Algebra 2 practice test: 10 free questions with worked answers

Each daily paper is a short timed practice test of 8 original questions. The AP Precalculus paper is the closer match for Algebra 2: exponentials and logarithms, polynomials and the factor theorem, sequences and series, transformations and trig equations. The Geometry, Algebra 2 and SAT Math paper covers the groundwork, such as quadratics, exponents, surds (radicals) and systems. Neither covers complex numbers.

Free Algebra 2 practice test: 10 questions

We wrote these questions for this page. Give yourself 40 minutes. Use a calculator only for question 6.

1. Solve |2x − 3| = 7.
2. Multiply (4 + 3i)(2 − 5i) and simplify.
3. Solve x² − 4x + 13 = 0.
4. Use the factor theorem to check whether (x + 2) divides p(x) = x³ + x² − 8x − 12, then find all the zeros of p.
5. Solve log₂(x) + log₂(x − 2) = 3.
6. $2,000 is invested at 4% interest compounded continuously. How much is it worth after 10 years?
7. Find the inverse of f(x) = (2x + 1)/3.
8. Find the sum of the first 8 terms of the geometric sequence 3, 6, 12, ...
9. Find the exact value of sin(5π/6), and the amplitude and period of y = 3 sin(2x).
10. Solve √(x + 7) = x − 5.

Algebra 2 practice test answers

1. The expression inside can be 7 or −7. 2x − 3 = 7 gives x = 5, and 2x − 3 = −7 gives x = −2. So x = 5 or x = −2.

2. Multiply out as with any two brackets, then use i² = −1: 8 − 20i + 6i − 15i² = 8 − 14i + 15 = 23 − 14i. The Complex Number Calculator checks these.

3. The discriminant is 16 − 52 = −36, so the roots are complex.

Complex roots of a quadratic with real coefficients always come in conjugate pairs like 2 + 3i and 2 − 3i. Practice the formula itself with this question from our Algebra course, then press Mark.

4. p(−2) = −8 + 4 + 16 − 12 = 0, so (x + 2) divides p(x) exactly. Dividing gives p(x) = (x + 2)(x² − x − 6) = (x + 2)²(x − 3). The zeros are x = −2, a double zero where the graph touches the x-axis, and x = 3, where it crosses. The Polynomial Division Calculator shows the division.

Here x is the input and y is p(x).

5. The sum of two logs with the same base is the log of the product, so log₂(x(x − 2)) = 3, which means x(x − 2) = 2³ = 8. Then x² − 2x − 8 = 0, so (x − 4)(x + 2) = 0. Reject x = −2, because you can't take the log of a negative number. The answer is x = 4. The Logarithm Calculator checks values.

6. Continuous compounding uses A = Pe^rt: A = 2,000e^{0.04 × 10} = 2,000e^0.4 = $2,983.65. Using (1.04)¹⁰ instead gives yearly compounding, a different answer.

7. Write y = (2x + 1)/3, swap x and y, and solve for y: 3x = 2y + 1, so f⁻¹(x) = (3x − 1)/2. Check: f(5) = 11/3, and f⁻¹(11/3) = (11 − 1)/2 = 5.

8. The first term is 3 and the common ratio is 2.

The sum is 765. The Sequences and Series Calculator works these out.

9. 5π/6 is 150°, in the second quadrant, where sine is positive, with a reference angle of π/6. So sin(5π/6) = 1/2. For y = 3 sin(2x), the amplitude is 3 and the period is 2π ÷ 2 = π.

10. Square both sides: x + 7 = x² − 10x + 25, so x² − 11x + 18 = 0 and (x − 9)(x − 2) = 0. Check both, because squaring can add false solutions. For x = 9, √16 = 4 and 9 − 5 = 4, so it works. For x = 2, √9 = 3 but 2 − 5 = −3, so it is extraneous. The answer is x = 9 only.

Algebra 2 Regents and other state tests

Whether you sit an Algebra 2 exam at the end of the course depends on your state and school, so ask your teacher. New York publishes its past Regents Examinations in Algebra II with scoring keys, rating guides, model responses and conversion charts, which makes them the most complete free official practice tests. The June 2026 exam ran on Wednesday, June 10, 2026, from 9:15 a.m. to 12:15 p.m., with 36 questions in four parts, and its conversion chart turned a top raw score of 82 into a scale score of 100.

Use the daily paper as a short timed practice test

1. Open today's AP Precalculus paper and set the suggested time, 35 to 45 minutes.
2. Show every step, especially when you square both sides or combine logs, so you can check for extraneous solutions.
3. Mark it and note the topic behind each lost mark.
4. Mix in the Geometry, Algebra 2 and SAT Math paper if quadratics or exponents keep costing you marks.

Common Algebra 2 mistakes

• Not checking for extraneous solutions after squaring or using logs.
• Forgetting that i² = −1 when multiplying complex numbers.
• Splitting a log of a sum: log(a + b) is not log a + log b.
• Mixing up compound interest formulas: Pe^rt is continuous, P(1 + r)^t is yearly.
• Using degrees in a radians question, or the other way round.

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United States · High school mathAlgebra 1 Practice Test: 12 Free Questions With AnswersA free Algebra 1 practice test: 12 questions on equations, functions, systems, exponents and quadratics, with full worked answers and a short daily paper.