8.1 Systems of Linear Equations in Two Variables
Method I: Graphing
Method II: Substitution
Ex: Solve each system by graphing
Ex: Solve each system by substitution
Method III: Addition
Ex: Solve each system by addition.
1.1 Equations in One Variable
Using properties of equalities:
Addition property of equality
Subtraction property of equality
Multiplication property of equality
Division property of equality
5.1 AREAS BETWEEN CURVES
5.1 Areas Between Curves
In chapter 5 we defined and calculated areas of regions that
lie under the graphs of functions. Here we use integrals to
find areas of regions that lie between the graphs of two
Consider the reg
Functions: a relationship between sets, such that each member of the first set corresponds to exactly
one member of the second set. The first set is called the _ and the second set is called
Functions will pa
4.1 Exponential Functions and Their Applications
f(x) = ax, a > 0 and a 1.
Ex: Let ( )
, ( )
, and ( )
( ) . Find the following values.
Domain of an Exponential Function
Chapters 3 & 4 Review
No work no credits
Find all real and imaginary solutions.
1) x4 + 81x2 = 0
Discuss the symmetry of the graph of the polynomial function.
2) f(x) = x3 - x
State the domain of the rational function.
Ch 8 & 9 Review
No work no credits!
9) Michael's bank contains only nickels, dimes,
and quarters. There are 48 coins in all, valued
at $3.80. The number of nickels is 4 short of
being three times the sum of the number of
3.1 Quadratic Functions and Inequalities
Two Ways to Write Quadratic Functions:
Ex: Rewrite the function in the form ( )
and sketch its graph
Theorem: Quadratic Functions
The graph of any quadrat
9.1 Solving Linear Systems Using Matrices
A matrix with m rows and n columns has size m n (read m by n).
o The number of rows is always given first.
A square matrix has an equal number of rows and columns.
5.1 Angles and Their Measurements
Definition: Degree Measure
The degree measure of an angle is the number of degrees in the intercepted arc of a circle centered at the
vertex. The degree measure is positive if the rotation is _an
A function whose domain is the set of counting numbers: 1,2,3,4,
Sequences can be infinite or finite.
It represented by its nth term, an.
Sometimes listed as a set, in set notation: cfw_an
Ex: Find all terms of the sequence
Math 180 Class Work Name:
Evaluateeach limit. \ 3_ as? -\f\
(3+h)1 31 hm 3W z \m aw :v\m gm.)
. z -" as j
1 m h has \A Wm M b?
, M L
z \W SLI = "'"
Wm 729% 56
x25x+6 = - dwe " K
x5 #15 (X 5080 \Nm
l W) W W \m_
Math 180 Class Work Sections 4.2, 4.3
1. The graph of f is shown. Evaluate (approximate) each of the following integrals by interpreting them in
terms of area.
2'. Write the integral as the limit of a sum, and then evaluate the integral, interpreti
Math 180 Class Work 4 Name: 8
Sections 2.3, 2.4, 2.5, 2.6
1. Find the equations of the tangent line and normal line to the curve y = 1
at the point
_ I: .1 "1- . &.5 _._."*2x iii-J-
mmh (KHZX ML 25; T ._. Ni 2
3.1 MAXIMUM AND MINIMUM VALUES
3.1 Maximum and Minimum Values
Some of the most important applications of differential calculus are
optimization problems, in which we are required to find the optimal (best)
way of doing something. These problems can be red
Math 180 5.1, and 5.2 Class Work Name:
'1. Sketch the region enclosed by the given curves and find its area. )6 = 2y2, and x = 4 + yz.
my X 5
2. The region enclosed by the curves y = x and y = x2 is rotated about the X-axis. Find the
volume of t
Ch. 10 & 11 Exam Review
No work no credits
Write out the first five terms of the sequence.
1) a n = (-1)n - 1
2n - 1
Identify the sequence as arithmetic, geometric, or neither.
2) 9, 11, 15, 21, 29, . . .
Find the required part of the geo
Chapters 1 & 2 Review
Show ALL work for full credits.
Solve the equation by factoring.
1) 49x2 - 98x + 45 = 0
For the given pair of variables determine whether a is a function of b, b is a function of a, both,
Chapters 5, 6 & 7 Review
No work no credits!
Find the exact value of the indicated trigonometric
function of .
10) cot = , cos < 0
Find csc .
Convert the angle to D M' S' form. Round the answer to
the nearest second.
2.1 DERIVATIVES AND RATES OF CHANGE
2.1 Derivatives and Rates of Change
If a curve C has equation y = f(x) and we want to find the tangent
line to C at the point P(a, f(a), then we consider a nearby point Q(x,
f(x), where x a, and compute the slo