MATHEMATICS 100
Rectilinear Motion (Motion Along A Line)
1. A particle moves along a horizontal coordinate line in such a way that its position at time t is specied
by s = t3 12t2 + 36t 30 where s is measured in feet and t in seconds. Find the instantaneo
University of the Philippines, Manila
College of Arts and Sciences
Department of Physical Sciences and Mathematics
MATH 100: INTRODUCTION TO CALCULUS
First Departmental Exam
July 23, 2009
I-Denitions: Give the complete formal denitions for the following:
1
UN IVERSIT Y OF T HE PHILIPPIN ES MAN ILA
MAT H 73 : FUN DAMEN T ALS OF AN ALYSIS I
FIRST
DEPART MEN T AL EX AM
GENERAL INSTRUCTION:
This is a two-hour closed notes, individual examination covering concepts and applications on precalculus topics,
analyt
University of the Philippines, Manila
College of Arts and Sciences
Department of Physical Sciences and Mathematics
MATHEMATICS 74 Second Laboratory Exam
September 13, 2012
I. Note that an integral may be evaluated directly by using a single technique or b
DERIVATIVES
Let u be a function of x.
2. Dx [cos u] = sin u Dx u
1
16. Dx [csc 1 u] =
Dx u
u u2 1
3. Dx [tan u] = sec 2 u Dx u
17. Dx [sinh u] = cosh u Dx u
4. Dx [cot u] = csc 2 u Dx u
18. Dx [cosh u] = sinh u Dx u
5. Dx [sec u] = sec u tan u Dx u
19. D
1
UN IVERSIT Y OF T HE PHILIPPIN ES MAN ILA
MAT H 73 : FUN DAMEN T ALS OF AN ALYSIS I
FIRST
I. TRUE or FALSE
DEPART MEN T AL EX AM
(1 point each)
II. MULTIPLE CHOICE
(2 points each)
1. FALSE
6. TRUE
1. A
4. A
7. D
2. FALSE
7. TRUE
2. B
5. B
8. C
3. FALSE
Self- Learning Kit
Social Science Grade 6
Location: Boon or Bane?
Introduction
It is true that knowledge on geography of the country is important because it can
help in understanding the events surrounding the area. In this lesson, we will focus on
locati
UPDATED-FEBRUARY 2005
APPENDIX IV
LABELLING
A Labelling Parameters required for UNIT CARTON
1. Product Name
2. Dosage Form
3. Name of Active Ingredient(s)
4. Strength of Active Ingredient(s)
5. Batch Number
6. Manufacturing Date
7. Expiration Date
8. Rout
Lines and the Derivative
Mathematics 100
Institute of Mathematics
Math 100 (Inst. of Mathematics)
Lines and the Derivative
1 / 24
Outline
1
Lines
Equations of a Line
Parallel and Perpendicular Lines
2
The Derivative
Limit Denition of the Derivative
Findin
MAXIMUM AND MINIMUM FUNCTION VALUES
Denition (Relative Maximum Value). The function f has a relative maximum value
at the number c if there exists an open interval containing c, on which f is dened, such that
f (c) f (x) for all x in this interval.
Deniti
The Derivative as Rate of Change
Mathematics 100
Institute of Mathematics
Math 100 (Inst. of Mathematics)
The Derivative as Rate of Change
1 / 18
The Derivative as instantaneous rate of change
Denition:
Given y = f (x ), the average rate of change of y wi
Higher Order Derivatives, Implicit Differentiation and
Equations of Tangent & Normal Lines
Mathematics 100
Institute of Mathematics
Math 100 (Inst. of Mathematics)
Higher Order Derivatives, Implicit Differentiation and Equations of Tangent & Normal1Lines
Some Types of Functions and their Graphs
Mathematics 100
Institute of Mathematics
Math 100 (Institute of Mathematics)
Functions
1 / 36
Outline
1
Functions and their Graphs
Graphs of Relations and Functions
Polynomial Functions
Rational Functions
Split Fun
University of the Philippines, Manila
College of Arts and Sciences
Department of Physical Sciences and Mathematics
MATH 100: INTRODUCTION TO CALCULUS
First Departmental Exam
July 15, 2010
I- TRUE OR FALSE: For each of the following, write TRUE if the give
University of the Philippines, Manila
College of Arts and Sciences
Department of Physical Sciences and Mathematics
MATH 100: INTRODUCTION TO CALCULUS
First Departmental Exam
December 16, 2008
I- Dene the following terms:
1. Parabola
(3 pts)
2. lim f (x) =
PROBLEM SET: RADICALS
SOLUTIONS:
I1.
p
3
128x5 y 17 z 23
p
3
27 x5 y 17 z 23
p
= 22 xy 5 z 7 3 2x2 y 2 z 2
p
= 4xy 5 z 7 3 2x2 y 2 z 2
=
2.
3.
p
4
5
5184x10 y 16 z 42
p
= 4 26 34 x10 y 16 z 42
4
= 2 3x2 y 4 z 10 22 x2 z 2
Note that the exponents in the ra
University of the Philippines, Manila
College of Arts and Sciences
Department of Physical Sciences and Mathematics
MATHEMATICS 17: College Algebra and Trigonometry
First Departmental Exam
July 12, 2012
I. Write TRUE if the given statement is always accura
Mathematics 17
Problem Set
First Semester AY 2012-2013
Due on July 2, 2011
General Instructions. Write your answers in a bluebook. Use only blue or black ballpen. Show
all necessary solutions and box all final answers. Do not consult anyone except your in
Mathematics 17
Problem Set
First Semester AY 2013-2014
Due on July 8, 2013
General Instructions. Write your answers in a bluebook. Use only blue or black ballpen. Show
all necessary solutions and box all final answers. Do not consult anyone except your in
True or False
1. (A B) A = A, for any finite sets A and B.
2. For any set A, A is a subset of the power set of A.
3. (Z Z) Z is null.
4. Two equivalent sets should always have the same number of elements.
5. If A and B are disjoint, then n(A B) = n(A) + n
University of the Philippines, Manila
College of Arts and Sciences
Department of Physical Sciences and Mathematics
MATH 74: FUNDAMENTALS OF ANALYSIS II
Second Lecture Exam
September 6, 2012
GENERAL INSTRUCTIONS: Show all necessary solutions for each of th
University of the Philippines, Manila
College of Arts and Sciences
Department of Physical Sciences and Mathematics
MATH 74: FUNDAMENTALS OF ANALYSIS II
First Lecture Exam
July 19, 2012
GENERAL INSTRUCTIONS: Show All Necessary Solutions for each of the fol
University of the Philippines, Manila
College of Arts and Sciences
Department of Physical Sciences and Mathematics
MATH 74: FUNDAMENTALS OF ANALYSIS II
First Laboratory Exam
GENERAL INSTRUCTIONS: Show All Necessary Solutions for each of the
following. Dis
Technology Integrated Coursepack on Selected Topics in Probability
PROBABILITY
Objectives:
1. Define probability and be familiar with its properties.
2. Find the probability of complementary events.
3. Solve problems involving probability.
4. Apply knowle
University of the Philippines, Manila
College of Arts and Sciences
Department of Physical Sciences and Mathematics
MATH 100: INTRODUCTION TO CALCULUS
First Departmental Exam
January 18, 2011
I- TRUE OR FALSE: For each of the following, write TRUE if the g
University of the Philippines, Manila
College of Arts and Sciences
Department of Physical Sciences and Mathematics
MATH 100: INTRODUCTION TO CALCULUS
First Departmental Exam
January 8, 2010
I- TRUE OR FALSE: Write TRUE if the given statement is accurate;