Companion: III. Number and Quantity; Probability and Statistics (32% of the test), F. creating and interpreting linear regression models
  • The data 12, 14, 15, 15, 16, 18 gains one more value, 60. Which statistic changes least? ETS, Praxis Algebra I (5162) Study Companion: III. Number and Quantity; Probability and Statistics (32% of the test), D. summarizing and interpreting data on a single variable
  • Home prices in a town are skewed far to the right by a few very costly houses. Which pair of statistics best describes center and spread? ETS, Praxis Algebra I (5162) Study Companion: III. Number and Quantity; Probability and Statistics (32% of the test), D. summarizing and interpreting data on a single variable
  • The points of a scatterplot lie close to a line that slopes downward from left to right. How are the two variables related? ETS, Praxis Algebra I (5162) Study Companion: III. Number and Quantity; Probability and Statistics (32% of the test), E. summarizing and interpreting data on two variables
  • Simplify √50 + √18. ETS, Praxis Algebra I (5162) Study Companion: III. Number and Quantity; Probability and Statistics (32% of the test), A. properties of radicals and exponents
  • What is (6 × 10⁸) ÷ (3 × 10⁻²) in scientific notation? ETS, Praxis Algebra I (5162) Study Companion: III. Number and Quantity; Probability and Statistics (32% of the test), A. properties of radicals and exponents
  • What is the interquartile range of the data 2, 4, 6, 8, 10, 12, 14, 20? ETS, Praxis Algebra I (5162) Study Companion: III. Number and Quantity; Probability and Statistics (32% of the test), D. summarizing and interpreting data on a single variable
  • What is the value of 8^(−2/3)? ETS, Praxis Algebra I (5162) Study Companion: III. Number and Quantity; Probability and Statistics (32% of the test), A. properties of radicals and exponents
  • Which expression equals ∛(x²) for x > 0? ETS, Praxis Algebra I (5162) Study Companion: III. Number and Quantity; Probability and Statistics (32% of the test), A. properties of radicals and exponents
  • Which sum is an irrational number? ETS, Praxis Algebra I (5162) Study Companion: III. Number and Quantity; Probability and Statistics (32% of the test), B. properties of rational and irrational numbers

How this list was compiled: Our own questions, written to the content topics of the ETS Study Companion for Praxis Algebra I (5162) (https://www.ets.org/pdfs/praxis/5162.pdf, read 2026-10-06; test page https://praxis.ets.org/test/5162.html): I. Principles of Algebra, about 23 questions (38%); II. Functions, about 18 (30%); III. Number and Quantity; Probability and Statistics, about 19 (32%). The bank holds 23, 18 and 19. Every computed answer is algebra or arithmetic on what the question itself prints, and each was worked out a second time on 2026-10-06. Licence: Questions, choices and explanations are original work of this site.

How it works

This free Praxis 5162 practice test has 60 Algebra I questions of our own, spread like the three categories of the ETS Study Companion, each worked out. It is unofficial and not affiliated with, endorsed by or sponsored by ETS.

Read the full guide

What the test covers

The ETS Study Companion for Algebra I (5162), read October 6, 2026, lists about 23 questions on principles of algebra (38%), 18 on functions (30%) and 19 on number and quantity with probability and statistics (32%). This bank holds 23, 18 and 19.

Timing

The real test has 60 selected-response questions in 150 minutes, and some may not count toward your score. Exam mode uses the same 60 and 150.

How the math is written

Whole-number powers are written x² or 10⁻². Other exponents use a caret, as in 9^t or x^(2/3). √ is a square root, ∛ a cube root, and ŷ a value predicted by a regression line.

  • ETS provides an on-screen graphing calculator for this test, so keep a graphing calculator beside you as you practice.
  • Some real questions ask you to select more than one answer choice. Every question here has exactly one right answer.

Questions and answers

Is this free Praxis 5162 practice test the real exam?

No. Every question is our own, written to the content topics ETS publishes for Algebra I. None is copied or reworded from a real test or an ETS sample question, and a score here does not predict a score there.

What is on the Praxis Algebra I test?

Three categories: principles of algebra (expressions, equations, inequalities, systems, slope), functions (notation, graphs, sequences, and linear, quadratic and exponential models), and number and quantity with probability and statistics. The Algebra I outline lists no calculus and no geometry.

What is a passing score on Praxis 5162?

ETS does not set one. Each state or licensing agency sets its own qualifying score, so look up your state on the ETS site. Exam mode here gives the number right and no pass verdict.

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