Free Fundamentals of College Algebra Practice Questions

Sample Practice Questions

Try these 10 sample questions from the Fundamentals of College Algebra practice bank. Each includes the answer and explanation. Continue with the interactive practice above to review the full question set.

1. 1Which expression is equivalent to 4(2x − 3)?

   1. A.eight x minus three
   2. B.eight x minus twelveCorrect answer: B
   3. C.six x minus twelve
   4. D.eight x plus twelve

   Explanation: The distributive property states that "the product of a factor times a sum is the sum of the factor times each term in the sum." Multiplying 4 by both terms gives 8x − 12.

   Reference: College Algebra 2e: Real Numbers: Algebra Essentials — Distributive Property

2. 2For the complex number −3 + 5i, identify the number obtained by conjugation.

   1. A.negative three minus five iCorrect answer: A
   2. B.positive three plus five i
   3. C.positive three minus five i
   4. D.negative five plus three i

   Explanation: A conjugate is found "by changing the sign of the imaginary part of the complex number. The real part of the number is left unchanged." Thus −3 + 5i has conjugate −3 − 5i.

   Reference: College Algebra 2e: Complex Numbers — The Complex Conjugate

3. 3Find the value that satisfies the linear equation 3(x − 2) = 2x + 5.

   1. A.positive elevenCorrect answer: A
   2. B.negative eleven
   3. C.positive one
   4. D.negative one

   Explanation: Solving uses "the fundamental properties of equality and basic algebraic operations." Expanding and subtracting 2x gives x − 6 = 5, so x = 11.

   Reference: College Algebra 2e: Linear Equations in One Variable — Solving Linear Equations in One Variable

4. 4On which axis does the point (0, −5) lie?

   1. A.The x-axis
   2. B.The y-axisCorrect answer: B
   3. C.Neither coordinate axis
   4. D.Both coordinate axes

   Explanation: The text states, "If the x-coordinate is zero, the point is on the y-axis." The x-coordinate is 0 and the y-coordinate is nonzero.

   Reference: College Algebra 2e: The Rectangular Coordinate Systems and Graphs — Plotting Ordered Pairs in the Cartesian Coordinate System

5. 5What is the value of 3x² − 2y when x = −2 and y = 3?

   1. A.positive eighteen
   2. B.negative eighteen
   3. C.positive sixCorrect answer: C
   4. D.negative six

   Explanation: To evaluate an expression, "Replace each variable in the expression with the given value, then simplify the resulting expression using the order of operations." Substitution gives 3(−2)² − 2(3) = 12 − 6 = 6.

   Reference: College Algebra 2e: Real Numbers: Algebra Essentials — Evaluating Algebraic Expressions

6. 6What is the product of 4 + 3i and its complex conjugate?

   1. A.7
   2. B.7 + 24i
   3. C.25Correct answer: C
   4. D.25 + 24i

   Explanation: The text states, "When a complex number is multiplied by its complex conjugate, the result is a real number." Here (4 + 3i)(4 − 3i) = 16 − 9i² = 25.

   Reference: College Algebra 2e: Complex Numbers — The Complex Conjugate

7. 7What is the solution set of 2(x + 3) = 2x + 6?

   1. A.{0}
   2. B.{3}
   3. C.All real numbersCorrect answer: C
   4. D.The empty set

   Explanation: An identity equation "is true for all values of the variable." Both sides simplify to 2x + 6, so every real x is a solution.

   Reference: College Algebra 2e: Linear Equations in One Variable — Solving Linear Equations in One Variable

8. 8What is the distance between (1, 2) and (4, 6) in a rectangular coordinate plane?

   1. A.five unitsCorrect answer: A
   2. B.seven units
   3. C.twenty-five units
   4. D.the square root of seven units

   Explanation: The distance formula is "Derived from the Pythagorean Theorem". The horizontal and vertical changes are 3 and 4, so the distance is √(3² + 4²) = 5.

   Reference: College Algebra 2e: The Rectangular Coordinate Systems and Graphs — Using the Distance Formula

9. 9The expression 7 + x can be written as x + 7. Which addition property permits this change?

   1. A.Associative property of addition
   2. B.Distributive property
   3. C.Identity property of addition
   4. D.Commutative property of additionCorrect answer: D

   Explanation: The text states that "numbers may be added in any order without affecting the sum." The two addends change order while the grouping and values remain unchanged.

   Reference: College Algebra 2e: Real Numbers: Algebra Essentials — Commutative Properties

10. 10For z = 6 − 2i, what is z plus its complex conjugate?

    1. A.12Correct answer: A
    2. B.4
    3. C.−4i
    4. D.12 − 4i

    Explanation: The book says, "When a complex number is added to its complex conjugate, the result is a real number." Here (6 − 2i) + (6 + 2i) = 12.

    Reference: College Algebra 2e: Complex Numbers — The Complex Conjugate