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Final Review
Solve the equation.
____
____
____
____
____
1.
a. d = –13
b. d = –25
c. d = –29
d. d = –11
a. k = 16
b. k = 63
c. k = –63
d.
7
k = 
9
a. n = –4
b. n = 10
c. n = –10
d. n = 8
a. k = 3
b.
1
k =
3
c. k = 3
d.
1
k = 
3
a. y = , y =
b. no solution
c. y =
d. y = , y =
2.
3.
4.
5.
Solve the equation. Determine whether the equation has one solution, no solution, or infinitely many
solutions.
____
6.
a.
b.
____
–4; one solution
infinitely many solutions
c.
d.
no solution
0 ; one solution
7.
a.
b.
1
; one solution
8
0; one solution
c. infinitely many solutions
d. no solution
Solve the equation. Graph the solution(s), if possible.
____
8.
a. no solution
c.
;
–4
–2
0
2
4
b.
,
;
–4
____
d.
–2
0
2
;
–4
4
–2
0
2
4
9.
a.
c. no solution
;
–2
0
2
b.
4
6
8
d.
;
–2
0
2
4
6
;
–2
8
0
2
4
6
8
____ 10. In a speech class, students must give a final speech for their exam. The speech can be 15 minutes, or within
that time by 4 minutes. Write an absolute value equation that represents the minimum and maximum lengths
of the final speech.
a.
c.
b.
d.
11. The height of a tree is 38 inches. After 4 years, the height is 9 feet 10 inches. How many inches did the tree
grow each year?
Write the sentence as an inequality.
____ 12.
a.
b.
c.
d.
____ 13. A number b times
a.
17
b.
is at least 17.
c.
d.
17
17
17
Graph the inequality.
____ 14.
a.
c.
–8
–4
0
4
8
–8
–4
0
4
8
b.
–4
0
4
8
–8
–4
0
4
8
d.
Solve the inequality. Graph the solution.
____ 15.
–8
a.
c.
–2
0
2
4
6
–20
8
b.
–18
–16
–14
–12
–10
d.
–20
–2
0
2
4
6
–18
–16
–14
–12
8
____ 16.
a.
c.
1
–1
b.
0
1
2
3
0
4
d.
0
2
4
6
4
4
6
8
–6
–4
–2
0
–4
–8
8
2
Solve the inequality.
____ 17.
a.
7
b. no solution
c.
7
d. all real numbers
____ 18.
5
5
a.
b.
c. no solution
d. all real numbers
____ 19. Which of the inequalities are represented by the graph?
–12 –10 –8
–6
–4
–2
0
2
4
6
8
10
12
d. 0  x – 10
e. 2  x – 11
a.
b. x + 5  15
c.
Find the domain and range of the function represented by the graph.
y
____ 20.
1
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
a. domain: 1, 2, 3, 4; range: –3, –2, –1, 0
–10
b. domain: 0, 1, 2, 3; range: –3, –2, –1, 0
c. domain: 1, 2, 3, 4; range: 0, 1, 2, 3
d. domain: –3, –2, –1, 0; range: 0, 1, 2, 3
____ 21. The amount of calories you consume after eating x pieces of candy is represented by the function
Find the domain of the function and determine whether it is discrete or continuous.
a.
; continuous
c.
; continuous
b.
d.
; discrete
; discrete
Find the value of x so that the function has the given value.
____ 22.
c. –343
d. 343
a. 7
b. –7
Graph the linear function.
____ 23.
a.
5
c.
y
–5
5
–5
5 x
–5
b.
5
–5
5 x
–5
d.
y
5 x
–5
y
5
–5
y
5 x
–5
____ 24. You spend $3.50 on fruit. Apples cost $0.20 each while oranges cost $0.30 each. The equation
models the situation, where x is the number of apples and y is the number of oranges.
Which of the following is not a possible solution in the context of the problem?
a. 1 apple; 11 oranges
c. 11 apples; 1 orange
.
b. 7 apples; 7 oranges
d. 4 apples; 9 oranges
Describe the slope of the line. Then find the slope.
y
____ 25.
4
(1, 3)
2
–4
4
–2
x
(1, –2)
–4
a. positive; 1
b. negative;
c. undefined
d. zero; 0
____ 26. The depth d (in feet) of a manmade lake is represented by the function
month with t = 1 corresponding to January. What is the lowest depth of the lake?
a. 21 ft
c. 2 ft
b. 8 ft
d. 13 ft
____ 27. Which equations represent linear functions?
a.
b.
c.
d.
e.
f.
Write an equation of the line with the given slope and y-intercept.
____ 28. slope: –3
y-intercept: –6
a.
b.
c.
d.
Write an equation of the line in slope-intercept form.
, where t is the
____ 29.
y
5
(–4, 4)
4
3
(0, 4)
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
a.
b.
c.
d.
____ 30.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
–2
(0, 0)
1
2
3
4
5
x
(4, –2)
–3
–4
–5
a. y = 2x
b. y = 2x – 2
c.
1
y=  x
2
d.
1
y=  x+2
2
Write an equation of the line that passes through the given points.
____ 31. (–5, –1), (0, –1)
a. y = –5
b.
2
y= x+ 1
5
____ 32. Write a linear function f with the values
a.
b.
c. y = –1
d.
5
23
y= x+
2
2
.
c.
d.
Write an equation in point-slope form of the line that passes through the given point and has the given
slope.
____ 33. (–3, 2); m = –3
a.
b.
c.
d.
____ 34. Write an equation of the line that passes through the given point and is parallel to the given line.
3
(4, 5); y =  x + 3
2
a.
c.
3
y= x–1
2
b.
3
y= x+3
2
3
y =  x + 11
2
d.
3
y = x + 11
2
____ 35. Write an equation of the line that passes through the given point and is perpendicular to the given line.
1
(–6, –4); y = x + 1
3
c. y = 3x + 14
a.
1
y= x+1
3
b.
1
y = x – 22
3
d. y = 3x – 22
____ 36. The city council members of a small coastal town want to construct a new boardwalk along the beach. They
want the boardwalk (shown in bold) to be perpendicular to the road leading to the beach. Write an equation
that represents the boardwalk.
y
8
4
–8
(4, 4)
–4
4
–4
8
x
(0, –4)
–8
a.
b.

1
2
c.
d.
–2
____ 37. The table shows the ages and prices of used cars from an online site. Write an equation that models price as a
function of age.
Age of car (in years), x
Price (in thousands of dollars), y
a.
b.
1
20.5
3
18.4
c.
d.
____ 38. Which two pairs of points lie on perpendicular lines?
a.
b.
c.
5
16.1
7
13.5
9
11.4
11
8.8
13
6
Final Review
Answer Section
1. ANS: D
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 1.1
NAT: HSA-REI.B.3
KEY: equation | linear equations in one variable | solution of an equation | solving simple linear equations |
solving equations by adding or subtracting
NOT: Example 1
2. ANS: C
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 1.1
NAT: HSA-REI.B.3
KEY: equation | linear equations in one variable | solution of an equation | solving simple linear equations |
solving equations by multiplying or dividing
NOT: Example 2
3. ANS: C
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 1.2
NAT: HSA-REI.B.3
KEY: equation | linear equations in one variable | solution of an equation | solving multi-step linear equations
NOT:
Example 2
4. ANS: C
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 1.3
NAT: HSA-REI.B.3
KEY: solving linear equations with variables on both sides | one solution | equation | solution of an equation |
linear equations in one variable
NOT: Example 2
5. ANS: A
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 1.4
NAT: HSA-REI.B.3
KEY: absolute value equation | solving absolute value equations
NOT: Example 2
6. ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 1.3
NAT: HSA-REI.B.3
KEY: solving linear equations with variables on both sides | infinitely many solutions | equation | no solution
| linear equations in one variable | solution of an equation
NOT: Example 3
7. ANS: C
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 1.3
NAT: HSA-REI.B.3
KEY: solving linear equations with variables on both sides | infinitely many solutions | equation | no solution
| linear equations in one variable | solution of an equation
NOT: Example 3
8. ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 1.4
NAT: HSA-REI.B.3
KEY: absolute value equation | solving absolute value equations | graphing absolute value solutions
NOT: Example 1
9. ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 1.4
NAT: HSA-REI.B.3
KEY: absolute value equation | solving absolute value equations | graphing absolute value solutions
NOT: Example 1
10. ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 1.4
NAT: HSA-CED.A.1
KEY: absolute value equation | application | writing absolute value equations
NOT: Example 3-1
11. ANS: 20
PTS:
NAT:
KEY:
NOT:
12. ANS:
1
DIF: Level 2
REF: Algebra 1 Sec. 1.2
HSN-Q.A.1 | HSA-CED.A.1 | HSA-REI.B.3
equation | linear equations in one variable | application | solving multi-step linear equations
Example 4
D
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 2.1
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
NAT: HSA-CED.A.1
KEY: writing linear inequalities | inequality
NOT: Example 1
ANS: D
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 2.1
NAT: HSA-CED.A.1
KEY: writing linear inequalities | inequality
NOT: Example 1
ANS: C
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 2.1
NAT: HSA-CED.A.1
KEY: graph of an inequality | inequality
NOT: Example 3
ANS: A
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 2.2
NAT: HSA-REI.B.3
KEY: solving inequalities by adding or subtracting | solving inequalities | inequality | graph of an inequality
NOT: Example 1
ANS: C
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 2.3
NAT: HSA-REI.B.3
KEY: solving inequalities | solving inequalities by multiplying or dividing by negative numbers | inequality |
graph of an inequality
NOT: Example 2
ANS: D
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 2.4
NAT: HSA-REI.B.3
KEY: solving multi-step inequalities | inequality | solving inequalities
NOT: Example 3
ANS: A
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 2.4
NAT: HSA-REI.B.3
KEY: solving multi-step inequalities | inequality | solving inequalities
NOT: Example 3
ANS: B, C, D
PTS: 1
DIF: Level 2
REF: Algebra 1 Sec. 2.2
NAT: HSA-CED.A.1 | HSA-REI.B.3
KEY: solving inequalities by adding or subtracting | solving inequalities | inequality | graph of an inequality |
writing linear inequalities
NOT: Combined Concept
ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 3.1
NAT: HSF-IF.A.1 KEY: function | domain | range
NOT: Example 3
ANS: D
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 3.2
NAT: HSA-REI.D.10 | HSF-IF.B.5 | HSF-IF.C.7a | HSF-LE.A.1b
KEY: linear function | discrete domain | continuous domain | application
NOT: Example 5-1
ANS: A
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 3.3
NAT: HSA-CED.A.2 | HSF-IF.A.1 | HSF-IF.A.2
KEY: function
NOT: Example 3
ANS: D
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 3.3
NAT: HSA-CED.A.2 | HSF-IF.A.1 | HSF-IF.A.2 | HSF-IF.C.7a KEY: function | linear function
NOT: Example 4
ANS: C
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 3.4
NAT: HSA-CED.A.2 | HSF-IF.C.7a
KEY: standard form | x-intercept | y-intercept | application | linear equation
NOT: Example 3-1
ANS: C
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 3.5
NAT: HSA-CED.A.2
KEY: slope | rise | run
NOT: Example 1
ANS: D
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 3.7
NAT: HSA-CED.A.2
KEY: absolute value function
NOT:
27. ANS:
NAT:
NOT:
28. ANS:
NAT:
KEY:
29. ANS:
NAT:
KEY:
NOT:
30. ANS:
NAT:
KEY:
NOT:
31. ANS:
NAT:
KEY:
NOT:
32. ANS:
NAT:
KEY:
33. ANS:
NAT:
KEY:
NOT:
34. ANS:
NAT:
KEY:
NOT:
35. ANS:
NAT:
KEY:
NOT:
36. ANS:
NAT:
KEY:
37. ANS:
NAT:
KEY:
NOT:
38. ANS:
NAT:
NOT:
Application-1
A, C, D
PTS: 1
DIF: Level 2
REF: Algebra 1 Sec. 3.2
HSF-LE.A.1b
KEY: linear function | nonlinear function
Example 3
D
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 4.1
HSA-CED.A.2 | HSF-BF.A.1a | HSF-LE.A.2
writing equations | slope | y-intercept | equation
NOT: Example 1
B
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 4.1
HSA-CED.A.2 | HSF-BF.A.1a | HSF-LE.A.2
writing equations | linear equation in two variables | slope-intercept form | equation
Example 2
C
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 4.1
HSA-CED.A.2 | HSF-BF.A.1a | HSF-LE.A.2
writing equations | linear equation in two variables | slope-intercept form | equation
Example 2
C
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 4.1
HSA-CED.A.2 | HSF-BF.A.1a | HSF-LE.A.2
writing equations | linear equation in two variables | equation
Example 3
D
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 4.1
HSA-CED.A.2 | HSF-BF.A.1a | HSF-LE.A.2
writing linear functions | linear function
NOT: Example 4
B
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 4.2
HSA-CED.A.2 | HSF-BF.A.1a | HSF-LE.A.2
writing equations of lines using a slope and a point | point-slope form | writing equations | equation
Example 1
C
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 4.3
HSA-CED.A.2 | HSF-LE.A.2
parallel lines | writing equations of parallel lines | equation | writing equations
Example 2
D
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 4.3
HSA-CED.A.2 | HSF-LE.A.2
perpendicular lines | writing equations | writing equations of perpendicular lines | equation
Example 4
A
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 4.3
HSA-CED.A.2 | HSF-LE.A.2
application | perpendicular lines | writing equations of perpendicular lines | equation | writing equations
NOT:
Example 5-1
B
PTS: 1
DIF: Level 1
REF: Algebra 1 Sec. 4.4
HSF-LE.B.5 | HSS-ID.B.6a | HSS-ID.B.6c | HSS-ID.C.7
application | line of best fit | finding lines of best fit | equation | writing equations | slope | y-intercept
Example 3-1
A, C
PTS: 1
DIF: Level 2
REF: Algebra 1 Sec. 4.3
HSA-CED.A.2 | HSF-LE.A.2
KEY: parallel lines | perpendicular lines | equation
Combined Concept