Algebra 2 SOL Practice Test — Set 2 of 6

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

1. 1. (y=x^2-8x+15). What are the x-intercepts of the graph that represents the equation?

   A((0,3)) and ((0,5))B((3,0)) and ((5,0))C((-8,0)) and ((15,0))D((0,-8)) and ((0,15))
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   Answer: B — ((3,0)) and ((5,0))

2. 2. If (y) varies jointly with (x) and (z), what is the constant of proportionality when (y=30), (x=4), and (z=5)?

   A1B((3)/(2))C6D24
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   Answer: B — ((3)/(2))

3. 3. The height of an object when projected upward can be described by the equation (h=270t-4.9t^2). The relationship between the height of the object and the elapsed time is —

   Aan exponential functionBa linear functionCa quadratic functionDa step function
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   Answer: C — a quadratic function

4. 4. These are the first three terms of an arithmetic sequence: ( 12, 34,1). What are the fourth and fifth terms of the sequence?

   A( 54, 32)B( 54, 74)C( 32,2)D( 74,2)
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   Answer: B — ( 54, 74)

5. 5. If (f(x)=x^5) and (g(x)=-2-3x^2), which is (f(g(x)))?

   A((-2-3x^2)^5)B(-2x-3x^10)C((-2-3x)^5)D(-2x^5-3x^7)
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   Answer: A — ((-2-3x^2)^5)

6. 6. Which equation represents the statement “(z) varies directly with (x) and inversely with (y)”?

   A(z=kxy)B(z=(k)/(xy))C(z=(kx)/(y))D(z=(ky)/(x))
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   Answer: C — (z=(kx)/(y))

7. 7. Which is the solution set for (2x^2-7x+6=0)?

   A(1.5,2)B(-1.5,2)C(1.5,-2)D(-1.5,-2)
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   Answer: A — (1.5,2)

8. 8. The width of a rectangular window is 2 feet more than its height. If the area is 35 square feet, what is the height?

   A9 ftB7 ftC5 ftD3 ft
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   Answer: C — 5 ft

9. 9. Which value of (x) is a solution to ( sqrt2x+24=3)?

   A12.5B25C50D70
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   Answer: B — 25

10. 10. Which is the solution set of (|5s-5|=3)?

    A(16)B(-16,16)C(-1,11)D(4,16)
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    Answer: C — (-1,11)

11. 11. When (x 0), what is the solution set for ((x)/(x)=x-3)?

    A(4)B(6)C(2,6)D(3,4)
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    Answer: D — (3,4)

12. 12. What are all the roots for (|2u-9|=5)?

    A−2 and −7B−2 and 7C2 and −7D2 and 7
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    Answer: D — 2 and 7

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

    A((2,-5))B((2,5))C((-2,5))D((-2,-5))
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    Answer: A — ((2,-5))

14. 14. A polynomial function has a zero at (x=6). Which expression must be a factor of the polynomial?

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

15. 15. What are the x-intercepts for the graph of (y=x^2+5x-6)?

    A((0,1)) and ((0,-6))B((1,0)) and ((-6,0))C((0,-1)) and ((0,6))D((-1,0)) and ((6,0))
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    Answer: B — ((1,0)) and ((-6,0))

16. 16. The dimensions of matrix (A) are (2 3). The dimensions of matrix (B) are (3 17). What are the dimensions of matrix (AB)?

    A(2 17)B(3 3)C(17 2)D(3 17)
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    Answer: A — (2 17)

17. 17. Which of the following represents the system 2x-3y=7 5x+4y=1

    A( 2&-35&4 x = 71 )B( 7&12&-3 )C( x&y 25 )D( 2&5-3&4 )
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    Answer: A — ( 2&-35&4 x = 71 )

18. 18. A matrix shows the number of flowers in four types of arrangements. Roses cost $3, daisies $1, lilies $2. Which product represents the cost of each type?

    A( 3&0&03&4&00&4&31&3&2 312 )B( 312 3&0&03&4&00&4&31&3&2 )C( 3&1&2 3&0&03&4&00&4&31&3&2 )D( 3&0&03&4&00&4&31&3&2 132 )
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    Answer: A — ( 3&0&03&4&00&4&31&3&2 312 )

19. 19. Which set of ordered pairs represents the vertices of the region that is the solution to y<1, x>-2, y 0

    A(-2,1),(0,1),(-2,0)B(2,-1),(0,-1),(2,0)C(2,-1),(2,0),(1,0)D(1,-2),(1,0),(0,-2)
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    Answer: A — (-2,1),(0,1),(-2,0)

20. 20. Which expression is equivalent to ((z^6 e)/(z^4))?

    A(z^2e)B(z^10e)C(z^2)D(ze^2)
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    Answer: C — (z^2)

21. 21. What value of (x) makes (x - 3 = 6) true?

    A9B3C–9D–3
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    Answer: A — 9

22. 22. Which expression is equivalent to (sqrt20x^4y^5) for positive (x) and (y)?

    A(2x^2y^2sqrt5y)B(5x^2y^5/2)C(2x^3y^1/2sqrt5y)D(5x^3y^1/2* 2y)
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    Answer: A — (2x^2y^2sqrt5y)

23. 23. Which expression is equivalent to ((3)/(6w^7)-(3)/(4w^5))?

    A((2)/(w^8))B((2)/(w^6))C((2y^7)/(3y^2))D((2w^7)/(6y^2))
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    Answer: A — ((2)/(w^8))

24. 24. The steps used to solve an equation are shown: Step 4: (1 * r = 21i) Step 5: (r = 21i) What property justifies the work between Step 4 and Step 5?

    AIdentity property of multiplicationBInverse property of multiplicationCCommutative property of multiplicationDAssociative property of multiplication
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    Answer: A — Identity property of multiplication

25. 25. Which expression is equivalent to ((1)/(30w^2)-(w-1)/(5w)), if no denominator equals zero?

    A((1-w)/(30w^2))B((6-w)/(30w))C((1-6w)/(30w^2))D((6w-1)/(30w^2))
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    Answer: B — ((6-w)/(30w))

26. 26. What is the complete factorization of (18x^4 + 12x^3 - 6x)?

    A(6x^3(3x+2))B(6x(3+x^2x^2))C(6x(3x-1)(x+1))D(6x(3x^3+2x^2-1))
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    Answer: D — (6x(3x^3+2x^2-1))

27. 27. Which of these is equivalent to (i^75)?

    A(i)B(-i)C(-1)D(1)
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    Answer: B — (-i)

28. 28. For which value of (b) is (x^2 + bx - 60) factorable over the integers?

    A61B23C–7D–16
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    Answer: C — –7

29. 29. If no denominator equals zero, which expression is equivalent to (25-4x^2)/(6x^2-2x-4) (6x^2+9x-15)/(2x^2-x-10)?

    A–2B2C(-(2(3x+2))/(3(x+2)))D((2(3x+2))/(3(x+2)))
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    Answer: C — (-(2(3x+2))/(3(x+2)))

30. 30. Assuming the denominators do not equal zero, which expression is equivalent to (12)/(13x-47)+(3)/((x+1)(x-4))?

    A((13)/((x+1)(x-4)))B((13x-47)/(13))C((2x-3)/(13))D((13)/(2x^3))
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    Answer: A — ((13)/((x+1)(x-4)))

31. 31. Which expression is equivalent to (36x^6y^5), where (x>0) and (y>0)?

    A(6x^3y^9/2)B(6x^2y^2)C(18x^3y^5)D(18x^2y^2)
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    Answer: B — (6x^2y^2)

32. 32. What nonzero value of (x) is a solution to (x+2)/(x)-(x-6)/(3x)=(2x+9)/(5x)?

    A14B–14C6D–6
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    Answer: A — 14

33. 33. How many values of (x) satisfy (|3x-5|=0)?

    A0B1C2DInfinitely many
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    Answer: B — 1

34. 34. What is a solution of (|7-2x|+5=8)?

    A(x=-26)B(x=-1)C(x=(9)/(2))D(x=-1)
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    Answer: D — (x=-1)

35. 35. What is the solution set for the system of equations (y=4x+2) and (y=x^2+4x-8)?

    A((-5,18),(2,10))B((-1,-2),(6,26))C((-6,22),(1,6))D((-4,0),(0,-8))
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    Answer: D — ((-4,0),(0,-8))

36. 36. The function (f(x)=(1-x)^2-4) is decreasing throughout which interval?

    A(-4<x<0)B(-0<x<1)C(-1<x<3)D(- <x< )
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    Answer: B — (-0<x<1)

37. 37. A normally distributed data set has mean 0 and standard deviation 0.5. Which is closest to the percent of values between –1 and 1?

    A34%B50%C68%D95%
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    Answer: C — 68%

38. 38. The volume of a cone varies jointly with its height and the square of its radius. If (k) is the constant of proportionality, which equation represents this relationship?

    A(V=k(rh)^2)B(V=(kr^2)/(h))C(V=kr^2h)D(V=krh)
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    Answer: C — (V=kr^2h)

39. 39. What is the equation of the horizontal asymptote of (f(x)=(4)/(x)-10)?

    A(y=4)B(y=0)C(y=-1)D(y=-10)
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    Answer: D — (y=-10)

40. 40. As (x) approaches negative infinity, what is the end behavior of (f(x)=-x^7+bx^3+c)?

    AApproaches (c)BApproaches 0CApproaches positive infinityDApproaches negative infinity
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    Answer: D — Approaches negative infinity

41. 41. Jessica paid $23,000 for her car. Assuming exponential depreciation, which equation best models the data?

    A(y=21,000(1.20)^x)B(y=22,300(2.60)^x)C(y=23,100(0.85)^x)D(y=23,500(0.70)^x)
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    Answer: C — (y=23,100(0.85)^x)

42. 42. Which number is a zero of (f(x)=7x^2+16x-48)?

    A12B4C–4D–12
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    Answer: C — –4

43. 43. Which function is the inverse of (g(x)=x^3+11)?

    A(g^-1(x)=sqrt 3 x-11)B(g^-1(x)=3x+11)C(g^-1(x)=x^3-11)D(g^-1(x)=x+11)
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    Answer: A — (g^-1(x)=sqrt 3 x-11)

44. 44. What is the domain of (g(x)= (x-1))?

    A(x x>10)B(x x>9)C(x x>1)D(x x 1)
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    Answer: C — (x x>1)

45. 45. What property is illustrated by the equation 3x(x + 2) = 3x² + 6x?

    AAssociative Property of AdditionBReflexive Property of EqualityCAssociative Property of MultiplicationDDistributive Property
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    Answer: D — Distributive Property

46. 46. Which of the following statements is an example of the transitive property of inequalities?

    FIf k ≥ 0, then |k| ≥ k.GIf k ≤ 6 and 6 ≤ m, then k ≤ m.HIf k ≤ 6, then k + 2 ≤ 8.JIf k ≤ 6 and j ≥ 0, then kj ≤ 6j.
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    Answer: G — If k ≤ 6 and 6 ≤ m, then k ≤ m.

47. 47. Which expression is equal to (4y⁵ − 3y²) / (5y²)?

    A4y³ − 2y²B(4/5)y³ − 3C5y − 3/5D(4/5)y³ − 3/5
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    Answer: D — (4/5)y³ − 3/5

48. 48. Which is equivalent to 7a²b / 15b⁵?

    Fa / (5b³)G7a / (15b⁴)H7a² / (15b⁴)J7a / (15b⁵)
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    Answer: H — 7a² / (15b⁴)

49. 49. Which is equivalent to (−2)³?

    A−2B2C−8D6
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    Answer: C — −8

50. 50. Which is equivalent to −6a²b³?

    Fa²b³ / 6G−a³b²Ha³b²J−6a²b³
    Show answer

    Answer: J — −6a²b³

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.