Free Praxis Algebra I (5162) Practice Questions

Sample Practice Questions

Try these 10 sample questions from the Praxis Algebra I (5162) practice bank. Each includes the answer and explanation. Continue with the interactive practice above to review the full question set.

1. 1In the polynomial -7x² + 5x - 3, what is the coefficient of x²?

   1. A.negative 3
   2. B.positive 7
   3. C.positive 5
   4. D.negative 7Correct answer: D

   Explanation: OpenStax states, "The coefficient of a term is the constant that multiplies the variable in a term." The factor multiplying x² is -7; 5 multiplies x, and -3 is the constant term.

   Reference: Elementary Algebra 2e: Use the Language of Algebra — Coefficient

2. 2Which relation, represented as ordered pairs, is a function of x?

   1. A.{(0, 1), (0, 2), (1, 3)}
   2. B.{(1, 2), (1, 3), (2, 4)}
   3. C.{(1, 2), (2, 3), (2, 4)}
   4. D.{(1, 2), (2, 2), (3, 4)}Correct answer: D

   Explanation: OpenStax states, "If each input value leads to only one output value, classify the relationship as a function." The relation {(1, 2), (2, 2), (3, 4)} assigns one output to every input; repeating an output for different inputs is allowed.

   Reference: College Algebra 2e: Functions and Function Notation — Section 3.1, Determining Whether a Relation Represents a Function

3. 3Rewrite x⁻³ using a positive exponent, assuming x is a nonzero real number.

   1. A.The reciprocal of x³Correct answer: A
   2. B.The negative reciprocal of x³
   3. C.The reciprocal of x multiplied by 3
   4. D.The negative of x³

   Explanation: OpenStax states, "The negative exponent tells us we can rewrite the expression by taking the reciprocal of the base and then changing the sign of the exponent." Thus x⁻³ = 1/x³ for x ≠ 0.

   Reference: Intermediate Algebra 2e: Properties of Exponents and Scientific Notation — Properties of Negative Exponents

4. 4Which expression is equivalent to x⁴ - 16 for every real x?

   1. A.(x² minus 4)²
   2. B.(x² minus 8)(x² plus 8)
   3. C.(x² minus 4)(x² plus 4)Correct answer: C
   4. D.(x² plus 4)²

   Explanation: OpenStax states, "A difference of squares factors to a product of conjugates." Here x⁴ - 16 = (x²)² - 4², so the conjugate factors are x² - 4 and x² + 4.

   Reference: Intermediate Algebra 2e: Factor Special Products — Factor Differences of Squares

5. 5For f(x) = 1/(x - 4), what is the largest real domain?

   1. A.All real x except negative 4
   2. B.All real x greater than 4
   3. C.All real x less than 4
   4. D.All real x except positive 4Correct answer: D

   Explanation: OpenStax says to "exclude values in the domain that force the denominator to be zero." The denominator x - 4 is zero only at x = 4, so all other real inputs are allowed.

   Reference: College Algebra 2e: Domain and Range — Section 3.2, Finding the Domain of a Function Defined by an Equation

6. 6Evaluate the real-number expression 27 raised to the power 2/3.

   1. A.6
   2. B.9Correct answer: B
   3. C.18
   4. D.3

   Explanation: OpenStax explains, "We usually take the root first—that way we keep the numbers in the radicand smaller, before raising it to the power indicated." The cube root of 27 is 3; squaring gives 9.

   Reference: Intermediate Algebra 2e: Simplify Rational Exponents — Simplify Expressions with a Rational Exponent

7. 7Which completed-square form is equivalent to x² - 10x + 13?

   1. A.(x minus 5)² plus 12
   2. B.(x minus 10)² minus 87
   3. C.(x minus 5)² minus 12Correct answer: C
   4. D.(x plus 5)² minus 12

   Explanation: OpenStax explains, "Now to complete the perfect square trinomial, we will find the last term by squaring b"; the half of -10 is -5, whose square is 25. Thus x² - 10x + 13 = (x - 5)² - 25 + 13 = (x - 5)² - 12.

   Reference: Intermediate Algebra 2e: Solve Quadratic Equations by Completing the Square — Complete the Square of a Binomial Expression

8. 8What is the range of f(x) = x² + 3 when the domain is all real numbers?

   1. A.All real numbers at least 3Correct answer: A
   2. B.All real numbers at most 3
   3. C.All real numbers greater than 3
   4. D.All real numbers except 3

   Explanation: OpenStax explains of the square function, "Because the graph does not include any negative values for the range, the range is only nonnegative real numbers." Adding 3 shifts every output up by 3; x = 0 attains 3.

   Reference: College Algebra 2e: Domain and Range — Section 3.2, Finding Domains and Ranges of the Toolkit Functions

9. 9For every real x, which expression equals the principal square root √(x²)?

   1. A.The absolute value of xCorrect answer: A
   2. B.The opposite of x
   3. C.The value x
   4. D.The square of x

   Explanation: OpenStax states, "We must use the absolute value signs when we take an even root of an expression with a variable in the radical." The principal square root is nonnegative, so √(x²) = |x|.

   Reference: Intermediate Algebra 2e: Simplify Expressions with Roots — Simplifying Odd and Even Roots

10. 10For every integer n, which expression equals 3^(n+2)?

    1. A.9 · 3^nCorrect answer: A
    2. B.3 · 3^(2n)
    3. C.3^n + 9
    4. D.3n + 6

    Explanation: OpenStax states, "To multiply with like bases, add the exponents." Hence 3^n · 3² = 3^(n+2), and 3² = 9.

    Reference: Intermediate Algebra 2e: Properties of Exponents and Scientific Notation — Product Property for Exponents