Algebra 2 SOL Practice Test — Set 4 of 6

Set 4 of 6 — 50 more free Algebra 2 SOL practice questions from official VDOE released tests.

1. 1. The domain of (f(x) = (x + 3)/(x^2 + 5x - 2)) is all real numbers except —

   A(-8, -3, 3)B(-8, 3)C(-3, 8)D(8)
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   Answer: B — (-8, 3)

2. 2. The amount of work (W) varies jointly with mass (M) and distance (D). Which equation models this?

   A(W = (k)/(MD))B(W = (kM)/(D))C(W = kMD)D(W = (kD)/(M))
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   Answer: C — (W = kMD)

3. 3. Madison deposited $1,000 into an account that compounds yearly. Using exponential regression, which is closest to the expected amount after 30 years?

   A$2,854B$3,291C$5,743D$16,854
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   Answer: C — $5,743

4. 4. The number of permutations of 8 objects taken 3 at a time is —

   A40,320B6,720C4,920D336
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   Answer: D — 336

5. 5. If (y) varies inversely as the square root of (x), what is the constant of proportionality if (y = 16) when (x = 4)?

   A4B8C32D64
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   Answer: D — 64

6. 6. Which describes the roots of (9x^2 - 6x - 1 = 0)?

   AExactly one real rootBTwo distinct real rootsCExactly one imaginary rootDTwo distinct imaginary roots
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   Answer: A — Exactly one real root

7. 7. What is the next term in the arithmetic sequence 2, 5, 8, 11, …?

   A3B13C14D17
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   Answer: D — 17

8. 8. Which of the following equations is an example of the distributive property?

   F4(x² + z) = 4x² + zG7y² + 1 = 7y²H6p³ + 9 = 3(2p³ + 3)J9y⁵ + 0 = 9y⁵
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   Answer: H — 6p³ + 9 = 3(2p³ + 3)

9. 9. Which is equivalent to x² + 4x + 4?

   Ax + 1B(x + 2)²Cx + 2Dx − 4
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   Answer: B — (x + 2)²

10. 10. Which property is illustrated by the equation x + 0 = x?

    ACommutative Property for AdditionBDistributive PropertyCAdditive InverseDAdditive Identity
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    Answer: D — Additive Identity

11. 11. Which is equivalent to (3x⁵y)/(14x⁸y)?

    A21/x²B14/(6x² + 5y)C3/(14x³)D14x/(3x² + 5y)
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    Answer: C — 3/(14x³)

12. 12. Which is equivalent to 16a⁴ ÷ a³?

    F4aG8aHa²J32
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    Answer: G — 8a

13. 13. Which is equivalent to a²b⁴ ÷ ab?

    Aab³Bab³C3a²b⁴D4a²b³
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    Answer: D — 4a²b³

14. 14. Which of the following expressions cannot be factored into a product of lower-degree terms over the set of real numbers?

    F8a³ + b³G4x² − 12xy + 9y²Hx² + 5x + 25J16a² − 9b²
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    Answer: H — x² + 5x + 25

15. 15. What is the sum of (2 − 5i) and (3 + i)?

    A−4 − 4iB1C5D5 − 4i
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    Answer: D — 5 − 4i

16. 16. Which is equivalent to (5 − i)/(1 − 3i)?

    F4 − 8iG4 − 7iH(1 − 7i)/5J9
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    Answer: G — 4 − 7i

17. 17. The table below shows some elements of a function. Which equation is most likely a rule for the function? x | f(x) −3 | 2 0 | 5 3 | 10

    Af(x) = x + 5Bf(x) = −5x + 5Cf(x) = 5 − 2x − x²Df(x) = x² − 5x + 5
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    Answer: C — f(x) = 5 − 2x − x²

18. 18. Which is a zero of the function f(x) = x² − 6x + 8?

    F−8G−4H2J4
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    Answer: G — −4

19. 19. If the domain of y = 2 − x² is −2, −1, 1, 3, what is the range?

    A−1, 2, 7B6, 3, 3, 11C7, 2, 1, 1D11, 3, 3, 6
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    Answer: A — −1, 2, 7

20. 20. The volume (V) of a sphere varies directly with the cube of its radius (r). If k is the constant of proportionality, which is the formula for this relationship?

    AV = krBV = kr³CV = k/r³Dr = kV³
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    Answer: B — V = kr³

21. 21. Two arithmetic means between 3 and 24 are —

    F8 and 12G8 and 16H9 and 16J10 and 17
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    Answer: J — 10 and 17

22. 22. Driving a piling into a harbor bottom, a pile driver sinks the piling 24 inches on the first stroke, 18 inches on the second stroke, and 13½ inches on the third stroke. If the sequence is continued, how far will the piling be driven down on the fifth stroke?

    A1 in.B4 in.C6 in.D7 in.
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    Answer: D — 7 in.

23. 23. Hooke’s law states that the force required to stretch a spring varies directly with the distance the spring is stretched. If a 10-pound force stretches a spring 2 inches, what force is required to stretch the spring 5 inches?

    F15 poundsG20 poundsH25 poundsJ30 pounds
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    Answer: H — 25 pounds

24. 24. If f(n) = −2n² − n, then f(3) =

    A3B5C9D11
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    Answer: B — 5

25. 25. Which is the solution to |2x − 4| ≤ 8?

    F−2 ≤ x ≤ 6Gx ≤ −6 or x ≥ 2Hx ≥ 2 or x ≤ 6Jx ≤ −2 or x ≥ 6
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    Answer: J — x ≤ −2 or x ≥ 6

26. 26. What are the solutions to (y − 3)² − 81 = 0?

    Fy = −12 or y = −6Gy = −12 or y = 6Hy = 12 or y = −6Jy = 12 or y = 6
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    Answer: G — y = −12 or y = 6

27. 27. What is the solution to −x/3 = 5?

    Ax = 3Bx = 9Cx = 15Dx = 33
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    Answer: C — x = 15

28. 28. What are the solutions to x² − 3x − 4 = 0?

    Fx = 1 or x = −4Gx = −1 or x = 4Hx = (3 ± √7)/2Jx = 2
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    Answer: G — x = −1 or x = 4

29. 29. The height of a right triangle is 5 units more than twice its base. If the area of the triangle is 21 square units, what is its height?

    A7 unitsB(5 + √193)/4 unitsC(5 − √193)/2 unitsD12 units
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    Answer: D — 12 units

30. 30. What is the solution to x/2 = 4/(2x + 1)?

    Fx = −5Gx = −5Hx = −4/5Jx = 4/5
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    Answer: H — x = −4/5

31. 31. What are the solutions to 4x + 16 = 2x²?

    Ax = 4i or x = −2Bx = −4 or x = 2Cx = 4 or x = 2iDx = 4 or x = 2
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    Answer: B — x = −4 or x = 2

32. 32. What is the solution to 5x − 1 = 2?

    Fx = 1/5Gx = 3/5Hx = 9/9Jx = 5
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    Answer: J — x = 5

33. 33. A pendulum L inches in length takes t seconds to make one full cycle according to the equation t = 2π√(L/384). To the nearest tenth of an inch, what is the length of a pendulum that completes one full cycle every 1.5 seconds?

    A9.6 in.B14.6 in.C21.9 in.D29.2 in.
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    Answer: C — 21.9 in.

34. 34. A polynomial function has a zero at x = −4. Which expression must be a factor of the polynomial?

    Fx − 4Gx − 2Hx + 2Jx + 4
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    Answer: J — x + 4

35. 35. What are the coordinates of the vertex of the graph of y = 2 − (x − 3)²?

    A(2, 3)B(−3, 2)C(3, 2)D(2, 3)
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    Answer: B — (−3, 2)

36. 36. Which describes the graph of x²/4 − y²/16 = 1?

    FParabolaGCircleHEllipseJHyperbola
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    Answer: J — Hyperbola

37. 37. If S = 3 1 and T = 2 −2, which matrix is the product S · T?

    F8G6 2H2 5J4 −2
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    Answer: J — 4 −2

38. 38. Matrix P = 1 2 3 6 represents the point values for scoring in football (1-point safety, 2-point conversion, 3-point field goal, 6-point touchdown). Matrix S = 2 0 3 2 represents how many times each scoring method occurred. What was the total number of points scored?

    A19B24C26D27
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    Answer: C — 26

39. 39. In 1990, sales at ABC Electronics totaled 4.9 million dollars. During 1996, total sales amounted to 12.1 million. Assuming the growth in sales is linear, what total sales can the company expect in 2001?

    F16.9 millionG18.1 millionH24.2 millionJ25.3 million
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    Answer: G — 18.1 million

40. 40. The table shows the number of students enrolled in the advanced algebra program at Fairoaks High School during the 6 years since its initiation. Year (x): 1, 2, 3, 4, 5, 6 Students (n): 66, 72, 82, 90, 100, 106 Which equation most closely describes the relationship between n and x?

    An = x + 65Bn = 6x + 60Cn = 8x + 58Dn = 10x + 46
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    Answer: C — n = 8x + 58

41. 41. Which is an equivalent form of the following expression? (2i^9)/(i^3)

    A( -6i )B( 5i )C( i )D( 2i^6 )
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    Answer: D — ( 2i^6 )

42. 42. What is the factored form of the following expression? 9h^2 + 24h + 16

    A( (3h+1)^2 )B( (3h-4)(3h-4) )C( (4h+3)^2 )D( (3h+4)^2 )
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    Answer: D — ( (3h+4)^2 )

43. 43. Which is a simplified form of the following expression? 3sqrt2 + 4sqrt2 - sqrt2

    A( 6sqrt2 )B( 7sqrt2 )C( 6+sqrt2 )D( 6sqrt6 )
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    Answer: A — ( 6sqrt2 )

44. 44. Which property is illustrated by the following statement? a(b+c)=ab+ac

    ACommutative property of multiplicationBDistributive propertyCMultiplicative identity propertyDMultiplicative inverse property
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    Answer: B — Distributive property

45. 45. Assuming (k=0), which expression is equivalent to the following complex fraction? 2k(5)/(6k)

    A( (2)/(3) )B( (3)/(2) )C( (6k^2)/(25) )D( (25)/(6k^2) )
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    Answer: B — ( (3)/(2) )

46. 46. When completely factored, 2x^2 - 16x + 32 is equivalent to —

    F(2(x-4)(x+4))G(2(x-2)(x-8))H(2(x+8)(x+2))J(2(x-4)^2)
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    Answer: J — (2(x-4)^2)

47. 47. Which is an equivalent form of the following expression? sqrt-64

    A(8i)B(-8i)C(8)D(-8)
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    Answer: A — (8i)

48. 48. Which is not an equivalent form of the following expression? (s)/(w)

    A((1)/(w)s)B(s w)C(sw^-1)D((w)/(s))
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    Answer: D — ((w)/(s))

49. 49. If defined, which is an equivalent form of this expression? (3^5yz^4)/(10xy^4z^3)

    A((243z)/(2xy^3))B((3yz)/(2x))C((3y^3)/(9))D((10xy^2z^5)/(9))
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    Answer: A — ((243z)/(2xy^3))

50. 50. Which is an equivalent form of the following expression? sqrt-100-sqrt4

    F(-12i)G(8i)H(8)J(-8)
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    Answer: H — (8)

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.