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← Algebra II
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Practice deliberately

Work through Algebra II unit by unit, then test yourself under time.

Practice mode gives one hint and a worked explanation after every question. Test mode mixes all 7 units, holds the explanations until you submit, and then reports which units need another pass. The 8 questions printed further down this page are fixed, so you can read them and their worked answers without starting a set.

Algebra II coverage and review map

Connect every question to the exact skill it rehearses. Work through the units in order, then return to any topic that still needs a hint or a second attempt.

This page follows the Algebra II syllabus unit by unit. For shorter mixed retrieval outside the course sequence, use algebra ii practice questions with answers.

01

Polynomial functions

Connect formulas, tables, and graphs; identify domain and parameters; then interpret how changing an input or coefficient changes the output.

Goal: recognise a polynomial functions problem from its wording, carry out the governing method, and check that the result is reasonable.

02

Rational functions

Connect formulas, tables, and graphs; identify domain and parameters; then interpret how changing an input or coefficient changes the output.

Goal: recognise a rational functions problem from its wording, carry out the governing method, and check that the result is reasonable.

03

Radicals

Define the central objects, connect at least two representations, solve direct and unfamiliar applications, and explain how the result can be checked.

Goal: recognise a radicals problem from its wording, carry out the governing method, and check that the result is reasonable.

04

Complex numbers

Build number sense with exact representations, estimation, and inverse-operation checks before applying the skill in multi-step contexts.

Goal: recognise a complex numbers problem from its wording, carry out the governing method, and check that the result is reasonable.

05

Exponential models

Connect formulas, tables, and graphs; identify domain and parameters; then interpret how changing an input or coefficient changes the output.

Goal: recognise a exponential models problem from its wording, carry out the governing method, and check that the result is reasonable.

06

Logarithms

Translate between exponential and logarithmic forms, identify the base and rate, and interpret parameters and domain in the original context.

Goal: recognise a logarithms problem from its wording, carry out the governing method, and check that the result is reasonable.

07

Sequences and series

Identify the generating pattern, distinguish term values from accumulated sums, and validate formulas with base cases and long-run behavior.

Goal: recognise a sequences and series problem from its wording, carry out the governing method, and check that the result is reasonable.

Algebra II questions with worked answers

These 8 questions are printed in full on this page and are drawn across all 7 course units. Nothing here is generated on the fly. Cover the options, solve each one on paper, and only then open the worked answer to compare your method with the one shown.

Question 1: Use the remainder theorem to find the remainder when 2x^3 - 5x^2 + 3x - 7 is divided by x - 2.

Algebra II · Polynomial functions

  1. -5
  2. 5
  3. -7
  4. 0
Show the worked answer
  1. The remainder theorem says the remainder equals the polynomial evaluated at x = 2.
  2. 2(2)^3 = 2 x 8 = 16, and -5(2)^2 = -5 x 4 = -20.
  3. 3(2) = 6, and the constant is -7.
  4. 16 - 20 + 6 - 7 = -5, so the remainder is -5.

Answer: -5

Question 2: Where is the vertical asymptote of f(x) = (x^2 - 9) / (x^2 - x - 6)?

Algebra II · Rational functions

  1. x = -2
  2. x = 3
  3. x = -3
  4. x = 2
Show the worked answer
  1. Factor the top: x^2 - 9 = (x - 3)(x + 3).
  2. Factor the bottom: x^2 - x - 6 = (x - 3)(x + 2).
  3. The factor (x - 3) cancels, so x = 3 is a hole, not an asymptote.
  4. The factor (x + 2) is left in the bottom, so the vertical asymptote is x = -2.

Answer: x = -2

Question 3: Solve the square root of (2x + 7) = x - 4.

Algebra II · Radicals

  1. x = 9 only
  2. x = 1 and x = 9
  3. x = 1 only
  4. no solution
Show the worked answer
  1. Square both sides: 2x + 7 = (x - 4)^2 = x^2 - 8x + 16.
  2. Bring everything to one side: x^2 - 10x + 9 = 0.
  3. Factor: (x - 1)(x - 9) = 0, so x = 1 or x = 9.
  4. Check both. At x = 1 the right side is -3, and a square root cannot be negative, so x = 1 fails. Only x = 9 works.

Answer: x = 9 only

Question 4: Multiply (3 + 2i)(4 - 5i).

Algebra II · Complex numbers

  1. 22 - 7i
  2. 2 - 7i
  3. 22 + 7i
  4. 12 - 10i
Show the worked answer
  1. Multiply each part: 3 x 4 = 12 and 3 x (-5i) = -15i.
  2. Then 2i x 4 = 8i and 2i x (-5i) = -10i^2.
  3. Because i^2 = -1, the term -10i^2 becomes +10.
  4. Add the real parts 12 + 10 = 22 and the imaginary parts -15i + 8i = -7i, giving 22 - 7i.

Answer: 22 - 7i

Question 5: An account holds $500 and grows 6% per year. To the nearest cent, what is the balance after 12 years?

Algebra II · Exponential models

  1. $1,006.10
  2. $860.00
  3. $1,060.00
  4. $948.30
Show the worked answer
  1. Growth of 6% per year multiplies the balance by 1.06 each year.
  2. After 12 years the balance is 500 x 1.06^12.
  3. 1.06^12 is about 2.012196.
  4. 500 x 2.012196 = 1006.098, which rounds to $1,006.10.

Answer: $1,006.10

Question 6: Solve log base 2 of x plus log base 2 of (x - 2) = 3.

Algebra II · Logarithms

  1. x = 4
  2. x = 4 and x = -2
  3. x = 2
  4. x = 8
Show the worked answer
  1. Adding two logs with the same base means multiplying the inputs: log base 2 of x(x - 2) = 3.
  2. Rewrite in exponential form: x(x - 2) = 2^3 = 8.
  3. That gives x^2 - 2x - 8 = 0, which factors as (x - 4)(x + 2) = 0.
  4. x = -2 makes the logs undefined, so the only solution is x = 4.

Answer: x = 4

Question 7: An arithmetic sequence starts at 7 and increases by 4 each term. What is the sum of the first 20 terms?

Algebra II · Sequences and series

  1. 900
  2. 830
  3. 1,540
  4. 460
Show the worked answer
  1. The sum of n terms is n/2 times (twice the first term plus (n - 1) times the difference).
  2. Twice the first term is 2 x 7 = 14.
  3. (20 - 1) x 4 = 76, and 14 + 76 = 90.
  4. 20 / 2 = 10, and 10 x 90 = 900.

Answer: 900

Question 8: What is the sum of the infinite geometric series 9 + 3 + 1 + 1/3 + ...?

Algebra II · Sequences and series

  1. 13.5
  2. 12
  3. 18
  4. 27
Show the worked answer
  1. Each term is one third of the term before, so the common ratio is 1/3.
  2. An infinite geometric series with a ratio between -1 and 1 sums to first term / (1 - ratio).
  3. 1 - 1/3 = 2/3.
  4. 9 divided by 2/3 is 9 x 3/2 = 13.5.

Answer: 13.5

Which unit each printed question belongs to

Use this map after marking your work. If two misses share a unit, review that unit before starting a generated set.

The 8 printed Algebra II questions, the unit each one tests, and its answer.
QuestionUnitWhat it asksAnswer
1Polynomial functionsUse the remainder theorem to find the remainder when 2x^3 - 5x^2 + 3x - 7 is divided by x - 2.-5
2Rational functionsWhere is the vertical asymptote of f(x) = (x^2 - 9) / (x^2 - x - 6)?x = -2
3RadicalsSolve the square root of (2x + 7) = x - 4.x = 9 only
4Complex numbersMultiply (3 + 2i)(4 - 5i).22 - 7i
5Exponential modelsAn account holds $500 and grows 6% per year. To the nearest cent, what is the balance after 12 years?$1,006.10
6LogarithmsSolve log base 2 of x plus log base 2 of (x - 2) = 3.x = 4
7Sequences and seriesAn arithmetic sequence starts at 7 and increases by 4 each term. What is the sum of the first 20 terms?900
8Sequences and seriesWhat is the sum of the infinite geometric series 9 + 3 + 1 + 1/3 + ...?13.5

How the generated Algebra II sets are created

The 8 questions above are fixed and checked. The generator at the top of the page is different: it writes fresh questions with AI from the course and unit information shown here, then the application checks each one for a complete prompt, four choices, one keyed answer, and an explanation. Generated questions are original practice—not official or released exam questions—and AI can still make mathematical mistakes. Verify a disputed answer with the stated method, your course materials, or the MathGPT solver, and follow the site's academic-integrity guidance.

Questions about this Algebra II practice page

What does this page cover?

It covers all 7 Algebra II units listed above. Choose one unit for focused work, or mixed review to test method selection, and switch to test mode when you want all units mixed under time.

When can I see correct answers and explanations?

The 8 printed questions on this page keep their worked answers behind a toggle, so you can check any one of them straight away. In the generator above, practice mode explains each question as soon as you answer it, while test mode holds every explanation until you submit.

What should I do with a missed question?

Classify the miss as a definition, setup, calculation, interpretation, or timing error. Re-solve it from a blank page, then use the MathGPT tutor for a hint or method check.