Algebra 1 SOL Practice Test — Set 1 of 6

348 free Algebra 1 Virginia SOL practice questions drawn from official Virginia Department of Education released tests. Pick an answer to check it instantly, or open “Show answer” to review. No signup required.

1. 1. If ( (t - 6)/(3) = 15 ), what is the value of ( t )?

   A21B27C53D63
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   Answer: D — 63

2. 2. What is the solution to the following system of linear equations? 4x - y = -6 x - 2y = -5

   F(−1, 2)G(0, 6)H(1, 2)J(2, −1)
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   Answer: F — (−1, 2)

3. 3. What is the solution set for the equation ( (x+5)(x+3)=0 )?

   A0, 8B3, 5C−2, 8D−5, −3
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   Answer: D — −5, −3

4. 4. What is the slope of the line that passes through the points (5, 0) and (10, 0)?

   F0G1H5JUndefined
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   Answer: F — 0

5. 5. Which is the solution to the system of equations? x - y = 7 2x + y = -1

   A(x=-5, y=2)B(x=-2, y=5)C(x=-1, y=-7)D(x=2, y=-5)
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   Answer: D — (x=2, y=-5)

6. 6. A line is shown that passes through the point (0,5) and is horizontal, remaining at y = 5 for all x-values. Which is most likely the equation of the line?

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

7. 7. A line passes through the y-intercept (0,2) and decreases so that when x increases by 2, y decreases by 1. Which could be an equation for the line?

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

8. 8. Which is an equation for the line with slope ( (1)/(2) ) and y-intercept of 3?

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

9. 9. Which property justifies rewriting (3x-5x) as ((3-5)x)?

   AAssociative property of multiplicationBDistributive propertyCCommutative property of multiplicationDAssociative property of addition
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   Answer: B — Distributive property

10. 10. Which graph best represents a line with an undefined slope? A vertical line where x is constant for all y-values.

    FVertical lineGHorizontal lineHLine with positive slopeJLine with negative slope
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    Answer: F — Vertical line

11. 11. What is the solution to the system of equations? y=4x+2 y=x-1

    A(x=-1,y=2)B(x=-1,y=-2)C(x=1,y=-2)D(x=1,y=2)
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    Answer: B — (x=-1,y=-2)

12. 12. While solving an equation, Lenny rewrote ((2x+1)+5=9) as (2x+(1+5)=9). What property of real numbers guarantees the equations are equivalent?

    FAssociative property of additionGAdditive inverse propertyHCommutative property of additionJDistributive property
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    Answer: F — Associative property of addition

13. 13. What is the solution to the equation (5(x+2)=7(4-x))?

    A−9.0B1.5C3.2D9.0
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    Answer: B — 1.5

14. 14. What are the x-intercepts of the graph of (y=x^2+5x+4)?

    F−4 and −1G−2 and 3H−1 and 1J−1 and 2
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    Answer: F — −4 and −1

15. 15. What values of x make the inequality ( -3(x+1) 15 ) true?

    A(x 6)B(x 6)C(x>=-6)D(x<=-6)
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    Answer: C — (x>=-6)

16. 16. The profit equation for a manufacturing firm is (P=x^2-2500). For what number of units sold does the company break even?

    F50G100H500J1,250
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    Answer: F — 50

17. 17. What is the value of ( (4x-5y)/(2y) ) if (x=-6) and (y=2)?

    A−26.5B−8.5C−3.5D−0.5
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    Answer: B — −8.5

18. 18. The expression ( sqrt175 ) is in simplest radical form of which number?

    F1,225G245H175J35
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    Answer: H — 175

19. 19. A shaded region is formed by a rectangle of area (x^2) with a smaller rectangle of area (6) removed. Which expression represents the shaded area?

    A(4x-10)B(x^2-6)C(x^2-5x+6)D(x^2+5x-6)
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    Answer: B — (x^2-6)

20. 20. Which is a factored form of (5x^2-20x)?

    F(5(x^2-4))G(5(x-2)^2)H(5x(x-4))J((5x-4)(x+5))
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    Answer: H — (5x(x-4))

21. 21. Which binomial is a factor of (2x^2+x-1)?

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

22. 22. Which polynomial is equivalent to ((2x^2-5x+6)+(5x^2-3x+4))?

    F(7x^2-8x+10)G(7x^2-2x+10)H(7x^2-8x+2)J(7x^2-2x+2)
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    Answer: F — (7x^2-8x+10)

23. 23. What is ( sqrt180 ) written in simplest radical form?

    A(5 6)B(4sqrt45)C(6 5)D(6sqrt30)
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    Answer: C — (6 5)

24. 24. What is the value of (3x+4y) if (x= 13) and (y= 12)?

    F17G3H2J1
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    Answer: G — 3

25. 25. Which is a simplified form of ((4xy^3)(xy^4))?

    A(x^2y^7)B(x^4y^12)C(x^5y^7)D(x^5y^12)
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    Answer: C — (x^5y^7)

26. 26. Which is equivalent to (2.3 10^4-6.5 10^3)?

    F−42G165H1,650J16,500
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    Answer: J — 16,500

27. 27. What is the value of ( (mn)/(r^2) ) if (m=7), (n=18), and (r=6)?

    A3.5B10.5C21D63
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    Answer: A — 3.5

28. 28. When factored completely, (x^2-9) equals

    F((x+3)^2)G((x-3)^2)H((x+1)(x-9))J((x+3)(x-3))
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    Answer: J — ((x+3)(x-3))

29. 29. For objects made of the same material, weight varies directly with volume. If a volume of 20 cubic inches weighs 28 ounces, what is the constant of variation?

    A( 57 )B( 75 )C20D28
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    Answer: B — ( 75 )

30. 30. What is the range of (f(x)=x^2-3) when the domain is 1, 3, 5?

    F−2, 22G−2, 0, 2H−2, 6, 22J2, 4, 6
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    Answer: H — −2, 6, 22

31. 31. Which is a zero of (f(x)=x^2-x-12)?

    F1G2H3J4
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    Answer: J — 4

32. 32. In which set of ordered pairs is y not a function of x?

    A(1,4),(2,4),(3,4),(4,4)B(2,0),(4,1),(6,2),(8,3)C(11,2),(12,4),(13,6)D(-6,37),(-6,10),(-5,26)
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    Answer: D — (-6,37),(-6,10),(-5,26)

33. 33. If (f(x)=8x+6), what is (f(-1))?

    F−14G−2H2J14
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    Answer: G — −2

34. 34. If (f(x)=5x-2), what is (f(3))?

    F0G8H13J15
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    Answer: H — 13

35. 35. Which is a zero of (f(x)=5x-20)?

    A−20B0C4D5
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    Answer: C — 4

36. 36. The ordered pairs of a function are (−4,1), (−2,0), and (8,−1). What is the range?

    F−1,1G−1,0,1H−4,−2,8J−4,−2,−1,0,1,8
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    Answer: G — −1,0,1

37. 37. A table shows brochure orders: 100 → 49, 500 → 45, 1000 → 40, 2000 → 30 (prices in cents). Which equation best represents this relationship?

    A(P=-(1)/(100)n+50)B(P=(1)/(10)n+39)C(P=-(1)/(10)n+59)D(P=(1)/(100)n+48)
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    Answer: A — (P=-(1)/(100)n+50)

38. 38. Distance varies directly with time. If 240 miles are traveled in 8 hours, what is the constant speed?

    F1,920 mphG232 mphH30 mphJ( (1)/(30) ) mph
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    Answer: H — 30 mph

39. 39. If the mean of 12 numbers is 13, what is the sum of the numbers?

    A25B144C156D169
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    Answer: C — 156

40. 40. Phone call times (minutes): 9, 15, 5, 7, 9, 12, 11, 4. Which statement is true?

    FThe mode is greater than 7.GThe mean is less than 8.HThe range is less than 10.JThe median is greater than 10.
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    Answer: F — The mode is greater than 7.

41. 41. Clothing purchases and tax charged are shown: (35,3.15), (40,3.60), (22,1.98), (68,6.12), (74,6.66), (31,2.79). Which equation best fits the data?

    A(t=0.09c+2.89)B(t=0.91c)C(t=0.09c)D(t=1.09c)
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    Answer: C — (t=0.09c)

42. 42. Builders constructed the following numbers of homes: 51, 25, 12, 10, 43, 50, 41, 39, 25. Which statement is true?

    FThe range is less than the mean.GThe mode is greater than the mean.HThe mode is greater than the median.JThe median is greater than the mean.
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    Answer: J — The median is greater than the mean.

43. 43. Given (P= 10&2515&3020&35 ), (Q= 40&7050&8060&90 ), what is (Q-P)?

    F( 30&6020&6525&70 )G( 30&4535&5040&55 )H( 50&9565&11080&125 )J( -30&-45-35&-50-40&-55 )
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    Answer: G — ( 30&4535&5040&55 )

44. 44. Given (M= 3&2 ) and (N= -14 ), which matrix equals (M+N)?

    A( 2&6 )B( 26 )C( 2&-38&6 )DM and N cannot be added.
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    Answer: D — M and N cannot be added.

45. 45. A graph shows profit increasing linearly with bags of popcorn sold. Profit reaches about $70 at 140 bags. Approximately how many bags must be sold to earn $200 profit?

    F250G300H350J400
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    Answer: J — 400

46. 46. What is the value of the expression 5sqrta - csqrtb + b^9 when (a = 8), (b = 16), and (c = -4)?

    A30B35C50D51
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    Answer: D — 51

47. 47. What is the quotient of ((15x^2 - 8x - 12)) and ((3x + 2))? Assume the denominator is not equal to zero.

    F(45x^2 + 6x^2 - 52x - 24)G(15x^2 - 5x - 10)H(5x + 6)J(5x - 6)
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    Answer: J — (5x - 6)

48. 48. Which represents the following expression in simplest form? (15(x^2)^3)/(3(x^4)^3)

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

49. 49. For which value of (x) does ((3)/(x)) simplify to ((5)/(7))?

    F35G245H875J1715
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    Answer: F — 35

50. 50. What is (sqrt13,456) in simplest radical form?

    A(2sqrt12)B(6sqrt16)C(12sqrt2)D116
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    Answer: D — 116

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.