Download Chapter 1 2 Review (with answers)

Alg 2 Chapter 1/2 Review
Short Answer
Graph the number on a number line.
1.
2.
Insert <, >, or = to make the sentence true.
3.
4.
5. 20.28
6.
7.
Evaluate the expression for the given value of the variable(s).
8.
; x = –3
9.
10. The expression
models the height of an object t seconds after it has been dropped from a height
of 1800 feet. Find the height of an object after falling for 4.8 seconds.
Simplify by combining like terms.
11.
12.
13.
Solve the equation.
14.
15.
16.
17.
Solve for x. State any restrictions on the variables.
18.
19.
Solve the inequality. Graph the solution set.
20. 2 + 2k  8
21. 2r – 9  –6
22. –4k + 5  21
23.
2(4y – 5)  –10
24. 2(2m – 5) – 6  –36
25. 4(3b – 5) < –31 + 12b
Solve the compound inequality. Graph the solution set.
26.
Solve the equation. Check for extraneous solutions.
27.
28.
Solve the inequality. Graph the solution.
29.
30.
31. Write the ordered pairs for the relation. Find the domain and range.
y
4
2
–4
–2
O
2
4
x
–2
–4
32. Find the domain and range of the relation and determine whether it is a function.
y
4
2
–4
–2
O
2
4
x
–2
–4
33. Graph the equation
.
34. Graph the equation –3x – y = 6.
Write in standard form an equation of the line passing through the given point with the given slope.
35. slope = –8; (–2, –2)
36. slope =
; (5, –3)
Find the slope of the line.
37.
38.
39. x = a
Find an equation for the line:
5
40. through (2, 6) and perpendicular to y =  x + 1.
4
41. through (–4, 6) and parallel to y = 3 x + 4.
42. A balloon takes off from a location that is 158 ft above sea level. It rises 56 ft/min. Write an equation to model
the balloon’s elevation h as a function of time t.
Graph the absolute value equation.
43.
44.
45. What is the vertex of the function
?
46. Write the equation for the translation of
.
y
6
4
2
–6
–4
–2 O
–2
2
4
6 x
–4
–6
Write an equation for the vertical translation.
47.
; 4 units down
48. The equation
describes a function that is translated from a parent function.
a. Write the equation of the parent function.
b. Find the number of units and the direction of translation.
c. Sketch the graphs of the two functions.
49. Graph the function
Graph the inequality.
50. –3x + y  5
.
51. A doctor’s office schedules 15-minute appointments and half-hour appointments for weekdays. The doctor
limits these appointments to, at most, 30 hours per week. Write an inequality to represent the number of
15-minute appointments x and the number of half-hour appointments y the doctor may have in a week.
52. An electronics store makes a profit of $20 for every portable DVD player sold and $45 for every DVD recorder
sold. The manager’s target is to make at least $180 a day on sales of the portable DVD players and DVD
recorders. Write and graph an inequality that represents the number of both kinds of DVD players that can be
sold to reach or beat the sales target. Let p represent the number of portable DVD players and r represent the
number of DVD recorders.
Graph the absolute value inequality.
53. y  |x + 3| – 2
Write an inequality for the graph.
54.
y
6
3
–6
–3
O
3
6
x
–3
–6
55. Graph the function
.
Simplify the expression.
56.
57. Graph the relation.
58. Is the relation {(–2, 5), (–1, 5), (–1, 4), (–1, –3), (–2, 0)} a function? Explain.
59. Is the relation {(3, 5), (–4, 5), (–5, 0), (1, 1), (4, 0)} a function? Explain.
60. Find the slope of the line. Show your work.
Rx + Sy = T
Other
61. What is the maximum number of 3.5-to-5-min songs that can fill a 120-min CD? What is the minimum number?
Write your answer as a compound inequality. Explain your reasoning.
62. Describe the vertical-line test for a graph and tell how it can determine whether a graph represents a function.
Alg 2 Chapter 1/2 Review
Answer Section
SHORT ANSWER
1. ANS:
–5 –4 –3 –2 –1 0 1 2 3 4 5
PTS: 1
DIF: L2
REF: 1-1 Properties of Real Numbers
OBJ: 1-1.1 Graphing and Ordering Real Numbers
STA: CO 1.2 | CO 1.1
TOP: 1-1 Example 2
KEY: rational numbers | graphing | number line
2. ANS:
–5 –4 –3 –2 –1 0 1 2 3 4 5
PTS: 1
DIF: L2
REF: 1-1 Properties of Real Numbers
OBJ: 1-1.1 Graphing and Ordering Real Numbers
STA: CO 1.2 | CO 1.1
TOP: 1-1 Example 2
KEY: square root | irrational numbers | graphing | number line
3. ANS:
>
PTS: 1
DIF: L2
REF: 1-1 Properties of Real Numbers
OBJ: 1-1.1 Graphing and Ordering Real Numbers
STA: CO 1.2 | CO 1.1
TOP: 1-1 Example 3
KEY: comparing fractions
4. ANS:
<
PTS: 1
DIF: L2
REF: 1-1 Properties of Real Numbers
OBJ: 1-1.1 Graphing and Ordering Real Numbers
STA: CO 1.2 | CO 1.1
TOP: 1-1 Example 3
KEY: irrational numbers | compare
5. ANS:
>
PTS: 1
DIF: L4
REF: 1-1 Properties of Real Numbers
OBJ: 1-1.1 Graphing and Ordering Real Numbers
STA: CO 1.2 | CO 1.1
TOP: 1-1 Example 3
KEY: compare | square root | rational numbers | real numbers
6. ANS:
<
PTS: 1
DIF: L3
OBJ: 1-1.2 Properties of Real Numbers
KEY: compare | absolute value | integers
7. ANS:
>
REF: 1-1 Properties of Real Numbers
STA: CO 1.2 | CO 1.1
PTS: 1
DIF: L3
OBJ: 1-1.2 Properties of Real Numbers
KEY: compare | absolute value | integers
8. ANS:
48
REF: 1-1 Properties of Real Numbers
STA: CO 1.2 | CO 1.1
PTS: 1
DIF: L3
REF: 1-2 Algebraic Expressions
OBJ: 1-2.1 Evaluating Algebraic Expressions
TOP: 1-2 Example 1
KEY: algebraic expression | order of operations
9. ANS:
32
PTS: 1
DIF: L3
REF: 1-2 Algebraic Expressions
OBJ: 1-2.1 Evaluating Algebraic Expressions
TOP: 1-2 Example 2
KEY: algebraic expression
10. ANS:
1431.36 ft
PTS: 1
DIF: L2
REF: 1-2 Algebraic Expressions
OBJ: 1-2.1 Evaluating Algebraic Expressions
TOP: 1-2 Example 3
KEY: algebraic expression | word problem | problem solving
11. ANS:
PTS: 1
DIF: L2
REF: 1-2 Algebraic Expressions
OBJ: 1-2.2 Simplifying Algebraic Expressions
TOP: 1-2 Example 4
KEY: like terms | combine like terms | algebraic expression
12. ANS:
PTS: 1
DIF: L3
REF: 1-2 Algebraic Expressions
OBJ: 1-2.2 Simplifying Algebraic Expressions
TOP: 1-2 Example 4
KEY: like terms | combine like terms | algebraic expression
13. ANS:
PTS: 1
DIF: L4
REF: 1-2 Algebraic Expressions
OBJ: 1-2.2 Simplifying Algebraic Expressions
TOP: 1-2 Example 4
KEY: like terms | algebraic expression
14. ANS:
17
PTS: 1
DIF: L2
OBJ: 1-3.1 Solving Equations
KEY: solve an equation
15. ANS:
REF: 1-3 Solving Equations
STA: CO 2.1
TOP: 1-3 Example 1
PTS: 1
DIF: L3
OBJ: 1-3.1 Solving Equations
KEY: solve an equation
16. ANS:
1
x = 1 or x = 2
3
REF: 1-3 Solving Equations
STA: CO 2.1
TOP: 1-3 Example 1
PTS: 1
DIF: L2
OBJ: 1-5.1 Absolute Value Equations
TOP: 1-5 Example 1
17. ANS:
2
x = 0 or x = 2
3
REF: 1-5 Absolute Value Equations and Inequalities
STA: CO 2.1 | CO 2.5
KEY: absolute value
PTS: 1
DIF: L2
OBJ: 1-5.1 Absolute Value Equations
TOP: 1-5 Example 2
18. ANS:
REF: 1-5 Absolute Value Equations and Inequalities
STA: CO 2.1 | CO 2.5
KEY: absolute value
;
PTS: 1
DIF: L2
REF: 1-3 Solving Equations
OBJ: 1-3.1 Solving Equations
STA: CO 2.1
TOP: 1-3 Example 4
KEY: solve an equation | restrictions on a variable
19. ANS:
;
PTS: 1
DIF: L3
REF: 1-3 Solving Equations
OBJ: 1-3.1 Solving Equations
STA: CO 2.1
TOP: 1-3 Example 4
KEY: solve an equation | restrictions on a variable
20. ANS:
k3
–8 –6 –4 –2
0
2
4
6
8
PTS: 1
DIF: L2
REF: 1-4 Solving Inequalities
OBJ: 1-4.1 Solving and Graphing Inequalities
STA: CO 2.1 | CO 2.5
TOP: 1-4 Example 1
KEY: inequality | graphing
21. ANS:
1
r 1
2
–8 –6 –4 –2
0
2
4
6
8
PTS: 1
DIF: L2
REF: 1-4 Solving Inequalities
OBJ: 1-4.1 Solving and Graphing Inequalities
STA: CO 2.1 | CO 2.5
TOP: 1-4 Example 1
KEY: inequality | graphing
22. ANS:
k  –4
–8 –6 –4 –2
0
2
4
6
8
PTS: 1
DIF: L2
REF: 1-4 Solving Inequalities
OBJ: 1-4.1 Solving and Graphing Inequalities
STA: CO 2.1 | CO 2.5
TOP: 1-4 Example 1
KEY: inequality | graphing
23. ANS:
y0
–8 –6 –4 –2
0
2
4
6
8
PTS: 1
DIF: L2
REF: 1-4 Solving Inequalities
OBJ: 1-4.1 Solving and Graphing Inequalities
STA: CO 2.1 | CO 2.5
TOP: 1-4 Example 1
KEY: inequality | graphing
24. ANS:
m  –5
–8 –6 –4 –2
0
2
4
6
8
PTS: 1
DIF: L3
REF: 1-4 Solving Inequalities
OBJ: 1-4.1 Solving and Graphing Inequalities
STA: CO 2.1 | CO 2.5
TOP: 1-4 Example 1
KEY: inequality | graphing
25. ANS:
no solutions
–8 –6 –4 –2
0
2
4
6
8
PTS: 1
DIF: L2
REF: 1-4 Solving Inequalities
OBJ: 1-4.1 Solving and Graphing Inequalities
STA: CO 2.1 | CO 2.5
TOP: 1-4 Example 2
KEY: inequality | graphing | no solutions
26. ANS:
–8 –6 –4 –2
PTS:
OBJ:
TOP:
KEY:
27. ANS:
0
2
4
6
8
1
DIF: L3
REF: 1-4 Solving Inequalities
1-4.2 Compound Inequalities
STA: CO 2.1 | CO 2.5
1-4 Example 4
compound inequality containing AND | compound inequality | graphing
PTS: 1
DIF: L3
REF: 1-5 Absolute Value Equations and Inequalities
OBJ: 1-5.1 Absolute Value Equations
TOP: 1-5 Example 3
28. ANS:
x = 3 or 2
STA: CO 2.1 | CO 2.5
KEY: absolute value | extraneous solutions
PTS: 1
DIF: L2
OBJ: 1-5.1 Absolute Value Equations
TOP: 1-5 Example 3
29. ANS:
REF: 1-5 Absolute Value Equations and Inequalities
STA: CO 2.1 | CO 2.5
KEY: absolute value | extraneous solutions
–20 –15 –10 –5
0
5 10 15 20
PTS: 1
DIF: L2
REF: 1-5 Absolute Value Equations and Inequalities
OBJ: 1-5.2 Absolute Value Inequalities STA: CO 2.1 | CO 2.5
TOP: 1-5 Example 4
KEY: absolute value | graphing | compound inequality containing OR
30. ANS:
–18 < x < 8
–20 –15 –10 –5
0
5 10 15 20
PTS: 1
DIF: L2
REF: 1-5 Absolute Value Equations and Inequalities
OBJ: 1-5.2 Absolute Value Inequalities STA: CO 2.1 | CO 2.5
TOP: 1-5 Example 5
KEY: absolute value | graphing | compound inequality containing AND
31. ANS:
{(–2, 5), (–1, 2), (0, 1), (1, 2), (2, 5)}; domain: {–2, –1, 0, 1, 2}; range: {1, 2, 5}
PTS: 1
DIF: L2
REF: 2-1 Relations and Functions
OBJ: 2-1.1 Graphing Relations
STA: CO 2.2 | CO 2.4 | CO 2.6 | CO 2.11
TOP: 2-1 Example 2
KEY: ordered pair | domain | range | relation
32. ANS:
Domain: x > 0; range: y > 0; yes, it is a function.
PTS: 1
DIF: L3
OBJ: 2-1.2 Identifying Functions
TOP: 2-1 Example 5
33. ANS:
REF: 2-1 Relations and Functions
STA: CO 2.2 | CO 2.4 | CO 2.6 | CO 2.11
KEY: domain | range | relation
y
4
2
–4
–2
O
2
4
x
–2
–4
PTS: 1
DIF: L2
OBJ: 2-2.1 Graphing Linear Equations
TOP: 2-2 Example 1
34. ANS:
REF: 2-2 Linear Equations
STA: CO 2.1 | CO 2.2 | CO 2.4 | CO 2.5 | CO 2.6
KEY: linear equation | graphing
y
12
8
4
–12
–8
–4 O
–4
4
8
12 x
–8
–12
PTS: 1
DIF: L3
OBJ: 2-2.1 Graphing Linear Equations
TOP: 2-2 Example 1
35. ANS:
8x + y = –18
REF: 2-2 Linear Equations
STA: CO 2.1 | CO 2.2 | CO 2.4 | CO 2.5 | CO 2.6
KEY: graphing | linear equation
PTS: 1
DIF: L2
OBJ: 2-2.2 Writing Equations of Lines
TOP: 2-2 Example 4
36. ANS:
 8 x + y =  61
7
7
REF: 2-2 Linear Equations
STA: CO 2.1 | CO 2.2 | CO 2.4 | CO 2.5 | CO 2.6
KEY: point-slope form | standard form of linear equation
PTS: 1
DIF: L3
OBJ: 2-2.2 Writing Equations of Lines
TOP: 2-2 Example 4
REF: 2-2 Linear Equations
STA: CO 2.1 | CO 2.2 | CO 2.4 | CO 2.5 | CO 2.6
KEY: point-slope form | standard form of linear equation
37. ANS:
3
5
PTS: 1
DIF: L2
OBJ: 2-2.2 Writing Equations of Lines
TOP: 2-2 Example 6
38. ANS:
REF: 2-2 Linear Equations
STA: CO 2.1 | CO 2.2 | CO 2.4 | CO 2.5 | CO 2.6
KEY: point-slope form | standard form of linear equation | slope
PTS: 1
DIF: L2
OBJ: 2-2.2 Writing Equations of Lines
TOP: 2-2 Example 6
39. ANS:
undefined
REF: 2-2 Linear Equations
STA: CO 2.1 | CO 2.2 | CO 2.4 | CO 2.5 | CO 2.6
KEY: point-slope form | standard form of linear equation | slope
PTS: 1
DIF: L3
OBJ: 2-2.2 Writing Equations of Lines
TOP: 2-2 Example 7
40. ANS:
4
22
y= x 
5
5
REF: 2-2 Linear Equations
STA: CO 2.1 | CO 2.2 | CO 2.4 | CO 2.5 | CO 2.6
KEY: vertical line | horizontal line | undefined slope | slope
PTS: 1
DIF: L2
OBJ: 2-2.2 Writing Equations of Lines
TOP: 2-2 Example 7
41. ANS:
y = 3 x  6
REF: 2-2 Linear Equations
STA: CO 2.1 | CO 2.2 | CO 2.4 | CO 2.5 | CO 2.6
KEY: slope | perpendicular | equation of a line
PTS: 1
DIF: L2
OBJ: 2-2.2 Writing Equations of Lines
TOP: 2-2 Example 7
42. ANS:
h = 56t + 158
REF: 2-2 Linear Equations
STA: CO 2.1 | CO 2.2 | CO 2.4 | CO 2.5 | CO 2.6
KEY: slope | equation of a line
PTS: 1
DIF: L2
OBJ: 2-4.1 Modeling Real-World Data
TOP: 2-4 Example 1
43. ANS:
REF: 2-4 Using Linear Models
STA: CO 2.1 | CO 2.6 | CO 2.2
KEY: linear equation
y
16
12
8
4
–8
–4
O
4
8
x
–4
PTS: 1
DIF: L2
REF: 2-5 Absolute Value Functions and Graphs
OBJ: 2-5.1 Graphing Absolute Value Functions
STA: CO 2.2 | CO 2.6 | CO 2.3
TOP: 2-5 Example 1
KEY: absolute value
44. ANS:
4 y
–8
–4
O
4
8
x
–4
–8
–12
–16
PTS: 1
DIF: L2
REF: 2-5 Absolute Value Functions and Graphs
OBJ: 2-5.1 Graphing Absolute Value Functions
STA: CO 2.2 | CO 2.6 | CO 2.3
TOP: 2-5 Example 1
KEY: absolute value
45. ANS:
2
( , –4)
3
PTS: 1
DIF: L3
REF: 2-5 Absolute Value Functions and Graphs
OBJ: 2-5.1 Graphing Absolute Value Functions
STA: CO 2.2 | CO 2.6 | CO 2.3
TOP: 2-5 Example 1
KEY: absolute value | vertex
46. ANS:
PTS: 1
DIF: L2
OBJ: 2-6.1 Translating Graphs
TOP: 2-6 Example 1
REF: 2-6 Families of Functions
STA: CO 2.3 | CO 2.4 | CO 4.7
KEY: horizontal translation | vertical translation
47. ANS:
PTS: 1
DIF: L2
OBJ: 2-6.1 Translating Graphs
TOP: 2-6 Example 1
48. ANS:
; 5 units left;
REF: 2-6 Families of Functions
STA: CO 2.3 | CO 2.4 | CO 4.7
KEY: vertical translation
y
6
4
2
–6
–4
–2 O
–2
2
4
6 x
–4
–6
PTS: 1
DIF: L2
OBJ: 2-6.1 Translating Graphs
TOP: 2-6 Example 3
49. ANS:
REF: 2-6 Families of Functions
STA: CO 2.3 | CO 2.4 | CO 4.7
KEY: horizontal translation | multi-part question
y
6
3
–6
–3
O
3
6
x
–3
–6
PTS: 1
DIF: L2
OBJ: 2-6.1 Translating Graphs
TOP: 2-6 Example 2
50. ANS:
REF: 2-6 Families of Functions
STA: CO 2.3 | CO 2.4 | CO 4.7
KEY: horizontal translation
y
6
4
2
–6 –4 –2 O
–2
2
4
6
x
–4
–6
PTS: 1
DIF: L2
OBJ: 2-7.1 Graphing Linear Inequalities
TOP: 2-7 Example 1
51. ANS:
REF: 2-7 Two-Variable Inequalities
STA: CO 2.1 | CO 2.5
KEY: inequality | graphing
PTS: 1
DIF: L3
OBJ: 2-7.1 Graphing Linear Inequalities
TOP: 2-7 Example 2
52. ANS:
20p + 45r  180
REF: 2-7 Two-Variable Inequalities
STA: CO 2.1 | CO 2.5
KEY: inequality | word problem | problem solving
r
6
4
2
0
2
4
6
p
PTS: 1
DIF: L2
OBJ: 2-7.1 Graphing Linear Inequalities
TOP: 2-7 Example 2
53. ANS:
REF: 2-7 Two-Variable Inequalities
STA: CO 2.1 | CO 2.5
KEY: inequality | word problem | problem solving
y
6
3
–6
–3
O
3
6
x
–3
–6
PTS: 1
DIF: L2
REF: 2-7 Two-Variable Inequalities
OBJ: 2-7.2 Graphing Two-Variable Absolute Value Inequalities
STA: CO 2.1 | CO 2.5
TOP: 2-7 Example 3
KEY: absolute value
54. ANS:
y  |x – 3| – 1
PTS:
OBJ:
STA:
KEY:
55. ANS:
1
DIF: L2
REF: 2-7 Two-Variable Inequalities
2-7.2 Graphing Two-Variable Absolute Value Inequalities
CO 2.1 | CO 2.5
TOP: 2-7 Example 4
absolute value
y
6
3
–6
–3
O
3
6
x
–3
–6
PTS: 1
DIF: L2
REF: 2-6 Families of Functions
OBJ: 2-6.2 Stretches | Shrinks | and Reflections
STA: CO 2.3 | CO 2.4 | CO 4.7
TOP: 2-6 Example 5
KEY: stretch and shrink | reflection
56. ANS:
–13
PTS: 1
DIF: L2
OBJ: 1-1.2 Properties of Real Numbers
REF: 1-1 Properties of Real Numbers
STA: CO 1.2 | CO 1.1
TOP: 1-1 Example 6
57. ANS:
KEY: absolute value | real numbers
y
6
4
2
–6
–4
–2
O
2
4
6
x
–2
–4
–6
PTS: 1
DIF: L2
REF: 2-1 Relations and Functions
OBJ: 2-1.1 Graphing Relations
STA: CO 2.2 | CO 2.4 | CO 2.6 | CO 2.11
TOP: 2-1 Example 1
KEY: relation | graphing | ordered pair
58. ANS:
No; a domain value corresponds to two or more range values.
PTS: 1
DIF: L2
REF: 2-1 Relations and Functions
OBJ: 2-1.1 Graphing Relations
STA: CO 2.2 | CO 2.4 | CO 2.6 | CO 2.11
TOP: 2-1 Example 4
KEY: relation | domain | range
59. ANS:
Yes; for each element in the domain there is exactly one element in the range.
PTS: 1
DIF: L2
OBJ: 2-1.1 Graphing Relations
TOP: 2-1 Example 4
60. ANS:
The slope of the line is
REF: 2-1 Relations and Functions
STA: CO 2.2 | CO 2.4 | CO 2.6 | CO 2.11
KEY: relation | domain | range
.
PTS: 1
DIF: L3
OBJ: 2-2.2 Writing Equations of Lines
TOP: 2-2 Example 6
REF: 2-2 Linear Equations
STA: CO 2.1 | CO 2.2 | CO 2.4 | CO 2.5 | CO 2.6
KEY: standard form of linear equation | slope
OTHER
61. ANS:
if all of the songs on the CD are the maximum length, 5 minutes long, then the minimum number
of songs will fit on the CD. 120 divided by 5 is 24, so the CD can contain a minimum of 24 songs. The shortest
possible song is 3.5 minutes. Since 120 divided by 3.5 is approximately 34.29, the CD can contain at most 34
complete songs.
PTS: 1
DIF: L3
REF: 1-4 Solving Inequalities
OBJ: 1-4.2 Compound Inequalities
STA: CO 2.1 | CO 2.5
KEY: compound inequality | reasoning | writing in math
62. ANS:
Answers may vary. Sample: Imagine drawing a vertical line through every point on the graph. If no line
intersects the graph more than once, the graph is a function. It works because if a vertical line intersects the
graph twice, then two points have the same x-value but two different y-values.
PTS: 1
DIF: L3
OBJ: 2-1.2 Identifying Functions
TOP: 2-1 Example 5
REF: 2-1 Relations and Functions
STA: CO 2.2 | CO 2.4 | CO 2.6 | CO 2.11
KEY: vertical-line test | graphing | writing in math | reasoning