Algebra 1 SOL Practice Test — Set 4 of 6

Set 4 of 6 — 50 more free Algebra 1 SOL practice questions from official VDOE released tests.

1. 1. A box-and-whisker plot of soccer goals shows minimum 2 and maximum 20. What is the range?

   A24B18C6D4
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   Answer: B — 18

2. 2. Which equation best represents the scatterplot data?

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

3. 3. A repairman estimated that the cost of replacing a part in Mrs. James’s computer would be at most $225. The estimate included $35 for the part, a $40 service charge, and $30 per hour for labor. What is the maximum number of hours the repairman estimated for the job?

   A4B5C6D7
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   Answer: B — 5

4. 4. What is the solution to the equation (4x - 1 = 2 + 5x)?

   F(x = 1)G(x = 2)H(x = 3)J(x = 4)
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   Answer: H — (x = 3)

5. 5. If (f(x) = x^2 + 2x + 3), what is the value of (f(x)) when (x = 6)?

   A51B27C42D60
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   Answer: A — 51

6. 6. The statement “If ((1)/(x) = 5), then (x = 10)” is justified by the —

   Fassociative property of multiplicationGcommutative property of multiplicationHaddition property of equalityJmultiplication property of equality
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   Answer: J — multiplication property of equality

7. 7. What are the x- and y-intercepts of the line with equation (4x + 5y = 40)?

   Ax-intercept 10, y-intercept 8Bx-intercept 8, y-intercept 10Cx-intercept −10, y-intercept −8Dx-intercept −8, y-intercept −10
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   Answer: A — x-intercept 10, y-intercept 8

8. 8. Which is an equation for the line that passes through the origin and has a slope of ((2)/(3))?

   A(y = (3)/(2)x)B(x = (2)/(3)y)C(y = (2)/(3))D(y = (2)/(3)x)
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   Answer: D — (y = (2)/(3)x)

9. 9. What is the slope of the line (y = 4x - 2)?

   F4G2H((1)/(4))J−2
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   Answer: F — 4

10. 10. Which line has a y-intercept of −5 and an x-intercept of 1?

    A(y = 5x - 5)B(y = -5x + 1)C(y = x - 5)D(y = 5x - 1)
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    Answer: D — (y = 5x - 1)

11. 11. The difference in cost between a large bag of chips and a small bag of chips was $0.90. Alicia bought 5 large bags and 3 small bags of chips for her party and spent $17.22. What was the cost of a small bag of chips?

    F$5.74G$2.49H$2.15J$1.59
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    Answer: J — $1.59

12. 12. Which is an equation for the line that passes through the points (3, 0) and (0, 2)?

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

13. 13. What is the solution to the system of equations: (x - 6y = -2) (-4x + 8y = 27)?

    A(8, 7)B(−8, −7)C(7, 8)D(−7, −8)
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    Answer: A — (8, 7)

14. 14. Which is a solution to the equation (x^2 - 12x - 28 = 0)?

    F14G−2H12J−14
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    Answer: F — 14

15. 15. What is the slope of the line through (3, 2) and (−1, −4)?

    A3B2C((2)/(3))D−2
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    Answer: B — 2

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

    F0, 3G−3, 0H3J0
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    Answer: F — 0, 3

17. 17. What is the value of ((4m + 8)/(4m + 4)) when (m = 4)?

    A1B2C((3)/(2))D((4)/(3))
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    Answer: B — 2

18. 18. Joe is 5 years less than one-half the age of the coach. If the coach is (n) years old, which expression describes Joe’s age?

    F((1)/(2)n - 5)G(2n + 5)H((1)/(2)n + 5)J(2n - 5)
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    Answer: F — ((1)/(2)n - 5)

19. 19. Which expression is equivalent to (-4a(3a - 5b))?

    A(-12a^2 + 20ab)B(-12a^2 - 20ab)C(-12a^2 + 20a)D(-12a^2 + 9ab)
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    Answer: A — (-12a^2 + 20ab)

20. 20. Which is equivalent to ((2a + 3b - 2c) + (8a - 4b - c) + (a - 5b + 4c))?

    F(5a - 6b + c)G(6a - 6b - c)H(6a - 6b + c)J(6a^2 - 6b^2 + c)
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    Answer: H — (6a - 6b + c)

21. 21. Which expression represents ((x + 2)(x + 3))?

    A(x^2 + 5x + 6)B(x^2 + 6x + 5)C(x^2 + x + 6)D(x^2 + 2x + 3)
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    Answer: A — (x^2 + 5x + 6)

22. 22. Which is equivalent to ((x - 3)(2x - 3))?

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

23. 23. When simplified, ((2x^4y^2)^2) equals —

    F(4x^8y^4)G(8x^8y^4)H(16x^4y^2)J(4x^8y^4)
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    Answer: J — (4x^8y^4)

24. 24. What are factors of (2x^2 + 9x + 9)?

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

25. 25. Which is equivalent to (x^2 - 81y^2)?

    F((x + 8y)(x - 27y))G((x - 9y)(x - 9y))H((x + 9y)(x - 9y))J((x - 8y)(x + 27y))
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    Answer: H — ((x + 9y)(x - 9y))

26. 26. What is the greatest common monomial factor of (16x^3y^2 + 6x^2y + 9x^2 + 12x)?

    A(xy^2)B(3x^2y)C(3x)D3
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    Answer: C — (3x)

27. 27. The following ordered pairs follow a linear pattern: (95, 182), (96, 180), (97, 176), (98, 172). What is the missing y-value when x = 99?

    A168B170C174D176
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    Answer: A — 168

28. 28. A club has the following data relating members (g) to boxes of cookies sold (b): (5, 350), (10, 650), (15, 950), (20, 1250). Which equation could be used to predict the number of boxes sold?

    F(b = 60g)G(b = 70g)H(b = 60g + 50)J(b = 50g + 50)
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    Answer: H — (b = 60g + 50)

29. 29. Which equation represents a direct variation?

    F(y = (8)/(x))G(y = 8x)H(y = 8x + 4)J(y = 8x - 1)
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    Answer: G — (y = 8x)

30. 30. What is the range of the function (f(x) = x^2 - 2) when the domain is 2, 4, 6?

    A8, 12, 16B0, 1, 2C2, 14, 34D−1, 0, 1
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    Answer: C — 2, 14, 34

31. 31. Which is a zero of (f(x) = x^2 - 15x + 54)?

    F3G5H9J15
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    Answer: H — 9

32. 32. If (f(a) = 7(a - 2) + 4a + 4), what is (f(2))?

    A2B10C11D12
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    Answer: D — 12

33. 33. The cost of fabric varies directly with the amount purchased. If 15 yards cost $10.00, how much would 45 yards cost?

    F$45G$30H$24J$14
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    Answer: G — $30

34. 34. If (m) varies directly as (p), and (m = 5) when (p = 7), what is the constant of variation?

    A35B((12)/(7))C((5)/(7))D7
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    Answer: D — 7

35. 35. The miles per gallon (m) of an experimental car is given by (m = 75 - 0.3s), where (s) is speed in miles per hour. What is the car’s miles per gallon when its speed is 100 miles per hour?

    F10 mpgG30 mpgH45 mpgJ50 mpg
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    Answer: H — 45 mpg

36. 36. Given a table relating year of birth (x) and life expectancy (y), which equation best estimates life expectancy?

    F(y = 0.45x + 919)G(y = 0.45x - 819)H(y = 0.40x + 893)J(y = 0.40x - 716)
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    Answer: J — (y = 0.40x - 716)

37. 37. Two softball teams sold the following numbers of boxes of cookies: Hawks: 14, 17, 32, 37, 67 Tigers: 28, 37, 24, 27, 18 What is the difference in the mean number of cookies sold by the two teams?

    A2.5B4.5C6D14
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    Answer: A — 2.5

38. 38. Travis would like to buy some toys to donate to charity. He plans to buy 9 dolls at d dollars each, 2 toy cars at c dollars each, and 3 train sets at f dollars each. Which expression represents the total cost, in dollars, of these items that Travis wants to buy?

    A9c + 2f + 3dB9d − 2c − 3fC9d + 2c + 3fD9c − 2f − 3d
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    Answer: C — 9d + 2c + 3f

39. 39. Which expression is equivalent to ((18c^8 d^8)/(9c^6 d^6))? Assume the denominator is not equal to zero.

    A(2c^2 d^2)B(9c^3 d^3)C(c^2 d^2)D(9c d)
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    Answer: A — (2c^2 d^2)

40. 40. Identify each expression that is a factor of the polynomial (4x^2 - 2x - 2). Select all that apply.

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

41. 41. What is (sqrt18) written in simplest radical form?

    A((2)/(3))B((3)/(2))C( 3sqrt2)D(3sqrt2)
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    Answer: D — (3sqrt2)

42. 42. Which binomial is a factor of (c^2 - 12c + 32)?

    A(c - 12)B(c - 8)C(c - 2)D(c - 1)
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    Answer: B — (c - 8)

43. 43. What is the value of the expression (7x^4 + 3x - 2) when (x = 0)?

    A−2B0C1D−2
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    Answer: A — −2

44. 44. Which expression is equivalent to ((3x^7)(5x^7))?

    A(30x^14)B(30x^7)C(15x^49)D(45x^14)
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    Answer: A — (30x^14)

45. 45. Which polynomial is equivalent to ((18n^2 - 9n + 1) (3n - 1))? Assume the divisor is not equal to zero.

    A(6n - 1)B(6n + 1)C(6n^2 - 3)D(18n^2 - 3)
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    Answer: A — (6n - 1)

46. 46. When (n > 0), which expression is equivalent to (sqrt42n^9) in simplest form?

    A(sqrt42)B(nsqrt42n)C(6n^4sqrt7)D(6n^4sqrt7n)
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    Answer: C — (6n^4sqrt7)

47. 47. Look at the system of equations: (y = -x + 2) (7x + 4y = -1) What is the value of (x) for the solution to this system of equations?

    A−5B−3C3D5
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    Answer: B — −3

48. 48. Pierre solved an inequality as shown: Step 1: (-8 > 2n + 3) Step 2: (-8 + (-3) > 2n + 3 + (-3)) Step 3: (-11 > 2n) Step 4: (-11 > n) What property justifies the work between Step 3 and Step 4?

    AInverse property of additionBIdentity property of additionCAddition property of inequalityDCommutative property of addition
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    Answer: C — Addition property of inequality

49. 49. Which property of real numbers justifies the work shown? (13x - 1 = (12x + 15) + 7x) (13x - 1 = 7x + (12x + 15))

    ACommutative property of additionBAssociative property of additionCIdentity property of additionDDistributive property
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    Answer: A — Commutative property of addition

50. 50. Which inequality represents all the solutions of (9(4x - 8) < 4(6x + 9))?

    A(x < -3)B(x > 7)C(x < 9)D(x > 9)
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    Answer: C — (x < 9)

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.