Name
Class
1-1
Date
Practice
Patterns and Expressions
Describe each pattern using words. Draw the next figure in each pattern.
1.
2.
3.
Copy and complete each table. Include a process column.
4.
5.
Input
6.
Input
Output
Output
Input
Output
1
4
1
–2
1
0.5
2
9
2
–4
2
1.0
3
14
3
–6
3
1.5
4
19
4
–8
4
2.0
5
5
5
6
6
6
n
n
n
7. Describe the pattern using words.
Name
1-1
Class
Date
Practice (continued)
Patterns and Expressions
A gardener plants a flower garden between his house and
a brick pathway parallel to the house.The table at the right
shows the area of the garden, in square feet, depending on
the width of the garden, in feet.
Width
Area
1
3.5
2
7
3
10.5
4
14
8. What is the area of the garden if the width is 8 feet?
9. What is the area of the garden if the width is 15 feet?
Identify a pattern and find the next three numbers in the pattern.
10. 5, 10, 20, 40, . . .
11. 5, 8, 11, 14, . . .
12. 3, 1, 1, 3, . . .
13. 1, 3, 6, 10, 15, . . .
14.
2 3 4 5
, , , , ...
3 4 5 6
15. 10, 9, 6, 1, 6, . . .
The graph shows the cost depending on the
number of DVDs that you purchase.
16. What is the cost of purchasing 5 DVDs?
17. What is the cost of purchasing 10 DVDs?
18. What is the cost of purchasing n DVDs?
Keesha earns $320 a week working in a clothing store. As a bonus, her employer
pays her $15 more than she earned the previous week, so that at the end of the
second week she earns $335, and after 3 weeks, she earns $350.
19. How much will Keesha earn at the end of the fifth week?
20. How much will Keesha earn at the end of the tenth week?
Name
Class
Date
Practice
1-2
Properties of Real Numbers
Classify each variable according to the set of numbers that best describes its
values.
1. the number of students in your class
To start, make a list of some numbers that could describe the number of
students in your class.
2. the area of the circle A found by using the formula A = r2
To start, make a list of some numbers that could describe the area of a circle.
3. the elevation e of various land points in the United States measured to the nearest foot To
start, make a list of some numbers that could describe elevation levels.
Graph each number on a number line.
4. 5
1
2
5. −4
7. 6
6. 2.25
8.
1
3
8
To start, use a calculator to approximate the square root.
Compare the two numbers. Use  or .
9.
50 and 8.8
11. 6.2 and
40
10. 5 and
23
12.  3 and −3
Name
1-2
Class
Date
Practice (continued)
Properties of Real Numbers
Name the property of real numbers illustrated by each equation.
13.
2 3
 1
3 2
14. 6(2 + x) = 6 · 2 + 6 · x
15. 2 · 20 = 20 · 2
16. 8 + (−8) = 0
17. 2(0.5 · 4) = (2 · 0.5) · 4
18. −11 + 5 = 5 + (−11)
Estimate the numbers graphed at
the labeled points.
19. point A
20. point B
21. point C
22. point D
To find the length of the side b of the square base of a rectangular prism, use the
V
formula b 
, where V is the volume of the prism and h is the height. Which
h
set of numbers best describes the value of b for the given values of V and h?
23. V = 100, h = 1
24. V = 100, h = 10
Write the numbers in increasing order.
25.
5
5
, 28,  ,  0.8,1
6
2
26.
2
,  4, 32, 13,  0.4
3
Name
Class
1-3
Date
Practice
Algebraic Expressions
Write an algebraic expression that models each word phrase.
1. seven less than the number t
2. the sum of 11 and the product of 2 and a number r
Write an algebraic expression that models each situation.
3. Arin has $520 and is earning $75 each week babysitting.
4. You have 50 boxes of raisins and are eating 12 boxes each month.
Evaluate each expression for the given values of the variables.
5. 4v + 3(w + 2v)  5w; v = 2 and w = 4
6. c(3  a)  c2; a = 4 and c = 1
7. 2(3e  5f) + 3(e2 + 4f); e = 3 and f = 5
Surface Area The expression 6s2 represents the surface area of a cube with edges of
length s. What is the surface area of a cube with each edge length?
8. 3 inches
9. 1.5 meters
The expression 4.95 + 0.07x models a household’s monthly long-distance
charges, where x represents the number of minutes of long-distance calls during
the month. What are the monthly charges for each number of long-distance
minutes?
10. 73 minutes
11. 29 minutes
Simplify by combining like terms.
12. 5x  3x2 + 16x2
14. t 
t2 2
t t
2
16. 2(j2  k)  6(j2 + 3k )
13.
3 a  b 
9
+
4
b
9
15. 4a  5(a + 1)
17. x(x  y) + y(y  x)
Name
1-3
Class
Date
Practice (continued)
Algebraic Expressions
18. In a soccer tournament, teams receive 6 points for winning a game, 3 points
for tying a game, and 1 point for each goal they score. What algebraic
expression models the total number of points that a soccer team receives in a
tournament? Suppose one team wins two games and ties one game, scoring a
total of five goals. How many points does the team receive?
Evaluate each expression for the given value of the variable.
19. t2  (3t + 2); t = 5
20. i2  5(i3  i2); i = 4
21. Perimeter Write an expression for the perimeter of the figure at
the right as the sum of the lengths of its sides. What is the
simplified form of this expression?
22. Simplify (2x  5y) + 3(4x + 2y) and justify each step in your
simplification.
23. Error Analysis Alana simplified the expression as shown. Do you agree
with her work? Explain.
24. Open-Ended Write an example of an algebraic expression that always
has the same value regardless of the value of the variable.
Match the property name with the appropriate equation.
25. Opposite of a Difference
A. [(r) + 2p] = (r)  2p
26. Opposite of a Sum
B. 16d  (3d + 2)(0) = 16d  0
27. Opposite of an Opposite
C. 5(2  x) = 10  5x
28. Multiplication by 0
D. (4r + 3s) + t = (1)(4r + 3s) + t
29. Multiplication by –1
E. (8  3m) = 3m  8
30. Distributive Property
F. [(9  2w)] = 9  2w
Name
1-4
Class
Date
Practice
Solving Equations
Solve each equation.
1. 7.2 + c = 19
3.
d
 31
4
2. 8.5 = 5p
4. s  31 = 20.6
Solve each equation. Check your answer.
5. 9(z  3) = 12z
6. 7y + 5 = 6y + 11
7. 5w + 8  12w = 16  15w
8. 3(x + 1) = 2(x + 11)
Write an equation to solve each problem.
9. Two brothers are saving money to buy tickets to a concert. Their combined
savings is $55. One brother has $15 more than the other. How much has each
saved?
10. Geometry The sides of a triangle are in the ratio 5 : 12 : 13. What is the length
of each side of the triangle if the perimeter of the triangle is 15 inches?
11. What three consecutive numbers have a sum of 126?
Determine whether the equation is always, sometimes, or never true.
12. 6(x + 1) = 2(5 + 3x)
13. 3(y + 3) + 5y = 4(2y + 1) + 5
Solve each formula for the indicated variable.
14. S = L(1  r), for r
15. A = lw + wh + lh, for w
Solve each equation for y.
16.
4
( y  3)  g
9
17. a(y + c) = b(y  c)
18.
y3 2
t
t
19. 3y  yz = 2z
Name
Class
1-4
Date
Practice (continued)
Solving Equations
Solve each equation.
20. 0.5(x  3) + (1.5  x) = 5x
22. 0.5(c + 2.8)  c = 0.6c + 0.3
21. 1.2(x + 5) = 1.6(2x + 5)
23.
u u u
  1
5 10 6
Solve each formula for the indicated variable.
24. V 

3
r 2 h, for h
 T2  T1 
 for T1
 L 
25. D  kA 
Write an equation to solve each problem.
26. Two trains left a station at the same time. One traveled north at a certain
speed and the other traveled south at twice that speed. After 4 hours, the
trains were 600 miles apart. How fast was each train traveling?
27. Geometry The sides of one cube are twice as long as the sides of a second cube.
What is the side length of each cube if the total volume of the cubes is 72 cm3?
28. Error Analysis Brenna solved an equation
for m. Do you agree with her? Explain your
answer.
Solve each problem.
29. You and your friend left a bus terminal at the same time and traveled in opposite
directions. Your bus was in heavy traffic and had to travel 20 miles per hour slower
than your friend’s bus. After 3 hours, the buses were 270 miles apart. How fast was
each bus going?
30. Geometry The length of a rectangle is 5 centimeters greater than its width.
The perimeter is 58 centimeters. What are the dimensions of the rectangle?
31. What four consecutive odd integers have a sum of 336?
Name
1-5
Class
Date
Practice
Solving Inequalities
Write the inequality that represents the sentence.
1. Four less than a number is greater than –28.
2. Twice a number is at least 15.
3. A number increased by 7 is less than 5.
4. The quotient of a number and 8 is at most –6.
Solve each inequality. Graph the solution.
6. 5t – 2(t + 2) ≥ 8
5. 3(x + 1) + 2 < 11
7. 2[(2y − 1) + y] ≤ 5(y + 3)
9. 5 – 2(n + 2) ≤ 4 + n
1
(7a  1)  2a  7
3
10. −2(w – 7) + 3 > w – 1
8.
Solve each problem by writing an inequality.
11. Geometry The length of a rectangular yard is 30 meters. The perimeter is at
most 90 meters. Describe the width of the yard.
12. Geometry A piece of rope 20 feet long is cut from a longer piece that is at least 32
feet long. The remainder is cut into four pieces of equal length. Describe the length of
each of the four pieces.
13. A school principal estimates that no more than 6% of this year’s senior class
will graduate with honors. If 350 students graduate this year, how many will
graduate with honors?
14. Two sisters drove 144 miles on a camping trip. They averaged at least 32 miles per
gallon on the trip. Describe the number of gallons of gas they used.
Name
1-5
Class
Date
Practice (continued)
Solving Inequalities
Is the inequality always, sometimes, or never true?
15. 3(2x + 1) > 5x − (2 − x)
16. 2(x − 1) ≥ x + 7
17. 7x + 2 ≤ 2(2x − 4) + 3x
18. 5(x − 3) < 2(x − 9)
Solve each compound inequality. Graph the solution.
19. 3x > – 6 and 2x < 6
20. 4x ≥ − 12 and 7x ≤ 7
21. 5x > − 20 and 8x ≤ 32
22. 6x < − 12 or 5x > 5
23. 6x ≤ − 18 or 2x > 18
24. 2x > 3 − x or 2x < x − 3
Solve each problem by writing and solving a compound inequality.
25. A student believes she can earn between $5200 and $6250 from her summer job. She
knows that she will have to buy four new tires for her car at $90 each. She estimates
her other expenses while she is working at $660. How much can the student save
from her summer wages?
26. Before a chemist can combine a solution with other liquids in a laboratory, the
temperature of the solution must be between 39°C and 52°C. The chemist places the
solution in a warmer that raises the temperature 6.5°C per hour. If the temperature is
originally 0°C, how long will it take to raise the temperature to the necessary range of
values?
27. The Science Club advisor expects that between 42 and 49 students will attend the next
Science Club field trip. The school allows $5.50 per student for sandwiches and
drinks. What is the advisor’s budget for food for the trip?
Name
1-6
Class
Practice
Absolute Value Equations and Inequalities
Solve each equation. Check your answers.
1. 3x  18
2. 5 y  35
3. t  5  8
4. 3 z  7  12
5. 2 x  1  5
6. 4  2 y  5  9
Solve each equation. Check for extraneous solutions.
7. x  5  3x  7
8. 2t  3  3t  2
9. 4w  3  2  5
10. 2 z  1  3  z  2
Solve each inequality. Graph the solution.
11. 5 y  3  15
12. 2t  3  5
13. 4b  3  9
14.
15. 2 4 x  1  5  1
1
2w  1  3  1
2
16. 3z  2  5  9
Write each compound inequality as an absolute value inequality.
17. 7.3  a  7.3
18. 11  m  19
19. 28.6  F  29.2
20. 0.0015  t  0.0018
Write an absolute value equation or inequality to describe each graph.
21.
22.
Date
Name
1-6
Class
Date
Practice (continued)
Absolute Value Equations and Inequalities
Solve each equation.
23. 3 2 x  5  9 x  6
24. 4  3m  m  10
3
8t  12  6(t  1)
4
25. 2 4w  5  12w  18
26.
27. 5 p  3  4  2 p
28. 7 y  3  1  0
Solve each inequality. Graph the solution.
29. 3 2t  1  9
31.
y2
1  2
3
30. 2 x  4  4
32.
1
4z  5  2  5
7
Write an absolute value inequality to represent each situation.
33. To become a potential volunteer donor listed on the National Marrow Donor Program
registry, a person must be between the ages of 18 and 60. Let a represent the age of a
person on the registry.
34. Two friends are hiking in Death Valley National Park. Their elevation ranges
from 228 ft below sea level at Badwater to 690 ft above sea level at Zabriskie
Point. Let x represent their elevation.
35. The outdoor temperature ranged between 37°F and 62°F in a 24-hour period. Let t
represent the temperature during this time period.
The diameter of a ball bearing in a wheel assembly must be between 1.758 cm and
1.764 cm.
36. What is the tolerance?
37. What absolute value inequality represents the diameter of the ball bearing? Let
d represent the diameter in cm.