Download Algebra 2

Bell Ringer
Which of the following mathematical
expressions is equivalent to the verbal
expression “A number, x, squared is 39 more
than the product of 10 and x”?
F. 2x = 39 + 10x
Note: Write all bell ringers
from a given week on a
G. 2x = 39x + 10x
single piece of paper. Turn
this piece of paper in on the
2
last day of the week.
H. x = 39 – 10x
Title: Bell Ringers
J. x2 = 39 + x10
Label individual bell ringers
K. x2 = 39 + 10x
by date
1.2 Properties of Real Numbers
In this class there are real numbers and
imaginary numbers, for the first 5 units we will
only deal with real numbers!
We will always start with vocabulary. Only write vocabulary terms you
DO NOT know.
Subsets of Real Numbers
Natural Numbers
Ex. 1, 2, 3, 4 …
The numbers used for counting
Subsets of Real Numbers
Whole Numbers
Ex. 0, 1, 2, 3, 4 …
The natural numbers and 0
Subsets of Real Numbers
Integers
Ex. … -3, -2, -1, 0, 1, 2, 3 …
The natural numbers, their opposites, and zero
Subsets of Real Numbers
Rational Numbers
Ex. 7/5, -3/2, -4/5, 0, 0.3, -1.2, 9
Any number that can be written as a quotient;
any number that terminates or repeats
Subsets of Real Numbers
Irrational numbers
Ex. √2, √7 , √2/3, 1011011101111011111…
Numbers that cannot be written as quotients of
integers
Subsets of Real Numbers
This diagram represents how all the subsets are
related.
Graphing numbers on the number line
To be able to graph on a number line you need
to understand what integers numbers fall
between
Practice: Name the 2 numbers each number
falls between
-3/2 =
-2 ¼ =
0.33333333…. =
The opposite or additive inverse of any number
a is –a. The sum of opposites is 0.
Practice:
1. ⅙ =
2. -⅝ =
3. -(-3.2) =
The reciprocal or multiplicative inverse of any
nonzero a is 1/a. The product of reciprocals is 1.
Practice:
1. ⅙ =
2. -⅝ =
3. -(-3.2) =
Finding Absolute Value
The absolute value of a real number is its
distance from zero on the number line.
Practice: Find |-4|, |0|, and |-1(-2)| and graph
on a number line.
1.3 Patterns and Expressions
Vocabulary:
A variable is a symbol, usually a letter, that
represents one or more numbers.
Ex.
x, y, a, b….
Vocabulary continued …
Algebraic Expression or a Variable Expression:
an expression that contains one or more
variables
Ex. 3x + 2b
*Note: An expression has no equation sign!!!!
Vocabulary continued …
Evaluate: When you substitute numbers for the
variables in an expression and follow the order
of operations to simplify
Practice:
a – 2b + ab for a = 4 and b = -2
Evaluating Practice
1. –x2 + 3(x – 3) for x = 2
Evaluating Practice
x(4x – x) – x2 for x = -5 and x = -2
Term: A number, a variable, or the product of a
number and one or more variables
Coefficient: The numerical factor in a term
5x2 + 6x
Like terms = the same variables raised to the
same powers
Ex. 3x2 and 5x2
or
-7x3 and 8x3
Combining like terms
Practice:
1. 5x2 – 10x + 3x2
2. -(m + n) + 2(m – 3n)
Finding the perimeter by combining
like terms
3x
2x - y
2x
y
y
3x - y
Practice
Evaluate the expression for the given values of
the variables.
4a + 7b + 3a – 2b + 2a; a = -5 and b=3
Practice
Evaluate the expression for the given value of
the variable.
|x| + |2x| - |x – 1|; x = 2
Evaluate |2x + 3| + |5 – 3x|for x = -3
1.4 Solving Equations
Equations with variables on both sides
Solve 13y + 48 = 8y - 47
Practice
8x + 12 = 5x - 21
Practice
2x – 3 = 9 – 4x
Using the Distributive Property
3x – 7(2x – 13) = 3(-2x + 9)
Practice
2(y – 3) + 6 = 70
Practice
6(x – 2) = 2(9 – 2x)
Solving a Formula for One of it’s Variables
Solve the formula for the area of a trapezoid for h:
A = ½ h (b1 + b2)
Solve the same equation for b1
A = ½ h (b1 + b2)
Homework
• Study vocabulary terms used in todays class
• Review sections 1 – 3 from Chapter 1 in your
textbook if you need the extra practice
1.5 Solving Inequalities
Solving an Graphing Inequalities
3x – 12 < 3
Practice
6 + 5(2 – x) < 41
Practice
12 > 2(3x + 1) + 22
Special Cases
Solve each inequality and graph the solution.
2x – 3 > 2(x – 5)
Special Cases
Solve each inequality and graph the solution.
7x + 6 < 7(x – 4)
Real World Connection
Revenue: A band agrees to play for $200 plus 25%
of the ticket sales. Find the ticket sales needed for
the band to receive at least $500.
Write an inequality and solve:
Practice
A salesperson earns a salary of $700 per month
plus 2% of the sales. What must the sales be if
the salesperson is to have a monthly income of
at least $1800?
Compound Inequalities (AND)
A compound inequality is a pair of inequalities
joined by AND or Or.
Example: 3x – 1 > -28 and 2x + 7 < 19
Practice (AND)
2x > x + 6 and x – 7 < 2
Compound Inequalities (OR)
4y – 2 > 14 or 3y – 4 < -13
1.6 Absolute Value Equations and
Inequalities
The absolute value of a number is its distance
from zero on the number line and distance is
nonnegative.
Example: |2x – 4| = 12
Practice
|3x + 2|= 7
Solving Multi-Step AV Equations
3|4x – 1| - 5 = 10
Practice
2|3x – 1| + 5 = 33
Practice
|2x + 7| = -2
An extraneous solution is a solution of an
equation derived from an original equation that
is not a solution of the original equation
Checking for extraneous Solutions
|2x + 5| = 3x + 4
Solve like normal
Check your answers
Practice
|2x + 3| = 3x + 2
Solving Absolute Value Inequalities
Solve |3x + 6| > 12. Graph the solution.
Practice
Solve 3|2x + 6| - 9 < 15 . Graph the solution.
Practice
Solve |5x + 3| - 7 < 34 . Graph the solution.
Bell Ringer
The expression (3x – 4y2)(3x + 4y2) is equivalent
to:
A. 9x2 – 16y4
B. 9x2 – 8y4
C. 9x2 + 16y4
D. 6x2 – 16y4
E. 6x2 – 8y4
Bell Ringer
The expression -8x3(7x6 – 3x5) is equivalent to:
A. -56x9 + 24x8
B. -56x9 - 24x8
C. -56x18 + 24x15
D. -56x18 – 24x15
E. -32x4
Bell Ringer
Marlon is bowling in a tournament and has the
highest average after 5 games, with scores of 210,
225, 254, 231, and 280. In order to maintain this
exact average, what must be Marlon’s score for his
6th game?
F. 200
G. 210
H. 231
J. 240
K. 245