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← College Algebra
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Practice deliberately

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

Practice mode gives one hint and a worked explanation after every question. Test mode mixes all 6 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.

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

01

Equations and inequalities

Represent the constraints symbolically, choose an equivalence-preserving solution method, and verify the result in every original relationship.

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

02

Functions

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

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

03

Polynomial models

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

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

04

Rational models

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

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

05

Exponential and logarithmic 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 and logarithmic models problem from its wording, carry out the governing method, and check that the result is reasonable.

06

Systems

Represent the constraints symbolically, choose an equivalence-preserving solution method, and verify the result in every original relationship.

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

College Algebra questions with worked answers

These 8 questions are printed in full on this page and are drawn across all 6 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: Solve the absolute value equation |2x - 5| = 9.

College Algebra · Equations and inequalities

  1. x = 7 or x = -2
  2. x = 7 only
  3. x = 2 or x = -7
  4. x = 4.5 or x = -4.5
Show the worked answer
  1. An absolute value of 9 means the inside is 9 or -9.
  2. Case one: 2x - 5 = 9 gives 2x = 14, so x = 7.
  3. Case two: 2x - 5 = -9 gives 2x = -4, so x = -2.
  4. Both check out: |2(7) - 5| = 9 and |2(-2) - 5| = 9.

Answer: x = 7 or x = -2

Question 2: Solve the inequality x^2 - x - 12 < 0.

College Algebra · Equations and inequalities

  1. -3 < x < 4
  2. x < -3 or x > 4
  3. -4 < x < 3
  4. x < 4
Show the worked answer
  1. Factor the quadratic: x^2 - x - 12 = (x - 4)(x + 3).
  2. The expression is zero at x = 4 and x = -3, which split the number line into three pieces.
  3. Test x = 0 in the middle piece: (0 - 4)(0 + 3) = -12, which is less than 0.
  4. Only the middle piece works, so the solution is -3 < x < 4.

Answer: -3 < x < 4

Question 3: What is the domain of f(x) = the square root of (x - 3), divided by (x - 7)?

College Algebra · Functions

  1. x is at least 3 and x is not 7
  2. all real numbers except 7
  3. x is greater than 3
  4. x is at least 3
Show the worked answer
  1. A square root needs a value that is zero or positive, so x - 3 must be at least 0.
  2. That gives x is at least 3.
  3. A fraction cannot have a zero denominator, so x - 7 cannot be 0, which rules out x = 7.
  4. Combine both rules: x is at least 3 and x is not 7.

Answer: x is at least 3 and x is not 7

Question 4: Find every zero of p(x) = x^3 + 2x^2 - 11x - 12.

College Algebra · Polynomial models

  1. -4, -1, and 3
  2. -3, 1, and 4
  3. -4, 1, and 3
  4. -2, 2, and 3
Show the worked answer
  1. Test factors of 12. At x = 3: 27 + 18 - 33 - 12 = 0, so x = 3 is a zero.
  2. Divide by (x - 3) to get x^2 + 5x + 4.
  3. That factors as (x + 1)(x + 4).
  4. The zeros are x = 3, x = -1, and x = -4.

Answer: -4, -1, and 3

Question 5: What is the slant asymptote of f(x) = (x^2 + 3x + 5) / (x + 1)?

College Algebra · Rational models

  1. y = x + 2
  2. y = x + 3
  3. y = x - 2
  4. y = x
Show the worked answer
  1. The top has degree exactly one more than the bottom, so there is a slant asymptote.
  2. Divide x^2 + 3x + 5 by x + 1.
  3. The quotient is x + 2 with a remainder of 3.
  4. The remainder term shrinks toward 0 for large x, so the asymptote is y = x + 2.

Answer: y = x + 2

Question 6: You invest $4,000 at 5% annual interest compounded quarterly. What is the balance after 6 years?

College Algebra · Exponential and logarithmic models

  1. $5,389.40
  2. $5,200.00
  3. $5,360.38
  4. $4,800.00
Show the worked answer
  1. Quarterly compounding means the rate per period is 0.05 / 4 = 0.0125.
  2. Six years at four periods per year is 24 periods.
  3. The balance is 4000 x 1.0125^24, and 1.0125^24 is about 1.347351.
  4. 4000 x 1.347351 = 5389.40, so the balance is $5,389.40.

Answer: $5,389.40

Question 7: Solve log base 3 of (2x + 1) = 4.

College Algebra · Exponential and logarithmic models

  1. x = 40
  2. x = 13.5
  3. x = 4
  4. x = 81
Show the worked answer
  1. Rewrite the log statement as a power: 2x + 1 = 3^4.
  2. 3^4 = 81.
  3. So 2x = 81 - 1 = 80.
  4. x = 40. Check: 2(40) + 1 = 81 and log base 3 of 81 is 4.

Answer: x = 40

Question 8: Solve the system x^2 + y^2 = 25 and y = x + 1.

College Algebra · Systems

  1. (3, 4) and (-4, -3)
  2. (4, 3) and (-3, -4)
  3. (3, 4) only
  4. (5, 6) and (-5, -4)
Show the worked answer
  1. Substitute y = x + 1 into the circle: x^2 + (x + 1)^2 = 25.
  2. Expand: x^2 + x^2 + 2x + 1 = 25, so 2x^2 + 2x - 24 = 0.
  3. Divide by 2 and factor: x^2 + x - 12 = (x + 4)(x - 3) = 0, so x = -4 or x = 3.
  4. Use y = x + 1 for each: (3, 4) and (-4, -3).

Answer: (3, 4) and (-4, -3)

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 College Algebra questions, the unit each one tests, and its answer.
QuestionUnitWhat it asksAnswer
1Equations and inequalitiesSolve the absolute value equation |2x - 5| = 9.x = 7 or x = -2
2Equations and inequalitiesSolve the inequality x^2 - x - 12 < 0.-3 < x < 4
3FunctionsWhat is the domain of f(x) = the square root of (x - 3), divided by (x - 7)?x is at least 3 and x is not 7
4Polynomial modelsFind every zero of p(x) = x^3 + 2x^2 - 11x - 12.-4, -1, and 3
5Rational modelsWhat is the slant asymptote of f(x) = (x^2 + 3x + 5) / (x + 1)?y = x + 2
6Exponential and logarithmic modelsYou invest $4,000 at 5% annual interest compounded quarterly. What is the balance after 6 years?$5,389.40
7Exponential and logarithmic modelsSolve log base 3 of (2x + 1) = 4.x = 40
8SystemsSolve the system x^2 + y^2 = 25 and y = x + 1.(3, 4) and (-4, -3)

How the generated College Algebra 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 College Algebra practice page

What does this page cover?

It covers all 6 College Algebra 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.