Algebra 2 SOL Practice Test — Set 3 of 6

Set 3 of 6 — 50 more free Algebra 2 SOL practice questions from official VDOE released tests.

1. 1. Which is a factored form of 9x² − 25?

   A(3x − 5)(3x + 5)B(3x − 5)²C(3x + 5)²D(9x − 25)²
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   Answer: A — (3x − 5)(3x + 5)

2. 2. Which is a factor of x² − 2x − 15?

   F(x − 3)G(x − 15)H(x + 3)J(x + 5)
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   Answer: H — (x + 3)

3. 3. Which is equivalent to (3 − 2i)(2 − 5i)?

   A−4 + 19iB16 + 19iC6 + 29iD6 − 10i
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   Answer: A — −4 + 19i

4. 4. Which is equivalent to −3 + (−3)?

   F−6G0H3J9
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   Answer: F — −6

5. 5. Which function includes the values in the table? x: −2, −1, 0, 1, 2 y: 3, 0, −1, 0, 3

   Fy = x − 1Gy = x + 1Hy = x² − 1Jy = (x − 1)²
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   Answer: H — y = x² − 1

6. 6. What is the zero of the function f(x) = 12x − 27?

   F27G4H0J9/4
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   Answer: J — 9/4

7. 7. If the domain of f(x) = 3x − 5 is −1, 0, 1, 2, 3, what is the range?

   A0, 2, 9, 11, 14B8, 5, 2, 1, 4C4, 2, 1, 5, 8D2, 5, 8, 11, 14
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   Answer: D — 2, 5, 8, 11, 14

8. 8. The polynomial function y = x³ − 3x² − x + 1 has a zero between —

   F−4 and −3G−2 and −1H−1 and 0J3 and 4
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   Answer: H — −1 and 0

9. 9. What is the value of 2ⁿ if n = 7?

   F62G128H252J21
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   Answer: G — 128

10. 10. If a = 1/n, then what is a⁻¹?

    A10BnC1/nDn²
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    Answer: B — n

11. 11. In which of the following is z directly proportional to x and inversely proportional to the square of y?

    Fz = kx²Gz = kxy²Hz = kx / y²Jz = ky / x
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    Answer: H — z = kx / y²

12. 12. The time required to complete a job varies inversely as the number of people working. It took 4 hours for 7 electricians to wire a building. How long would it have taken 3 electricians to have done the job?

    A1 hr 43 minB5 hr 15 minC7 hr 30 minD9 hr 20 min
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    Answer: D — 9 hr 20 min

13. 13. What are the solutions to x² − 12x + 16 = 0?

    A12 ± 4√5B6 ± 2√5C6 ± √20D12 ± 4
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    Answer: C — 6 ± √20

14. 14. Which is the solution set for 3x² − 4x − 15 = 0?

    F5, −3G3, −5H−3, 5J3, 5
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    Answer: H — −3, 5

15. 15. What is the solution set for (1/4)(9 − x) = 1?

    A−7, 7B5, −5C7D5
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    Answer: C — 7

16. 16. For which value of x does (x − 2)/18 = (x − 3)/15?

    F8G13/3H5/3J8
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    Answer: J — 8

17. 17. The length, s, (in feet) of the skid mark left by an automobile traveling at r miles per hour can be approximated by the relation r = 2√(5s). At the scene of an accident, police measured a skid mark of 361 feet. About how many miles per hour was the car traveling when the brakes were applied?

    A42 mphB54 mphC76 mphD85 mph
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    Answer: D — 85 mph

18. 18. Which function of x would have x-intercepts −1, 2, and 3?

    Fy = 2x² − 5x − 3Gy = x² − x − 6Hy = 2x² + 5x − 3Jy = 2x² + 7x + 3
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    Answer: F — y = 2x² − 5x − 3

19. 19. When graphed, which of the following equations would produce a circle?

    Ax² − y² = 9Bx + y = 9Cy = x² − 9Dx² + y² = 9
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    Answer: B — x + y = 9

20. 20. If f(x) is a polynomial with only factors (x − 1), (x + 2), and (x − 4), what is the solution set of f(x) = 0?

    F0, 2, 4G4, 0, 2H−2, 1, 4J4, 2, 0
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    Answer: H — −2, 1, 4

21. 21. Q = 1 2, R = 1 3, T = 1 2 4. Which product is not possible?

    AQ × RBQ × TCR × QDR × R
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    Answer: A — Q × R

22. 22. What is the multiplicative inverse of the matrix 4 1; 7 8?

    A1/25 −1/25; −7/25 4/25B8/25 −1/25; −7/25 4/25C1/25 4/25; 7/25 8/25D8/25 1/25; 7/25 4/25
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    Answer: B — 8/25 −1/25; −7/25 4/25

23. 23. What is the solution set for the system 2y = x² − 6x + 9 2y = −x² + 2x + 1?

    A(5, −7), (−1, −1)B(1, 1), (−5, 23)C(1, 7), (−5, 23)D(1/2, 2)
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    Answer: A — (5, −7), (−1, −1)

24. 24. The chart gives the average number of students per computer in public schools in America from 1990–1991 to 1997–1998. Assuming a linear relationship, which is the best estimate for the number of students per computer during 1989–1990?

    F5.4G10.8H20.2J21.9
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    Answer: J — 21.9

25. 25. The chart shows city real estate taxes paid by four families and the assessed value of their homes. The tax on the Miller home was $1,700. What was the assessed value?

    A$60,000B$65,000C$68,000D$70,000
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    Answer: D — $70,000

26. 26. Which expression is equivalent to ( sqrt16x^2 )?

    A(4x)B(-4x)C(8x)D(2x)
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    Answer: B — (-4x)

27. 27. Which expression is equivalent to ((3n^2 - 7n + 15)/((n + 3)(n - 4))), assuming no denominator equals zero?

    A((3n^2 - 7n + 3)/((n + 3)(n - 4)))B((3n^2 - 7n + 15)/((n + 3)(n - 4)))C((3n^2 + 5n + 3)/((n + 3)(n - 4)))D((3n^2 + 5n + 15)/(2(n + 3)(n - 4)))
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    Answer: B — ((3n^2 - 7n + 15)/((n + 3)(n - 4)))

28. 28. Which number is equivalent to (( -6 - i ) + 5i - (11 + 13i))?

    A(-17 - 9i)B(-17 + 17i)C(-5 - 9i)D(-5 + 17i)
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    Answer: A — (-17 - 9i)

29. 29. Which of the following is the factored form of (x^3 - 216)?

    A((x - 6))B((x - 6)(x^2 + 36))C((x - 6)(x^2 + 12x + 36))D((x - 6)(x^2 + 6x + 36))
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    Answer: D — ((x - 6)(x^2 + 6x + 36))

30. 30. Which expression is equivalent to (sqrt75x^3 - sqrt27x^3), if (x > 0)?

    A(4xsqrt6x)B(4xsqrt3x)C(2xsqrt6x)D(2xsqrt3x)
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    Answer: D — (2xsqrt3x)

31. 31. Which is equivalent to ((6 + sqrt7)(5 + sqrt7))?

    A(11 + 2sqrt7)B(30 + 11sqrt7)C(30 + 18sqrt7)D(37 + 11sqrt7)
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    Answer: D — (37 + 11sqrt7)

32. 32. Which expression is equivalent to (x^7/5y^7/5)?

    A(x^1.4y^1.4)B(x^7y^7)C((xy)^7/5)D(x^5y^5)
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    Answer: C — ((xy)^7/5)

33. 33. Which statement illustrates the symmetric property of equality?

    AIf (7x + 17i = 49i), then (7x + 17i = 49i).BIf (7x + 17i = 49i), then (49i = 7x + 17i).CIf (7x + 17i = 49i) and (49i = 12x - 3i), then (7x + 17i = 12x - 3i).DIf (7x + 17i = 49i) and (7x + 17i - y = -35i), then (49i - y = -35i).
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    Answer: B — If (7x + 17i = 49i), then (49i = 7x + 17i).

34. 34. What is the solution set to (x^2 = 16 - 4x)?

    A(4)B(2 2sqrt5)C(-2 2sqrt5)D(-2 2isqrt3)
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    Answer: C — (-2 2sqrt5)

35. 35. What is the solution to (|x + 4| < 2)?

    A(x < -6) or (x > -2)B(-6 < x < -2)C(x < -2)D(2 < x < 6)
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    Answer: B — (-6 < x < -2)

36. 36. Given the system of equations (x^2 + y + 10 = 0) (x^2 - 4y - 2 = 0) What are the x-values for the solutions to the system?

    A(-3, -7)B(-3, 4)C(-4, 3)D(4, -14)
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    Answer: B — (-3, 4)

37. 37. Which is a solution for (sqrtw - 4 + 11 = 14)?

    A(w = 8)B(w = 16)C(w = 77)D(w = 85)
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    Answer: D — (w = 85)

38. 38. Which is a solution to ((4n - 37)/(3) = 10), if (n > 0)?

    A(-10)B(-2)C(7)D(17)
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    Answer: D — (17)

39. 39. Which is a solution of (|2x - 7| + 1 = 9)?

    A(x = -1)B(x = 1)C(x = 7)D(x = 3)
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    Answer: C — (x = 7)

40. 40. A solution to a quadratic equation is ((13 - 11i)/(7)). Which of the following must also be a solution?

    A(-(13 - 11i)/(7))B((13 + 11i)/(7))C(-(13 + 11i)/(7))D((13 - 11i)/(7))
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    Answer: D — ((13 - 11i)/(7))

41. 41. Which of the following functions does NOT have a range of only the real numbers greater than or equal to zero?

    A(f(x) = sqrt4 - x)B(f(x) = x^2)C(f(x) = |x|)D(f(x) = x)
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    Answer: D — (f(x) = x)

42. 42. What is the equation of the horizontal asymptote of (f(x) = 6(1 - 9)^x - 4)?

    A(y = 6)B(y = 0)C(y = -4)D(y = -5)
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    Answer: C — (y = -4)

43. 43. The graph of (g(x) = (2x)) has —

    Ano x-intercept or y-interceptBone x-intercept and no y-interceptCtwo x-intercepts and no y-interceptDone x-intercept and one y-intercept
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    Answer: B — one x-intercept and no y-intercept

44. 44. Throughout which interval is (f(x) = (x - 1)(x - 4)) only decreasing?

    A(- < x < 0)B(- < x < 1)C(1 < x < 4)D(2 < x < 4)
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    Answer: D — (2 < x < 4)

45. 45. Given (f(x) = (x - 16) + 15), what is the equation of an asymptote?

    A(x = 16)B(y = 16)C(x = 15)D(y = 15)
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    Answer: A — (x = 16)

46. 46. The heights of a large population of ostriches are normally distributed. Which is closest to the percentage of heights within 3 standard deviations of the mean?

    A0.3%B5%C95%D99.7%
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    Answer: D — 99.7%

47. 47. Which situation involves a combination?

    AChoosing 3 employees from 10BSeating 7 people around a tableCAssigning lanes to 8 runnersDCreating 6-letter passwords from “pencil”
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    Answer: A — Choosing 3 employees from 10

48. 48. What is the 14th term of an arithmetic sequence with first term 7 and common difference 10?

    A130B137C147D221
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    Answer: A — 130

49. 49. Which describes the end behavior of (y = -x^2 + bx + c) as (x) approaches positive or negative infinity?

    A(y) approaches positive infinityB(y) approaches negative infinityC(y) approaches (c)D(y) approaches 0
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    Answer: B — (y) approaches negative infinity

50. 50. If (f(x) = 2x^2 + 1) and (g(x) = 6x - 15), which polynomial is equivalent to (g(f(x)))?

    A(4x^2 - 13)B(4x^2 - 9)C(4x^3 - 10x^2 + 6x - 15)D(16x^2 - 80x + 101)
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    Answer: B — (4x^2 - 9)

Practice items adapted from Virginia Department of Education released SOL tests. Practice items are provided for study purposes and are not affiliated with or endorsed by the Virginia Department of Education.