Math 1513 College Algebra
C. Hook
Quadratic Equations
1.3
Standard Quadratic Form
Methods used to solve quadratic equations
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Factori
MTWR Caicuius 1
Chapter 4 Section 1 C. Hook
Extrema on an interval
Whats 1the highest point in a certain interval?
Maximum and minimum are Extreme Vaiues
(Extrema) plural
l
Given ion interval | with c
Chapter 9 and 10 Review
1. Solve the system by graphing and report answer as an ordered pair.
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y=%x+2
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MTWR Calculus 1
Chapter 4 Section 4 C. Hook
Concavity and the Second Derivative Test
Advertising a product
Net Profit
Advertising 5
Profit per Add S - slope of tangent (rate at which add S are bri
Math 1513 - College Algebra
C. Hook
The Real Number System
Section 13.1
Classification ofthe sets of numbers:
Naturai numbers/Counting Numbers cfw_1, 2, 3, 4, .
integers cfw_., -3, -Z, -1, 0, 1, 2, 3,
Chapter 4 Review
1. Find the inverse of f(x) = 3x2 + 2
2
Kg 2 x i l
,2
X 1: 3.3% "t l
m 2. " 2.
Sketch the graph of each equation. w WWWWWW M
2. y x 2"H 4. Use a calculator to find the value
Math 1513 College Algebra
C. Hook
Linear and Absolute Value Equations
1.1
Equations Expression =Expression
What you do to one side you have to do to the otherl!
Linear Equation
Form
called fik o
Math 1513 Coilege Algebra
0. Hook
4.4 Properties of Logs
Ex) Expand or contract depen ' on what is gveu. . . ._
xzyz ] \La 04: g. 'f:
1. log [
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Find the first three terms and th:' _ I _ the sequence with the given nth term.
_1 n+2
1 a" a ( )
n
2. Findthe3383termof211,4,7- Q; at? (mcfw_\)C
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Math 1513 Coilege Algebra
C. Hook
Introduction to Functions
2.2
Function a correspondence between x and y
(formai definition) a set of ordered pairs in which no two ordered pairs have the same
first c
Math 1513 College AEgebra
C.Hook
9.3 Non linear system of Equations Math 1513 Coliege Algebra
C. Hook
y=x3 2x2 +5x+l
2. L.
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2
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MTWR Calculus 1 E
Chapter 3 Section 6 C. Hook i
Let f be a function with domain of interval i. iffhas an inverse, then
i
1. iff is continuous then f'1 is continuous
2. Iffis increasing then f1 is incr
3.1 The Remainder Theorem and the Factor Theorem
if P is a polynomial function, then the values of x for which PM is equal to 0 are cailed the
zeros of P.
A To divide a polynomial by a monomial dived
Math 1513 College Algebra
C. Hook
3.3 Zeros of Polynomial Functions
Multiple zeros of a polynomial function
If a polynomial function P has (x r) as a factor k times, then r is a zero of multiplicity k
MTWR Caiculus 1
Chapter 3 Section 1 _ C. Hook
The Derivative and the Tangent Line Problem
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W.wa-mm,w .
. rise _
Rate of change is = m : yz y1
mm xzxl
Exampie: The pig puiation
MTWR Caicuius 1
Chapter 3 Section 7 _C. Hook
Related Rates
Sometimes two variabies are both changing in a problem.
lf you are standing in front of a train watching it as it goes by. The rate in which
Math 1513 College Algebra
C. Hook
8.1 Sequences and Summation Notation
A _ is a list of terms, and the terms are related to each other by a
function, rule or formula. The set of counting numbers is th
Math 1513 Coliege Aigebra
2 f C. Hook
3 I3?
Cramers Rule
Using determinants of equations to solve for x and y.
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Math 1513 College Algebra
C. Hook
9.1 System of Linear Equations in two variables
is an ordered pair that is a solution of both equations.
Three ways to solve: 1) Graphing
2) Elimination
3) Substitu
Math 1513 College Algebra
C. Hook
5 4.6 Exponential Growth and Decay
Also, used for infinite compounding.
Compound Interest for Finite Compounding Periods
_ n!
A = A0 (1+?)
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Ex)
1. C
Math 1513 College Algebra
C. Hook
Quadratic Functions
2.4
a> O the parabola opens kw and the vertex is a 5% ig
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sea;
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a< 0 the parabola opens cfw_jggand the vertex is 3 E
Math 1513 College Algebra
C. Hook
Complex Numbers
P.6
There really is nothing complex" about itil The definition of complex in dealing with
mathematics is: consisting of two parts. The two parts are:
'(ntln ~
9.4 Partial Fractions
A
Case 1 : Nonrepeated Linear Factors of the form Tum
C
3x4 A B
ex :
01: + 4)(x - 2) x
+
3x+4 x2
each iinear factor of the denominator occurs only once
Case 2: Repe
Math 1513 College Algebra
C.Hook
10.1 Matrices and determinants
Matrix a rectangular array of numbers (matrices plural)
Order m x n
Given a system of linear equations the Augmented matrix is:
g . .
x3
Math 1513 _ Coilege Algebra
C. Hook
Two Dimensional Coordinate System and Graphs
I tank)
Distance Formula
The distance between two points PE(xi,yi) and Pz(x2,y2) is
Ex)
1. Find the distance and midp
Math 1513 College Algebra
C.Hook
11.1 Sequences and Summation Notation - l
_ _ is a list of terms, and the terms are related to each other by a
function rule or formula. The set of counting numbers
Math 1513 College Algebra
C. Hook
11.3 Infinite Geometric series
a A geometric series is characterized by a common ratio r.
o The terms in a geometric series or sequences are reiated by a common ratio
Math 1513 - College Algebra
C.Hook
(3" =
(51.5)" = 61%" l
Exampie 2: Simplify
Scientific Notation: A number written in scientific notation has the form ax 10 where n is an integer
and 15a<10.
Math 1513 Coilege Algebra
C. Hook
10.4- Determinants
Each square matrix ( m x n ) has a number associated with it called the Determinant.
Determinant notation is paralief bars I i
A 2 x 2 determinant
Sum:
Difference:
Product
Quotient
Ex) If f(x) 25_and g(x)
x #254215
Math 1513 Coliege Aigebra
C. Hook
Algebra of Functions
2.6
ind the domalns 0f(f+ 5Q" ggj >
245%
EX] Let f(x)=x2+2 and g(x
MTWR Calculus 1
Chapter 4 Section 2 C. Hook
Rolies Theorem and the Mean Vaiue Theorem
M
Thore is no way to draw a continuous graph from a to b without
creating a max or a min. Thats what the next th
Math 1513 College Algebra
C. Hook
Factoring can also be done using the grouping method.
4x217x21
95:2 3661 + 35
6x211x+4
6.
8. Math 1513 College Algebra
C. Hook
Factoring trinomials that do no
MTWR Calculus 1
Chapter 3 Section 5 C. Hook
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Implicit Differentiation
0 = 2x2 4y + 3 this is the impiicit form ofy as a function ofx
We can write it into function form by solving for y.
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Math 1513 College Algebra
C.Hook
Radical Equation
Ex)
3y
1 cfw_lbxm4%& z x+2wa =
ZE
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l5x1x/3x2 =1
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