Algebra 2 SOL Practice Test — Set 6 of 6

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

1. 1. What are the coordinates of the vertex of (y = (x - 4)^2 + 1)?

   A(4, 1)B(−4, 1)C(4, −1)D(−4, −1)
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   Answer: A — (4, 1)

2. 2. What is the graph of ((x - 2)^2 - (y - 3)^2 = 4)?

   AAn ellipseBA circleCA parabolaDA hyperbola
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   Answer: B — A circle

3. 3. Which matrix product is not defined?

   FA (4 * 2) matrix multiplied by a (2 * 3) matrixGA (2 * 2) matrix multiplied by a (2 * 2) matrixHA (2 * 4) matrix multiplied by a (4 * 3) matrixJA (1 * 3) matrix multiplied by a (1 * 3) matrix
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   Answer: J — A (1 * 3) matrix multiplied by a (1 * 3) matrix

4. 4. A football scoring system awards: touchdown = 6 points, field goal = 3 points, safety = 2 points, extra point = 1 point. Team Alton scored 3 touchdowns, 0 field goals, 1 safety, and 2 extra points. Team Bakey scored 2 touchdowns, 2 field goals, 0 safeties, and 1 extra point. Which matrix product gives the final scores?

   A( 6&3&2&1 3012 )B( 3&0&1&22&2&0&1 6321 )C( 6&3&2&1 3&0&1&22&2&0&1 )D( 3&0&1&2 6321 )
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   Answer: C — ( 6&3&2&1 3&0&1&22&2&0&1 )

5. 5. Mel paid $3.28 for 3 eggs and 1 sausage patty. Ann paid $3.56 for 2 eggs and 3 sausage patties. Which system models this situation?

   F(3x + y = 3.28,; 2x + 3y = 3.56)G(3x + 3y = 3.28,; x + 2y = 3.56)H(x + y = 3.28,; 2x + 3y = 3.56)J(3x + y = 3.56,; 2x + 3y = 3.28)
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   Answer: F — (3x + y = 3.28,; 2x + 3y = 3.56)

6. 6. Which matrix equation represents the system (3x + 2y = 5) (8x + 9y = 2)?

   A( x&y 3&28&9 = 5&2 )B( 3&28&9 x = 52 )C( x 3&28&9 = 52 )D( 3&28&9 x&y = 5&2 )
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   Answer: D — ( 3&28&9 x&y = 5&2 )

7. 7. Which set of ordered pairs is the solution to the system (y = -x^2 + 2x + 1) and (y = x^2 - 4x + 1)?

   F((0,3),(-1,2))G((0,-1),(3,2))H((0,1),(6,23))J((3,2),(6,11))
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   Answer: G — ((0,-1),(3,2))

8. 8. Given paired data relating hours of sleep (x) to minutes of naptime (y), which is most likely the line of best fit?

   A(y = -23.39x + 296.04)B(y = -0.03x + 11.26)C(y = 11.26x - 0.03)D(y = 296.04x - 23.39)
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   Answer: A — (y = -23.39x + 296.04)

9. 9. A table shows the number of students enrolled in an advanced algebra program for the first 6 years: Year: 1, 2, 3, 4, 5, 6 Students: 66, 72, 82, 90, 100, 106 Assuming the trend continues, what is the best prediction for year 12?

   F212G157H142J126
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   Answer: G — 157

10. 10. Which is a simplified form of the following expression? (27^3)

    A419,683B36C81D177,147
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    Answer: C — 81

11. 11. Which is a true statement?

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

12. 12. Which is equivalent to the following expression? (2-x)/(x-3)

    A0B((2x)/(x-3))C((2-x)/(x-3))D((2)/(x-3))
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    Answer: C — ((2-x)/(x-3))

13. 13. If no denominator is equal to zero, which is a simplified form of the following expression? (5xy(x-y))/((x-y)(x+y))

    F((5xy)/(x+y))G((5)/(x+y))H(5xy(x-y)(x+y))J((5xy)/((x-y)(x+y)))
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    Answer: J — ((5xy)/((x-y)(x+y)))

14. 14. Which is equivalent to 2sqrt27+3sqrt75-sqrt18?

    A(18 6)B(4sqrt120)C(21 3-3 2)D(24 3-9 2)
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    Answer: C — (21 3-3 2)

15. 15. Which statement is a result of applying the transitive property of inequalities? Given: (2x-1<7x) and (7x<x+72)

    F(2x-1<x+72)G(x+72<7x)H(x+72<2x-1)J(7x<2x-1)
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    Answer: F — (2x-1<x+72)

16. 16. Which is equivalent to the expression below? (1+3i)(3+i)

    A(3-10i)B(6+6i)C(6+10i)D(10i)
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    Answer: D — (10i)

17. 17. What is the completely factored form of the following expression? (6x^2+7x-3)

    F((2x+3)(3x-1))G((2x-3)(3x+1))H((6x-3)(x+1))J((6x-1)(x+3))
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    Answer: F — ((2x+3)(3x-1))

18. 18. If (x -3), which is an equivalent form of the following expression? (6x+7)/(2(x+3))-(2x+5)/(2(x+3))

    A((2)/(x+1))B((x+3)/(2x+1))C((x+3)/(2(2x+3)))D((x+3)/(9))
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    Answer: C — ((x+3)/(2(2x+3)))

19. 19. Which is an equivalent form of the following? (-1-5i)-4i

    F(-8i)G(-9i)H(i+10)J(-9)
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    Answer: G — (-9i)

20. 20. Which equation represents the statement below? “(a) is inversely proportional to (b).”

    A(a=k+b)B(a=kb)C(a=(k)/(b))D(a=(b)/(k))
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    Answer: D — (a=(b)/(k))

21. 21. What type of function is f(x)=3(x-2)^2+1?

    FQuadraticGLinearHExponentialJStep
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    Answer: F — Quadratic

22. 22. Ohm’s Law states that resistance is directly proportional to voltage and inversely proportional to current. One circuit has resistance 8 ohms when voltage is 48 volts and current is 6 amperes. What is the resistance of a second circuit with voltage 128 volts and current 8 amperes?

    A120 ohmsB64 ohmsC28 ohmsD16 ohms
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    Answer: D — 16 ohms

23. 23. If (f(x)=x^3+x^2-8), what is (f(-8))?

    A−568B−456C456D568
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    Answer: B — −456

24. 24. The table shows the value of a collectible baseball card over eight years: Year (x): 1, 2, 3, 4, 5, 6, 7, 8 Value (y): 3, 5, 9, 18, 29, 43, 51, 69 Which exponential equation best represents the data?

    F(y=2.18^x+6.1)G(y=14.8^x+9.58)H(y=0.53^x+1.01)J(y=2.25^x+1.59)
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    Answer: J — (y=2.25^x+1.59)

25. 25. What are the first three terms of the sequence defined by a_n=7+5(n-1)?

    A12, 17, 22B7, 2, −3C7, 12, 17D7, 35, 175
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    Answer: C — 7, 12, 17

26. 26. This table contains ordered pairs of a function: x: 0, 1, 2, 3, 4 y: 11, 6, 3, 2, 3 Which equation could define the function?

    F(y=-5x+11)G(y=-2x+11)H(y=(x-3)^2+2)J(y=(x-2)^2+7)
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    Answer: H — (y=(x-3)^2+2)

27. 27. Which lists four consecutive terms of a geometric sequence?

    F1, 4, 8, 16G6, 9, 12, 15H12, 48, 192, 768J7, 14, 42, 168
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    Answer: H — 12, 48, 192, 768

28. 28. Which is a root of (f(x)=0) if (f(x)=(x+5)(x-4))?

    A−5B−4C0D5
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    Answer: A — −5

29. 29. Given (f(x)=2x-1) (g(x)=3x) What is (g(f(x)))?

    F(5x-1)G(6x-3)H(6x-1)J(6x^2-3)
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    Answer: G — (6x-3)

30. 30. Assuming the domain is all real numbers, what is the range of (y=x^2+2)?

    FAll integersGAll real numbersHAll real numbers greater than or equal to 0JAll real numbers greater than or equal to 2
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    Answer: J — All real numbers greater than or equal to 2

31. 31. The table shows paired data: x: 4, 4.5, 5, 5.5, 6 y: 0.5, 0.6, 0.8, 0.9, 1.2 Which is most likely the line of best fit?

    A(y=0.34x-0.9)B(y=0.25x-0.7)C(y=0.45x-1)D(y=0.50x-0.6)
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    Answer: A — (y=0.34x-0.9)

32. 32. Assuming (k) is a constant, which equation represents joint variation of (y) as (a) and (b)?

    F(y=kab)G(y=(ab)/(k))H(y=(k)/(ab))J(y=(b)/(a))
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    Answer: F — (y=kab)

33. 33. Solve the inequality: (x-3>2)

    A(x>5)B(x>3)C(x<5)D(x<3)
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    Answer: A — (x>5)

34. 34. What is the solution set for (x-2)/(8)-(x-2)/(x)=-1

    F2, 8G10/3H4J6
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    Answer: H — 4

35. 35. What is the solution to (x+4)/(x)=(3)/(7)?

    A(x=-7)B(x=-4)C(x=-(1)/(14))D(x=(5)/(14))
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    Answer: A — (x=-7)

36. 36. What is the solution of (x-6+5=8)?

    A(x=9)B(x=15)C(x=19)D(x=65)
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    Answer: B — (x=15)

37. 37. What is the solution set of (x^2+6x-7=0)?

    F−1, 7G−2, 3H−3, 2J−7, 1
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    Answer: J — −7, 1

38. 38. What is the solution set of (6=x^2-x)?

    A( 1 isqrt232)B( -1 isqrt232)C−2, 3D−3, 2
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    Answer: C — −2, 3

39. 39. If (-6x+11=4), then —

    F(x=-(5)/(2)) or (x=-(7)/(6))G(x=-(7)/(6)) or (x=(5)/(2))H(x=-(5)/(2)) or (x=(7)/(6))J(x=(7)/(6)) or (x=(5)/(2))
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    Answer: J — (x=(7)/(6)) or (x=(5)/(2))

40. 40. A polynomial has zeros −3 and 4. Which is a factor?

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

41. 41. The matrix equation 4&59&10 x = 2030 is equivalent to which system?

    A(4x+9y=20,;5x+10y=30)B(4x+5y=20,;9x+10y=30)C(4x+5x=20,;9y+10y=30)D(4x+5y=20,;5x+10y=30)
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    Answer: B — (4x+5y=20,;9x+10y=30)

42. 42. Which matrix equals 1&11&1 11?

    F( 11 )G( 1&11&1 )H( 22 )J( 2&22&2 )
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    Answer: H — ( 22 )

43. 43. Charlie bought (j) jeans at $28 each and (t) T-shirts at $12 each. He bought 7 items for $116 total. Which system models this?

    A(7j+12t=28,;j+t=116)B(28j+12t=116,;j+t=7)C(28j+12t=7,;j+t=116)D(12j+28t=116,;j+t=7)
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    Answer: B — (28j+12t=116,;j+t=7)

44. 44. Solve the system: (y=x^2+6x+1) (y=-2x-14)

    F(-3, -8), (-5, -4)G(-7, 0), (0, 1)H(-5, -4), (0, 1)J(-3, -8)
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    Answer: F — (-3, -8), (-5, -4)

45. 45. Given A= 5&1025&30,; B= 25&305&10 Which matrix is (B* A)?

    F( 175&250775&1050 )G( 250&600425&1050 )H( 125&300125&300 )J( 875&1150275&350 )
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    Answer: J — ( 875&1150275&350 )

46. 46. Which of the following operations is the commutative property not valid for?

    AMultiplication of real numbersBMultiplication of complex numbersCMultiplication of matricesDMultiplication of negative real numbers
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    Answer: B — Multiplication of complex numbers

47. 47. Which is equivalent to the expression ((4x^7)/(x^3))?

    A(4x^4)B(x^4)C(4x^10)D(x^10)
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    Answer: C — (4x^10)

48. 48. Which expression is equivalent to (3a^2)?

    A(a^2)B(a^3)C(a^6)D(a^6)
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    Answer: B — (a^3)

49. 49. Which is a factored form of (8x^3 + 1)?

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

50. 50. Which is equivalent to ((4 - 3i)^2)?

    A25B(25 + 2i)C7D(7 - 24i)
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    Answer: D — (7 - 24i)

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.