Unit 3: Permutations and Combinations (Day 1)
Section 8.1 Fundamental Counting Principle
i) An ice cream parlor has 3 types of cones (plain, sugar and waffle)
and 10 kinds of ice cream. How many choices do you have for
single scoop cones?
ii) How many cho
MTH 1210 2.4 Average Rate of Change of a Function Fall 2013
Rates of change are very important in applications. We are often interested in how a quantity is
changing over time. That is the rate of change of the quantity. You are already familiar with rat
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MTH 1210 3.5 Complex Numebrs Fall 2013
A complex number is an expression in the form
a + bi
Where a and b are real numbers and i = \/1.
The real part is the number a and the imaginary part is the number 1).
Adding, Subtracting, and Multiplyi
1:1,
«
Mlll 1210 3.4 Real Zeros of Polynomials Fall 2013
Rational Zeros of Polynomials
We know how to nd zeros of polynomials of degree two. We can factor or use the quadratic formula.
We can even nd the zeros of degree 3 polynomials. But once
Lauren Doherty
Math
Mrs. Glass
4/2/2014
Simple vs. Damped harmonic motion
Simple harmonic motion is repetitive movement back and forth through an
equilibrium, or central, position, so that the maximum displacement on one side of this
position is equal to
Unit 4: Graphing Quadratic Functions
Unit Review
Topics Covered:
1. Graphing Quadratic Functions
- Properties of the graph (vertex, axis of symmetry, intercepts)
- Graphing y a ( x p) 2 q
- Completing the Square
2. Finding the zeros/roots of a quadratic b
Unit 4: Exponents and Logarithms (Day 1)
Exponents Review
Exponent Laws:
Multiplication Law: When multiplying powers with the same base, ADD the exponents.
Division Law: When dividing powers with the same base, SUBTRACT the exponents.
Power Law: When a po
Unit 4: Exponents and Logarithms (Day 11)
Graphing Logarithmic Functions
i) Make a table of values and sketch a graph of
y log 2 x
Properties of the graph:
x-intercept:
y-intercept:
Domain:
Range:
Asymptotes:
Transforming the graph:
y a log b( x p ) q
a e
Unit 4: Exponents and Logarithms (Day 3)
Defining Logarithms
Use your calculator to evaluate
log10
log100
log1000
log10000
log x is the exponent 10 has if x is written as a power of ten.
Definition:
log to the base a of x equals y:
The answer, y, is the e
Unit 4: Quadratic Functions
Lesson 1
Properties of the Graph of a Quadratic
A quadratic function is defined as having an equation with degree 2.
Its equation can be written as:
y ax 2 bx c
where a, b, c are constants (a, b, c )and a 0 .
Which of the follo
Unit 3: Permutations and Combinations (Day 2)
Section 8.3 Permutations Involving Identical Objects
Consider: How many permutations are there of the word ROSE?
The word ROSS
The letters RSSS
The number of permutations of n objects taken n at a time if ther
Unit 3: Permutations and Combinations (Day 5)
Section 8.6 The Binomial Theorem
Expand the following:
( a b) 0
(a b)1
( a b) 2
( a b) 3
( a b) 4
Predict
( a b) 5
The Binomial Theorem:
(a b) n n C0 a n n C1a n 1b n C2 a n 2b 2 n C3a n 3b 3 n Cn 1a1b n 1 n C
Unit 8: Functions (Day 6)
Analyzing Rational Functions
Discontinuities:
On a graph, the non-permissible values of a rational function correspond to either a
vertical asymptote or a point discontinuity (hole) in the graph.
If the numerator and the denomina
Unit 3: Permutations and Combinations (Review)
Unit Review
Topics Covered:
1. The Fundamental Counting Principle
2. Permutations
Different Objects
n
Pr
Identical Objects
P
n!
(n r )!
n!
a!b!c!
3. Combinations
n
Cr
n!
r!(n r )!
4. Pascals Triangle
rth
Unit 8: Functions (Day 1)
Adding and Subtracting Functions
Domain and Range:
Domain is a list of all the possible x values.
Polynomials, exponentials, odd indexed roots, sine and cosine
all have domain all real numbers
The inside of a an even indexed ro
Unit 4: Exponents and Logarithms (Day 4)
Section 5.5 Laws of Logarithms
Multiplication Law:
Division Law:
Power Law:
Exponents
Logarithms
a x a y a x y
log a xy log a x log a y
a x a y a x y
log a ( xy ) log a x log a y
(a x ) n a xn
log a x n n log a x
U
Unit 4: Graphing Quadratic Functions
Graphing y a ( x p) 2 q
Recall:
We can quickly graph any quadratic, by hand, if the function is in the form
f ( x) a ( x p) 2 q
a:
p:
q:
Graph:
i) f ( x) x 2
Vertex:
Domain:
ii) y ( x 2) 2 6
Axis/Symmetry:
Range:
Verte
Final Exam Review III
January 18, 2012
UNIT 5: SYSTEMS OF EQUATIONS AND INEQUALITIES
1. Solve. Answer both algebraically and on a number line:
x 2 5 x 14 0
2. Graph the region defined by:
2 x 3 y 6
3. Solve algebraically:
y 3 x 2
y x 2 4 x 2
UNIT 6: TRIGO