• 50 questions

Fundamentals of College Algebra DSST Practice Test

Unofficial practice on the four areas of the DSST Fundamentals of College Algebra outline, every answer worked out.

Simplify the cube root of 54x⁴, written ∛(54x⁴).

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

Exam mode: 50 questions, 60 minutes.

More options

Unofficial practice questions, not affiliated with Prometric, which owns the DSST program. Bank checked October 12, 2026.

Next step DSST Math for Liberal Arts practice testCollege algebra final exam practice

All 50 questions

Fundamental algebraic operations 8

  • Add 2/(x − 1) + 3/(x + 2) and write the sum as one fraction. Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: I. Fundamental Algebraic Operations (16% of the exam), c. rational expressions
  • Expand (2x − 3)(x² + 4x − 1). Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: I. Fundamental Algebraic Operations (16% of the exam), b. polynomials (including factoring and expanding polynomials)
  • Simplify (x² − 25) / (x² − 3x − 10), for x ≠ 5 and x ≠ −2. Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: I. Fundamental Algebraic Operations (16% of the exam), c. rational expressions
  • Simplify 3(2x − 5) − 4(x − 7). Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: I. Fundamental Algebraic Operations (16% of the exam), a. algebraic expressions
  • Simplify the cube root of 54x⁴, written ∛(54x⁴). Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: I. Fundamental Algebraic Operations (16% of the exam), d. rational exponents and nth roots
  • What is the value of 8^(5/3) · 81^(−1/2)? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: I. Fundamental Algebraic Operations (16% of the exam), d. rational exponents and nth roots
  • What is the value of x² − 3xy + 2y² when x = −2 and y = 3? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: I. Fundamental Algebraic Operations (16% of the exam), a. algebraic expressions
  • Which product is the factored form of 8x² + 2x − 15? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: I. Fundamental Algebraic Operations (16% of the exam), b. polynomials (including factoring and expanding polynomials)
Show all 50 questions (42 more)

Complex numbers 3

  • Divide (5 + i) by (2 − i) and write the result in the form a + bi. Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: II. Complex Numbers (5% of the exam), b. basic operations
  • Multiply (3 + 2i)(1 − 4i) and write the result in the form a + bi. Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: II. Complex Numbers (5% of the exam), b. basic operations
  • What is the conjugate of the complex number −3 + 8i? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: II. Complex Numbers (5% of the exam), a. conjugate of a complex number

Equations and inequalities 23

  • A café sells 90 drinks for $330. A coffee costs $3 and a smoothie costs $5. How many smoothies did it sell? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), d. systems of linear equations and inequalities
  • Completing the square turns x² + 8x − 3 = 0 into which equation? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), b. quadratic equations and inequalities
  • The discriminant of 3x² − 6x + 5 = 0 tells you which fact about its solutions? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), b. quadratic equations and inequalities
  • The equations 3x + 6y = 9 and x + 2y = 3 form a system. How many solutions does it have? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), d. systems of linear equations and inequalities
  • Solve 2^(3x − 1) = 32. Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), e. exponential and logarithmic equations
  • Solve 3(x − 4) − 2(2x + 1) = 5x + 4. Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), a. linear equations and inequalities
  • Solve 5e^(2x) = 40 for x. Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), e. exponential and logarithmic equations
  • Solve log₂(x) + log₂(x − 6) = 4. Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), e. exponential and logarithmic equations
  • Solve log₄(3x + 4) = 3. Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), e. exponential and logarithmic equations
  • Solve the quadratic inequality x² + x − 20 > 0. Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), b. quadratic equations and inequalities (including solving quadratic inequalities)
  • Solve x/3 − (x − 2)/4 = 1. Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), a. linear equations and inequalities
  • Solve |3x + 2| = 10. Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), c. absolute value equations and inequalities
  • Solve −3x + 7 ≤ 22. Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), a. linear equations and inequalities
  • Solve √(3x + 10) = x. Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), f. equations involving radicals
  • Solve ∛(2x + 3) = −3, where ∛ is the real cube root. Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), f. equations involving radicals
  • Use the quadratic formula to solve 2x² − 4x − 3 = 0. Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), b. quadratic equations and inequalities
  • What are all the real solutions of x⁴ − 10x² + 9 = 0? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), b. quadratic equations and inequalities (including quadratic forms)
  • What are the solutions of x² + 5x − 36 = 0? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), b. quadratic equations and inequalities
  • Which interval is the solution of −5 < 2x + 3 ≤ 11? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), a. linear equations and inequalities
  • Which ordered pair solves both 3x − 2y = 16 and x + 4y = −4? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), d. systems of linear equations and inequalities
  • Which point is a solution of the system y > 2x − 1 and x + y ≤ 4? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), d. systems of linear equations and inequalities
  • Which values of x satisfy |2x + 7| ≥ 3? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), c. absolute value equations and inequalities
  • Which values of x satisfy |x − 6| < 2? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: III. Equations and Inequalities (47% of the exam), c. absolute value equations and inequalities

Functions and their graphs 16

  • Divide 2x³ − 3x² − 5x + 4 by x − 2. What is the remainder? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: IV. Properties of Functions and their Graphs (32% of the exam), g. polynomial functions (including long and synthetic division methods)
  • Given that x − 1 is a factor of f(x) = x³ − 2x² − 5x + 6, what are the zeros of f? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: IV. Properties of Functions and their Graphs (32% of the exam), g. polynomial functions (including long and synthetic division methods)
  • The height in feet of a model rocket t seconds after launch is h(t) = −16t² + 96t + 6. How high does it get? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: IV. Properties of Functions and their Graphs (32% of the exam), f. quadratic functions
  • How far apart are the points (−3, 2) and (9, −3)? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: IV. Properties of Functions and their Graphs (32% of the exam), a. coordinate systems
  • If f(x) = 3x + 1 and g(x) = x² − 4, what is (f ∘ g)(3)? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: IV. Properties of Functions and their Graphs (32% of the exam), c. operations of functions
  • If f(x) = 3x² − x + 4 and g(x) = x² + 5x − 2, what is (f − g)(x)? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: IV. Properties of Functions and their Graphs (32% of the exam), c. operations of functions
  • What is the domain of f(x) = √(x − 3) / (x − 7)? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: IV. Properties of Functions and their Graphs (32% of the exam), b. domain and range
  • What is the inverse of f(x) = (4x + 1) / 5? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: IV. Properties of Functions and their Graphs (32% of the exam), d. inverse functions
  • What is the midpoint of the segment that joins (−6, 1) and (2, 9)? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: IV. Properties of Functions and their Graphs (32% of the exam), a. coordinate systems
  • What is the range of f(x) = |x| − 3? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: IV. Properties of Functions and their Graphs (32% of the exam), b. domain and range
  • What is the vertex of the graph of f(x) = 3x² + 12x − 5? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: IV. Properties of Functions and their Graphs (32% of the exam), f. quadratic functions
  • Where does the graph of f(x) = (2x² − 8) / (x² − x − 6) have a vertical asymptote? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: IV. Properties of Functions and their Graphs (32% of the exam), h. rational functions
  • Which equation is the line through (−1, 4) and (3, −8)? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: IV. Properties of Functions and their Graphs (32% of the exam), e. linear functions
  • Which line is the horizontal asymptote of the graph of f(x) = 3^(x − 2) + 4? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: IV. Properties of Functions and their Graphs (32% of the exam), i. exponential and logarithmic functions
  • Which line passes through (4, −2) and is perpendicular to y = (2/5)x − 1? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: IV. Properties of Functions and their Graphs (32% of the exam), e. linear functions
  • Which of these functions, with all real numbers as its domain, is one-to-one and so has an inverse function? Prometric, DSST Fundamentals of College Algebra fact sheet, content outline: IV. Properties of Functions and their Graphs (32% of the exam), d. inverse functions

How this list was compiled: Our own questions, written to the content outline of the DSST Fundamentals of College Algebra fact sheet (Prometric, Rev 11/2021, https://getcollegecredit.com/wp-content/uploads/2022/09/DSST_FundamentalsofCollegeAlgebra.pdf, read 2026-10-12): fundamental algebraic operations 16%, complex numbers 5%, equations and inequalities 47%, properties of functions and their graphs 32%. The bank holds 8, 3, 23 and 16 questions, the same shares of 50. Every answer is algebra on what the question itself prints, worked out again on 2026-10-12. Licence: Questions, choices and explanations are original work of this site.

How it works

This free Fundamentals of College Algebra DSST practice test has 50 questions of our own in the fact sheet's four areas, each worked step by step. It is unofficial and not affiliated with Prometric, which owns the DSST program.

Read the full guide

Four areas and their weights

The fact sheet (Rev 11/2021, read October 12, 2026) weights them: equations and inequalities 47%, properties of functions and their graphs 32%, fundamental algebraic operations 16%, complex numbers 5%. The bank holds 23, 16, 8 and 3 questions.

100 questions, 2 hours

That is the real exam. A timed run here is 50 questions in 60 minutes, the same pace.

How the math is written

Powers appear as x² or 2^(3x − 1), ∛ is a cube root, and log₂ is a logarithm to base 2.

  • Equations and inequalities are nearly half the exam: linear, quadratic, absolute value, systems, exponential and logarithmic, and radical.
  • Put each answer to a radical or logarithmic equation back into the original: squaring both sides or combining logarithms can add a false solution.
  • Dividing an inequality by a negative number reverses its sign.

Questions and answers

Is there a DSST Principles of College Algebra exam?

Not under that name. Prometric's list of DSST exams has one college algebra title, Fundamentals of College Algebra, and this practice test follows its outline.

Is there a DSST Fundamentals of College Algebra study guide?

The free one is Prometric's fact sheet: the content outline and three reference textbooks. Here the questions are grouped by the outline's four areas, and every answer shows its steps.

Is there a DANTES study guide for college algebra?

DANTES is the Defense Department office that funds DSST exams for eligible service members. The exams have been owned by Prometric since 2004, so its fact sheet for Fundamentals of College Algebra is the study guide under either name.

Can you use a calculator on the DSST college algebra exam?

Yes. The fact sheet says a non-programmable calculator may be used in this exam. The numbers here are chosen so that each answer can also be worked by hand.

What score do you need on the DSST Fundamentals of College Algebra exam?

There is no percent to aim for. The American Council on Education recommends 3 semester hours of lower-level baccalaureate credit at a score of 400. The DSST site says to ask an advisor whether your school accepts the exam.

More tests

Show 8 more

Browse Civics and Law