Algebra 1 SOL Practice Test — Set 2 of 6

Set 2 of 6 — 50 more free Algebra 1 SOL practice questions from official VDOE released tests.

1. 1. A function (f) is described by f(x) = (x - 2)^4 + 3 The domain of (f) is all real numbers greater than 0. The range of (f) is all real numbers greater than or equal to —

   A3B0C−3D−5
   Show answer

   Answer: A — 3

2. 2. Which function does not have a y-intercept of 2?

   A(y = 4x + 2)B(y = 4(x + 0.5))C(y = x^2 + 7x + 2)D(y = (x - 2)(x + 5))
   Show answer

   Answer: D — (y = (x - 2)(x + 5))

3. 3. Given: f(x) &= 7x + 5 g(x) &= 2x - 5 h(x) &= (x + 2)(x - 5) Which functions have at least one equivalent x-intercept?

   F(f(x)) and (g(x)) onlyG(f(x)) and (h(x)) onlyH(g(x)) and (h(x)) onlyJ(f(x)), (g(x)), and (h(x))
   Show answer

   Answer: H — (g(x)) and (h(x)) only

4. 4. The correlation coefficient for the curve of best fit relating student cell phone use (hours per day) and GPA is −0.9921. Based on the data, there appears to be —

   Ano relationshipBa weak relationshipCa strong relationshipDa positive relationship
   Show answer

   Answer: C — a strong relationship

5. 5. Which conclusion about the relationship between student cell phone use and GPA is best supported by these data?

   FIncreased cell phone use prevents students from getting good grades.GDecreased cell phone use causes students to perform better in school.HThe more time students spend on their cell phones, the lower their GPA.JThere is no relationship between student cell phone use and GPA.
   Show answer

   Answer: H — The more time students spend on their cell phones, the lower their GPA.

6. 6. Using the quadratic curve of best fit, which equation most closely represents the set of data: (-8, 80.4), (-7, 57.8), (-6, 38.6), (-5, 22.8), (3, 18.8), (5, 51.8), (7, 98.4)

   A(y = x^2 + 2x - 5)B(y = x^2 - 3x + 45.2)C(y = 1.7x^2 - 3x + 45)D(y = 1.7x^2 + 2.9x - 5.2)
   Show answer

   Answer: D — (y = 1.7x^2 + 2.9x - 5.2)

7. 7. The table below shows the number of months used and the approximate distance driven for four buses in a school district: 6 months → 10,100 miles 10 months → 17,000 miles 20 months → 43,200 miles 27 months → 59,900 miles Using the line of best fit for these data, which value is the best prediction of the distance driven, in miles, by a bus that has been used for 40 months?

   F68,000G79,100H86,400J91,400
   Show answer

   Answer: G — 79,100

8. 8. Line ℓ has slope 2 and passes through the point (1, 3). Which is one form of the equation of line ℓ?

   A(y = x + 2)B(y = 2x + 1)C(y = 3x + 2)D(y = 2x + 5)
   Show answer

   Answer: B — (y = 2x + 1)

9. 9. What is the solution set for the quadratic equation (x^2 - 4x + 4 = 0)?

   F2G−2H−2, 2J1, 3
   Show answer

   Answer: F — 2

10. 10. What is the solution to the system of equations? 4x - 3y = 10 x + 4y = 7

    A(1, −2)B(−11, 1)C(−1, 2)D(−15, 2)
    Show answer

    Answer: A — (1, −2)

11. 11. What is the slope of the line given by the equation (y = (1)/(3)x - 3)?

    F3G((1)/(3))H((2)/(3))J−3
    Show answer

    Answer: G — ((1)/(3))

12. 12. What are the x-intercepts of the graph of the equation (y = x^2 + 6x - 7)?

    A−7 and −1B−1 and 7C1 and −7D−7 and 1
    Show answer

    Answer: D — −7 and 1

13. 13. What is the solution to the inequality (6(x + 1) > 7)?

    F(x < -(1)/(6))G(x > (1)/(6))H(x > 1)J(x > 6)
    Show answer

    Answer: G — (x > (1)/(6))

14. 14. Andrea has 37 coins, all nickels and dimes. The total value is $3.10. How many dimes does Andrea have?

    A12B19C25D31
    Show answer

    Answer: C — 25

15. 15. What is the slope of the line that passes through (−3, −5) and (4, −2)?

    F((1)/(3))G((3)/(7))H7J0
    Show answer

    Answer: G — ((3)/(7))

16. 16. What is the solution to the system of equations? x + 2y = 5 x - y = -1

    A(x = 3, y = 4)B(x = 1, y = 3)C(x = 1, y = 2)D(x = 3, y = 1)
    Show answer

    Answer: C — (x = 1, y = 2)

17. 17. Jerri solved the equation (17(x + 3) = 6 - 4). Step 1: (17x + 51 = 6 - 4) Which property justifies Step 1?

    FAssociative property of additionGCommutative property of additionHDistributive propertyJAdditive identity property
    Show answer

    Answer: H — Distributive property

18. 18. What value of (m) satisfies the equation (5(m - 5) = 3(m + 1))?

    A14B9C3.5D7.5
    Show answer

    Answer: A — 14

19. 19. Which expression is not equivalent to (3x * 3x * 3x * 3x * 3x * 3x)?

    A(3x^6)B(9^3x^6)C(27^2x^6)D(3^6x^6)
    Show answer

    Answer: A — (3x^6)

20. 20. Which is a factored form of (2x^2 - 6x)?

    F(2(x^2 - 3))G(2x(x - 3))H(2x(1 - 3x))J((2x + 3)(x - 2))
    Show answer

    Answer: G — (2x(x - 3))

21. 21. Written in simplest radical form, (sqrt32) is equal to —

    A(2sqrt4)B(2sqrt16)C(4sqrt2)D(8sqrt2)
    Show answer

    Answer: C — (4sqrt2)

22. 22. If 112 children sign up for a field trip and each vehicle carries (x) children, which expression represents the number of vehicles needed?

    A(112 - x)B(112x)C((112)/(x))D(x - 112)
    Show answer

    Answer: C — ((112)/(x))

23. 23. Which is equivalent to (3a(2a + b))?

    F(6a^2 + b)G(6a^2 + 3ab)H(5a^2 + b)J(5a^2 + 3ab)
    Show answer

    Answer: G — (6a^2 + 3ab)

24. 24. Which expression is equivalent to ((3x^2y)^2)?

    F(3x^5y^5)G(9x^5y^5)H(9x^6y^2)J(27x^2y^2)
    Show answer

    Answer: J — (27x^2y^2)

25. 25. Which is equivalent to ((3x + 1)(4x - 1))?

    A(12x^2 - 1)B(12x^2 - x - 1)C(12x^2 + x - 1)D(12x^2 + 7x - 1)
    Show answer

    Answer: C — (12x^2 + x - 1)

26. 26. Which is a factor of (a^2 - 81)?

    F(a + 3)G(a + 9)H(a + 27)J(a + 81)
    Show answer

    Answer: G — (a + 9)

27. 27. What is the value of the expression (x + y + z) if (x = 4), (y = 2), and (z = 2)?

    A5B9C10D16
    Show answer

    Answer: B — 9

28. 28. The equation (f(x) = n(2x) + 3) defines a function. If (6, 7) is on the graph, what is the value of (n)?

    A((1)/(6))B((1)/(3))C1D2
    Show answer

    Answer: A — ((1)/(6))

29. 29. The number of water bottles used varies directly with temperature. If 75 bottles are used at 60°, what is the temperature when 120 bottles are used?

    F96°G92°H84°J80°
    Show answer

    Answer: F — 96°

30. 30. If (f(2) = 13), which could be the equation for (f(x))?

    A(f(x) = x^2 + 8)B(f(x) = x + x^2)C(f(x) = 2x^3 + 5)D(f(x) = 3x^2 + 1)
    Show answer

    Answer: D — (f(x) = 3x^2 + 1)

31. 31. The points (1, 1), (2, 4), (3, 7), (4, 10), and (5, 13) lie on a linear function. Which could be the function?

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

    Answer: H — (y = 3x - 2)

32. 32. Which is a zero of the function (f(x) = 2x - 6)?

    A−6B−3C2D3
    Show answer

    Answer: D — 3

33. 33. In which set of ordered pairs is (y) a function of (x)?

    F(−3,4), (1,9), (1,4)G(0,5), (0,4), (0,5)H(1,−1), (2,1), (3,−3)J(0,1), (1,−1), (1,0)
    Show answer

    Answer: H — (1,−1), (2,1), (3,−3)

34. 34. If (f(x) = 3x^2 + 2x - 1), what is (f(0))?

    A−1B0C1D2
    Show answer

    Answer: A — −1

35. 35. The depth of a lake varies directly with the amount of rainfall. If (k) is the constant of variation, which equation represents the situation?

    A(d = (k)/(r))B(d = (r)/(k))C(d = k + r)D(d = kr)
    Show answer

    Answer: D — (d = kr)

36. 36. Kayla works four days as a waitress and nanny. Her original hours are: Waitress: (6, 5, 4, 7) Nanny: (4, 4, 6, 3) If she cuts all hours in half, which matrix represents the new schedule?

    A( 3 & 2.5 & 2 & 3.5 2 & 2 & 3 & 1.5 )B( 6 & 5 & 4 & 7 4 & 4 & 6 & 3 )C( 3 & 2.5 & 2 & 3.5 2 & 2 & 3 & 1.5 )D( 4 & 4 & 6 & 3 6 & 5 & 4 & 7 )
    Show answer

    Answer: C — ( 3 & 2.5 & 2 & 3.5 2 & 2 & 3 & 1.5 )

37. 37. An elementary school has 150 boys and 145 girls. If 60% of each group goes on a field trip, which matrix represents the number of students going?

    F( 90 58 )G( 150 145 )H( 60 58 )J( 90 87 )
    Show answer

    Answer: J — ( 90 87 )

38. 38. Consider the procedure used below to solve the equation Given: 3(x − 2) = 17 (1st step) 3x − 6 = 17 (2nd step) 3x = 23 (3rd step) x = 23⁄3 Which of the following properties justifies the 1st step?

    AAssociative property of additionBCommutative property of additionCDistributive propertyDTransitive property of equality
    Show answer

    Answer: C — Distributive property

39. 39. The volume of a rectangular solid is 960 cubic inches. The base of the solid measures 12 inches by 10 inches. What is the height of the solid?

    A4 in.B8 in.C120 in.D840 in.
    Show answer

    Answer: B — 8 in.

40. 40. The equation y = 1⁄2 x represents a straight line. If this line is shifted downward 3 units, which equation represents the new line?

    Ay = 1⁄2 x + 3By = 3⁄2 xCy = 1⁄2 x − 3Dy = 1⁄2 x + 1
    Show answer

    Answer: C — y = 1⁄2 x − 3

41. 41. Which line has a negative slope?

    AThe line that decreases from left to rightBThe line that increases from left to rightCThe horizontal lineDThe vertical line
    Show answer

    Answer: A — The line that decreases from left to right

42. 42. What is the slope of the line y = 2x − 3?

    A3B2C1⁄2D2
    Show answer

    Answer: D — 2

43. 43. The table below shows values of x and y. x: −2, −1, 0, 1, 2 y: −3, −1, 1, 3, 5 Which equation fits the data in the table?

    Ay = x − 2By = 2x + 1Cy = 3x + 3Dy = x + 1
    Show answer

    Answer: B — y = 2x + 1

44. 44. Solve the system of equations: x + y = 5 x − y = 7

    Ax = 6, y = −1Bx = 4, y = 3Cx = 1, y = 6Dx = −1, y = 7
    Show answer

    Answer: A — x = 6, y = −1

45. 45. What is the solution to the inequality −2x + 3 ≤ 7?

    Ax ≤ −5Bx ≤ −2Cx ≥ 2Dx ≤ 3
    Show answer

    Answer: B — x ≤ −2

46. 46. The formula for the surface area of a cylinder is SA = 2πr(h + r). What is the surface area when r = 3 cm and h = 4 cm?

    A28π cm²B32π cm²C36π cm²D42π cm²
    Show answer

    Answer: D — 42π cm²

47. 47. Which is equivalent to (−2ab³)(−3a²b⁵)?

    A−5abB6a²b¹⁵C6a³b²D6a³b⁸
    Show answer

    Answer: D — 6a³b⁸

48. 48. A diagram of algebra tiles represents six x² tiles, nine x tiles, and three unit tiles. Which polynomial is represented?

    A6x² + 12xB2x² + 3x + 1C6x² + 9x + 3D9x² + 6x + 3
    Show answer

    Answer: C — 6x² + 9x + 3

49. 49. If x ≠ 0, which expression is equivalent to (8x⁷ − 2x³) ÷ 2x?

    A6x⁶ − x²B4x⁶ − x²C6x⁷ − x³ + xD4x⁶ − x² + 1
    Show answer

    Answer: D — 4x⁶ − x² + 1

50. 50. When factored completely, x² − 9 equals —

    A(x + 3)(x − 3)B(x + 1)(x − 9)C(x − 3)²D(x + 3)²
    Show answer

    Answer: A — (x + 3)(x − 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.