Name: K E V
Discussion Section:
MATH 1715, Exam 2A
October 9, 2013
Only one calculator may be used on the exam. No TI-89, TI-Nspire (unless using
a TI-84 keyboard), or similar calculators may be used. Cell phone calculators and
computers/1aptops/table
Math 1715, L. Brown
Sec. 13.2: Arithmetic Sequences
Arithmetic Sequences
An arithmetic sequence is a sequence in which the difference between terms is
always constant.
Sequence
Difference
1, 5, 9, 13, 17,
4
12, 10, 8, 6, 4,
2
Example 1
Determine whether
Math 1715, L. Brown
Section 12.3: Hyperbolas
A hyperbola is the set of all points in the plane the difference of whose distances
from two fixed points (foci) is constant.
Vertex
Vertex
Focus
Conjugate
Axis
Focus
Transverse
Axis
Asymptotes
Standard Equatio
Math 1715, L. Brown
Section 13.1: Sequences and Summation Notation
Sequences
A sequence is a set of numbers written in a specific order.
The domain of the sequence is the set of natural numbers: cfw_1, 2, 3, 4, .
The values in the sequence are called the
Math 1715, L. Brown
Section 11.1: Systems of Linear Equations in Two Variables
A system of equations is a set of two or more equations, involving two or more
variables.
In a system of linear equations in two variables, each of the equations must have
the
Math 1715, L. Brown
Section 12.1: Parabolas
Conic sections are the shapes formed when a plane slices through a double-napped
cone.
Circle
Circle
Hyperbola
Ellipse
Parabola
The Parabola
A parabola is the set of all points in a plane equidistant from a fixe
Math 1715, L. Brown
Section 10.1: Vectors in Two Dimensions
Introduction to Vectors
Terminal Point Q
Vectors are line segments with an assigned direction.
They have both magnitude (length) and direction.
The vector shown is called v PQ , since it starts
a
Math 1715, L. Brown
Section 11.2: Systems of Linear Equations in Several Variables
A linear system of equations in three variables graphs as a plane.
A linear system of 3 equations in three variables can have 1 solution, no solution,
or an infinite number
Math 1715, L. Brown
Section 8.5: More Trigonometric Equations
Solving Equations Using Identities
Example 1
Solve the equation.
(a) 2cos2 3(1 sin )
(c) 4 sin cos 2sin 2cos 1 0
(b) sin 2 cos 0
Math 1715, Section 8.5
Multiple Angle Trigonometric Equations
Wh
Math 1715, L. Brown
Section 8.4: Basic Trigonometric Equations
The solution to a trig equation is the set of all values that make the equation true.
Example 1
1
Name one solution to the equation sin , in radians. How many solutions does
2
it have?
General
Math 1715, L. Brown
Section 8.3: Double-Angle, Half-Angle Formulas
The Double-Angle Formulas
The sine and cosine double-angle identities can be derived using the sum identities.
Derivation of Cosine Double-Angle Identity
Start with the sum identity for co
Math 1715, L. Brown
Section 7.5: Inverse Trigonometric Functions
Inverse Sine
Since sine is not one-to-one, its domain is restricted to
2
x
2
.
Graph of
y = arcsin(x)
Its inverse, y sin 1 x , also known as y arcsin x , has domain 1 x 1 and range
2
y
2
.
Math 1715, L. Brown
Section 7.3: Trigonometric Graphs
A function is periodic if there is a positive number p such that f(t + p) = f(t), for every t.
The smallest such number is called the period of f.
The period for both sine and cosine is 2.
sin(t+ 2) =
Math 1715, L. Brown
Section 7.4: More Trigonometric Graphs
Tangent Graph
y
Plot points to see the graph of tangent.
y = tanx
x
undefined
1
2
3
3
x
1
4
1
1
6
3
0
0
1
6
3
tan x as x from the right
2
1
tan x as x from the left
4
2
3
Tangent has vertical asym
Math 1613, L. Brown
Section 7.2: Trigonometric Functions of Real Numbers
A unit circle is a circle of radius 1. A point (a, b) is on the unit circle only if it
satisfies the equation x 2 y 2 1 .
Unit Circle
(x , y )
1
t
x
Let t be an arbitrary radian angl
Math 1715, L. Brown
Section 8.2: Addition and Subtraction Formulas
The addition and subtraction formulas allow us to find exact values of trig functions
at values we could not calculate exactly before.
Addition and Subtraction Formulas (Sum & Difference I
Math 1715, L. Brown
Section 6.6: The Law of Cosines
Remember: The Law of Cosines is used for SAS and SSS triangles.
Law of Cosines
a2 b2 c2 2bc cos
b2 a 2 c2 2ac cos
c2 a 2 b2 2ab cos
a
c
b
Example 1
Solve the triangle: a = 6.1 cm, b = 2.7 cm, and
= 62
Math 1715, L. Brown
Sec. 13.3: Geometric Sequences
Geometric Sequences
A geometric sequence is a sequence in which the ratio of terms is always constant.
Sequence
Common Ratio
3, 6, 12, 24, 48,
2
1,
1111
,
, .
2 4 8 16
5, 6, 7.2, 8.64,
1
2
1.2
Example 1
Name: _
Due Date: Friday 1/24/2014
MATH 1715, Section 1.3 Homework
Answer all questions completely and show all work to receive full credit.
1. (5 pts. each) Solve each equation by completing the square.
(a) x2 18x 19
(b) 3x2 6 x 1 0
Name: _
MATH 1715, Section 4.6 Homework
Answer all questions completely and show all work to receive full credit.
1. (3 pts. each) Find the intercepts and asymptotes, and then sketch a graph of the rational function. Show your work.
2x 1
3x 3
x2 5x 4
(a )
OKLAHOMA STATE UNIVERSITY
SYLLABUS ATTACHMENT
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http:/academicaffairs.okstate.edu/faculty-a-staff
YOUR SUCCESS AS A STUDENT IS OUR TOP PRIORITY.
THIS INFORMATION IS PROVIDED TO ANSWER QUESTIONS MOST OFTEN ASKED BY STUDENTS .
IMPORTANT DATES
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Please write both your first and last name.
Algebra Review
10 points
_
_
In questions involving numeric calculation, you must write down all steps.
1. (2 pts.) Simplify the expression and eliminate any negative exponents. Assume
that all let
Math 1715
Group Work: Sections 1.5, 1.6
Group Members (max. 3 per group)
Please write both your first and last name.
_
_
10 points
Remember to show all your work.
1. (5 pts.) Find all real solutions:
answers for extraneous solutions!
2. (5 pts.) Solve the
Name: _
Due Date: Friday 1/31
MATH 1715, Section 1.5/1.6 Bonus Group Work
Answer all questions completely and show all work to receive full credit.
Each group member must turn in their own work. Points per question will
replace your corresponding 1.5/1.6
Name:_
Discussion Section:_
MATH 1715, Exam 1(A)
September 14, 2012
Only one calculator may be used on the exam. No TI-89, TI-Nspire (unless
using a TI-84 keyboard), or similar calculators may be used. Cell phone
calculators and computers/laptops/tablets