Name: 
 

Pre-Algebra Chapter One Study Guide


Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
 
 
Identify the expression as a numerical expression or a variable expression. For a variable expression, name the variable.
 

 1. 
prealgebrastudyguid_files/i0030000.jpg × 12
a.
numerical expression
b.
variable expression; a is the variable.
c.
variable expression; there is no variable.
d.
variable expression; l is the variable.
 

 2. 
prealgebrastudyguid_files/i0040000.jpg ¸ 7
a.
variable expression; there is no variable.
b.
numerical expression
c.
variable expression; g is the variable.
d.
variable expression; f is the variable.
 

 3. 
prealgebrastudyguid_files/i0050000.jpg × 11
a.
variable expression; b is the variable.
b.
numerical expression
c.
variable expression; k is the variable.
d.
variable expression; there is no variable.
 

 4. 
Write a variable expression for 9 more than a number s.
a.
9 – s
b.
s + 9
c.
s + 10
d.
9 ¸ s
 

 5. 
Write a word phrase that can be represented by b – 6.
a.
the difference of 6 and b
c.
6 more than a number b
b.
the quotient of a number b and 6
d.
6 less than a number b
 

 6. 
Which word phrase could represent the variable expression 2p + 3?
a.
three more than Sam’s age doubled
b.
twice Sam’s age times three
c.
half Sam’s age times three
d.
three times Sam’s age
 
 
Simplify.
 

 7. 
3 - 15 × 5
a.
0
b.
78
c.
90
d.
–72
 

 8. 
17 – 6 × 10 ¸ 2 + 12
a.
27.8
b.
59
c.
67
d.
–1
 

 9. 
5 ´ (8 + 7) + 7
a.
83
b.
53
c.
54
d.
82
 

 10. 
[2 × (10 + 5)] - 5
a.
12.5
b.
20
c.
25
d.
120
 
 
Evaluate.
 

 11. 
6t - 6, for t = 6
a.
30
b.
43
c.
42
d.
29
 

 12. 
47 + 2d, for d = 3
a.
138
b.
53
c.
139
d.
54
 

 13. 
prealgebrastudyguid_files/i0170000.jpg for d = 8 and p = 1
a.
0.89
b.
1
c.
1.14
d.
8
 

 14. 
prealgebrastudyguid_files/i0180000.jpg for prealgebrastudyguid_files/i0180001.jpg and prealgebrastudyguid_files/i0180002.jpg
a.
120
b.
180
c.
185
d.
156
 

 15. 
Your job pays $8 per hour. Write a variable expression for your pay in dollars for working h hours. What is your pay if you work 36 hours?
a.
9h; $288
b.
8h; $288
c.
8h; $292
d.
8; $282
 

 16. 
Several people form groups with four people in each group. Write an expression for the number of groups formed by p people. How many groups are formed if there are 28 people?
a.
prealgebrastudyguid_files/i0200000.jpg; 4
b.
prealgebrastudyguid_files/i0200001.jpg; 7
c.
prealgebrastudyguid_files/i0200002.jpg; 28
d.
prealgebrastudyguid_files/i0200003.jpg; 7
 

 17. 
To print tickets, a printer charges a $70 setup fee plus $1.25 per ticket. Write an algebraic expression for the cost of t tickets. What is the cost of 650 tickets?
a.
prealgebrastudyguid_files/i0210000.jpg; $882.50
c.
prealgebrastudyguid_files/i0210001.jpg; $742.50
b.
prealgebrastudyguid_files/i0210002.jpg; $812.50
d.
prealgebrastudyguid_files/i0210003.jpg; $882.50
 
 
Write a number to represent the quantity.
 

 18. 
eighteen degrees above zero
a.
18
b.
–18
c.
–23
d.
23
 

 19. 
a loss  of five yards
a.
5
b.
–5
c.
–7
d.
7
 

 20. 
Graph –5, 6, and 9 on a number line. Order the numbers from least to greatest.
a.
prealgebrastudyguid_files/i0250000.jpg;
–9, –5, 9
c.
prealgebrastudyguid_files/i0250001.jpg;
–5, 4, 6
b.
prealgebrastudyguid_files/i0250002.jpg;
–5, 6, 9
d.
prealgebrastudyguid_files/i0250003.jpg;
3, 6, 9
 

 21. 
Simplify prealgebrastudyguid_files/i0260000.jpg.
a.
15
b.
prealgebrastudyguid_files/i0260001.jpg
c.
prealgebrastudyguid_files/i0260002.jpg
d.
–15
 
 
Compare. Use >, <, or = to complete the statement.
 

 22. 
7prealgebrastudyguid_files/i0280000.jpg| –3 |
a.
>
b.
=
c.
<
 

 23. 
| 10 |prealgebrastudyguid_files/i0290000.jpg–6
a.
=
b.
<
c.
>
 

 24. 
Write the numerical expression for the model. Find the sum. Let one white tile equal +1 and one black tile equal –1.
prealgebrastudyguid_files/i0300000.jpg
a.
–5 – 4; –1
b.
–4 + 5; 1
c.
5 + 4; 9
d.
4 + 5; 5
 

 25. 
What integer can be represented by 16 positive tiles and 26 negative tiles?
a.
42
b.
–6
c.
10
d.
–10
 

 26. 
Write an expression for the model. Find the sum.
prealgebrastudyguid_files/i0320000.jpg
a.
2 + 3; 5
b.
2 + (–3); 1
c.
2 + (–3); –1
d.
–3 + 2; 5
 
 
Find the sum.
 

 27. 
–10 + 1 + (–6)
a.
–15
b.
–17
c.
–3
d.
5
 

 28. 
172 + (–167) + (–10) + (–144)
a.
–129
b.
–149
c.
185
d.
139
 

 29. 
The temperature in your town is 31°F. The radio announcer says that the temperature will drop 15 degrees. Write an expression to compute the predicted temperature. What will the temperature be?
a.
31 + (–15); 16°F
c.
15 + 31; 46°F
b.
15 + (–31); –16°F
d.
31 + 15; 22°F
 

 30. 
Atoms contain charged particles called protons and electrons. Each proton has a charge of +1, and each electron has a charge of –1. A sulfur ion has 16 protons and 18 electrons. Find the net charge.
a.
–34
b.
+2
c.
34
d.
–2
 

 31. 
Write the difference 48 – (–14) as a sum. Then simplify.
a.
48 – 57; –9
b.
48 + 57; 105
c.
48 – 14; 34
d.
48 + 14; 62
 

 32. 
A submarine at the surface dives 375 ft and then another 175 ft. Express the final depth as an integer.
a.
–525 ft
b.
–550 ft
c.
550 ft
d.
525 ft
 

 33. 
A checking account is overdrawn if it has a negative balance. Marc’s account is overdrawn by $45. What will the balance be after he deposits $170 and writes a check for $59?
a.
–$184
b.
–$156
c.
$184
d.
$66
 
 
Draw the next figure in the pattern.
 

 34. 
prealgebrastudyguid_files/i0420000.jpg
a.
prealgebrastudyguid_files/i0420001.jpg
b.
prealgebrastudyguid_files/i0420002.jpg
c.
prealgebrastudyguid_files/i0420003.jpg
d.
prealgebrastudyguid_files/i0420004.jpg
 

 35. 
All tests for the first six chapters had 20–30 questions. The chapter 7 test will be given tomorrow. What reasonable conclusion can you make?
a.
The chapter 7 test will have less than 20 questions on it.
b.
The chapter 7 test will have exactly 25 questions on it.
c.
The chapter 7 test will have more than 30 questions on it.
d.
The chapter 7 test will have 20–30 questions on it.
 

 36. 
A display of gift boxes has 1 box in the top row, 3 boxes in the next row, 5 boxes in the next row, and so on. There are 7 rows in all. How many gift boxes are in the display?
a.
64 boxes
b.
47 boxes
c.
36 boxes
d.
49 boxes
 

 37. 
A basketball drops from a height of 76 in. On bounce 1, it rebounds to a height of 38 in. On bounce 2, it rebounds to a height of 19 in. How high does the basketball bounce on bounce 3?
a.
9 inches
b.
19 inches
c.
9.5 inches
d.
4.75 inches
 
 
Write the sum as a product. Simplify the product.
 

 38. 
(–2) + (–2) + (–2) + (–2)
a.
4 (–2); –8
c.
(–2) + (–2) + (–2) + (–2); –6
b.
5 (–2); –10
d.
2(–2) + 2(–2); 10
 

 39. 
(–6) + (–6) + (–6) + (–6) + (–6) + (–6)
a.
6(–6); –36
c.
2(–6) + 2(–6) + 2(–6); –34
b.
7(–6); –42
d.
3(–6) + 2(–6); –30
 
 
Simplify the product.
 

 40. 
4(–7)
a.
–28
b.
–30
c.
–26
d.
16
 

 41. 
–8(–9)
a.
74
b.
72
c.
71
d.
70
 

 42. 
prealgebrastudyguid_files/i0520000.jpg
a.
–240
b.
–241
c.
–238
d.
–40
 

 43. 
Find the quotient –88 ¸ 11.
a.
–10
b.
–7
c.
–8
d.
–3
 
 
In which quadrant does the point lie? Write the coordinates of the point.
prealgebrastudyguid_files/i0540000.jpg
 

 44. 
A
a.
quadrant II; ( 6, –4)
c.
quadrant III; (–4, –6)
b.
quadrant I; (4, 6)
d.
quadrant I; (6, 4)
 

 45. 
B
a.
quadrant II; (–2, –4)
c.
quadrant III; (–2, –4)
b.
quadrant III; (2, 4)
d.
quadrant IV; (–4, –2)
 

 46. 
C
a.
quadrant IV; ( –2, 2)
c.
quadrant III; ( 2, –2)
b.
quadrant III; ( –2, 2)
d.
quadrant IV; ( 2, –2)
 

 47. 
Graph A(–1, 0).
a.
prealgebrastudyguid_files/i0580000.jpg
c.
prealgebrastudyguid_files/i0580001.jpg
b.
prealgebrastudyguid_files/i0580002.jpg
d.
prealgebrastudyguid_files/i0580003.jpg
 

 48. 
Draw the shape that a mowing machine would make given these instructions. Go to (–7, 7). Lower blade. Cut to (–7, 1). Raise blade. Go to (–4, 7). Lower blade. Cut to (–4, 1). Raise blade. Go to (–7, 4). Lower blade. Cut to (–4, 4). Raise blade. What is the shape?
a.
I
b.
H
c.
T
d.
X
 

Short Answer
 
 
Write a rule for the pattern.
 

 49. 
1, 4, 7, 10, . . .
 
 
Write a rule for each pattern. Then find the next two numbers in each pattern.
 

 50. 
5, –30, 180, –1080, . . .
 
 
Is the conjecture correct or incorrect? If it is incorrect, give a counterexample.
 

 51. 
All odd numbers are prime.
 

 52. 
The sum of an odd number and an even number is always even.
 
 
Without computing, tell whether each product or quotient is positive or negative.
 

 53. 
(–4)(–4)(–4)
 



 
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