CUNY Elementary Algebra Final Exam
Problem Sets
November 2012
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Math 470, Fall 2005.
Topics in Geometry
Dr. Silvia Fernndez
Problem Set #1
Plane Euclidean Geometry
1. (Triangle Geometry) In triangle ABC, AB=AC. Point P strictly between A and B
such that AP=PC=CB. Find A .
2. (Triangle Geometry) Triangle ABC has a righ
INTRO TO ALGEBRAIC GEOMETRY, PROBLEM SET 6
Due Thursday October 28 in class (no lates). Hand in seven of the following
questions. Youre strongly encouraged to collaborate (although write up solutions
separately), and youre also strongly encouraged to ask
FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 17
RAVI VAKIL
This set is due Thursday, April 20. You can hand it in to Rob Easton, in class or via
his mailbox. It covers (roughly) classes 37 and 38.
Please read all of the problems, and ask me about any sta
Bashing Geometry with Complex Numbers Problem Set
Peng Shi
Reality may be a line, but a little imagination makes it a plane!
1
Slick Bashing
These problems are perfect for complex number solutions. Exploit the power of complex numbers in representing
tra
Accelerated Geometry Application
Problem Set
Overlake Summer Program will admit students to Accelerated Geometry on a rolling
basis. Applications for the course will be reviewed once all materials have been submitted;
students are encouraged to submit all
Descriptive Geometry
Problem Set A
Instructions:
For each drawing, there is a rod inside a cubic box. You are given two orthographic views: the top view
and the front view. First, you should precisely describe on a separate sheet and in your own words how
18.782 Introduction to Arithmetic Geometry
Problem Set #1
Fall 2013
Due: 09/17/2013
Description
These problems are related to the material covered in Lectures 1-2. I have made every
effort to proof-read these problems, but there are may be errors that I h
INTRO TO ALGEBRAIC GEOMETRY, PROBLEM SET 12
Due Monday December 13 by noon at my office. Read all of the problem set, and
hand in six of them, including one from each section. Youre strongly encouraged
to collaborate (although write up solutions separatel
Trigonometry - Problem Set
1. Find the acute angle that has the same sin-, cos-, and tan-values as 380 ,
450 , 1082 , 5 radians, 11
2 radians, and 26.
2. Convert the following angle to radians: 45 , 27 , and 120 .
3. Convert the following angles (given in
Inverse trig functions create right triangles
An inverse trig function has an angle (y or ) as its output. That angle
satisfies a certain trig expression and so we can draw a right triangle that
represents that expression.
Elementary Functions
One can alw
New York State Learning Standard for Mathematics
Revised by NYS Board of Regents March 15, 2005
Page 113
Algebra 2 and Trigonometry
In implementing the Algebra 2 and Trigonometry process and content performance indicators, it
is expected that students wil
Trigonometric Identities 1
Lecture Notes
page 1
Sample Problems
Prove each of the following identities.
1. tan x sin x + cos x = sec x
2.
1
1
+ tan x =
tan x
sin x cos x
3. sin x
4.
5.
sin x cos2 x = sin3 x
cos
1 + sin
+
cos x
1 sin x
6. cos2 x =
1 + sin
Math 103 Problem Set 1
1. Using Right Triangle Trigonometry
(1) A person stands 50 feet from a tree and looks up at the top of the tree. The angle of
elevation from eye level is 20 . If the persons eye level is 5 feet from the ground, how tall
is the tree
Trigonometric Limits
We will deal here with a set of problems posed at the end of Section 3.3. In order
to find the derivatives of sin x and cos x , using the definition of derivative, we
needed to prove the limits
sin x
= 1
x0 x
lim
and
lim
x0
cos x 1
=
Lesson 30
NYS COMMON CORE MATHEMATICS CURRICULUM
M2
GEOMETRY
Lesson 30: Trigonometry and the Pythagorean Theorem
Student Outcomes
Students rewrite the Pythagorean theorem in terms of sine and cosine ratios and use it in this form to solve
problems.
Studen
Problem Set (Derivatives of Trig Functions)
Part A- Find the derivatives of the following functions. These problems do
not involve the chain rule.
1. sin
5. tan cos csc
2. ab sin cos
6. ab sin cos sec
3. ab sin cos
7.
4. ab tan
sin
8. ab cos
Par
INTRO TO ALGEBRAIC GEOMETRY, PROBLEM SET 3
Due Thursday October 7 in class. No lates will be accepted, so Ana-Maria will
be able to return it in time for the next Tuesdays class. Do any 7 of the following
9 problems, including Problem 9 (which is, I think
MATH 1040 FUNDAMENTAL PROBLEMS OF GEOMETRY
PROBLEM SET 3, DUE WEDNESDAY FEBRUARY 24 5pm
graded out of: 11 max number of points: 13
1. (2pts) Prove that the image of a compact space under a continuous map is compact. You can
work with either metric or topo
Algebra Cheat Sheet
Basic Properties & Facts
Arithmetic Operations
Properties of Inequalities
If a < b then a + c < b + c and a c < b c
a b
If a < b and c > 0 then ac < bc and <
c c
a b
If a < b and c < 0 then ac > bc and >
c c
b ab
a =
c c
ab + ac = a (
Discrete Mathematics Problems
William F. Klostermeyer
School of Computing
University of North Florida
Jacksonville, FL 32224
E-mail: [email protected]
Contents
0 Preface
1 Logic
1.1 Basics . . . . . .
1.2 Truth Tables and
1.3 Quantiers . . .
1.4 Circuits .
18.8096 Problem 8et 1 Fall 2013
Due date : 9/24/2013
Collaboration on homework is encouraged, but you should think through the problems yourself
before discussing them with other people. You must write your solution in your own
words. Make sure to list al
The PRIMES 2015 Math Problem Set
Dear PRIMES applicant!
This is the PRIMES 2015 Math Problem Set. Please send us your
solutions as part of your PRIMES application. For complete rules, see
http:/web.mit.edu/primes/apply.shtml
Note that this set contains tw
Sample Problem Sets
KSEA National Mathematics Competition 2007
These sets cover : 4th Grade 11th Grade
Notes
These problems do not necessarily cover every aspect of the actual test. These
are problems chosen from the pool of old problem sets with some mo
Algebra - Problem Set
1. Simplify the following expression:
( 25 +
1
10
2
25 )
1
7
2
7
2. Simplify the following expression:
7(5 20 8 5 + 3 2)
3. Simplify the following expression:
14x2 y 3 z 5 + 6x1 y 5 z 3
1
+
2
10xyz
5xz
4. Find f (7) when f (x) = 3x
Principles of Mathematics 12
THE PROBLEM SET
September 2001
Assessment Department
ACKNOWLEDGEMENT
The Ministry of Education gratefully acknowledges the advice, assistance, and contribution of the
following professionals in the development of The Problem S
Applications of Mathematics 12
THE PROBLEM SET
September 2002
Student Assessment and Program Evaluation Branch
ACKNOWLEDGEMENT
The Ministry of Education gratefully acknowledges the advice, assistance, and contribution of the
following professionals in the
Set Theory: Venn Diagrams for Problem Solving
In addition to just being fun, we can also use Venn diagrams to solve problems. When doing
so, the key is to work from the inside out, meaning we start by putting information in the
regions of the diagram that
Problem Set Linear Algebra I
Vectors
In class we talked about how vectors are just a list of numbers that can be interpreted as a
direction or position in space. While this space can in some cases be literal physical space
(such as the example with