Algebra 2 SOL Practice Test — Set 5 of 6

Set 5 of 6 — 50 more free Algebra 2 SOL practice questions from official VDOE released tests.

1. 1. Which equation represents a situation in which (z) varies jointly as (x) and (y)?

   A(z=(x)/(y))B(z=(y)/(x))C(z=24y)D(z=kxy)
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   Answer: D — (z=kxy)

2. 2. Which is an arithmetic sequence?

   F(2,5,9,14, )G(100,50,12.5,1.6, )H(3,10,17,24, )J(-3,-2,-1,1,4, )
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   Answer: H — (3,10,17,24, )

3. 3. Which shows four consecutive terms of a geometric sequence?

   A(1,5,25,125, )B(10,20,30,40, )C(50,100,150,200, )D(1,-1,2,-2, )
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   Answer: A — (1,5,25,125, )

4. 4. Which of the following functions of (x) has the greatest number of roots in the complex number system?

   F(y=x^4+1)G(y=x^2-4x+2)H(y=x+x^2)J(y=x^4+3)
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   Answer: F — (y=x^4+1)

5. 5. The function defined by (f(x)=3(5^x)) is —

   Aan absolute value functionBan exponential functionCa linear functionDa quadratic function
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   Answer: B — an exponential function

6. 6. A farmer pumps water from an irrigation well. Time varies inversely with pumping rate. It takes 20 hours at 600 gallons per minute. How long will it take at 400 gallons per minute?

   F12.5 hoursG15 hoursH30 hoursJ40 hours
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   Answer: H — 30 hours

7. 7. What is the domain of the function defined by f(x)=(1)/(x)

   AAll real numbersBAll non-zero real numbersCAll real numbers greater than zeroDAll real numbers less than zero
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   Answer: B — All non-zero real numbers

8. 8. Each statement describes a transformation of the graph of (y=x^2). Which correctly describes (y=(x-5)^2+6)?

   A6 units down, 5 units rightB6 units down, 5 units leftC6 units up, 5 units rightD6 units up, 5 units left
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   Answer: C — 6 units up, 5 units right

9. 9. What is (a_3) in the sequence defined by a_n = 5 + 2^n-2

   A160B40C80D10
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   Answer: B — 40

10. 10. Which is a solution to the equation sqrtx+4 = -2-x

    A(x=-4)B(x=-3)C(x=-2)D(x=-1)
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    Answer: B — (x=-3)

11. 11. If the surface area of a cube is (140 cm^2), what is the length of one edge, to the nearest tenth?

    A4.8 cmB7.6 cmC12.3 cmD23.4 cm
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    Answer: A — 4.8 cm

12. 12. What is the solution to (x-3)^2=14

    A(x=5) or (x=1)B(x=1) or (x=5)C(x=-3 4sqrt14)D(x=3 14)
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    Answer: D — (x=3 14)

13. 13. What is the solution set for 3|x+4|=18

    A(-10,2)B(6)C(-6)D(0)
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    Answer: A — (-10,2)

14. 14. What is the solution to (2)/(5x)=(4)/(10)

    F(x=3)G(x=(3)/(5))H(x=-(2)/(3))J(x=(1)/(3))
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    Answer: J — (x=(1)/(3))

15. 15. Which is a root of (x^2-11x+30=0)?

    A3B6C10D11
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    Answer: B — 6

16. 16. Which conic section describes the graph of (x^2)/(4)+(y^2)/(9)=1

    ACircleBEllipseCParabolaDHyperbola
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    Answer: B — Ellipse

17. 17. Where does the graph of (f(x)=(x+1)(x-2)) cross the x-axis?

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

18. 18. The graph of (y=5(x+6)^2-5) is —

    Aa circleBan ellipseCa parabolaDa hyperbola
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    Answer: C — a parabola

19. 19. The zeros of a polynomial function are 1 and −1. Which could be the function?

    A(f(x)=(x-1)^2)B(f(x)=(x+1)(x-2))C(f(x)=(x-1)(2x+1))D(f(x)=(x+1)(2x-1))
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    Answer: D — (f(x)=(x+1)(2x-1))

20. 20. If P= 63, Q= 5-2, then (P* Q) equals —

    F( 030 )G( -911 )H( 20-13 )J( 2415 )
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    Answer: H — ( 20-13 )

21. 21. What is the solution set to the system? y=2x-3 y=-x^2+5x+1

    A(-1,−5),(4,5)B(1,5),(4,5)C(-6,−15),(9,15)D(1.5,0)
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    Answer: A — (-1,−5),(4,5)

22. 22. Which is a matrix form of the system -3x+y=11 5x-2y=-16

    F( 11-16 = -3&15&-2 x )G( 1&-2-3&0 x = 11-16 )H( -3&15&-2 x = 11-16 )J( -3&15&-16 x = 1-2 )
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    Answer: H — ( -3&15&-2 x = 11-16 )

23. 23. Which product cannot be determined using the given matrices?

    A(AB)B(BC)C(BA)D(CA)
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    Answer: D — (CA)

24. 24. Bernard spent $5,100 replacing flooring in a 1,800-square-foot house. Carpeting costs $5 per square foot, and vinyl tile costs $2 per square foot. If (c) represents square feet of carpeting and (v) square feet of vinyl tile, which system models the situation?

    A( c+v=18005c+2v=5100 )B( c+2v=18005v=5100 )C( c+5v=18002v=5100 )D( 5c+v=18002v=5100 )
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    Answer: A — ( c+v=18005c+2v=5100 )

25. 25. Which indicates a correct application of the distributive property?

    A(a(b + c) = ab + ac)B((a + b) + c = a + (b + c))C((a + b) + c = c + (a + b))D(a + (b + c) = (a + b) + c)
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    Answer: A — (a(b + c) = ab + ac)

26. 26. Which of the following may not be true?

    FIf (a > b) and (b > c), then (a > c).GIf (a b) and (b c), then (a c).HIf (a > b), then (b > a).JIf (a b), then (b a).
    Show answer

    Answer: G — If (a b) and (b c), then (a c).

27. 27. Which is equivalent to (((a - b)^3)/((a - b)^2))?

    A(a - b)B((a - b)^5)C(a^2)D(18a - 9b)
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    Answer: A — (a - b)

28. 28. Which is a factored form of (y^3 - 1)?

    F((1 - y)(1 - y + y^2))G((1 - y)(1 + y + y^2))H((1 + y)(1 - y + y^2))J((1 + y)(1 + y + y^2))
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    Answer: G — ((1 - y)(1 + y + y^2))

29. 29. Which is equivalent to (25^2/3)?

    A125B75C15D5
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    Answer: A — 125

30. 30. Which is equivalent to ((1 - 2i)^3)?

    F(-11 + 2i)G(13 - 10i)H(13 + 2i)J(1 + 8i)
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    Answer: F — (-11 + 2i)

31. 31. Which is a factored form of (x^2 - 18x + 81)?

    A((x + 9)^2)B((x - 3)(x + 27))C((x - 9)^2)D((x + 9)(x - 9))
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    Answer: C — ((x - 9)^2)

32. 32. Which expression is equivalent to ( 18^2/3 - 16^1/4)?

    F((3)/(20))G4H((1)/(6))J((24)/(12))
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    Answer: G — 4

33. 33. Which is equivalent to ((6!)/(2!(3!)))?

    A288B216C((6)/(2))D9
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    Answer: D — 9

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

    F(2 - 3i)G(2 - 7i)H(-2 + i)J(-2 - 3i)
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    Answer: J — (-2 - 3i)

35. 35. Which is a zero of the function (f(x) = x^2 - 2x - 24)?

    F(-6)G(-3)H4J6
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    Answer: J — 6

36. 36. Given (f(x) = x^3 - 3x) and (g(x) = x^2 - 8), what is (f(10) - g(10))?

    A608B783C862D878
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    Answer: D — 878

37. 37. What is the value of ( _n=0^3 2^n+1)?

    A12B14C28D30
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    Answer: A — 12

38. 38. If the fifth and eighth terms of an arithmetic sequence are 9 and 21, respectively, what are the first four terms of the sequence?

    F2, −1, −4, −7G3, −1, −5, −9H5, 2, −1, −4J7, 3, −1, −5
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    Answer: J — 7, 3, −1, −5

39. 39. Wind chill factor (W) varies directly with temperature (T) and inversely with wind velocity (v). Which formula represents this relationship?

    F(W = kTv)G(W = (kv)/(T))H(W = (kT)/(v))J(W = (kT)/(v^2))
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    Answer: H — (W = (kT)/(v))

40. 40. A function table contains the ordered pairs ((1, -2), (2, -5), (3, -8), (4, -11)). Which is a general rule for the function?

    A(y = -3x + 1)B(y = x^2 - 7)C(y = -x^2 + 1)D(y = -3x - 3)
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    Answer: C — (y = -x^2 + 1)

41. 41. What is the solution set for (|2x - 5| = 7)?

    A(-6, 1)B(1, 11)C(6)D(1)
    Show answer

    Answer: A — (-6, 1)

42. 42. What is the solution set for (x^2 - 16 = 0)?

    F(4)G(-4, 4)H(0, 4)J(4)
    Show answer

    Answer: G — (-4, 4)

43. 43. What is the solution set for ((3x - 1)^2 = 0)?

    A( (1)/(3) )B(1, 3)C( (1)/(3) )D(-1)
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    Answer: C — ( (1)/(3) )

44. 44. Which is a solution to (2x^2 - 7x - 3 = 0)?

    F(x = 3)G(x = (2)/(3))H(x = -2)J(x = -3)
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    Answer: F — (x = 3)

45. 45. What is the solution to (3x^2 - 26x - 2 = 0)?

    A6B2C−2D0
    Show answer

    Answer: B — 2

46. 46. What is the solution set for (|x - 2| = 4)?

    F(2)G(14)H(16)J(-2, 6)
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    Answer: J — (-2, 6)

47. 47. What is the solution set for (|3y - 4| = 5)?

    A(3)B(1)C(3, -(1)/(3))D(9)
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    Answer: C — (3, -(1)/(3))

48. 48. Two factors of a polynomial (P(x)) are ((x - 6)) and ((x + 3)). Which is a zero of (P(x))?

    F6G−3H1J3
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    Answer: G — −3

49. 49. What are the factors of a polynomial function if its graph has x-intercepts at −1, 0, and 4?

    A(x(x - 1)(x + 4))B(x(x + 1)(x - 4))C((x + 1)(x - 4))D((x - 1)(x + 4))
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    Answer: B — (x(x + 1)(x - 4))

50. 50. Which of the following is a zero of the function (f(x) = x^3 - x^2 - 14x + 24)?

    F−4G−3H2J0
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    Answer: F — −4

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.