Integrated Algebra/Geometry
Quarter 1 Final Exam Review
Do all work on a separate sheet of paper.
Writing expressions, equations, and inequalities
For each, write an expression, equation, or inequality that represents the situation.
1. Grapes cost $1.99 per pound. Write an expression for the cost of g pounds of grapes.
2. Barbara has saved d dollars for a $65 sweater. Write an expression for the amount of money she
still needs to buy the sweater.
3. Today’s temperature is 3 degrees warmer than yesterday’s temperature t. Write an expression
for today’s temperature.
4. Rita bought a sandwich, w bottles of water, and an apple for lunch. The sandwich cost $4.99, the
bottles of water cost $1.48 each, and the apple cost $0.89. If she spent a total of $11.80 on
lunch, write an equation to represent this.
5. Alyssa has $7 and would like to buy fruit snacks for as many of her friends as possible. Write an
inequality that can be used to find the number of fruit snacks f she can buy.
6. No more than 12 students were present.
7. Tammy wants to run at least 10 miles per week. So far this week she has run 4.5 miles. Write
and solve an inequality to determine who many more miles Tammy must run this week to reach her
goal.
8. The senior class is selling lanyards as a fundraiser. The profit for each lanyard is $0.75. Write
an inequality to determine the number of lanyards the class must sell to make a profit of at least
$250.
9. Carl’s Cable Company charges $55 for monthly service plus $4 for each pay-per-view movie.
Teleview Cable Company charges $110 per month with no fee for movies. For what number of
movies is the cost of Carl’s Cable Company less than the cost of Teleview?
10. Madison must run a mile in at most 9 minutes to qualify for a race.
11. If k represents Kathy’s age, write an expression to represent 8 less than a third of her age.
12. If w represents William’s age, write an expression to represent 5 times the quantity 9 more than
twice William’s age.
Evaluating expressions, simplifying expressions, equivalent expressions
Evaluate each expression.
13. For a = 7 and b = 15
b -a
a–b
14. x2 + 7 for x = 1
a
b
ab
15. x2 - 2for x = - 5
Simplify each expression.
16. 20x – 16x
19. -2(x2 – 1) + 4x2 – 9(x + 3)
17. 2y2 + 5y2
20. -2y + 3y2 – 3y + y
18. 6(x + 4) – 2x
21. 3(2x – 4) – (3 – 4x)
Match an expression in the first column with an equivalent expression in the second column.
Column 1
Column 2
-7(x – 9)
4(x + 3) – 3x
-5x - 63
7x + 9
6x + 9 + x
7x
9 – x – 9 + 8x
63 – 7x
x + 12
4x – 9(7 + x)
Solving for a variable
Solve each for the given variable.
22. r – 2s = 14 for s
23. V =
1
bh for b
3
Solving Equations and Inequalities
Solve each.
26. x – 12 = 4
24. -5x + 3y = 24 for y
25. A = lw for w
27. 13 = -9 + m
28. -6h = -36
29.
x
=2
3
30. 16 =
36. 0 = 6n – 36
4
d
5
31. 4t – 13 = 57
32. 5 – 2y = 15
33.
35. 4 + 3a – 6 = 43
k
-6=2
5
37. 4x + 2 = 3x
38. –a – 3 + 7 = 3a
39. -3r – 8 = -5r – 12
40. 5d = -3(d + 7)
41. 3(x – 2) + 2 = 5x – 7 – 2x
34. 7x – 19x = 6
Solve and graph each.
42. -11 + y > 8
43. 4 < p – 1
44. 15y < -30
47.
2k 3
>7
5
48. 6(n – 8) > -18
49. 10 – 2(3x + 4) < 11
3
45.
m>3
4
50. 2x + 6 < 5x – 3
46. -7x < 0
51. -3(3x + 5) > -5(2x – 2)
Functions
Sketch a graph to represent each statement.
52. The temperature of a water class rose steadily for several hours until it reached room
temperature , then remained constant.
53. A person leaves home, drives through town, then on the highway, and finally stops at a rest area.
Express each relation as a table, a mapping diagram and as sets of domain and range.
54. {(-2, 5), (-1, 1), (3, 1), (-1, -2)}
55. {(5, 3), (4, 3), (3, 3), (2, 3), (1, 3)}
Absolute Value Equations
56. |x + 2| - 4 = 9
57. |x – 8| + 3 = 12