Algebra 1 SOL Practice Test — Set 5 of 6

Set 5 of 6 — 50 more free Algebra 1 SOL practice questions from official VDOE released tests.

1. 1. A total of 243 adults and children are at a movie theater. There are 109 more adults than children. If (a) represents the number of adults and (b) represents the number of children, which system of equations could be used?

   A(a + b = 243), (a = 109b)B(a + b = 243), (b = 109a)C(a + b = 243), (a = b + 109)D(a + b = 243), (b = a + 109)
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   Answer: C — (a + b = 243), (a = b + 109)

2. 2. The formula (A = P + Prt) represents the amount of money in a savings account. Which equation is correctly solved for (r)?

   A(r = (A)/(Pt))B(r = (A - 2P)/(t))C(r = (A)/(2Pt))D(r = (A - P)/(Pt))
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   Answer: D — (r = (A - P)/(Pt))

3. 3. What are the real roots of (x^2 - 7x + 10 = 0)?

   A2 and 5B1 and 10C−1 and −10D−2 and −5
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   Answer: A — 2 and 5

4. 4. A data set has an even number of data points. The median is given by (m = (x_1 + x_2)/(2)). Which equation shows this formula solved for (x_2)?

   A(x_2 = 2m - x_1)B(x_2 = (m)/(x_1))C(x_2 = 2m - 2x_1)D(x_2 = m - 2x_1)
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   Answer: A — (x_2 = 2m - x_1)

5. 5. Which equation represents the horizontal line passing through ((7, 5))?

   A(x = 5)B(y = 5)C(x = 7)D(y = 7)
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   Answer: B — (y = 5)

6. 6. What value of (p) will make this equation true? ((6p + 4)/(6) = (4p - 8)/(3))

   A−10B−6C2D10
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   Answer: D — 10

7. 7. The length of a rectangle is 3 times its width. The perimeter is greater than 48 centimeters. Which inequality represents all possible lengths (l)?

   A(l > 6)B(l > 12)C(l > 18)D(l > 36)
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   Answer: C — (l > 18)

8. 8. This relation is an inverse variation: ((-1, 8), (4, -2), (-2, 4)) Which equation represents this relation?

   A(y = 7x + 5)B(y = 7x)C(y = -(8)/(x))D(y = -2x)
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   Answer: C — (y = -(8)/(x))

9. 9. Two relationships are described. Relationship S: 160 miles in 4 hours; 80 miles in 2 hours. Relationship T: 6 hamburgers in 10 minutes; 9 hamburgers in 15 minutes. Which statement is true?

   ANeither is a direct variationBBoth are direct variationsCOnly Relationship S is a direct variationDOnly Relationship T is a direct variation
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   Answer: B — Both are direct variations

10. 10. What is (f(-8)) for the function (f(x) = (11(x - 24))/(5))?

    A−56B−88C−176D−352
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    Answer: C — −176

11. 11. The manager compared two weeks of work hours. Week 1 had a standard deviation of 1.5 hours; Week 2 had a standard deviation of 2.0 hours. The conclusion that Week 2 has more variation is —

    AValid because the mean is greaterBValid because the standard deviation is greaterCInvalid because the mean is smallerDInvalid because the standard deviation is smaller
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    Answer: B — Valid because the standard deviation is greater

12. 12. A scientist dropped an object from 200 feet and recorded heights at 0.5-second intervals. Based on a quadratic model, which best approximates the height at 3 seconds?

    A52 feetB55 feetC65 feetD80 feet
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    Answer: A — 52 feet

13. 13. Look at the function (g(x) = 9x^2 - 16). Which set contains only the zeros of (g)?

    A(-4, 4)B(-4, 0, 4)C-16, 9D-16, 0, 9
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    Answer: A — (-4, 4)

14. 14. The mean of a data set is 18.1, and the z-score for 13.0 is −1.7. What is the standard deviation?

    A1.7B3.0C3.4D5.1
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    Answer: B — 3.0

15. 15. A function is defined by (f(x) = -4x + 2). What are the x-intercept and y-intercept?

    Ax-intercept ((0, -2)); y-intercept ((0, 0))Bx-intercept ((0, 2)); y-intercept ((0, 0))Cx-intercept (((1)/(2), 0)); y-intercept ((0, -2))Dx-intercept (((1)/(2), 0)); y-intercept ((0, 2))
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    Answer: D — x-intercept (((1)/(2), 0)); y-intercept ((0, 2))

16. 16. What value of (x) will make the equation (3(x+15) - 6x = -6(x-3)) true?

    A−9B−6C2D3
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    Answer: A — −9

17. 17. Which describes the graph of (g(x) = -3x + 5)?

    FA line with a slope of −3 and a y-intercept of −5GA line with a slope of −3 and a y-intercept of 5HA line with a slope of 3 and a y-intercept of −5JA line with a slope of 3 and a y-intercept of 5
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    Answer: G — A line with a slope of −3 and a y-intercept of 5

18. 18. Which ordered pair represents the solution to the system of equations? 2x - 7y = 0 x - 6y = -5

    F(7, 2)G(2, 7)H(1, 1)J(−11, −1)
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    Answer: F — (7, 2)

19. 19. What is the solution to the inequality (3(x-3) <= 3)?

    A(x <= 2)B(x >= 2)C(x <= 4)D(x >= 4)
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    Answer: C — (x <= 4)

20. 20. Which quadratic equation has solutions of 5 and 7?

    A(x^2 - 5x = 0)B(x^2 - 2x - 35 = 0)C(x^2 - 3x - 28 = 0)D(x^2 - 12x + 35 = 0)
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    Answer: D — (x^2 - 12x + 35 = 0)

21. 21. Which is an example of the distributive property?

    F(10 + 5x = 5x + 10)G(5(x + 2) = 5x + 10)H(5x + 10 = 5x + 10)J((5 + 10)x = x(5 + 10))
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    Answer: G — (5(x + 2) = 5x + 10)

22. 22. A school play cost $1,200 to produce. Tickets sold for $5 each. The profit (p), in dollars, made by selling (x) tickets is given by (p = 5x - 1,200). What is the slope of the line representing this equation?

    F−1,200G−240H1J5
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    Answer: J — 5

23. 23. Which of the following is a solution to (2x^2 + 2x - 12 = 0)?

    A−12B−3C−2D0
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    Answer: B — −3

24. 24. Which is an equation for the line that contains the point (1, 2) and has a slope of 4?

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

25. 25. Which inequality is equivalent to (4x - 2y <= 8)?

    A(y <= 2x - 4)B(y >= 2x - 4)C(y <= -2x - 4)D(y >= -2x - 4)
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    Answer: B — (y >= 2x - 4)

26. 26. What is the slope of the line that passes through (−2, 5) and (3, 9)?

    F(-(5)/(4))G(-(4)/(5))H((5)/(5))J((4)/(5))
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    Answer: H — ((5)/(5))

27. 27. In addition to an $80 bonus, Joan earned $8 per hour working last week. Her total earnings were $240. How many hours did she work?

    A10B20C30D40
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    Answer: B — 20

28. 28. Tommie paid $17.50 for 6 youth tickets and 1 adult ticket. Susan paid $22.50 for 3 youth tickets and 3 adult tickets. What was the price of an adult ticket?

    F$2.00G$2.90H$5.50J$7.50
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    Answer: H — $5.50

29. 29. What is the value of ((6x - 3y)/(xy)) when (x = 6) and (y = -4)?

    A−2B−1C2D3
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    Answer: A — −2

30. 30. Which equals ((2.3 * 10^3)(3.6 * 10^3))?

    F(8.28 * 10^9)G(8.28 * 10^6)H(5.90 * 10^9)J(5.90 * 10^6)
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    Answer: G — (8.28 * 10^6)

31. 31. Which expression is equivalent to ((4x^2 - 3x + 9) + (7x^2 - 11) + (-x^2 + 7x - 2))?

    A(10x^2 + 4x - 4)B(10x^2 - 10x - 22)C(10x^6 + 4x^2 - 4)D(11x^2 + 4x + 4)
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    Answer: A — (10x^2 + 4x - 4)

32. 32. In simplest radical form, (sqrt845) is equal to —

    F(13)G(13sqrt2)H(13sqrt3)J(13sqrt5)
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    Answer: J — (13sqrt5)

33. 33. Which polynomial is equivalent to ((8x^3 + 12x)/(2x)), where (x 0)?

    A(4x^2 + 6)B(4x^2 + 6x)C(4x^2 + 12x)D(4x^4 + 6x^2)
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    Answer: A — (4x^2 + 6)

34. 34. What is the complete factorization of (x^2 - 5x - 14)?

    F((x - 2)(x + 7))G((x + 2)(x - 7))H((x - 1)(x + 14))J((x + 1)(x - 14))
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    Answer: G — ((x + 2)(x - 7))

35. 35. Which statement could be represented by the expression (n^2 + 4n)?

    AThe square of a number increased by fourBThe square of the product of a number and fourCThe sum of two times a number and four times a numberDThe square of a number increased by four times the number
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    Answer: D — The square of a number increased by four times the number

36. 36. Which expression is equivalent to (4x(2x^2 - x - 3))?

    F(6x^2 - 5x - 7)G(6x^3 - 5x^2 + 7x)H(8x^2 - 4x + 12)J(8x^3 - 4x^2 - 12x)
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    Answer: J — (8x^3 - 4x^2 - 12x)

37. 37. A computer chip has two pins. One pin is (4.0 * 10^-3) inches long, and the other is (2.5 * 10^-3) inches long. What is the difference in their lengths?

    F(6.5 * 10^9) in.G(6.5 * 10^-3) in.H(1.5 * 10^-3) in.J(1.5 * 10^-6) in.
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    Answer: H — (1.5 * 10^-3) in.

38. 38. Which represents the complete factorization of (3v^2 + 9v)?

    A(v(3v + 9))B(3(v^2 + 3v))C(3v(v + 3))D(3v^2(1 + 3v))
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    Answer: C — (3v(v + 3))

39. 39. Lincoln High School earned $5,100 in ticket sales. Each ticket cost $12. Let (t) represent the number of tickets sold. Which equation could be used to determine (t)?

    F(12 = 5,100t)G(12t = 5,100)H(t = 5,100 - 12)J(t = 5,10012)
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    Answer: G — (12t = 5,100)

40. 40. The function (f(x) = 35 + 15x) represents the amount of money, in dollars, Mr. Lewis earns for working (x) hours. How much does he earn for 25 hours?

    A$75B$375C$410D$1,250
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    Answer: C — $410

41. 41. The table shows the relationship between time and distance traveled: 2 hours → 90 miles 3 hours → 135 miles 4 hours → 180 miles 5 hours → 225 miles Which equation represents the relationship between time (t) (hours) and distance (d) (miles)?

    F(d = t + 45)G(d = 45t)H(t = 45d)J(t = (45)/(d))
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    Answer: G — (d = 45t)

42. 42. What is the domain of the relation shown in the table? (−5, −23) (−2, −14) (0, −8) (3, 1) (6, 10)

    A(-5, -2, 0, 3, 6)B(-23, -14, -8, 1, 10)C(-23, -14, -8, -5, -2, 0, 1, 3, 6, 10)D(−5, −23), (−2, −14), (0, −8), (3, 1), (6, 10)
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    Answer: A — (-5, -2, 0, 3, 6)

43. 43. Which of the following sets of ordered pairs is a function?

    A(3, 4), (2, 3), (3, −2), (4, 1)B(2, 5), (−1, 9), (6, 3), (−1, −2)C(1, 3), (−2, 5), (4, 5), (3, −2)D(5, 6), (−2, 3), (10, 1), (−2, −9)
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    Answer: C — (1, 3), (−2, 5), (4, 5), (3, −2)

44. 44. What is (g(2)) for (g(x) = (1)/(2)x^3 + 2x)?

    F5G7H8J12
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    Answer: H — 8

45. 45. What are the range values of the function (f(x) = -3x^2 + 5) for the domain values (-2, 0, 1)?

    A-31, −4, 5B-7, 2, 5C5, 8, 17D5, 14, 41
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    Answer: B — -7, 2, 5

46. 46. The table shows the cost of a 12-inch pizza based on the number of toppings: 0 toppings: $15.50 1 topping: $17.35 2 toppings: $19.20 3 toppings: $21.05 4 toppings: $22.90 Which equation gives (C), the cost of a pizza with (t) toppings?

    A(C = 1.85t)B(C = 17.35t)C(C = 15.50 + 1.85t)D(C = 22.90 - 1.85t)
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    Answer: C — (C = 15.50 + 1.85t)

47. 47. The table shows high temperatures (°F) for four Virginia cities over one week in March: Arlington: 52, 70, 74, 66, 56, 50, 63 Norfolk: 52, 71, 75, 70, 53, 70, 73 Roanoke: 63, 70, 65, 57, 59, 48, 54 Virginia Beach: 50, 73, 78, 68, 55, 71, 72 Which city had the greatest mean high temperature?

    FArlingtonGNorfolkHRoanokeJVirginia Beach
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    Answer: J — Virginia Beach

48. 48. Which equation most closely represents the line of best fit for the data? (1,4), (2,6), (3,7), (4,9), (5,10), (6,10)

    A(y = -(5)/(4)x + 3)B(y = -(4)/(5)x + 3)C(y = (4)/(5)x + 3)D(y = (5)/(4)x + 3)
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    Answer: D — (y = (5)/(4)x + 3)

49. 49. What is 5 & -3 2 & 6 2 & 6 -2 & 4 3 & -2 4 & -4?

    A( 3 & 1 5 & 4 6 & 2 )B( 7 & -7 -1 & 8 -2 & 10 )C( 7 & 1 -1 & 4 -2 & 2 )D( 10 & 12 -6 & 12 -8 & 24 )
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    Answer: B — ( 7 & -7 -1 & 8 -2 & 10 )

50. 50. Jake earned $40, $80, $38, $40, $32, and $65 over six weeks. He then earned $25 in a seventh week. How were the mean and median affected?

    AThe mean decreased and the median remained the same.BThe median decreased and the mean remained the same.CThe median and the mean both remained the same.DThe mean and the median both decreased.
    Show answer

    Answer: A — The mean decreased and the median remained the same.

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.