By: Cristian Murguia and Roman Becerra
Definition: a solid geometric figure with straight parallel sides and a
circular or oval cross section.
Volume formula-V= r2 h
Coca cola is shaped as a cylinder
This very beautiful shaped c
Desarrollo Carlos Alberto Triana Livano
Ejercicio 1. Principio de sustitucin
x 2 x + x
Se realiza sustitucin:
Lo que provoca una indeterminacin con lo cual se procede a factorizar la expresi
Assessment for Learning: Peer Evaluation
1. Because the postal codes in the province of Ontario can start with one of five letters (K, L, M, N
or P) that means the first digit can be one of 5. The next digit is a number so it can be any from
one to nine m
sin D =
cos D =
tan D =
The trigonometric ratios sine, cosine, and tangent have reciprocal ratios:
cosecant, secant, and cotangent.
The reciprocal of sine is cosecant (csc).
The reciprocal of cosine is secant (sec).
The reciprocal of ta
CNRS, Institut Fourier
Universite de Grenoble I
100 Rue des Mathematiques BP74
38402 Saint-Martin-dH`eres Cedex, France
Email: [email protected]
Jan. 2015Charge de Recherche, CNRS, Fourier Institute, Grenoble.
Feb. 2015- Apr
Chapter 1 Review/Extra Credit Problems
Remember, no credit will be given for answers without justification.
Consider the multivariale function
f (x, y)
x2 + y 2
, if (x, y) 6= (0, 0)
, if (x, y) = (0, 0),
and the associated differentia
Formulas from Trigonometry
opp y sin
adj x cos
opp tan sin
sin + cos =1
1+ tan = sec
1+ cot =csc
Harolds Calculus Notes
26 April 2016
Definition of Limit
Let f be a function defined on an open
interval containing c and let L be a real
number. The statement:
lim () =
means that for each > 0 there exists a
> 0 such that
f ( g ( x) )
log a x
f + g
f g + f g
f g f g
f ( g ( x) ) g ( x)
nx n 1
a x ln a
x ln a
sec 2 x
csc x cot x
sec x tan x
Pre-Calculus 12 (30-1) Formula Sheet
Graphing Calculator Format
For ax 2 + bx + c = 0
b 2 4ac
For two points (x1 , y1 ) and (x2 , y2 )
(x 2 x 1 )2 + (y2 y1 )2
Exponential and Logarithmic Functions
x: [xmin, xmax, xscl]
y: [ymin, ymax,
Formula Sheet for Test 1
February 17, 2015
Product to Sum Formulas:
sin x sin y =
(cos(x y) cos(x + y)
cos x cos y =
(cos(x y) + cos(x + y)
sin x cos y =
(sin(x + y) + cos(x y)
Sum to Product Formulas:
sin x + sin y = 2 sin
Real Numbers and the Real Number Line
C Precalculus Review
C.1 Real Numbers and the Real Number Line
Represent and classify real numbers.
Order real numbers and use inequalities.
Find the absolute val
Calculus I Formulas
1. Limits and Derivatives
2. Differentiation rules
3. Applications of Differentiation
5. Applications of Integration
Professor: Dr. Mohammad Shakil
C0-Author: Jeongmin Correa
Miami Dade Co
Math 215 Precalculus Review Notes
area of circle: A = r2
circumference of a circle: C = 2r
volume of a sphere: V = 13 r3
surface of a right circular cylinder: S = 2r2 + 2rh
volume of a right circular cylinder: V = r2 h
Pythagorean Theorem: In a r
Functions to KNOW!
1. Polynomial Functions
and unique properties
Generalizations for Polynomial Functions
- The domain for all polynomial functions is ALWAYS _
- The deg
Lecture 1 : Precalculus Review
Hyperlinks are shown in blue, download the cdf player from the Wolfram Alpha website to view the
Wolfram Alpha interactive demonstrations. When you have downloaded the cdf player, click on
to view the demonstrati
Problems 1 & 2
DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO
This section of the competition consists of eight problems, which will be
presented in pairs. Work on one pair of problems will be completed a
Spring Level 5 | 07/31/2010
Trapezoid ABCD has vertices A( 1; 0), B (0; 4), C (m; 4) and D(k; 0), with
m > 0 and k > 0. The line y = x + 4 is perpendicular to the line containing side CD, and
the area of trapezoid ABCD is 34 square units. What is the
Spring Level 4 | 07/31/2010
What is the number of square feet in the area of a triangle with side lengths
A positive three-digit integer is formed by choosing three dierent digits
from the set f0; 2; 4; 6; 8g. The rs
Purpose of researchWhy
Graphing (Required for AP):
1. Always label the X and Y axis
2. Include tittle and units
3. Include a legend or k
f ( x )=e x
Dominio: cfw_x R
Rango: cfw_ y R y >0
Periodo: No tiene
Montona: S, decreciente.
Positiva o no: S
Par o impar?: impar ninguna.
Puntos mximos: No tiene
Puntos mnimos: No tiene
Para esta funcin usamos el graficador Symbo
A = B x,(x A x B).
B A x,(x B x A).
A = B (A B) (B A).
B = cfw_x A | p(x). ESPECIFICACIN
= cfw_x A | x 6= x.
F = cfw_x E | A F, x A.
Ac=cfw_x E | x A.
A B = cfw_x E | (x A) (x B).
A B = cfw_x E | (x A) (x B).
A \ B = cfw_x E | (x A) (x 6 B).
North Carolina Test of
Public Schools of North Carolina
State Board of Education
Department of Public Instruction
Division of Accountability Services/North Carolina Testing
Unit 1: Some Basic Figures
Section 1: A Game and Some Geometry
Chapter 01: Points, Lines, Planes, and Angles
How can you find the treasure?
3. is not the point X.
2. is 10 m (meters) from the building
1. is as far from the fountains
Math 151 (Finite Mathematics)
Rules of Engagement:
1. Communication between classmates is not allowed.
2. The only materials permitted for the exam are the exam booklet, a writing utensil, and the Sharp E
Math 151, Section 30: Midterm 1
Instructor: Asilata Bapat
October 22, 2013
This is a 60-minute exam.
Write your solutions in the space provided. Continue on the back if you run out of space.
Show your work. Incomplete work may get partial credit.
Fall 2006 Math 151
Final Exam Practice
(covering Sections 1.1 - 6.5)
courtesy: Amy Austin
NOTE: These problems are to serve merely as practice for
your nal exam. The nal exam for Math 151 is NOT a common exam. Each instructor makes up his or her own nal
MATH 151, FINAL EXAM
Winter Quarter, 16 March, 2015
Time: 3 hours, 12:15-3:15
(1) Write your name in blue-book provided and sign that you agree to abide by the
(2) The exam consists of 6 questions. The breakdown of points appears