Polar Coordinates
Another coordinate system that can be used to plot points in the plane.
y
Polar axis Origin Pole x
P = (r , )
r
O Pole
Polar axis
Plot the point 4, using polar coordinates. 6
4
6
Math 2: Final Exam Review Questions
1. Find the domain of f (x) =
1
.
x+4
2. Find the difference quotient of f (x) = x2 3x; that is, find
f (x + h) f (x)
, h 6= 0. Simplify fully.
h
3. David has 800
Math 2: Exam 1 Review Questions
1. For the circle given by the equation x2 + y 2 2x 4y 4 = 0, find the center (h, k) and
the radius r. Sketch a graph of the circle.
2. Determine whether y = x + 1 is a
Math 2
Review Problems for Week 6
Find the exact value of the expression. Do not use a calculator.
- 1 (- 0.9372)]
1) cos [cos
A) - 0.4686
2) cos- 1 cos A) -
B) 0.4686
C) - 0.9372
1)
D) 0.9372
3
5
2
5
Math 2
Review problems for Final
These problems cover only chap 8,9,10, and 11. You will need to rework the problems on the old reviews to be ready fo
cumulative final exam.
Solve the right triangle u
Math 2
Review Problems for Week 5
Convert the angle to a decimal in degrees. Round the answer to two decimal places.
1) 21014'51'
A) 210.31
B) 210.21
C) 210.25
D) 210.26
Convert the angle to D M' S' f
Math 2
Review problems for week 2
Analyze the graph of the given function f as follows:
(a) Determine the end behavior.
(b) Find the x- and y-intercepts of the graph.
(c) Determine the multiplicity at
Math 2: Exam 2 Review Solutions
1. (a) Max Number of Zeros = 4; Max Number of Positive Zeros = 3; Max Number of
Negative Zeros = 1
p
1 1
(b)
= 1, 2, 4, 8, ,
q
2 4
1
(c) 2, , 1, 4
4
(d) f (x) = (x + 2
The Fundamental Theorem of Algebra
Motivation
Over the set of real numbers not all polynomial equations have a root.
Example: x2 + 1 = 0 has no real solution.
We want to determine the conditions that
The Remainder Theorem and the Factor Theorem
Remainder Theorem
Let f be a polynomial function. If f (x) is divided by x - c, then the remainder is f (c). Find the remainder if f ( x ) = 3x 3+ 9 x 2 18
Curves in Polar Coordinates
An equation whose variables are polar coordinates is called a polar equation. The graph of a polar equation consists of all points whose polar coordinates satisfy the equat
Systems of Two Linear Equations in Two Unknowns
A system of equations is a collection of two or more equations, each containing one or more variables. A solution of a system of equations consists of v
Nonlinear Systems of Equations
We want to solve systems of equations that involve non-linear equations. Geometrically, what we want to do is to find the points of intersection of two curves. For examp
The Basic Equations
Know Facts
Distance between P = ( x1 , y1 ) and P2 = ( x2 , y2 ) : 1 d ( P , P2 ) = 1
( x2 x1 )
2
2
+ ( y2 y1 )
2
Equation of a circle centered at C = (h, k ) and radius r :
( x h)
Conic Sections
Conic sections, or conics, get their name because they result from intersecting a cone with a plane.
PARABOLA
A parabola is the set of points in a plane that are equidistant from a fixe
The Ellipse
Definition
An ellipse is the set of points in a plane the sum of whose distances from two fixed points F1 and F2 is a constant. These points are called the foci.
To obtain the equation for
The Hyperbola
Definition
A hyperbola is the set of all points in a plane the difference of whose distances from two fixed points F1 and F2 (the foci) is a constant.
The derivation of the equation of a
The Complex Number System
Imaginary Unit
Definition : i = 1 is the imaginary unit.
Hence, i2 = -1, so i clearly is NOT a real number.
Characteristics of the imaginary unit : i = 1 i = 1
2
i = i i = i
Division of Polynomials
Division Algorithm for Polynomials If f(x) and g(x) denote polynomial functions and if g(x) is not the zero polynomial, then there are unique polynomial functions q(x) and r(x)
Math 2
Review problems for Midterm
For the given functions f and g, find the requested composite function.
Find (f g)(x).
1) f(x) = x 2 - 2, g(x) = x 2 - 7;
A) x 4 + 47
B) x 4 - 14x 2 + 47
2) f(x) = -
IVC Math 2 (Prof. Pham)
WS 11
Name:
REVIEW.
1. Find the long-range behavior of the following functions. This is something you will be doing alot in
Calculus.
(
x if x > 3
(a) f (x) =
(b) f (x) = (4x 1
Math 2 accelerated Practice Exam 1
Show all your work.
Decide whether or not the points are the vertices of a right triangle.
1) (5, -7), (14, -7), (14, 1)
1)
Answer: Yes
2) (-6, 10), (0, 12), (-1, 7)
cp3 math 2
Name_
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question
Find the domain of the function.
2x
1) g(x) =
x2 - 81
2)
1)
x
x-5
2)
For the given fu
Math 2 Activity 4
Name_
Solve the following inequalities and write the solution set in interval notation. Use a sign chart.
1.
2.
3.
4.
5.
List the potential rational zeros of the polynomial function
Math 2 Activity 3
Name_
Read and follow all directions, and show your work to receive full credit.
1.
Write an equation of a polynomial with the degree and zeros given by:
Zeros: -1, 2, 5/2
2.
degree:
Math 2 Activity 2
Name_
Read and follow all directions, and show your work to receive full credit.
1. An equilateral triangle is inscribed in a circle of radius r. Express the circumference C of the c
Math 2 Activity 1
Name_
Read and follow all directions, and show your work to receive full credit.
1. Find the equation of the line that is perpendicular to the distance between the point (4, 4) and t
cp2 math 2
Name_
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question
Find the slope of the line and sketch its graph.
1) 3x + 4y = 18
1)
Find an equation
cp4 math 2
Name_
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question
The graph of a function f is given. Use the graph to answer the question.
1) Use the