Free ACCUPLACER Advanced Algebra and Functions Practice Questions

Sample Practice Questions

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

1. 1Solve the equation (2/3)x − 5 = 7 for x.

   1. A.x = 3
   2. B.x = 8
   3. C.x = 18Correct answer: C
   4. D.x = 24

   Explanation: The text says, "Make the coefficient of the variable term equal to 1." Adding 5 gives (2/3)x = 12; multiplying by 3/2 gives x = 18.

   Reference: Intermediate Algebra 2e, Key Concepts — Section 2.1, general strategy

2. 2Using the two points (1, 4) and (5, 10), calculate the rise divided by the run.

   1. A.2/3
   2. B.3/2Correct answer: B
   3. C.5/2
   4. D.3

   Explanation: The source explains, "The rise measures the vertical change and the run measures the horizontal change." The rise is 6 and the run is 4, so the slope is 6/4 = 3/2.

   Reference: Intermediate Algebra 2e, Key Concepts — Section 3.2, slope

3. 3Factor 12x³ − 18x² completely by taking out the greatest common factor.

   1. A.6x²(2x − 3)Correct answer: A
   2. B.6x(2x² − 3x)
   3. C.3x²(4x − 6)
   4. D.12x²(x − 18)

   Explanation: The source directs, "Find the GCF of all the terms of the polynomial." The GCF is 6x², leaving 2x − 3.

   Reference: Intermediate Algebra 2e, Key Concepts — Section 6.1, greatest common factor

4. 4Find both zeros of the quadratic polynomial x² − 5x + 6 by factoring.

   1. A.negative three or negative two
   2. B.negative three or positive two
   3. C.positive two or positive threeCorrect answer: C
   4. D.negative two or positive three

   Explanation: The source notes, "If the quadratic factors easily, this method is very quick." Factoring gives (x − 2)(x − 3) = 0, so x = 2 or x = 3.

   Reference: Intermediate Algebra 2e, Key Concepts — Section 9.3, methods to solve quadratic equations

5. 5If f(x) = 3x − 4, what is f(5)?

   1. A.7
   2. B.11Correct answer: B
   3. C.15
   4. D.19

   Explanation: The source says that function notation relates "the input to the output." Substituting 5 for x gives f(5) = 3(5) − 4 = 11.

   Reference: College Algebra 2e, Key Concepts — Section 3.1, function notation

6. 6Find every real zero of the factored cubic polynomial p(x) = x(x − 2)(x + 4).

   1. A.−4, 0, and 2Correct answer: A
   2. B.−2, 0, and 4
   3. C.−4 and 2 only
   4. D.0, 2, and 4

   Explanation: The source says to "set each factor equal to zero" to find zeros of a factored polynomial. The three factors vanish at x = 0, 2, and −4.

   Reference: College Algebra 2e, Key Concepts — Section 5.3, zeros

7. 7What is the value of the base-two logarithm log₂(32)?

   1. A.4
   2. B.5Correct answer: B
   3. C.6
   4. D.16

   Explanation: The source says, "Logarithmic equations can be written in an equivalent exponential form, using the definition of a logarithm." Since 2⁵ = 32, log₂(32) = 5.

   Reference: College Algebra 2e, Key Concepts — Section 6.3, logarithmic functions

8. 8A rectangle has area 24 square units. Its image under a dilation with scale factor 3 has what area?

   1. A.72 square units
   2. B.216 square unitsCorrect answer: B
   3. C.48 square units
   4. D.24 square units

   Explanation: The source says a dilation "scales all vectors away from the origin" by its factor. The rectangle area is "the length times the width". Both dimensions triple, so the area is 3² × 24 = 216 square units.

   Reference: Special Linear Transformations in Two and Three Dimensions — Dilations and Contractions, definition

9. 9A cone has radius 3 cm and height 4 cm. What is its volume?

   1. A.12π cm³Correct answer: A
   2. B.18π cm³
   3. C.36π cm³
   4. D.48π cm³

   Explanation: The source states, "the volume of a cone is exactly one-third of the volume of a cylinder with the same base and height." Thus V = (1/3)π(3²)(4) = 12π cubic centimeters.

   Reference: Prealgebra 2e, Volume and Surface Area — Find the Volume of Cones, paragraph following Figure 9.36

10. 10Calculate sin θ from a right triangle whose opposite leg measures 3 and whose hypotenuse measures 5.

    1. A.3/5Correct answer: A
    2. B.4/5
    3. C.3/4
    4. D.5/3

    Explanation: The source says, "Find the sine as the ratio of the opposite side to the hypotenuse." Thus sin θ = 3/5.

    Reference: Precalculus 2e, Right Triangle Trigonometry — Section 5.4, right-triangle ratios