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WorksheetsKEYSTONE REVIEW - Algebra 1 (Module 1)
Total questions: 60
Worksheet time: 5hrs 0mins
Order the following numbers from greatest to least.
Complete the comparison below.
-0.75 ______ 3/4
<
>
=
≠
Choose the correct comparison for the numbers below.
0.46, 104%, 5/14
0.46 < 5/14 < 104%
104% > 0.46 > 5/14
104% > 5/14 > 0.46
5/14 > 104% > 0.46
Which list of numbers is in order from least to greatest?
2, √5, √32, 3
2, √5, 3, √32
√32, 3, √5, 2
2, 3, √5, √32
Complete the comparison below.
16/17 _____ 99.8%
>
<
=
≥
Simplify:
√243
9
81
81√2
9√3
Simplify:
√162
54
9√2
81√2
6
Simplify:
√640
8√10
160√2
20√2
64√10
Which value of x makes the below expression equivalent to 21√53 ?
147
441
7
49
The expression below should be further simplified for which value of x?
59
94
3
235
What is the greatest common factor of the monomial:
78x2y2z4 , 12x2yz2
156x4y3z6
156x2y2z4
6x2y2z4
6x2yz4
What is the greatest common factor of the monomials: 21xy4z2 , 77x3y2
231x4y6z2
7x3y4z2
7xy2
231x3y4z2
What is the least common multiple of the monomials: 9xy4 , 5x2y2
45x3y6
x3y6
xy2
45x2y4
What is the least common multiple of the monomials: 18u4vw4, 30u4v3w3
90u4v3w4
90u8v4w7
6u8v4w7
6u4vw3
What is the least common multiple of the monomials:
9x3y3z4, 15x3y4z4, 5x2y3z3
3x3y3
45x6y7z8
3x3y3z4
45x3y4z4
Evaluate:
-2|n + 5|
when n = -11.
-8
12
0
-12
Simplify:
2(13 - |-11 + 2|) - |10 - 7|2
-10
8
-1
-9
Simplify:
25√3
25√6
50√3
10√6
George's car can travel about 28 miles per gallon of gas. If the car has used 10 gallons of gas, approximately how far has George driven?
2.8
38
18
280
It costs a shoe company $20.67 to produce one pair of running shoes. The company sells each pair of shoes for $75.07 in stores. If the company sells 145 pairs of running shoes in the month of March, what is the company's approximate profit from running shoes in March?
$7,830.00
$13,920.00
$10,875.00
$7,975.00
A fast food restaurant sells between 164 and 328 hamburgers per day. If the company profits $82.00 per 82 hamburgers sold, approximately how much does the company profit in one year from hamburgers?
$89,790.00
$179,580.00
$7,362,780.00
$29,930.00
Simplify:
(8x2 - 4x - 8) + (3x2 - 7x - 3)
11x2 - 11x – 11
11x2 - 3x + 11
5x2 - 11x – 5
11x2 - 3x – 11
Simplify:
(6x3 + 3x2 - 5) + (4x3 - 4x - 3)
10x3 + 3x2 - 4x – 8
2x3 + 3x2 - 4x – 2
10x3 - 4x + 8
10x3 + 3x2 - 4x + 8
Simplify:
(9x2 + 6x + 4) - (3x2 + 2x + 6)
6x2 + 4x - 2
12x2 + 4x - 10
6x2 + 8x - 2
12x2 + 4x - 2
Factor the following expression completely:
x4 – 1
(x2 - 1)(x2 + 1)
(x - 1)(x + 1)(x2 + 1)
(x - 1)(x3 + 1)
(x - 1)(x + 1)(x - 1)(x + 1)
Factor the following expression completely:
4x2 – 4
4(x - 1)2
4(x + 1)(x - 1)
(4x + 1)(x - 1)
4(x2 - 1)
Factor the polynomial expression:
x2 - 10x + 25
2x2 – 25
x2 – 25
(x - 10)2
(x - 5)2
Simplify the following expression:
3x3 + 18x2 - 5
19x2 + 5x
x2 + 6x - 5
x2 + 15x - 12
Simplify the following expression:
x7 - 12
x14 - 12
x7 - 4
x7 + 4
Simplify the following expression:
Erica went shopping for new clothes for school. She bought a pair of jeans for $70.19 and several shirts for $8.63 each. If x represents the number of shirts she bought, which of the following equations should be used to find y, the total cost of Erica's shopping trip?
x = $8.63y + $70.19
y = $70.19x + $8.63
y = $8.63x + $70.19
x = $70.19y + $8.63
LeAnne leaves town traveling at an average speed of 49 mph. After 4 hours, Bart leaves town traveling in the same direction at an average speed of 67 mph. Which of the following equations could be used to represent the distance between LeAnne and Bart after x hours?
(Let x represent the time in hours that Bart has been traveling and y represent the distance between LeAnne and Bart.)
y = 18x
y = 196 + 18x
y = 196 - 67x
y = 196 - 18x
A company has fixed operating costs of $2,137.00 per month with a production cost of $15.15 per unit. If each unit brings $33.09 in revenue, which of the following equations represents the profit for the month?
(Let x represent the number of units made per month and y represent the total profit for the month.)
y = 48.24x - 2,137
y = 15.15x - 2,137
y = 33.09x - 2,137
y = 17.94x - 2,137
Ann is moving from Houston to McKinney and rented a truck from U-Move truck rentals. The cost of a one-day truck rental is given by
C(m) = 0.5m + 50
where m is the number of miles driven. If Ann drives 280 miles, what is the cost of the truck rental?
$195
$190
$218
$140
Solve for x:
7(2x – 8) = 77x
Juan scored 24 points in the first half of the basketball game, and he scored p points in the second half of the game. Write an expression to determine the number of points he scored in all. Then, find the number of points he scored in all if he scored 11 points in the second half of the game.
24 + p; 35 points
24 – p; 13 points
24p; 35 points
24/p; 13 points
Write the equation that describes the line with slope = 2 and y-intercept = 3/2 in slope-intercept form.
2x + y = 3/2
y = 3/2x + 2
y = 2x + 3/2
x = 2y + 3/2
The water level of a river is 34 feet and it is receding at a rate of 0.5 foot per day. Write an equation that represents the water level, w, after d days. In how many days will the water level be 26 feet?
w = 34d - 0.5; In 120 days, the water level will be 26 feet.
w = -0.5d + 34; In 16 days, the water level will be 26 feet.
w = 34d + 0.5; In 16 days, the water level will be 26 feet.
w = -0.5d + 34; In 120 days, the water level will be 26 feet.
Write the equation that describes the line in slope-intercept form.
slope = 4, point (3, –2) is on the line
y = 4x + 14
y = 4x – 14
y = 4x + 10
y = 4x – 2
(8, –4)
(4, -8)
(-2, 4)
(4, 8)
(–2, –3)
(-2, 0)
(0, -2)
(-8, -6)
The Fun Guys game rental store charges a fee of $5 plus $5.50 per game rented. The Game Bank charges a fee of $17 plus $2.50 per game. For how many game rentals will the cost be the same at both stores? What is that cost?
3 games; $22
2 games; $16
4 games; $27
6 games; $38
Janice is going on vacation and needs to leave her dog at a kennel. Nguyen’s Kennel charges $15 per day plus $20 for a processing fee. The Pup Palace Kennel charges $12 per day, and has a $35 processing fee. After how many days is the Pup Palace Kennel cheaper than Nguyen’s Kennel?
The Pup Palace Kennel is always cheaper than Nguyen’s Kennel.
The Pup Palace Kennel is never cheaper than Nguyen’s Kennel.
The Pup Palace Kennel is cheaper than Nguyen’s Kennel after 15 days.
The Pup Palace Kennel is cheaper than Nguyen’s Kennel after 5 days.
At the local pet store, zebra fish cost $2.10 each and neon tetras cost $1.85 each. If Marsha bought 13 fish for a total cost of $25.80, not including tax, how many of each type of fish did she buy?
7 zebra fish, 6 neon tetras
8 zebra fish, 5 neon tetras
6 zebra fish, 7 neon tetras
5 zebra fish, 8 neon tetras
Write the compound inequality shown by the graph.
Solve and graph the solutions of the compound inequality:
Solve and graph the compound inequality:
Write the inequality shown by the graph.
Write the inequality shown by the graph.
To join the school swim team, swimmers must be able to swim at least 500 yards without stopping. Let n represent the number of yards a swimmer can swim without stopping. Write an inequality describing which values of n will result in a swimmer making the team. Graph the solution.
Denise has $365 in her saving account. She wants to save at least $635. Write and solve an inequality to determine how much more money Denise must save to reach her goal. Let d represent the amount of money in dollars Denise must save to reach her goal.
Marco’s Drama class is performing a play. He wants to buy as many tickets as he can afford. If tickets cost $2.50 each and he has $14.75 to spend, how many tickets can he buy?
0 tickets
5 tickets
6 tickets
4 tickets
Mrs. Williams is deciding between two field trips for her class. The Science Center charges $135 plus $3 per student. The Dino Discovery Museum simply charges $6 per student. For how many students will the Science Center charge less than the Dino Discovery Museum?
132 or more students
132 or fewer students
More than 45 students
Fewer than 45 students
Choose the system of inequalities that best matches the graph below.
Given the graph the system of linear inequalities.
Give two ordered pairs that are solutions and two that are not solutions.
Graph the system of linear inequalities
To join the school swim team, swimmers must be able to swim at least 500 yards without stopping. Let n represent the number of yards a swimmer can swim without stopping. Write an inequality describing which values of n will result in a swimmer making the team. Graph the solution.
Fly with Us owns a D.C.10 airplane that has seats for 240 people. The company flies this airplane only if there are at least 100 people on the plane. Write a compound inequality to show the possible number of people in a flight on a D.C.10 with Fly with Us. Let n represent the possible number of people in the flight. Graph the solutions.
Sam earned $450 during winter vacation. He needs to save $180 for a camping trip over spring break. He can spend the remainder of the money on music. Write an inequality to show how much he can spend on music. Then, graph the inequality.
