Algebra 2 SOL Practice Test — Set 1 of 6

333 free Algebra 2 Virginia SOL practice questions drawn from official Virginia Department of Education released tests. Pick an answer to check it instantly, or open “Show answer” to review. No signup required.

1. 1. For non-zero denominators, which of the following is equivalent to ((3a^3 - 75a)/(a(a+5)(a+5)))?

   A(-3)B(-(1)/(a^2))C((a-5)/(a+5))D((3(a-5))/(a+5))
   Show answer

   Answer: D — ((3(a-5))/(a+5))

2. 2. What is the factored form of (x^2 - 36z^2)?

   F((x+6z)(x-6z))G((x+z)(x-36z))H((x+6z)^2)J((x-6z)^2)
   Show answer

   Answer: F — ((x+6z)(x-6z))

3. 3. Which of these is equivalent to (i^24)?

   A1B(i^4)C(i^6)D(i^8)
   Show answer

   Answer: A — 1

4. 4. Which complex number is equivalent to ((7-9i) - (-1+3i))?

   F(6-6i)G(6-12i)H(8-6i)J(8-12i)
   Show answer

   Answer: J — (8-12i)

5. 5. What is the simplified form of (6i^2)?

   A(-6)B(6i)C(12i)D(6i^3)
   Show answer

   Answer: A — (-6)

6. 6. The equation ((2 ^-1 - 17 )(1) = 2 ^-1 - 17 ) is an example of which property of real numbers?

   FAssociative propertyGTransitive propertyHIdentity propertyJReflexive property
   Show answer

   Answer: H — Identity property

7. 7. Which expression is equivalent to ( 5^3 x^10 y^25^2)?

   A(2x^2y^5)B(2x^5y^-3)C((1)/(5)x^2y^2)D((32)/(5)x^50y^10)
   Show answer

   Answer: A — (2x^2y^5)

8. 8. Which is equivalent to (sqrt13 - (-81))?

   F4G(13 - 9i)H(13 + 9i)J22
   Show answer

   Answer: G — (13 - 9i)

9. 9. Which property would justify the following statement? If (x+2=y) and (y=20), then (x+2=20).

   ADistributive propertyBReflexive property of equalityCSymmetric property of equalityDTransitive property of equality
   Show answer

   Answer: D — Transitive property of equality

10. 10. Which expression is equivalent to ((2x^8 * 5y)/(4x^2 * 25y^3)), where (x 0) and (y 0)?

    F((i)/(i))G((i)/(i))H((i)/(i))J((i)/(i))
    Show answer

    Answer: G — ((i)/(i))

11. 11. Using (a_n = ar^n-1), what is the 10th term in this geometric sequence? (0.2, 1, 5, 25, 125, )

    A78,125B390,625C1,953,125D9,765,625
    Show answer

    Answer: B — 390,625

12. 12. If (f(x)=2x^2-7x), what is the value of (f(-4))?

    F−44G−4H60J92
    Show answer

    Answer: H — 60

13. 13. Given (f(x)=(x-4)^2-1), what is the vertex of the graph of this function?

    A(−4, −1)B(−4, 1)C(4, −1)D(4, 1)
    Show answer

    Answer: C — (4, −1)

14. 14. Given (S_n = (n)/(2) 2a_1 + (n-1)d ). An outdoor theater has 37 seats in the first row, 40 seats in the second row, and 43 seats in the third row. If this pattern continues, what is the total number of seats in the first 10 rows?

    A120B320C505D520
    Show answer

    Answer: C — 505

15. 15. What is the value of ( _n=1^3 (17n - 15))?

    A2B19C36D57
    Show answer

    Answer: D — 57

16. 16. Which of the following equations best models the data in this table? | x | y | | ---: | --: | | −2 | 5 | | −0.5 | 2 | | 0 | 1 | | 1.5 | 0.5 | | 2.5 | 1.5 | | 3 | 2.5 |

    F(y=2 ((5)/(4) )^x)G(y=x^2+1)H(y=(x+2)/(4)-3)J(y=(1)/(2)x^2 - x + 1)
    Show answer

    Answer: J — (y=(1)/(2)x^2 - x + 1)

17. 17. The time it takes to do a job is inversely proportional to the number of workers. If 8 workers can do a job in 6 days, then 16 workers can do the same job in —

    A1.5 daysB3 daysC6 daysD12 days
    Show answer

    Answer: B — 3 days

18. 18. What type of function is (y=2x+8)?

    FExponentialGQuadraticHLinearJStep
    Show answer

    Answer: F — Exponential

19. 19. The graph of (y=4x-11) is translated up 8 units. Which equation represents the translated graph?

    F(y=4x-19)G(y=12x-3)H(y=12x-11)J(y=4x-3)
    Show answer

    Answer: J — (y=4x-3)

20. 20. Which equation represents the statement: “(r) is inversely proportional to (s) and directly proportional to the cube of (t)”?

    A(r=(kt^3)/(s^3))B(r=(k)/(st^3))C(r=(ks)/(t^3))D(r=(kt^3)/(s))
    Show answer

    Answer: D — (r=(kt^3)/(s))

21. 21. Which equation best represents the data in this table? | x | y | | --: | ----: | | 0.5 | −0.75 | | 1 | 0 | | 1.5 | 0.5 | | 2 | 0.75 | | 3 | 1 |

    F(y= x)G(y=(1)/(2)x)H(y=(1)/(2)x^2+2x-1)J(y=x+1)
    Show answer

    Answer: F — (y= x)

22. 22. Given (f(x)=-3x+4) and (g(x)=x+7), what is the value of (g(f(2)))?

    A−23B−18C5D7
    Show answer

    Answer: C — 5

23. 23. Which lists four consecutive terms of an arithmetic sequence?

    F3, 10, 17, 24G1, 4, 9, 16H1, 2, 4, 8J−5, 6, 10, 13
    Show answer

    Answer: F — 3, 10, 17, 24

24. 24. What are all the roots of the equation (3(w-14)-6=21)?

    A19B23C5 and 23D9 and 19
    Show answer

    Answer: C — 5 and 23

25. 25. What is the solution set for (k+64-8=-2)?

    A−28B−124C4D17
    Show answer

    Answer: A — −28

26. 26. What is the solution set of the equation (x^2-2x+5=0)?

    F−3, 1G−1, 3H1−2i, 1+2iJ−1−2i, −1+2i
    Show answer

    Answer: H — 1−2i, 1+2i

27. 27. What is the solution to (3^x-4=-5)?

    A(x=-(1)/(2))B(x=-1)C(x=2)D(x=(1)/(2))
    Show answer

    Answer: A — (x=-(1)/(2))

28. 28. Which is the solution set for ((x+5)^2=0)?

    F25G5H−5J−5, 5
    Show answer

    Answer: H — −5

29. 29. What is the solution set for (-(5)/(3x)=(8)/(x)), where (x 0)?

    A2B18/5C26/5D6
    Show answer

    Answer: D — 6

30. 30. Which of the following represents the solutions to (4x+9>11)?

    F(x<-(5)/(2)) or (x>(1)/(2))G(-(5)/(2)<x<(1)/(2))H(x<-(1)/(2)) or (x>5)J(-(1)/(2)<x<5)
    Show answer

    Answer: F — (x<-(5)/(2)) or (x>(1)/(2))

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

    A( (5)/(2) )B( (19)/(2) )C( (29)/(2) )D( (43)/(2) )
    Show answer

    Answer: C — ( (29)/(2) )

32. 32. What is the solution set of (2x^2+7x+5=0)?

    F( -1,-(5)/(2) )G( -(5)/(2),-1 )H( 1,(5)/(2) )J( (1)/(2),5 )
    Show answer

    Answer: G — ( -(5)/(2),-1 )

33. 33. Which is a zero of the function (f(x)=(x+3)(2x-1)(x+2))?

    A3B0C−1D−2
    Show answer

    Answer: D — −2

34. 34. What are the coordinates of the vertex of the graph of the function (-2(x-1)^2=y+5)?

    F(−1, 5)G(2, 5)H(1, −5)J(−2, −5)
    Show answer

    Answer: H — (1, −5)

35. 35. A polynomial function has a zero at (x=3). Which of the following expressions must be one factor of the polynomial?

    A(x−3)B(x+3)C3xD(x^3)
    Show answer

    Answer: A — (x−3)

36. 36. Where does the graph of (f(x)=(3x-5)(x+9)) cross the x-axis?

    F(((5)/(3),0)) and ((−9,0))G(((5)/(3),0)) and ((−3,0))H((−(5)/(3),0)) and ((9,0))J((−(5)/(3),0)) and ((−45,0))
    Show answer

    Answer: F — (((5)/(3),0)) and ((−9,0))

37. 37. If (M= -7 & 10 & 3 ), which matrix represents (M^2)?

    A( 49 & -40 & 9 )B( -14 & 20 & 6 )C( 49 & 10 & 9 )D( -14 & 20 & 9 )
    Show answer

    Answer: A — ( 49 & -40 & 9 )

38. 38. The dimensions of matrix (P) are (6 5). The dimensions of matrix (Z) are (5 1). What are the dimensions of matrix (PZ)?

    A(30 5)B(6 1)C(5 5)D(1 6)
    Show answer

    Answer: B — (6 1)

39. 39. If (P= 4 & -3-2 & 1 ) and (P^-1Q= 20 & -30-10 & 12 ), what is the value of (Q)?

    F( 110 & -156-50 & 72 )G( 20 & 30-7 & -9 )H( 5 & 105 & 12 )J( 5 & -30 & 6 )
    Show answer

    Answer: J — ( 5 & -30 & 6 )

40. 40. What is the solution set for the system of equations? (x^2+y^2=5) (x+y=1)

    A(1, −2), (1, 2)B(−2, 1), (2, 1)C(−1, −2), (1, 2)D(−1, 2), (2, −1)
    Show answer

    Answer: D — (−1, 2), (2, −1)

41. 41. Which ordered pair represents a solution to the system of inequalities? (2x+4y 12) (3x-y<2)

    A(6, 4)B(2, 6)C(−3, 2)D(−4, −14)
    Show answer

    Answer: C — (−3, 2)

42. 42. The matrix equation ( 4 & -3-1 & 1 x = -26 ) represents which system of linear equations?

    F( 4x-y=-2-3x+y=6 )G( 4x-3y=-2-x+y=6 )H( 4x+3y=-2-x-y=6 )J( 4x+y=-2-x-3y=6 )
    Show answer

    Answer: G — ( 4x-3y=-2-x+y=6 )

43. 43. Which number is equivalent to ( (32)^5 )?

    A2B8C0D16
    Show answer

    Answer: C — 0

44. 44. If (x<0), which expression is equivalent to sqrtx^2x,?

    A1B−1C(x)D(-x)
    Show answer

    Answer: B — −1

45. 45. When completely factored, (2x^2+2x-24) is equivalent to —

    A((2x-3)(x+4))B(2(x+3)(x-4))C(2(x+6)(x-2))D((2x-3)(x+8))
    Show answer

    Answer: B — (2(x+3)(x-4))

46. 46. Which of the following is equivalent to (sqrt72+sqrt50)?

    A(11sqrt2)B(-11sqrt2)C( sqrt122)D( sqrt2)
    Show answer

    Answer: A — (11sqrt2)

47. 47. Which expression is equivalent to (sqrt 3 x^6y^9)?

    A(x^2y^3)B(x^2y^2)C(x^2y^4)D(x^3y^3)
    Show answer

    Answer: A — (x^2y^3)

48. 48. Which expression is equivalent to (64x^2-81y^2)?

    A((8x+9y)^2)B((8x-9y)^2)C((8x+9y)(8x-9y))D((8x+9)(8x-9))
    Show answer

    Answer: C — ((8x+9y)(8x-9y))

49. 49. For which of the following sets is multiplication not commutative?

    AComplex numbersBMatricesCReal numbersDWhole numbers
    Show answer

    Answer: B — Matrices

50. 50. The graph of (y=3x-2) is translated up 5 units. What is the equation of the new graph?

    A(y=8x-2)B(y=3x+3)C(y=3x-7)D(y=3x+5)
    Show answer

    Answer: B — (y=3x+3)

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.