• 48 questions

Algebra II SOL Practice Test

Virginia's end-of-course Algebra 2 test in practice form: rational and radical expressions, complex numbers, functions, and the normal curve.

What is the product (x² − 9)/(x² + 5x + 6) · (x + 2)/(x + 4) in simplest form, where no denominator is zero?

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 48 questions. Share this set copies a link to the same questions in the same order.

Exam mode: 48 questions, no time limit.

More options

Unofficial practice questions, not affiliated with the Virginia Department of Education. Bank checked October 13, 2026.

The real test: the Algebra 2 SOL

Questions
48
Items
48 operational items that count, plus 8 field-test items that do not.
Reporting categories
Expressions and Operations 11 items, about 23%; Equations and Inequalities 14, about 29%; Functions and Statistics 23, about 48%.
Standards
The fifteen 2023 Algebra 2 standards: A2.EO.1 to A2.EO.4, A2.EI.1 to A2.EI.6, A2.F.1, A2.F.2 and A2.ST.1 to A2.ST.3. Not every standard is on every test.
Calculator
Items come with the online Desmos Virginia Graphing calculator on the toolbar.
How it is given
Online. Students who take the same version answer the same questions. Paper is for students who meet the criteria for a paper test.
Scores
A scale of 0 to 600: 400 is the minimum for proficient and 500 is advanced. End-of-course levels: Pass/Advanced, Pass/Proficient, Fail/Does Not Meet.

Checked October 13, 2026 against the Test Blueprint, Algebra 2, 2023 Mathematics Standards of Learning, and the SOL Test Scoring & Performance Reports page, Virginia Department of Education. Rules change, so confirm with the agency itself before your test.

The state's own SOL practice items

Next step More advanced algebra practiceReview: Algebra 1 SOL practice

All 48 questions

Expressions and Operations 11

  • What is 6/(3 − √3) with a rational denominator? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EO.2b
  • What is the product (2 + 5i)(3 − i), written in a + bi form? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EO.4c
  • What is the product (x² − 9)/(x² + 5x + 6) · (x + 2)/(x + 4) in simplest form, where no denominator is zero? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EO.1a
  • What is the quotient (2x³ + x² − 13x + 6) ÷ (x − 2)? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EO.3c
  • What is the sum 3/(x + 2) + 2/(x − 1), written as one fraction? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EO.1a
  • What is √(50x⁵y²) in simplest radical form, for x ≥ 0 and y ≥ 0? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EO.2a
  • Which expression is equal to √(−48)? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EO.4b
Show all 48 questions (41 more)

Expressions and Operations, continued

  • Which expression is equivalent to the complex fraction (1/x + 1/3) ÷ (1/x − 1/3), for x ≠ 0 and x ≠ 3? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EO.1c
  • Which expression is equivalent to ∛(a²) · √a, for a ≥ 0? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EO.2c
  • Which is the complete factorization of 8x³ + 27? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EO.3b
  • Which is the complete factorization of x³ − 2x² − 9x + 18? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EO.3b

Equations and Inequalities 14

  • A cubic polynomial function has zeros −2, 1 and 5. Which equation, in factored form, has exactly those solutions? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EI.6a
  • A machine fills bottles to 500 milliliters. A bottle passes inspection when its volume v is within 4 milliliters of 500. Which inequality models the bottles that pass? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EI.1c
  • The height of a ball, in feet, t seconds after it is thrown is h = −16t² + 48t + 4. At what times is the ball 36 feet high? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EI.2a
  • How many solutions does the system y = x² + 4 and y = 2x + 3 have? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EI.3b
  • Multiplying both sides of x/(x − 3) = 3/(x − 3) + 2 by x − 3 leads to x = 3. What is the solution set of the equation? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EI.4d
  • Squaring both sides of √(2x + 3) = x gives x² − 2x − 3 = 0, with roots −1 and 3. What is the solution of the original equation? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EI.5c
  • What are the solutions of the system y = x² − 2x − 3 and y = x + 1? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EI.3c
  • What are the solutions of x² − 4x + 13 = 0 over the set of complex numbers? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EI.2b
  • What are the solutions of x³ − 3x² + 4x − 12 = 0 over the set of complex numbers? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EI.6c
  • What are the solutions of |2x − 5| = 9? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EI.1b
  • What is the solution of the radical equation ∛(x + 5) − 1 = 2? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EI.5a
  • What is the solution of x/(x − 2) + 1 = 8/(x − 2)? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EI.4b
  • Which interval is the solution set of |x + 4| ≤ 3? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EI.1d
  • Which values of x make x² − x − 12 < 0 true? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.EI.2c

Functions and Statistics 23

  • A curve of best fit for a club's sign-ups is y = 0.5x² − 2x + 10, where x is the week and y is the number of sign-ups. What does the model predict for week 8? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.ST.2g
  • A data set has the values y = 5, 10, 20, 40 and 80 for x = 0, 1, 2, 3 and 4. Which type of function best models the data? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.ST.2d
  • A table has the pairs (2, 18), (3, 12), (4, 9) and (6, 6). Which describes the relationship between x and y? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.F.1d
  • A teacher picks 3 of 8 students for a committee whose members all have the same role. How many different committees are possible? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.ST.3c
  • Ava scored 84 on a test with a mean of 76 and a standard deviation of 4. Ben scored 90 on a test with a mean of 80 and a standard deviation of 8. Who did better relative to their own class? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.ST.1g
  • The distance a spring stretches varies directly with the weight hung on it. A 6-pound weight stretches the spring 4 inches. How far does a 15-pound weight stretch it? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.F.1d
  • For f(x) = 4 + log₂ x, what is f(8)? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.F.2f
  • For f(x) = x² + 1 and g(x) = 2x − 3, what is f(g(x))? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.F.2k
  • The graph of a parent function passes through (0, 1), rises from left to right and has the x-axis as a horizontal asymptote. Which function is it? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.F.1a
  • The graph of f(x) = x³ − 3x has a relative maximum at (−1, 2) and a relative minimum at (1, −2). On which interval is f decreasing? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.F.2c
  • The graph of y = √x is shifted 3 units left and 2 units down. Which equation matches the new graph? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.F.1b
  • How does the graph of g(x) = −2∛x compare with the graph of the parent function f(x) = ∛x? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.F.1c
  • In how many ways can a president, a vice president and a treasurer be chosen from 9 club members, if no one holds two offices? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.ST.3b
  • The masses of apples in an orchard are approximately normal, with a mean of 150 grams and a standard deviation of 12 grams. About what percent of the apples have a mass between 126 and 174 grams? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.ST.1i
  • Test scores are normally distributed with a mean of 70 and a standard deviation of 8. What is the z-score of a score of 82? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.ST.1f
  • What are the asymptotes of the graph of f(x) = (2x + 1)/(x − 4)? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.F.2h
  • What are the zeros of f(x) = x³ − 4x² − 5x? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.F.2a
  • What is the domain of the square root function f(x) = √(3x + 12)? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.F.2a
  • What is the end behavior of the graph of f(x) = −2x⁴ + 3x² + 1? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.F.2g
  • What is the equation of the horizontal asymptote of the graph of f(x) = 3^x − 4? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.F.2h
  • Which function is the inverse of the linear function f(x) = 4x + 10? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.F.2i
  • Which statement is true of every normal distribution? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.ST.1d
  • Which statement is true of the functions f(x) = 3^x and g(x) = log₃ x? Virginia Department of Education, 2023 Mathematics Standards of Learning, Algebra 2, SOL A2.F.1e

How this list was compiled: Outline: Test Blueprint, Algebra 2, 2023 Mathematics Standards of Learning, Virginia Department of Education (effective with the spring 2025 SOL tests; July 2026 update), https://www.doe.virginia.gov/home/showpublisheddocument/56015/639215098562370000, linked from Test Blueprints, https://www.doe.virginia.gov/teaching-learning-assessment/student-assessment/virginia-sol-assessment-program/test-blueprints, read 2026-10-13. Each question names the standard it practices in the Mathematics Standards of Learning for Virginia Public Schools, 2023, Algebra 2 (August 2023), https://www.doe.virginia.gov/home/showpublisheddocument/48957/638315045918730000, linked from Standards of Learning for Mathematics, https://www.doe.virginia.gov/teaching-learning-assessment/instruction/mathematics/standards-of-learning-for-mathematics, read 2026-10-13. Every answer is algebra or arithmetic on the numbers in the question, worked out a second time. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from an SOL test, a released test, a practice item set of the state or another practice test. No released test or practice item was read.

How it works

Unofficial practice for Virginia's end-of-course Algebra II SOL test: 48 original questions on the 2023 Standards of Learning, as many as count on the real test. No released item is among them. Not affiliated with the Virginia Department of Education.

Read the full guide

What the Virginia Algebra 2 SOL practice test covers

The blueprint puts 48 scored items in three reporting categories, and this practice test keeps its split. Functions and Statistics, 23: root, rational, exponential and logarithmic functions, their transformations, domains, zeros, asymptotes, inverses and compositions, then z-scores, the Empirical Rule, curves of best fit, permutations and combinations. Equations and Inequalities, 14: absolute value, quadratics with complex solutions, systems, and rational, radical and polynomial equations. Expressions and Operations, 11: rational expressions, radicals, factoring and complex numbers.

Algebra 2 SOL study guide: fifteen standards, one pre test

Virginia's 2023 Algebra 2 standards number fifteen: A2.EO.1 to 4, A2.EI.1 to 6, A2.F.1 and 2, and A2.ST.1 to 3. Taken before a unit, the 48 questions work as a pre test: each wrong answer names the standard to study.

  • The standards name extraneous solutions twice, for rational and for radical equations, so put every answer back into the original equation.

Questions and answers

How many questions are on the Algebra 2 SOL test?

48 operational items count toward the score. Eight more are field-test items that do not count, so a student answers 56 in all.

What is a passing score on the Algebra 2 SOL?

The state grades SOL tests on a scale of 0 to 600, where 400 is the minimum for proficient and 500 marks advanced. An end-of-course result is one of three levels: Pass/Advanced, Pass/Proficient or Fail/Does Not Meet.

Can you use a calculator on the Algebra 2 SOL?

Yes. The blueprint says each Algebra 2 item comes with the online Desmos Virginia Graphing calculator on the toolbar of the test.

Is there a state Algebra 2 SOL practice test?

The Virginia Department of Education posts practice item sets for End-of-Course Algebra 2 on its SOL Practice Items page, online and as printable PDFs. Those are the state's own items; the 48 here are separate and unofficial.

More tests

Show 8 more

Browse Civics and Law