Algebra 2
Chapter 1 Notes
P.1 – Prerequisite skills – Basic Algebra Skills
Topics: Evaluate an algebraic expression for given values of variables
Combine like terms/simplify algebraic expressions
Solve equations for a specified variable
A: Evaluate Expressions for Given Values (Lesson 1.3)
Example: What is the value of the expression for the given values of the variables?
A1. 3𝑥(𝑥 + 2) − 3𝑥 2 for 𝑥 = 19
A2. 4(𝑦 2 − 3) + 7(𝑦 − 2) for 𝑦 = −5
A3. 𝑥2 − 5(3𝑥 − 12) for 𝑥 = 10
A4. What is the value of 𝑦 for each of the given
values of 𝑥.
𝑦 = −2𝑥 + 7
x
3
y
0
-8
B: Simplify Expressions using Order of Operations (Lesson 1.3)
Recall:
Example: Rewrite the expression in its simplest form.
B1. 𝑎2 + 𝑎 + 𝑎2
B2. 5(𝑥 − 2𝑦) − 3(𝑥 − 2𝑦)
B3. 7𝑥𝑦 − (10𝑥𝑦 − 3𝑥 2 )
Algebra 2
Chapter 1 Notes
C: Solving One-Variable Equations
(Lesson 1.4)
Example: Solve for the given variable
C1.
C3.
C5.
x+5=9
2a 3 6
6x 5 7 9x
C2.
C4.
C6.
-3y = 15
7 − 𝑥 = −10
5(6 4 y ) y 21
Expectations:
I want to see for any problem:
The original problem
Any key steps in getting to your
solution- “the work”
Clearly stated solution
Answers:
Should use original variable if
applicable x = 2 or y = 5, etc.
FRACTIONS should always be
reduced to lowest terms.
DECIMALS only if they are
terminating and you write the entire
thing… never round unless the
directions say so.
24 3
= ≈ .4285714 …
56 7
3
𝑌𝑜𝑢 𝑠ℎ𝑜𝑢𝑙𝑑 𝑎𝑛𝑠𝑤𝑒𝑟
7
14 1
= = 0.25
56 4
𝑌𝑜𝑢 𝑠ℎ𝑜𝑢𝑙𝑑 𝑎𝑛𝑠𝑤𝑒𝑟
C7.
53 = 3(y − 2) − (3y – 1)
C8.
2(−𝑥 + 5) + 2 = 5 − (2𝑥 − 7)
1
𝑜𝑟 0.25
4
Algebra 2
Chapter 1 Notes
P.2 – Prerequisite skills – Special Equations and Inequalities
Topics: Solving Formulas for a specified variable (Literal Equations”
Solve absolute value equations and inequalities
A: Solving Literal Equations (Lesson 1.4)
“Solve for __A__ in terms of __B__”
Goal: Use algebra to get “A =” on one side of the equation and a simplified
expression that contains “B” on the other side of the equation.
Example:
A1. 𝑆 = 2𝜋𝑟ℎ solve for 𝑟
A3. 𝑎𝑥 + 𝑏𝑥 = 𝑐 solve for 𝑥
A2. 3𝑥 − 5𝑦 = 15 solve for y
1
A4. 𝐴 = 2 (𝑏1 + 𝑏2 )ℎ solve for 𝑏1
B: Solving Absolute Value Equations (Lesson 1.6)
Perhaps you remember from a previous math class the concept of “absolute value.”
Solve this equation:
x 5
Algebra 2
Chapter 1 Notes
Strategy:
1.
Isolate the absolute value
|𝑠𝑡𝑢𝑓𝑓| = 𝑣𝑎𝑙𝑢𝑒
2. Set up 2 equations:
𝑠𝑡𝑢𝑓𝑓 = 𝑣𝑎𝑙𝑢𝑒 OR 𝑠𝑡𝑢𝑓𝑓 = −𝑣𝑎𝑙𝑢𝑒
3. Solve each new equation and check your solution.
Example: Solve the following absolute value equation. Be sure to check your answers.
B1.
x 18 5
B2.
3 a 9 30
B3.
5 2 x 4 7 17
B4.
5x 6 9 0
B5.
5 3 2 2w 7
B6.
x 6 3x 2
Algebra 2
Chapter 1 Notes
C: Inequalities (Lesson 1.5)
RECALL: Inequalities represent values that may not necessarily be equal.
Inequality Summary
greater than
less than
greater than or equal
less than or equal
Graphing Inequalities:
Solving inequalities is the same as
solving equations EXCEPT if you
multiply or divide by a negative
number, you have to FLIP the
inequality symbol.
Example: Solve each compound inequality. Graph the solution.
C1.
3x 12 and 8x 16
C2.
−3𝑥 + 4 > 16 or 2𝑥 > 14
Algebra 2
Chapter 1 Notes
D: Solving Absolute Value Inequalities (Lesson 1.6)
There are two types of absolute value inequalities: “Less than” and “Greater than”
“GO L.A.!”can help you remember the difference
Greater than = Rewrite and solve like an Or inequality.
Less than = Rewrite and solve like an And inequality.
Example: Solve each inequality. Graph the solution.
D1.
4 x 8 20
D2.
|3𝑥 − 12| + 8 ≥ 14
D3.
4s 1 27
D4.
2 10 2k 2
Algebra 2
Chapter 1 Notes
P.3 – Prerequisite skills – Binomials and Radicals
Topics: Multiplying Binomial Algebraic Expressions
Rewrite Square roots in simplest radical form
A: Multiplying Binomials – The FOIL Method
Example: Multiply and simplify the following expressions.
A1. (𝑥 + 3)(𝑥 + 5)
A2. (𝑥 − 6)2
A3. (2𝑥 − 5)(3𝑥 + 9)
A4.
(𝑥 2 + 5)(𝑥 + 2)
A6.
(2𝑥 − 3)(3𝑥 2 − 𝑥 + 4)
A5.
(𝑥 + 3)(𝑥 2 + 4𝑥 − 7)
Algebra 2
Chapter 1 Notes
B: Simplest Radical Form
Recall:
A “perfect square” is a number that has an integer square root
Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, . . .
Using the Multiplication Property to simplify square roots:
Strategy:
1. Break the square root into two factors, one of which is a perfect square.
2. Simplify the perfect square.
3. Continue until the radicand (number under the radical) has no more perfect
square factors.
Example.
B1.
√50
B2.
√160
B4.
B5.
−5√162
3√12
B3.
Using the Division Property to simplify square roots:
Strategy: It’s not simplified until there are no radicals left in the denominator
1. Break the square root into a quotient of two radicals, top & bottom
2. Multiply the numerator and denominator by the denominator of the fraction
3. Simplify
B6.
𝟐
𝟓
√
B7.
𝟕
𝟏𝟎
√
√27
Algebra 2
Chapter 1 Notes
P.4 – Prerequisite skills –Using a scientific
calculator
Topics: Use a scientific calculator properly and efficiently
A: Fraction Key
Examples:
14
A1.
Reduce 240
A3.
2
3
A6.
Solve
3
+7
B: F
A4.
2
𝑥
5
15
A2.
3
5
Reduce 25
1
4 6 ∙ 10
4
−8=5
A7.
Solve
5
1
A5.
−8 ÷ 22
1
𝑥
3
2
− 10 = 5 𝑥 + 4
D (Fraction to Decimal Shift)
Convert Decimals to fractions and fractions to decimals.
Example:
B1. Solve:
14𝑥 = 10
B3. Convert to a fraction in lowest terms:
B2.
0.372
Solve:
90𝑥 = 80
.45
0. 3̅
Algebra 2
Chapter 1 Notes
C: Exponents
Example: Simplify the following expressions
4𝟐
C1.
C2.
(−8)2
C3.
53
C4.
(−5)3
C5.
−72
Example: Evaluate the following expressions when 𝑥 = 6 and 𝑦 = −2.
𝑥𝑦 3
C6.
C7.
5𝑦 4
C8.
10
𝑥2
D: General Calculations
Simplify the following expressions
√52 − 4(1)(3)
D1.
D4. 2(−1)2 + 3(−1) + 6
D6.
2
3
4
(24𝑥 + 5)
D2.
√(−3)2 − 4(2)(−5)
D5. 2(5)2 − 7(5) − 1
D7.
1
𝑥+10
4
2
D3.
2−10
12+14
0
