Name: ______________________
Class: _________________
Date: _________
First Semester Final Review Algebra 1
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Evaluate u + xy, for u = 18, x = 10, and y = 8.
a. 188
b. 36
c.
98
d.
224
Simplify the expression.
____
____
____
2.
3.
1
(–12m + 38)
2
a. −6m + 38
b. –24m + 19
c.
d.
−6m + 76
−6m + 19
1 ÊÁ
n Ë −6 + 27m − 51p ˆ˜¯
3
a. –18n + 81m n – 153np
b. –2n + 9m – 17p
c.
d.
–2n + 9m n – 17np
–2n – 9m n + 17np
4. Evaluate x(–y + z) for x = 3, y = 3, and z = 1.
a. –6
b. 10
c.
Name the property the equation illustrates.
____
5. 8 + 3.4 = 3.4 + 8
a. Inverse Property of Addition
b. Associative Property of Addition
c. Commutative Property of Addition
d. Inverse Property of Multiplication
____
6. 7 + (4 + 4) = (7 + 4) + 4
a. Inverse Property of Addition
b. Associative Property of Addition
c. Commutative Property of Multiplication
d. Commutative Property of Addition
____
ÁÊ 3 ˜ˆ ÁÊ 3 ˜ˆ
7. 2 ÁÁÁÁ − ˜˜˜˜ = ÁÁÁÁ − ˜˜˜˜ 2
ÁË 9 ˜¯ ÁË 9 ˜¯
a. Associative Property of Addition
b. Commutative Property of Multiplication
c. Inverse Property of Multiplication
d. Commutative Property of Addition
1
12
d.
–8
ID: A
Name: ______________________
____
ID: A
8. (ab)3 = a(b3)
a. Inverse Property of Multiplication
b. Associative Property of Addition
c. Associative Property of Multiplication
d. Commutative Property of Multiplication
Solve the equation.
____
9.
y
= −10
4
1
a. −2
2
b.
–14
c.
40
d.
–40
b.
–9
c.
–5
d.
–6
b.
16
c.
–16
d.
1.8
b.
1
2
7
c.
−7
d.
7
____ 13. 3(y + 6) = 30
a. 5
b.
16
c.
4
d.
–16
____ 14. 37 – 18 + 8w = 67
a. –6
b.
4
c.
7
d.
6
b.
3. 3
c.
0. 6
d.
3
____ 16. 3p − 1 = 5(p − 1) − 2(7 − 2p)
a. 3
b. 0
c.
–9
d.
–10
____ 17. 5x – 5 = 3x – 9
a. –2
1
c.
–1
d.
–3
−1
c.
−2
d.
–4
____ 10. 9d = –54
a. 6
x
+ 4
8
–80
____ 11. −6 =
a.
____ 12.
3
x+5=8
7
a.
7
2
3
____ 15. 6(4.5y − 12) = 9
a.
28
b.
____ 18. 8d – 4d – 6d – 8 = 2d
a. 0
b.
____ 19. Two angles are complementary if the sum of their measures is 90°. ∠P and ∠Q are complementary. The
measure of ∠P is 61°. Write and solve an equation to find the measure of ∠Q.
a. 61° + 90° = Q°; 151°
c. Q° + 90° = 61°; −29°
b. 61° + Q° = 90°; 29°
d. 61° + Q° = 90°; 39°
2
Name: ______________________
ID: A
____ 20. You are driving to visit a friend in another state who lives 440 miles away. You are driving 55 miles per
hour and have already driven 275 miles. Write and solve an equation to find how much longer in hours
you must drive to reach your destination.
a. 55h + 275 = 440; h = 3
c. 440h − 275 = 55; h = 110
b. 55h − 275 = 440; h = 13
d. 55h + 275h = 440; h = 1. 3
____ 21. Steven wants to buy a $565 bicycle. Steven has no money saved, but will be able to deposit $30 into a
savings account when he receives his paycheck each Friday. However, before Steven can buy the bike, he
must give his sister $65 that he owes her. For how many weeks will Steven need to deposit money into
his savings account before he can pay back his sister and buy the bike?
a. 25 weeks
b. 19 weeks
c. 22 weeks
d. 21 weeks
____ 22. Find the value of y.
−6y + 14 + 4y = 32
a. 18
b.
1.8
c.
–9
d.
9
____ 23. Find the measure of ∠x. (Hint: The sum of the measures of the angles in a triangle is 180°.)
a.
6°
b.
180°
c.
90°
d.
86°
____ 24. John and 2 friends are going out for pizza for lunch. They split one pizza and 3 large drinks. The pizza
cost $14.00. After using a $7.00 gift certificate, they spend a total of $12.10. Write an equation to
model this situation, and find the cost of one large drink.
a. 3d + $14.00 – $7.00 = $12.10; $1.70
b. 2d + $14.00 – $7.00 = $12.10; $2.55
c. 3d – $14.00 + $7.00 = $12.10; $9.55
d. 3d + $14.00 – $7.00 = $12.10; $1.90
____ 25. The sum of two consecutive integers is 59.
values of the two integers.
a. n + 2n = 59; n = 19; 2n = 38
b. n + n + 1 = 59; n = 29; n + 1 =
c. n + n + 1 = 59; n = 30; n + 1 =
d. n + n + 1 = 59; n = 29; n + 1 =
Write an equation that models this situation and find the
28
31
30
____ 26. The sum of four consecutive odd integers is −72. Write an equation to model this situation, and find the
values of the four integers.
a. n + (n − 2) + (n − 4) + (n − 6) = − 72;
n = − 21; n − 2 = − 23; n − 4 = − 25; n − 6 = − 27
b. n + n + 2 + n + 4 + n + 6 = − 72;
n = − 21; n + 2 = − 23; n + 4 = − 25; n + 6 = − 27
c. n − (n + 2) − (n + 4) − (n + 6) = − 72;
n = −20; n + 2 = − 18; n + 4 = − 16; n + 6 = − 14
d. n + n + 2 + n + 4 + n + 6 = − 72;
n = − 21; n + 2 = − 19; n + 4 = − 17; n + 6 = − 15
3
Name: ______________________
ID: A
____ 27. Carlos and Maria drove a total of 258 miles in 5 hours. Carlos drove the first part of the trip and
averaged 53 miles per hour. Maria drove the remainder of the trip and averaged 51 miles per hour. For
approximately how many hours did Maria drive? Round your answer to the nearest tenth if necessary.
a. 3.5 hours
b. 2.5 hours
c. 1.8 hours
d. 1.5 hours
9
C + 32. Solve the
5
formula for degrees Celsius (C). Then find the temperature in degrees Celsius (C) when the temperature in
degrees Fahrenheit (F) is –4.
a. –20° C
b. –29° C
c. –14° C
d. –7° C
____ 28. The formula for converting degrees Celsius (C) to degrees Fahrenheit (F) is F =
____ 29. At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle
path.The bicyclist heading north is riding 6 km/hour faster than the bicyclist heading south. At 10:15,
they are 42.5 km apart. Find the two bicyclists’ rates.
a. northbound bicyclist = 20 km/h; southbound bicyclist = 14 km/h
b. northbound bicyclist = 23 km/h; southbound bicyclist = 17 km/h
c. northbound bicyclist = 18 km/h; southbound bicyclist = 11 km/h
d. northbound bicyclist = 20 km/h; southbound bicyclist = 13 km/h
Solve the inequality.
____ 30. –2w < –18
a. w > 9
b.
w < –16
____ 31. | d + 2 | ≥ 6
a. d ≤ − 4 or d ≥ 4
b.
d ≥ − 8 or d ≥ 4
____ 32. | 2x + 9 | < 25
a. –36 < x < 14
b.
–17 < x < 8
c.
w<9
d.
w > –16
c.
d ≤ − 8 or d ≥ 4
d.
d ≤ − 8 or d ≥ 4
c.
–17 > x > 8
d.
–8 < x < 8
4
Name: ______________________
ID: A
Solve the inequality.
____ 33. –5x – 7 < 28
a.
x > –7
b.
____ 34. a + 8 – 2(a – 12) > 0
a. a < 32
b.
21
5
x < –7
c.
x>
a > –16
c.
a < –16
21
5
d.
x<−
d.
a > 32
____ 35. The French club is sponsoring a bake sale. If their goal is to raise at least $140, how many pastries must
they sell at $3.50 each in order to meet that goal? Write and solve an inequality.
a. 3.50p ≥ 140; p ≥ 490
c. 3.50p ≥ 140; p ≥ 136.5
b. 140p ≥ 3.50; p ≥ 40
d. 3.50p ≥ 140; p ≥ 40
Solve the equation. If there is no solution, write no solution.
____ 36. −2 |h − 7 | = − 28
a. no solution
b. h = 21
|
1|
____ 37. 4 | x + | = 20
|
3|
11
11
a. x = 4
or −4
12
12
11
b. x = 4
12
____ 38. $7.80/hour = ____ cents/minute?
a. 13
b. 8.8
c.
d.
h = –7, h = 21
h = 7, h = –21
c.
x=4
d.
no solution
c.
780
d.
4.7
c.
110
d.
1.8
2
1
or −5
3
3
Solve the proportion.
____ 39.
2
11
=
10
x
a. 55
b.
2.2
____ 40. A van travels 220 miles on 10 gallons of gas. Write and solve a proportion to find how many gallons the
van needs to travel 550 miles.
220
550
10
550
a.
=
; 31 gallons of gas
c.
=
; 115 gallons of gas
10
g
220
g
10
550
220
550
b.
=
; 121 gallons of gas
d.
=
; 25 gallons of gas
220
g
10
g
____ 41. During the month of February, Fabulous Feet Shoe Mart sold 50 pairs of red loafers. After an ad
campaign to boost sales, they sold 60 pairs in March. Find the percent of increase in sales.
a. 12%
b. 20%
c. 15%
d. 23%
5
Name: ______________________
ID: A
____ 42. The circulation of a newsletter decreased from 5200 to 3140. Find the percent of decrease in circulation
to the nearest percent.
a. 66%
b. 40%
c. 166%
d. 6%
____ 43. Suppose you choose a marble from a bag containing 2 red marbles, 5 white marbles, and 3 blue marbles.
You return the first marble to the bag and then choose again. Find P(red and blue).
3
7
1
3
a.
b.
c.
d.
5
10
2
50
____ 44. You have three $1 bills, four $5 bills, and two $10 bills in your wallet. You select a bill at random.
Without replacing the bill, you choose a second bill at random. Find P($10 then $1).
1
5
5
2
a.
b.
c.
d.
12
81
72
27
____ 45. A car is driving at a speed of 60 mi/h. What is the speed of the car in feet per minute?
a. 5,280 ft/min
c. 316,800 ft/min
b. 3,600 ft/min
d. 2,580 ft/min
____ 46. Evaluate f ( x) = −2x − 5 for x = 3.
a. –11
b. 1
____ 47. Evaluate f(x) =
a.
1
1
3
1
x for x = 4.
3
1
b.
12
c.
–6
d.
11
c.
3
4
d.
−12
c.
–8
d.
4
2
____ 48. Evaluate f ( x) = −x + 1 for x = –3.
a. –9
b. –4
____ 49. A taxi company charges passengers $2.00 for a ride, no matter how long the ride is, and an additional
$0.20 for each mile traveled. The rule c = 0.20m + 2.00 describes the relationship between the number
of miles m and the total cost of the ride c.
a. What is the charge for a 1-mile ride?
b. What is the charge for a 2.7-mile ride?
a. $2.20; $2.54
b. $2.00; $2.20
c. $0.20; $5.60
d. $0.20; $0.54
Find the slope and y-intercept of the line.
____ 50. y =
a.
4
x–3
3
4
3;
3
b.
–3;
4
3
c.
6
3
;3
4
d.
4
; –3
3
Name: ______________________
ID: A
Write the slope-intercept form of the equation for the line.
____ 51.
a.
y = 3x − 1
c.
b.
y = −3x − 1
d.
7
1
x+1
3
1
y= x−1
3
y=
Name: ______________________
ID: A
____ 52. Use the slope and y-intercept to graph the equation.
3
y= x– 3
4
a.
c.
b.
d.
Find the x- and y-intercept of the line.
____ 53. 2x + 3y = –18
a. x-intercept is 18; y-intercept is 18.
b. x-intercept is –6; y-intercept is –9.
c.
d.
8
x-intercept is 2; y-intercept is 3.
x-intercept is –9; y-intercept is –6.
Name: ______________________
ID: A
Match the equation with its graph.
____ 54. –7x + 7y = –49
a.
b.
c.
d.
9
Name: ______________________
ID: A
Graph the equation.
____ 55. y = –3
a.
b.
c.
d.
10
Name: ______________________
____ 56. x = –4
a.
ID: A
c.
b.
d.
____ 57. A line passes through (1, –5) and (–3, 7).
a. Write an equation for the line in point-slope form.
b. Rewrite the equation in slope-intercept form.
a.
y – 5 = 3(x + 1); y = 3x + 8
b.
y−1=
1
1
8
(x + 5); y = x + ;
3
3
3
1
1
16
(x + 1); y = x +
3
3
3
c.
y−5=
d.
y + 5 = –3(x – 1); y = –3x – 2
Are the graphs of the lines in the pair parallel? Explain.
1
x+8
6
–2x + 12y = –11
a. Yes, since the slope are the same and the y-intercepts are the same.
b. No, since the y-intercepts are different.
c. Yes, since the slope are the same and the y-intercepts are different.
d. No, since the slopes are different.
____ 58. y =
11
Name: ______________________
ID: A
____ 59. y = 5x + 6
–18x + 3y = –54
a. No, since the slopes are different.
b. Yes, since the slopes are the same and the y-intercepts are different.
c. No, since the y-intercepts are different.
d. Yes, since the slope are the same and the y-intercepts are the same.
Write an equation for the line that is parallel to the given line and that passes through the
given point.
____ 60. y = –5x + 3; (–6, 3)
a. y = –5x + 27
b. y = –5x – 27
c.
d.
y = 5x – 9
y = –5x + 9
Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
____ 61. 7x – 4y = 4
x – 4y = 3
a. perpendicular
b.
parallel
c.
neither
1
____ 62. y = − x – 11
2
16x – 8y = –8
a. neither
b.
perpendicular
c.
parallel
Write the equation of a line that is perpendicular to the given line and that passes through
the given point.
____ 63. 4x – 12y = 2; (10, –1)
a. y = 3x + 29
1
b. y = − x + 29
3
c.
d.
y = −3x + 29
1
y=− x+7
3
Short Answer
64. Find the range of f ( x) = −x + 4 for the domain {–3, –2, –1, 1}.
12
Name: ______________________
ID: A
Use the vertical line test to determine whether the relation is a function.
ÔÏ
Ô¸
65. ÔÌ (−1, −2), (3, −1), (−5, 2), (−3, −5) Ô˝
Ó
˛
Other
66. Is the following statement true or false for all values of a and b? If false, give a counterexample.
|a + b | > |b |
13
First Semester Final Review Algebra 1 [Answer Strip]
C
_____
8.
A
_____20.
ID: A
A
_____27.
B
_____42.
A
_____33.
D
_____43.
C
_____
1.
D
_____21.
A
_____28.
D
_____
9.
D
_____
2.
C
_____34.
D
_____35.
C
_____22.
A
_____29.
D
_____10.
C
_____
3.
A
_____11.
A
_____
4.
A
_____12.
A
_____44.
A
_____45.
D
_____23.
C
_____36.
A
_____30.
C
_____37.
A
_____46.
A
_____47.
A
_____24.
C
_____
5.
C
_____13.
C
_____48.
A
_____38.
D
_____14.
D
_____31.
D
_____15.
B
_____
6.
D
_____25.
A
_____39.
A
_____16.
A
_____17.
B
_____
7.
C
_____18.
A
_____49.
D
_____26.
B
_____32.
D
_____40.
D
_____50.
B
_____19.
B
_____41.
First Semester Final Review Algebra 1 [Answer Strip]
D
_____52.
A
_____51.
ID: A
B
_____56.
A
_____54.
A
_____59.
C
_____55.
B
_____60.
C
_____61.
B
_____62.
C
_____63.
D
_____57.
D
_____53.
C
_____58.