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Name: _______________________________
Period: ________
Honors Algebra 2 – Assignment Sheet
Chapter 1: Equations and Inequalities
Date
1.
HOMEWORK
Read and
Study
1.1
Pages 1 - 5
Problem Sets
Pages 6–7; #6, 7, 11–16, 27–30, 33–36, 41–48
2.
1.2
Pages 13–15; #5, 6, 8, 9, 12, 13, 15, 21–23, 30–32, 39–42, 47–50, 57, 58, 60
Pages 10 - 13
3.
1.3
Pages 21–24; #29–31, 37–40, 48–50, 53–54, 59–60, 63, 64, 68–70, 75–76
Pages 18 – 21
4.
1.2 & 1.3 Page 17; #1–13
Pages 17 & 25 Page 25; #1–8
5.
6.
7.
1.4
Pages 30–32; #3–6, 11–14, 23–26, 33–34, 36
Pages 26–29
1.1 – 1.4
Review
Page 16; #7–13, Page 33; #2, 4, 5, 8, 9, 10, Page 40; #3–8
Quiz 1.1 – 1.4 Read Section 1.5 on Pages 34–36.
8.
1.5
Pages 37–39; #3–17 odd, 24–26, 29–31, 33
Pages 34–36
9.
1.6
Pages 45–47; #11, 12, 18, 21, 31–33, 39–41, 44–46, 52–53, 58
Pages 41–44
10.
1.7
Page 55; #24–32, 34–38
Pages 51–52
11.
1.7
Pages 56–57; #53–61 odd, 66–69, 74, 75, 77, 79, 80
Page 53–54
12.
1.1 – 1.7
Pages 61–64; #14–16, 21–24, 27, 30–33, 37–40, 42, 43, 45–47
Pages 60–61 Page 65; #1, 2, 30, 31
13.
1.1 – 1.7
Review
Optional Additional Review: Page 59; #1–8, Pages 66–69; #1–21, Page
1010; #1–53, Practice Workbook Pages 1–14
14.
1.1 – 1.7
Chapter 1 Test
Honors Algebra 2
Name _________________________
Date ______________ Period _____
1.1 – Apply Properties of Real Number – Day 1
Real Numbers
Irrational Numbers
Rational Numbers
Integers
Whole Numbers
Natural Numbers
Natural Numbers are the counting numbers beginning with 1.
1, 2,3,...
Whole Numbers include the natural numbers and zero.
0,1, 2,...
Integers are positive and negative whole numbers.
...  2, 1, 0,1, 2,...
Rational Numbers are any numbers that can be written as the ratio or quotient of integers (fractions).
3
1
  1.5 or  0.1666...
When written as decimals they either terminate or repeat.
2
6
Irrational Numbers are real numbers that are not rational. When written as decimals they neither
terminate nor repeat.
 3  1.73205..., 5  2.23606... or   3.14159...
Real numbers are the numbers used most often in algebra. They include rational and irrational
numbers.
Example 1: Classify each real number. Identify all that apply.
a)
2
b)
3
4
c)
7
d)
0
e)
3.14
f)
9
A Number Line is a line on which numbers increase from left to right.
Example 2: Plot the points 4.2,
12 5
,  and 3 on the number line.
5
4
0
Properties of Addition and Multiplication
Let a, b and c be real numbers.
Addition
Multiplication
Closure Property
a  b is a real number
ab is a real number
Commutative Property
a b  ba
ab  ba
Associative Property
(a  b)  c  a  (b  c)
(ab)c  a (bc)
Identity
a  0  a or 0  a  a
a 1  a or 1 a  a
0 is called the additive identity and 1 is called the multiplicative identity.
Inverse
a  (a)  0
a
1
1
a
Distributive Property (of multiplication over addition)
a(b  c)  ab  ac
Distributive Property (of multiplication over subtraction)
a(b  c)  ab  ac
Subtraction is defined as adding the opposite or additive inverse.
a  b  a  (b)
Division is defined as multiplying by the reciprocal or multiplicative inverse.
a b  a
Example 3: Identify the property that the statement illustrates.
a)
3(2  5)  3 2  3 5
b)
1
5 1
5
1
,b  0
b
Unit Analysis: When using operations in real-life problems unit analysis helps verify that the units for
the answer make sense for the problem.
Example 4
a) You work 4 hours and earn $36. What is your earning rate?
b) You travel for 2.5 hours at 50 miles per hour. How far do you go?
c) You drive 45 miles per hour. What is your speed in feet per second?
Example 4
The distance form Montpelier, Vermont, to Montreal, Canada is about 132 miles. The distance from
Montreal to Quebec City is about 253 kilometers. One mile equals 1.61 kilometers.
a) Convert the distance from Montpelier to Montreal to kilometers.
b) Convert the distance from Montreal to Quebec City to miles.
HW: Pages 6–7; #6, 7, 11–16, 27–30, 33–36, 41–48.
Honors Algebra 2
Name _________________________
Date ______________ Period _____
1.2 – Algebraic Expressions and Models – Day 1
A numerical expression consist of numbers, operations and grouping symbols. An expression formed
with repeated multiplication is called a power. A power is made up of a base and an exponent. The
base is multiplied by itself the number of times shown by the exponent.
Example 1: Evaluate each power.
a)
(3)4 
b)
34 
ORDER OF OPERATIONS (GEMDAS)
1)
_____________________________________________________________________________.
2)
_____________________________________________________________________________.
3)
_____________________________________________________________________________.
4)
_____________________________________________________________________________.
Example 2: Using Order of Operations.
a)
4  2(2  5) 2
b)
2 (7  5)  (13  9)2
EVALUATING AN ALGEBRAIC EXPRESSION
1)
___________________________________________________________________.
2)
___________________________________________________________________.
3)
___________________________________________________________________.
Example 3: Evaluate each expression.
a)
3x 2 5 x  7 when x  2
b)
x  2y
when x  3, and y  1
2x  y
Example 4: You have $50 and are buying some movies on DVD that cost $15 each. Write an
expression that shows how much money you will have left after buying n movies. Evaluate the
expression when n  2 and n  3 .
Example 5: Simplify each expression.
a)
7 x  4x
b)
3n 2  n  n 2
c)
2( x  1)  3( x  4)
d)
3x( x  4)  2 x 2  5 x  3
HW: Pages 13–15; #5, 6, 8, 9, 12, 13, 15, 21–23, 30–32, 39–42, 47–50, 57, 58, 60
Honors Algebra 2
Name _________________________
Date ______________ Period _____
1.3 – Solve Linear Equations – Day 1
SOLVING EQUATIONS
1.
______________________________________________________________________________
2.
______________________________________________________________________________
3.
______________________________________________________________________________
4.
______________________________________________________________________________
5.
______________________________________________________________________________
If the equation has a one coefficient that is a fraction, multiply by the reciprocal to remove it.
If an equation has several fractions, multiply by the least common denominator on both sides.
4
Example 1: Solve the equation x  8  20 .
5
Example 2: During one shift, a waiter earns wages of $30 and gets an additional 15% in tips on
customers’ food bills. The waiter earns $105. What is the total of the customer’s food bills?
Example 3: Solve the equation 7 p  13  9 p  5 .
Example 4: Solve the equation 3(5 x  8)  2( x  7)  12 x .
2
5
1
Example 5: Solve the equation x   x  .
3
6
2
Example 6: It takes you 8 minutes to wash a car and it takes a friend 6 minutes to wash a car. How
long does it take the two of you to wash 7 cars if you work together?
Example 7: If another friend can wash a car in 12 minutes, how long will it take all three of you to
wash 3 cars if you work together?
Example 8: Solve the equation 3( x  2)  3x  4
Example 9: Solve the equation 2( x  4)  2 x  8
HW: Pages 21–24; #29–31, 37–40, 48–50, 53–54, 59–60, 63, 64, 68–70, 75–76
Honors Algebra 2
Name _________________________
Date ______________ Period _____
1.2 & 1.3 – Graphing Calculators – Day 1
Notes
HW: Page 17; #1–13 and Page 25; #1–8
Honors Algebra 2
Name _________________________
Date ______________ Period _____
1.4 – Rewrite Formulas and Equations – Day 1
Rewriting Formulas and Equations
Example 1: Solve the formula C  2 r for the variable r. Then find the radius of a circle with a
circumference of 88 centimeters.
Example 2: The formula for the distance d between opposite vertices of a regular hexagon is d 
2a
3
where a is the distance between opposite sides. Solve the formula for a. Then find a when d  10
centimeters.
Example 3: Solve P  2l  2w for l. Then find the length of a rectangle with a width of 7 inches and a
perimeter of 30 inches.
Example 4: Solve the formula A 
1
(b1  b2 )h for the variable h. Then find h if b1  6 inches, b2  8
2
inches and A  70 square inches.
Example 5: Solve the equation y  6 x  7 for y. Then find the value of y when x  2 .
Example 6: Solve the equation 3  2xy  x for y. Then find the value of y when x  2 .
Example 7: Solve the equation 4 y  xy  28 for y. Then find the value of y when x  2 .
Homework: Pages 30–32; #3–6, 11–14, 23–26, 33–34, 36.
Honors Algebra 2
Name _________________________
Date ______________ Period _____
1.5– Using Problem Solving Strategies and Models
Strategies for Solving Problems
Example 1: A jet flies at an average speed of 540 miles per hour. How long will it take to fly from
New York to Tokyo, a distance of 6760 miles?
Example 2: The table shows the height h of a paramotorist after t minutes. Find the height of the
paramotorist after 8 minutes.
Time (min), t
0
1
2
3
4
Height (ft), h
2400
2190
1980
1770
1560
Example 3: You are hanging four championship banners on a wall in your school’s gym. The banners
are 8 feet wide. The wall is 62 feet long. There should be an equal amount of space between the ends of
the wall and the banners, and between each pair of banners. How far apart should the banners be
placed?
Example 4: A truck used 28 gallons of gasoline and traveled a total distance of 428 miles. The truck’s
fuel efficiency is 16 miles per gallon on the highway and 12 miles per gallon in the city. How many
gallons of gasoline were used in the city?
HW: Pages 37–39; #3–17 odd, 24–26, 29–31, 33
Honors Algebra 2
Name _________________________
Date ______________ Period _____
1.6 – Solving Linear Inequalities – Day 1
Simple Linear Inequalities:
Compound Inequalities:
Example 1: Graph each inequality.
a) x  4
b) x  1
c) x  2 or x  3
d) 2  x  5
Example 2: You have budgeted $66 a month to spend on yoga classes. Your yoga studio charges a $22
per month membership fee, plus $5.50 per class attended. Describe the possible number of classes that
you can attend each month.
Example 3: Solve each inequality and graph the solution.
a) 4x  3  6x  5
b) 10  3x  5  8
c) 2x 1  7 or 4x  3  7
Example 4: In Pennsylvania, the lowest temperature on record is –42°F in January, 1904, in Smethport,
while the highest temperature on record is 111°F in July, 1936, in Phoenixville. Write the range of
temperatures as an inequality. Then write the an inequality giving the temperature range in degrees
Celsius.
HW: Pages 45–47; #11, 12, 18, 21, 31–33, 39–41, 44–46, 52–53, 58
Honors Algebra 2
Name _________________________
Date ______________ Period _____
1.7 – Solving Absolute Value Equations and Inequalities – Day 1
Absolute Value
Solving an Absolute Value Equations
1)
2)
3)
Example 1: Solve 2 x  9  15 .
Example 2: Solve 4 x  12  28 .
Extraneous Solutions
Example 3: Solve 4 x  10  6 x .
HW: Page 55; #24–32, 34–38
Honors Algebra 2
Name _________________________
Date ______________ Period _____
1.7 – Solving Absolute Value Equations and Inequalities – Day 2
Solving Absolute Value Inequalities
Example 1: Solve and graph:
a)
4 x  5  13
b)
h  10  10
Mean of the Extremes
Tolerance
Acceptable Values
Examples 2: A food manufacturer specifies that every family-sized box of cereal should have a net weight
of 25 ounces, with a tolerance of 1.2 ounces. Write and solve an absolute value inequality that describes the
acceptable net weights for the cereal in a family-size box.
Example 3: You have found that your new winter coat is comfortable to wear when the outdoor
temperature is between 10º F and 42º F, inclusively. Write an absolute value inequality for this temperature
range, where t represents the temperature in degrees Fahrenheit.
HW: Pages 56–57; #53–61 odd, 66–69, 74, 75, 77, 79, 80