Pre Algebra
Final Exam Study Guide
Name:_________________________________
Section 1: Writing words, expressions, equations, and inequalities.
Write an expression or equation for each word problem. Then Solve.
1. Thirty-one increased by fourteen
3. Twice as many potatoes
2. Six less than nine
4. 2 dollars more than the cost of a drink
5. Seven times a number is eighteen less than the number.
6. A number divided by two is ten more than six.
7. Eight times a number equal to thirty-two.
8. Seven less than three times a number is equal to fourteen.
9. The total cost of a meat and three sides is $10. If the meat costs $6 and each
side costs the same amount, how much does each side cost (round to the
nearest cent)?
10. At the Christmas party, Maria ate 10 cookies. This is 4 more than twice the
amount of cookies that Lizzie ate. How many cookies did Lizzie eat?
Section 2: Graphing ordered pairs.
Identify the x and y coordinate for each ordered pair, or place each ordered pair in
the correct spot on the graph.
11. A (1, 3)
12. B (2,5)
13. C (0, 4)
14. D (1,1)
15. W (____ , ____)
16. X (____ , ____)
17. Y (____ , ____)
18. Z (____ , ____)
Section 3: Integers.
Solve each problem using addition, subtraction, multiplication, or division.
50
19. 8 + (−7)
20. −6 − 1
21.
22. 10 − (−3)
23. 5(−30)
24. −12 + 44
26. −4(6)
27. −8 − (−15)
28.
−5
−45
9
Section 4: Fractions and Rational Numbers.
Solve each problem using addition, subtraction, multiplication, or division. Make
sure to simplify your answer!
2
1
3
6
29. ×
30. −2 ÷
2
1
5
5
32. 5 − 1
16
4
35. 36 ÷ 6
7
3
1
5
4
8
33. 3 ×
3
9
5
10
36.− +
3
1
5
5
31. +
2
5
5
12
34. − ×
9
1
37. 15 − 5
Convert each number to a fraction or decimal.
38. 0.55555(𝑡ℎ𝑒 5 𝑖𝑠 𝑟𝑒𝑝𝑒𝑎𝑡𝑖𝑛𝑔)
40.
34
39. 0.75
41. −
99
3
5
Section 5: Solving one, two, and multi-step equations.
Solve each equation for the variable given. Show your work, and write your answers
in simplest form where necessary.
Use the distributive property to simplify each expression. Then evaluate the
expression if possible.
42. 4(20 − 9)
43. 3(2 + 7)
Simplify each expression.
44. 9𝑗 + 3𝑗 − 6
45. 5𝑦 + 2 + 3𝑦
Solve each equation.
46. 𝑥 + 3 = 7
47. 2𝑥 = 12
49. 6y – 5 = 31
50. 3 + 1 = 10
𝑟
48.
𝑡
5
= 13
51. 3x + 12 = 2x + 25
52. 4𝑡 + 16 = 2𝑡 − 20
53. 2𝑐 − 4 = 8𝑐 + 16
54. 𝑔 + 6 = 7𝑔 + 22
Solve the problem by writing and solving an equation.
55. You bought 2 shirts that cost x dollars each, some shoes for $10, and a hat for $3.
If you spent $25 total, what is the value of x?
Find the area and perimeter for each figure. Include units for full credit.
56.
57.
Area = __________________
Area = __________________
Perimeter = __________________
Perimeter = __________________
Section 6: Solving one, two, and multi-step inequalities.
Solve each inequality for the variable given. Show your work, and write your
answers in simplest form where necessary.
Write an inequality for the sentence.
58. The maximum age to order from the children’s menu is 12 years old.
Graph the inequality on the number line provided.
59. 𝑥 ≥ 4
Solve each inequality.
60. 𝑥 + 5 > 7
61. 𝑦 − 3 ≤ 10
62. −2𝑠 < 11
63. ≥ 3
𝑡
4
Section 7: Ratios, Rates, and Proportions
Express each ratio as a fraction in simplest form.
64. 5 singers to 25 dancers
65. 9 made shots out of 12 attempted
BONUS: explain the meaning of this ratio.
Express each rate as a unit rate. Round to the nearest tenth or nearest cent (if
the unit is money), if necessary.
66. $10 for 5 slices of pizza
67. 27 Christmas cookies in 3 days
Complete each conversion using dimensional analysis. Round to the nearest
hundredth if necessary.
68. 18 in = _________ ft
69. 3.5 hours = _________ minutes
70. 8 meters/second = _________ cm/second
Solve the following proportions.
71.
𝑥
10
72.
=
2.5
7
5
𝑐
=
5
10
BONUS: Word Problems.
Alfredo’s Pizza Cafe charges $10 for 8 slices of pizza. Pizza by Alfredo charges $12
for 6 slices of pizza. Which restaurant gives the better deal per slice of pizza?
The area of a rectangle is 36 square in. If the length of the rectangle is 9 in, what is
the width? (remember units)
The elves at Santa’s workshop can make 150 new toys in 5 hours. At this same rate,
how many new toys could the elves make in 24 hours?
In a school survey, 34 out of 50 students said their favorite sport is basketball. Is this
figure more or less than 2/3 of those surveyed? Explain.