REVIEW FOR FALL SEMESTER ALGEBRA 1
(Non-calculator part)
SIMPLIFY.
1. 9 + 2(4 +3)
4.
7 4 2
9 3 2
7.
3
10. (17 - 15) - (44 - 55)
13. -
1
5
1
10
2. 6
5.
1+7+5
6
3. 0
6 4 3 8
3(9 5)
9 + 6 - 10
6. 32 - (8 - 3) + 3
8. 8 12
9. - 4 - 2
11. -14 + 10 - 11 - 3 + 22
12. -36
1
( )
6
14. (-2)(-6)(-5)
SIMPLIFY.
15. -7t + 6 - 8t + t2
16. -9a + b - 5a + 2b
18. 4(x - 2) + 6x
19. 3( 2r + p) – 3(r – 2p)
17. 7 - 2( 3 + 2b)
EVALUATE.
20. -z - 6 + y for y=8 and z=5
21. 6y - 2xy for x=3 and y=4
22. -a - b + y for a= -3, b= -2, y=5
23.
c b
for a= -1, b=5, c= -2
a b c
SOLVE.
24. y - 9 = 17
25. 8 = -x + 18
26. 3t = 27
27. -12a = -36
28.
x
= -7
5
29.
2
x = 12
3
5+2
2
REVIEW FOR FALL SEMESTER EXAM - ALGEBRA 1
(Calculator Part)
Translate each statement into an equation.
1. Six less than twice a number is ten._________________________________
2. Six times the quantity two less than a number is ten.____________________
3. Six diminished by twice a number is ten._____________________________
4. Two less than two thirds times a number is ten.________________________
5. Six times the difference between two and a number is ten.________________
Equations
2
x-7=5
3
6. 5x + 9 = -16
7.
8. -8m + 3m = 35
9. 2y - y + 4y - 6 = 0
10. 8(w + 1) - 6 = 26
11. 3(a - 2) + 8(a - 3) = -8
12. 8 = 10 - (5 - w)
13. 5 -
14. 4(y - 3) = 7y
15. 2(x + 3) + 3(x - 5) = 8(x - 6)
a
=3
2
Word problems
16. Four more than three times a number is 175. Find the number.
17. Seven less than two thirds of a number is 5. Find the number.
18. The perimeter of a rectangle is 24 m and the length is 8. Find the dimensions of the
rectangle.
19. The length of a rectangle is 5 more than the width. If the perimeter is 42 ft, what are the
dimensions of the rectangle?
20. 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.
21. Two sides of a pentagon have a length of (3x – 2) and three sides have a length of
(2x + 4). If the perimeter is 104 cm., find the length of the longest side.
22. Bill sold 2 times as many boxes of candy as Jim. Together they sold 99 boxes. How
many boxes of candy did each guy sell?
23. Phillip can eat four times as many chocolate kisses as Grant. Together they can eat 150
chocolate kisses. (make a table if it helps)
a. How many kisses does Grant eat?
b. How many kisses does Phillip eat?
24. 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?
25. 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?
26. Mrs. Hester drove to the beach at 68 km/h. The return trip took 2 hours longer because
she traveled at only 52 km/h due to their bad sunburn. How long did it take Mrs. Hester to
get home?
27. John started out on his bicycle at a rate of 8 km/h. One hour later Jim left from the same
point along the same road at 12 km/h. How long did it take Jim to catch up with John?
28. The formula for volume of a rectangular prism is V = lwh, where V is the volume, l is the
length, w is the width, and h is the height of the prism. Find the height is the length is 15 ft.,
the width is 12 ft., and the volume is 3420 ft3.
Proportions
3x 2 x 4
29.
4
2
30.
5x 3
3x 3
9
7
31. Five out of every six of Mrs. Jones’ students passes the EOC exam in Algebra I. If 70
students passed the test, how many students does Mrs. Jones have?
Percent
32. 32% of 300 is what number?
33. 21 is 6% of what number?
34. Laura makes 10.5% commission on each of her sales. How much does she make when
she sells a house of $85,000?
35. Joe goes to the Hallmark store to buy his girlfriend a teddy bear for Christmas. The bear
costs $15 and the tax is 8.25%. What was the total price that Joe paid for the teddy bear?
36. Allison, Joe’s girlfriend, goes to Circuit City to buy Joe his Christmas present. She wants
to buy NFL Quarterback Club, which costs $59.99. They are having a big sale and all games
are 15% off. If the tax is 6%, how much did Allison pay for the game?
37. Barry’s Toy Store had 250 Furbies in stock on Sunday. After they closed on Monday,
they had only 55 left. What was the percent decrease in the amount of Furbies in stock?
Probability
A bag contains 8 red, 7 white and 5 blue balls. A ball is drawn from the bag. Find the
following:
38. P(white) = ____________________
39. P(red or blue) = ________________
40. If the first two marbles drawn were blue and not replaced, what is the probability that the
next marble will be blue?________________
41. A card is drawn from a standard deck of 52 cards and then a die is tossed. What is the
probability of: P(red queen, 5) ________________
Domain and Range
42. Determine if the relation {(2, 3), (4, 7), (1, 7), (5, 9)} is a function. __________________
43. State the domain of the relation above. _____________________
44. State the range of the relation above. ______________________
45. Find the range of the function f(x) = x2 + 2x + 1 when the domain is {-7, -5, 2}.
46. Find the domain and range of the function graphed below. D: ___________________
R: ___________________
Equations of lines
47. Find the slope and y-intercept of x – 3y = 18.
48. What is the slope of the line through (-2, 7) and (-5, -7)?
Find the equation of the lines below.
49.
50.
52. Write the equation of a line parallel to y = -
51.
1
x + 2 but has a y-intercept of –3.
2
53. Write the equation of a line perpendicular to y = (0,5).
54. Graph the line 8x + 4y = 12 on the grid.
1
x + 3 but passes through the point
2
Write the equation of each line described below.
55. Slope –3, y –intercept 4
56. Slope
1
, passes through (4, -1)
2
57. Passes through (-1, -2) and (0, 3)
58. Horizontal line through (-2, -1)
59. If (x, -3) is a solution to 3x – y = 15, what is the value of x?
60. If (4, y) is a solution to x – 2y = 6, what is the value of y?
61. Use the data below to draw a line of best fit and then determine the best estimate of the
weight of an Algebra book if it contains 200 pages.
35
Weight (lbs)
25
15
5
25
__________________
75
125
# of pages
175
225
Systems of Equations
62. Where do the lines y = 2x and 5x – y = 30 intersect?
63. If (x, 3) is the solution for the following system of equations, what is the value of x?
x + y = 10
y=x–4
64. What are the solutions to the following systems below?
a.
b.
c.
65.
x+y=9
x – 3y = -3
66.
3x + y = 4
x – 2y = 6
67.
Given f(x) = 3 – 5x
f(1) =
68.
For g(x) = {(4, -3) (2, 1) (-1, 5) (-3, -6)}
g(-1) =
69.
x
2
3
4
6
7
f(x)
5
7
9
(a) Rate:
(b) Rule:
Use the graph below to answer questions 70 – 74.
A
B
C
70. If you reflect ABC across the x-axis what would be the coordinates of
points A, B, and C?
71. If you reflect ABC across the y-axis what would be the coordinates of
points A, B, and C?
72. If you shift ABC across the 4 units to the right and 1 unit down what
would be the coordinates of points A, B, and C?
72. If you shift ABC across the 2 units to the left and 3 units up what would
be the coordinates of points A, B, and C?
72. If ABC is enlarged to create a triangle with sides twice as long, what
would be the coordinates of points B and C with point A as the vertex of the
larger triangle?
ANSWERS
Non-Calculator
1. 23
2. 43
3. 6
4. 5
5. 4
6. 10
7. 3
8. 4
9. -6
10. 13
11. 4
12. -216
13. -2
14. -60
15. t2 - 15t + 6
16. -14a + 3b
17. 1 - 4b
18. 10x - 8
19. 3r + 9p
20. -3
21. 0
22. 10
23.
24.
25.
26.
27.
28.
29.
3
2
26
10
9
3
-35
18
Calculator
1.
1.
2.
3.
4.
6.
7.
8.
2X - 6 = 10
6(x - 2) = 10
6 - 2x = 10
2/3x - 2 = 10
6(2 - x) = 10
-5
18
-7
6
9.
5
10. 3
11. 2
12. 3
13. 4
14. -4
15. 13
16. 57
17. 18
18. 8m by 4m
19. 8 ft by 13 ft
20. 27, 14, 29
21. 22,20
22. Bill: 66, Jim: 33
23. a. 30
b. 120
24. a. $100
b. 15x + 25
c. 8
25. 17 miles
26. 8.5 hours
27. 2 hours
28. 19 ft.
29. 10
30. 6
31. 84
32. 96
33. 350
34. $8925
35. $16.24
36. $54.05
37. 78%
38.
7
20
39.
40.
41.
42.
13/20
1/6
1/156
yes
43. {1, 2, 4, 5}
44. {3, 7, 9}
45. {36, 16, 9}
46. D: –7 < x < 2
R: -3 < y < 5
1
, b = -6
3
47. m =
48.
14
3
49. x = 3
50. y = -4
51. y = -2x + 3
52. y = -
1
x-3
2
53. y = 2x + 5
54. m = -2, b = 3
55.y = -3x + 4
56. y =
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
1
x–3
2
y = 5x + 3
y = -1
x=4
y = -1
about 33
(10, 20)
7
a. no solution
b. (3, -1)
c. infinitely many
(6, 3)
(2, -2)
f(1) = -2
g(-1) = 5
(a) rate = 2
(b) f(x) = 2x + 1
(6, 13), (7,15)
A(2,-5) B(0,-2) C(3,-3)
A(-2,5) B(0,2) C(-3,3)
A(6,4) B(4,1) C(7,2)
A(0,8) B(-2,5) C(1,6)
B(-2,-1) C(4,1)