REVIEW FOR FALL SEMESTER ALGEBRA 1



REVIEW FOR FALL SEMESTER ALGEBRA 1

1. WHICH PROPERTY IS BEING ILLUSTRATED? (Commutative, Associative, Distributive)

a) 3a + 2b = 2b + 3a b) 3(a + 2) = 3a + 6 c) 3(2 + a) = 3(a + 2) d) (3· 2)a = 3(2a)

SIMPLIFY.

2. -7t + 6 - 8t + t2 3. -9a + b - 5a + 2b 4. 7 - 2( 3 + 2b)

5. 4(x - 2) + 6x 6. 3( 2r + p) – 3(r – 2p)

EVALUATE.

7. -z - 6 + y for y=8 and z=5 8. 6y - 2xy for x=3 and y=4

9. -a - b + y for a= -3, b= -2, y=5 10. [pic] for a= -1, b=5, c= -2

SOLVE.

11. y - 9 = 17 12. 8 = -x + 18

13. 3t = 27 14. -12a = -36

15. [pic] = -7 16. [pic]x = 12

Translate each statement into an equation.

17. Six less than twice a number is ten._________________________________

18. Six times the quantity two less than a number is ten.____________________

19. Six diminished by twice a number is ten._____________________________

20. Two less than two thirds times a number is ten.________________________

21. Six times the difference between two and a number is ten.________________

Equations

22. 5x + 9 = -16 23. [pic]x - 7 = 5

24. -8m + 3m = 35 25. 2y - y + 4y - 6 = 0

26. 8(w + 1) - 6 = 26 27. 3(a - 2) + 8(a - 3) = -8

28. 8 = 10 - (5 - w) 29. 5 - [pic] = 3

30. 4(y - 3) = 7y 31. 2(x + 3) + 3(x - 5) = 8(x - 6)

Word problems

32. Four more than three times a number is 175. Find the number.

33. Seven less than two thirds of a number is 5. Find the number.

34. The perimeter of a rectangle is 24 m and the length is 8. Find the dimensions of the rectangle.

35. The length of a rectangle is 5 more than the width. If the perimeter is 42 ft, what are the dimensions of the rectangle?

36. The sides of a triangle have lengths of x, x + 2, and 2x - 40. The perimeter is 70 cm. Find the length of each side of the triangle.

37. Two sides of a pentagon have a length of (3x – 2) cm and three sides have a length of

(2x + 4) cm. If the perimeter is 104 cm, find the length of the longest side.

38. Emily is buying some graduation pictures. She pays $25 for the sitting and $15 for each sheet of pictures she buys. (make a table if it helps)

a. How much does she pay for 5 sheets of pictures?

b. How much does she pay for “x” sheets?

c. How many sheets can she buy for $145?

39. A taxi driver charges $2.50 for the first two miles and $.95 for each mile after two. If the taxi ride costs $16.75, how many miles did the taxi travel?

40. Find the radius of a circle if the circumference is 29π. (HINT: use the TAKS formula chart)

41. Find the lateral surface area of a cylinder if the radius is 12 in and the height of the cylinder is 14 in. Leave your answer in terms of π. (HINT: use the TAKS formula chart)

42. Find the length of the base of a triangle if the area of the triangle is 82 cm2 and the height is 4 cm. (HINT: use the TAKS formula chart)

Proportions

43. [pic] 44. [pic]

45. Five out of every six of Mrs. Jones’ students passes the Fall exam in Algebra I. If 70 students passed the test, how many students does Mrs. Jones have?

46. Adam has a monthly income of $210. He wants to buy a used car for $150 a month. What percent of his monthly income would his car payment be?

47. Sadie works at a car dealership and receives a 3.5% commission for each car she sells. She received $930.30 in commission for selling a car. What was the price of the car?

48. Laura makes 10.5% commission on each of her sales. How much does she make when she sells a house of $85,000?

49. An electronic store has a sale on televisions. The regular price of a television is $576. The sales price of the television is $432. What is the discount rate?

50. The total cost of a new pair of jeans that Matt bought was $42.76. If the tax rate is 8.25%, what was the ticket price of the jeans?

51. James hits the bullseye of the archery target with an arrow 72% of the time. If James shot his bow and arrow 30 times Friday afternoon, about how many times did he hit the bullseye?

Domain and Range

52. Tell whether each relation is a function.

a) (4,2), (6,-2), ( 2,4), (6,-3)

b) (8,1), (10,-3), ( 5,-6), (-6,4)

c) (1,3), (-5,3), ( 7,3), (-2,3)

d) (2,6), (2,-8), ( 2,19), (2,-12)

53. Find the domain and range of the function {(2, 3), (4, 7), (1, 7), (5, 9)}

54. Find the range of the function f(x) = x2 + 2x + 1 when the domain is {-7, -5, 2}.

55. Find the domain and range of the function.

D: ___________________

R: ___________________

Equations of lines

56. Find the slope and y-intercept of x – 3y = 18.

57. What is the slope of the line through (-2, 7) and (-5, -7)?

Find the equation of the lines below.

61. Write the equation of a line parallel to y = -[pic]x + 2 but has a y-intercept of –3.

62. Write the equation of a line perpendicular to y = -[pic]x + 3 but passes through the

point (0,5).

63. Graph the line 8x + 4y = 12 on the grid.

Write the equation of each line described below.

64. Slope –3, y –intercept 4 65. Slope [pic], passes through (4, -1)

66. Passes through (-1, -2) and (0, 3) 67. Horizontal line through (-2, -1)

68. If (x, -3) is a solution to 3x – y = 15, what is the value of x?

69. If (4, y) is a solution to x – 2y = 6, what is the value of y?

70. Given f(x) = 3 – 5x 71. For g(x) = {(4, -3) (2, 1) (-1, 5) (-3, -6)}

f(1) = g(-1) =

|72. |x |f(x) | | |

| | | | | |

| | | | |(a) Rate: |

| | | | | |

| | | | | |

| | | | | |

| | | | |(b) Rule: |

| |2 |5 | | |

| |3 |7 | | |

| |4 |9 | | |

| |6 | | | |

| |7 | | | |

ANSWERS

1. a) Commutative

b) Distributive

c) Commutative

d) Associative

2. t2 – 15t + 6

3. -14a + 3b

4. 1 - 4b

5. 10x - 8

6. 3r + 9p

7. -3

8. 0

9. 10

10. [pic]

11. 26

12. 10

13. 9

14. 3

15. -35

16. 18

17. 2x - 6 = 10

18. 6(x - 2) = 10

19. 6 - 2x = 10

20. 2/3x - 2 = 10

21. 6(2 - x) = 10

22. -5

23. 18

24. -7

25. [pic]

26. 3

27. 2

28. 3

29. 4

30. -4

31. 13

32.. 57

33. 18

34. 8m by 4m

35. 8 ft by 13 ft

36. 27, 14, 29

37. 22

38. a. $100

b. 15x + 25

b. 8

39. 17 miles

40. 14.5 cm

41. 336π

42. 41 cm

43. 10

44. 6

45. 84

46. 71%

47. $26,580

48. $8925

49. 25%

50. $39.50

51. 22

52. a) No b) Yes

c) Yes d) No

53. D = {1, 2, 4, 5}

R ={3, 7, 9}

54. {36, 16, 9}

55. D: –7 < x < 2

R: -3 < y < 5

56. m = [pic], b = -6

57. [pic]

58. x = 3

59. y = -4

60. y = -2x + 3

61. y = -[pic]x - 3

62. y = 2x + 5

63. m = -2, b = 3

64. y = -3x + 4

65. y = [pic]x – 3

66. y = 5x + 3

67. y = -1

68. x = 4

69. y = -1

70. f(1) = -2

71. g(-1) = 5

72. (a) rate = 2

(b) f(x) = 2x + 1

(6, 13), (7,15)

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NAME____________________________

REVIEW FOR FALL SEMESTER EXAM

REVIEW FOR FALL SEMESTER EXAM

REVIEW FOR FALL SEMESTER EXAM

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REVIEW FOR FALL SEMESTER EXAM

REVIEW FOR FALL SEMESTER EXAM

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