Name:_______________________________________________Period:_____
Date:_______________________________________
Advanced Algebra II
Ch. 1 Homework Packet
Section 1.1 – Patterns and Expressions
Describe each pattern using words. Draw the next figure in each pattern.
1.
2.
Complete the following table. Explain the process.
3.
4. Describe the pattern using words.
5. A gardener plants a flower garden between his house and a brick pathway parallel to the house. The
table below shows the area of the garden, in square feet, depending on the width of the garden, in feet.
What is the area of the garden if the width is 15 ft.?
Identify a pattern and find the next three numbers in the pattern.
6. 5, 8, 11, 14,…
7. 1, 3, 6, 10, 15,…
8. 10, 9, 6, 1, -6,…
9. The graph shows the cost depending on the number of DVDS that you purchase. What is the cost of
purchasing 10 DVDs?
10. Mr. Broerman earns $320 a week working in a clothing store. As a bonus, his employer pays him $15
more than he earned the previous week, so that at the end of the second week he earns $335, and after 3
weeks, he earns $350. How much will Mr. Broerman earn at the end of the fifth week?
Section 1.2 – Properties of Real Numbers
Classify each variable according to the set of numbers that best describes its values.
11. the area of the circle A found by using the formula πr2
12. the air temperature t in Brookville, OH, measured to the nearest degree Fahrenheit
Graph each number on a number line. Label appropriately!
13. -1
14. 2.8
Compare the two numbers using < or >.
15. −√2_____ − 2
16. √29_____5
17. 11_____√130
1
18. 7 2 _____√67
Name the property of real numbers illustrated by each equation.
1
19. 2(3 + √5) = 2 ∙ 3 + 2 ∙ √5
20. −7 ∙ −7 = 1
Estimate the numbers graphed at the labeled points.
21. point A
22. Point C
𝑽
To find the length of side b of a rectangular prism with a square base, use the formula 𝒃 = √𝒉 where V is
the volume of the prism and h is the height.
23. V = 100, h = 5
4
24. V = 100, h = 20
5
25. Write the numbers 2√2, 5 , − 4 , 0.9, −1 in increasing order.
Justify the equation by stating one of the properties of real numbers.
26. (x + 37) + (-37) = x + (37 + (-37))
27. x + (37 + (-37)) = x + 0
Section 1.3 – Algebraic Expressions
28. Write an algebraic expression that models the phrase, “seven less than the number t”
29. Write an algebraic expression that models the situation: “Emma has $520 and is earning $75 each
week babysitting.”
Evaluate each expression for the given values of the variables.
30. 4v + 3(w + 2v)  5w; v = 2 and w = 4
31. 2(3e  5f) + 3(e2 + 4f); e = 3 and f = 5
32. The expression 6s2 represents the surface area of a cube with edges of length s. What is the surface
area of a cube with an edge 1.5 meters long?
33. 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 is the monthly charge
for using 29 long distance minutes?
Simplify by combing like terms
3(𝑎−𝑏)
4
34. 9 + 9 𝑏
35. 4a – 5(a + 1)
36. x(x – y) + y(y – x)
37. Evaluate the expression for the given value of the variable.
-t2 – (3t + 2); t = 5
38. 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?
39. Alana simplified the expression as shown. Do you agree with her work? Explain.
Match the property name with the appropriate equation by connecting with a line segment.
40. Opposite of a Difference
A. [(r) + 2p] = (r)  2p
41. Opposite of a Sum
B. 16d  (3d + 2)(0) = 16d  0
42. Opposite of an Opposite
C. 5(2  x) = 10  5x
43. Multiplication by 0
D. (4r + 3s) + t = (1)(4r + 3s) + t
44. Multiplication by –1
E. (8  3m) = 3m  8
45. Distributive Property
F. [(9  2w)] = 9  2w
Section 1.4 – Solving Equations
Solve each equation. Check your answer.
46. 7.2 + c = 19
47.
48. 9(z – 3) = 12z
49. 5w + 8 – 12w = 16 – 15w
𝑑
4
= −31
50. 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? Use an equation.
51. What three consecutive numbers have a sum of 126? Use an equation.
52. Determine whether the equation is always, sometimes, or never true.
3(y + 3) + 5y = 4(2y + 1) + 5
53. Solve A = lw + wh + lh for w.
Solve each equation for y.
54. a(y + c) = b(y – c)
55. 3y – yz = 2z
Solve each equation.
56. 1.2(x + 5) = 1.6(2x + 5)
57.
58. Solve 𝐷 = 𝑘𝐴 [
𝑇2 −𝑇1
𝐿
𝑢
5
𝑢
𝑢
+ 10 − 6 = 1
] for T1
59. 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? Use an equation.
60. 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?
61. What four consecutive odd integers have a sum of 336?
Section 1.5 – Solving Inequalities
Write the inequality that represents the sentence.
62. Four less than a number is greater than -28.
63. A number increased by 7 is less than 5.
Solve each inequality. Graph the solution.
64. 3(x + 1) + 2 < 11
65. 2[(2y – 1) + y] < 5(y + 3)
66. 5 – 2(n + 2) < 4 + n
Solve each problem by writing an inequality.
67. The length of a rectangular yard is 30 meters. The perimeter is at most 90 meters. Describe the width
of the yard.
68. 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?
Is the inequality always, sometimes, or never true?
69. 3(2x + 1) > 5x − (2 − x)
70. 7x + 2 ≤ 2(2x − 4) + 3x
Solve each compound inequality. Graph the solution.
71. 3x > – 6 and 2x < 6
72. 5x > − 20 and 8x ≤ 32
73. 6x ≤ − 18 or 2x > 18
Solve each problem by writing and solving a compound inequality.
74. 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?
75. 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?
Section 1.6 – Absolute Value Equations and Inequalities
Solve each equation. Check your answers and extraneous solutions.
76. |-3x| = 18
77. |t + 5| = 8
78. |2x – 1| = 5
79. |x + 5| = 3x – 7
80. |4w + 3| - 2 = 5
81. 2|z + 1| - 3 = z – 2
Solve each inequality. Graph the solution.
82. 5|y + 3| < 15
83. 2|4x + 1| - 5 < 1
Write each compound inequality as an absolute value inequality.
84. −7.3 ≤ 𝑎 ≤ 7.3
85. 28.6 ≤ 𝐹 ≤ 29.2
86. Write an absolute value function or inequality to represent the graph.
Solve each equation.
87. 2|4w – 5| = 12w – 18
88. 3|2x + 5| = 9x – 6
89. |5p + 3| - 4 = 2p
Solve each inequality. Graph the solution.
90. -3|2t + 1| < 9
𝑦+2
91. |
3
|−1<2
Write an absolute value inequality to represent each situation.
92. 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.
93. The outdoor temperature ranged between 37°F and 62°F in a 24-hour period. Let t represent the
temperature during this time period.