Algebra 1 SOL Practice Test — Set 6 of 6

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

1. 1. A sports league charges $60 per person. The table shows registrations by age group: Ages 7–8: Soccer 350, Football 280 Ages 9–10: Soccer 320, Football 165 Ages 11–14: Soccer 180, Football 120 Which product represents the registration fees paid for soccer and football by age range?

   F(60 280165120 )G(60 350320180 )H(60 7 –89 –1011 –14 )J(60 350 & 280320 & 165180 & 120 )
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   Answer: J — (60 350 & 280320 & 165180 & 120 )

2. 2. Ron paid $75.00 for 5 compact disks and a case. If the price of each compact disk was $12.60, what was the price of the case?

   A$12.00B$12.50C$15.00D$63.00
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   Answer: A — $12.00

3. 3. What is the solution to (4(2x-3)-2(3x+1))?

   F5G1H7J10
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   Answer: H — 7

4. 4. What is the solution to (8-2x=-4)?

   A(x=-6)B(x=-2)C(x=2)D(x=6)
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   Answer: D — (x=6)

5. 5. What property makes the equation (6a^2-2a=2a(3a-1)) true?

   AThe reflexive propertyBThe associative propertyCThe commutative propertyDThe distributive property
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   Answer: D — The distributive property

6. 6. What is the y-intercept of (4x+8y=12)?

   A3B(-(3)/(2))C((3)/(2))D4
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   Answer: B — (-(3)/(2))

7. 7. What is the slope of the line through ((1,1)) and ((4,-1))?

   F5G(-2)H(-(2)/(3))J((2)/(3))
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   Answer: H — (-(2)/(3))

8. 8. What is the slope of the line (3y=4x+5)?

   A4B2C((3)/(4))D((4)/(3))
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   Answer: D — ((4)/(3))

9. 9. Which is an equation for the line with a y-intercept of 4 and a slope of ((1)/(3))?

   F(y=(1)/(3)x+4)G(y=2x)H(y=-5)J(x=0)
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   Answer: F — (y=(1)/(3)x+4)

10. 10. Which is an equation for the line that contains ((3,4)) and the origin?

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

11. 11. Which is the solution to the system of equations (3x+y=11) (y=x+3)?

    F(4, 7)G(2, 17)H(2, 5)J( ((1)/(2),(3)/(2) ))
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    Answer: H — (2, 5)

12. 12. Mrs. Crews bought 4 pencils and 3 pens for $5.60. Miss Houston bought 2 pencils and 3 pens of the same kind for $4.60. What was the price of each pencil and each pen?

    A$1.70 per pencil, $0.20 per penB$0.50 per pencil, $1.20 per penC$0.17 per pencil, $1.64 per penD$0.80 per pencil, $0.80 per pen
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    Answer: B — $0.50 per pencil, $1.20 per pen

13. 13. The perimeter of a rectangular playing field is 244 feet. If its length is 2 feet longer than twice its width, what are the dimensions of the field?

    F20 ft by 41 ftG21 ft by 40 ftH40 ft by 82 ftJ42 ft by 80 ft
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    Answer: H — 40 ft by 82 ft

14. 14. What are the solutions to (x^2-12=0)?

    A(x=-4) or (x=4)B(x=-12) or (x=9)C(x=-3) or (x=3)D(x=3) or (x=9)
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    Answer: A — (x=-4) or (x=4)

15. 15. Which is the solution set for (x^2-5x-14=0)?

    F(-7,2)G(7,-2)H(-2,7)J(2,7)
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    Answer: H — (-2,7)

16. 16. If (z 0), (24y^2z^3 6z =)

    A(18y^2z^2)B(16y^2z^2)C(4yz^3)D(4y^2z^2)
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    Answer: D — (4y^2z^2)

17. 17. ((3xy)(5x^2+2xy+3y^2)) is equivalent to —

    F(15x^3y+6x^2y^2+9xy^3)G(15x^3y+2xy+3y^2)H(15x^2y+6x^2y^2+9xy^2)J(15x^2+5xy+3y^2)
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    Answer: F — (15x^3y+6x^2y^2+9xy^3)

18. 18. What is the perimeter of a triangle with side lengths (7x+9), (8x+9), and (5x+1)?

    A(7x+9)B(8x+9)C(8x^3+9)D(10x^3+9)
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    Answer: B — (8x+9)

19. 19. (3.81 10^-4) may be written as —

    F0.0000381G0.000381H3,810J38,100
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    Answer: G — 0.000381

20. 20. Which is equivalent to (p^6p^2)?

    A(p^8)B(2p^8)C(p^10)D(p^12)
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    Answer: A — (p^8)

21. 21. If (y 0), which expression is equivalent to ((xy^2)/(y^4))?

    F((x)/(y^2))G((x^7)/(y^2))H((6x)/(y^8))J((y^2)/(x))
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    Answer: F — ((x)/(y^2))

22. 22. A board supports stairs with horizontal length 18 ft and vertical height 12 ft. The board length is (c). Using (c=sqrt12^2+18^2), what is (c) to the nearest tenth?

    A36.0 ftB30.0 ftC21.6 ftD13.4 ft
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    Answer: C — 21.6 ft

23. 23. When completely factored, (x^2-7x+10) equals —

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

24. 24. When (5x^2-5) is completely factored, which is one of its factors?

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

25. 25. Which is the simplest radical form of (sqrt52)?

    F(13sqrt2)G(sqrt52)H(4sqrt13)J(2sqrt13)
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    Answer: J — (2sqrt13)

26. 26. What is the value of (a(3-b)) if (a=2) and (b=5)?

    A(-4)B0C5D16
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    Answer: A — (-4)

27. 27. The base of a triangle is 3 units more than its height (h). Which expression represents its area?

    F(h(h+3))G((1)/(2)h(h+3))H(h(h-3))J((1)/(2)h(h-3))
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    Answer: G — ((1)/(2)h(h+3))

28. 28. Trina’s paycheck earnings (p) vary directly as the number of hours (h). If she works 19 hours and earns $187.15, what should she earn for 40 hours?

    A$394.00B$443.25C$472.80D$512.20
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    Answer: A — $394.00

29. 29. Given (f(x)=x^2-5), what is the output when the input is 2?

    F6G9H14J46
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    Answer: G — 9

30. 30. The ordered pairs are of the form ((x,y)). In which set is (y) a function of (x)?

    A((1,3),(2,6),(3,1),(6,3))B((1,3),(3,1),(3,4),(4,3))C((1,2),(1,0),(1,5),(1,7))D((0,3),(1,4),(2,4),(2,8))
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    Answer: A — ((1,3),(2,6),(3,1),(6,3))

31. 31. A table shows that when the base is constant, the rectangle has areas 8, 20, 28, and 48 for heights 2, 5, 7, and 12. Which equation represents the relationship?

    F(a=h+6)G(a=3h+2)H(a=4h)J(a=2h+4)
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    Answer: H — (a=4h)

32. 32. The number of employees is given by (n=10p+20), where (p) is yearly profit in millions of dollars. If profit declined from 20 million to 15 million, what was the decrease in employees?

    A50B70C120D220
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    Answer: A — 50

33. 33. Which pair could not lie on the graph of a function of (x)?

    F(1,1) and (3,1)G(1,1) and (2,1)H(1,1) and (1,2)J(1,1) and (2,2)
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    Answer: H — (1,1) and (1,2)

34. 34. The function (f=(6,5),(2,3),(1,4)). What is the range?

    F4G1,2,3,4,5,6H1,2,6J3,4,5
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    Answer: J — 3,4,5

35. 35. Which is a zero of (f(x)=2x-10)?

    A10B8C5D–5
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    Answer: C — 5

36. 36. If (f(x)=3-x^2), what is (f(2))?

    F2G–1H1J2
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    Answer: G — –1

37. 37. The point ((q,0)) lies on the graph of (f(x)=(3)/(x-6)). What is the value of (q)?

    A–8B6C–6D8
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    Answer: A — –8

38. 38. In a table, (y) varies directly with (x): when (x=10,15,20,25), (y=6,9,12,15). Which equation best describes the data?

    F(xy=(3)/(5))G(xy=(5)/(3))H(y=(3)/(5)x)J(y=(5)/(3)x)
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    Answer: J — (y=(5)/(3)x)

39. 39. A student scored 85, 49, 67, and 83 on four tests. What score is needed on the next test to have a mean of 75?

    F75G79H86J91
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    Answer: J — 91

40. 40. For the data set (5,6,6,8,9,10), which measure is greatest?

    AMeanBMedianCModeDRange
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    Answer: A — Mean

41. 41. Sam and Max sold peanuts and popcorn on two days. Day 1: Peanuts—Sam 136, Max 154; Popcorn—Sam 0, Max 38. Day 2: Peanuts—Sam 154, Max 167; Popcorn—Sam 2, Max 47. Which matrix shows how many more bags were sold on Day 2 than Day 1?

    F( 290&32182&85 )G( 18&132&9 )H( 18&134&7 )J( 18&132&7 )
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    Answer: G — ( 18&132&9 )

42. 42. If (A= 2&43&64&8 ) and (B= 1&52&73&6 ), what is (A+B)?

    A( 5&137&2 )B( 6&4212&48 )C( 9&912&3 )D( 1&-11&14 )
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    Answer: D — ( 1&-11&14 )

43. 43. A delivery company’s insurance costs are: 1 vehicle: $1,700; 2: $2,200; 3: $2,700; 4: $3,200; 5: $3,700; 6: $4,200. Using a line of best fit, estimate the cost for 8 vehicles.

    F$5,050G$5,200H$5,500J$5,950
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    Answer: G — $5,200

44. 44. Engine torque was tested at various RPMs, producing a roughly linear decreasing trend. Which equation most closely defines the line of best fit?

    A(y=4.1x+414)B(y=-4.1x+414)C(y=3.1x+383)D(y=-3.1x+383)
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    Answer: D — (y=-3.1x+383)

45. 45. Given data points ((70,4),(75,7),(80,8.5),(85,12),(90,11),(95,13.5),(100,15)), which equation best models the linear trend?

    F(y=19.5x-0.35)G(y=-0.35x+19.5)H(y=-19.5x+0.35)J(y=0.35x-19.5)
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    Answer: J — (y=0.35x-19.5)

46. 46. What is the solution to the inequality below? (2x - 7 > 15)

    A(x > 11)B(x > 4)C(x < 11)D(x < 4)
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    Answer: B — (x > 4)

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

    A−3B−2C2D3
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    Answer: A — −3

48. 48. If (2n = 6), what property of equality justifies writing (p + 2n = 4p + 15) as (p + 6 = 4p + 15)?

    AAddition propertyBTransitive propertyCSymmetric propertyDSubstitution property
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    Answer: D — Substitution property

49. 49. What is the slope of the line represented by the following equation? (y = 2x - 1)

    A−1B( 12)C1D2
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    Answer: D — 2

50. 50. Kristen heard that it is 82° Fahrenheit outside. She knows that (F = 1.8C + 32), where (F) represents the temperature in degrees Fahrenheit and (C) represents the temperature in degrees Celsius. Which is closest to the temperature outside, in degrees Celsius?

    F28G63H90J180
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    Answer: F — 28

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.