ALGEBRA
Math 10-3
LESSON 5
COMPLEX NUMBERS
INTRODUCTION TO COMPLEX NUMBERS
INTRODUCTION TO COMPLEX NUMBERS
Recall that 9 = 3 because 32 = 9.
Now consider the expression 9 .
To find 9 , we need to find a number c such that c2 = 9.
However, the square of an

Lesson 12:
Basic Combinatorics
Math 10-4
Advanced Algebra
What is Combinatorics?
A branch of mathematics concerned with the study of finite or
countable discrete structures (Wikipedia)
The branch of mathematics studying enumeration, combination
and perm

Lesson 10:
Mathematical Induction
Math 10-4
Advanced Algebra
The Induction Axiom
Suppose
S is a set of positive integers with the following two
properties:
i) 1 S
ii) If the positive integer k S then k + 1 S
Then S contains all positive integers.
The Pr

CO5
Analyze correctly and solve properly application
problems concerning the derivatives to include
writing equation of tangent/normal line, curve
tracing ( including all types of algebraic curves and
cusps), optimization problems, rate of change and
rela

PROBLEM SET
PHY11 / January 2016
IMPULSE AND MOMENTUM
1. A 100 g ball is dropped from a height of h = 2.00 m above the floor. It rebounds vertically to
a height of h'= 1.50 m after colliding with the floor. (a) Find the momentum of the ball
immediately be

FLUID MECHANICS
FLUID MECHANICS
Study of the behavior of fluids at rest or at motion refers
to fluid mechanics.
Fluids Substances that are either gas or liquid
Fluid Mechanics is divided into two:
HYDROSTATICS
HYDRODYNAMICS
FLUID MECHANICS
Important Prope

ELECTROCHEMICAL EQUILIBRIUM
Electrochemical reactions involves free electrons that are transferred from a metal
to a species in a solution.
Importance of EMF measurements
1. thermodynamics quantities for the reaction that occurs in the cell can be
obtaine

Lesson 1
Linear Equations
SPECIFIC OBJECTIVES:
At the end of the lesson, the student is expected to be able:
identify an equation,
distinguish an identity equation from a conditional equation,
solve linear equations in one variable
solve application p

MAPA INSTITUTE OF TECHNOLOGY
Department of Mathematics
VISION
The Mapua Institute of Technology shall be a global center of excellence in education by providing instructions that are current
in content and state-of-the-art in delivery; by engaging in cutt

Lecture 1
Linear Equations
Definition:
An equation is a statement that two quantities
are equal.
A solution to an equation is a value of the
unknown which satisfies the equation.
Types of Equation:
1. Identity
2. Conditional
Definitions
Two equations are

1. Calculate the following vector
[ ]
([ ]) [ ] [ ]
([ ])
T x
y
x y
x+ y
2x
x y
T 15 x + y
4
2x
=
11
19
30
2. Determine whether the following transformation are linear or not.
x y
T x
x+ y
y
2x
([ ])
[ ]
T ( u + v )=T ( u ) +T (v )
[] []
u = a1 , v = b1

Tabunan, Ira David M.
Math 12-1/ECE A1
HW-1 Expectations on Math 12 this Quarter
This quarter, I will be starting my freshman year in Mapua Institute of
Technology and I will be taking up ECE. In line with this, Math 12-1 is one of my
courses and I have s

THE NECKLACE
By Guy de Maupassant
The narrator introduces us to a girl. We don't know her name yet, but
apparently
she's charming, attractive, and, believes that she should have been
born into a rich
family.
The Necklace Summary
Instead she wound up in a

QUADRATIC EQUATIONS AND
APPLICATIONS
MATH10-3
ALGEBRA
GENERAL OBJECTIVE
At the end of the chapter the students are expected to:
Solve quadratic equations using different methods,
Solve equations in quadratic form,
Solve equations leading to quadratic equa

ALGEBRA
Math 10-3
LESSON 2
POLYNOMIALS
ALGEBRAIC EXPRESSIONS
ALGEBRAIC EXPRESSIONS
Mathematical statements use two types of quantities:
constants and variables.
A constant is a symbol whose value does not change .
Examples: 26, -6, 2.71828,
2
2,
5
A varia

ALGEBRA
Math 10-3
LESSON 5
COMPLEX NUMBERS
INTRODUCTION TO COMPLEX NUMBERS
INTRODUCTION TO COMPLEX NUMBERS
2
Recall that 9= 3 because 3 = 9.
Now consider the expression 9 .
9
2
To find
, we need to find a number c such that c = 9. However, the
square of a

ALGEBRA
Math 10-3
LESSON 1
SETS AND THE REAL NUMBER SYSTEM
CONCEPT OF SETS
SETS
Collection of things such as books on a shelf, baseball cards, stamps,
and toys are common. Mathematics greatly relies on that notion of
collection called a set. One of the mo

ALGEBRA
Math 10-3
LESSON 1
SETS AND THE REAL NUMBER SYSTEM
CONCEPT OF SETS
SETS
Collection of things such as books on a shelf, baseball cards, stamps,
and toys are common. Mathematics greatly relies on that notion of
collection called a set. One of the mo

ALGEBRA
Math 10-3
LESSON 7
QUADRATIC EQUATIONS
Definition of a Quadratic Equation
A quadratic equation in x is an equation that can be written in
the standard quadratic form
ax2 + bx + c = 0
where a, b and c are real numbers and a 0.
Several methods can b

ALGEBRA
Math 10-3
LESSON 3
RATIONAL EXPRESSIONS
RATIONAL EXPRESSIONS
A rational expression is a fraction in which the numerator and
denominator are polynomials.
For example, the expressions below are rational expressions.
The domain of a rational expressi

SOLVING WORD PROBLEMS
1.
2.
3.
4.
5.
6.
7.
Read the problem all the way through quickly, to see what kind of word problem it is and
what it is about.
Look for a question at the end of the problem. This is often a good way to find what you
are solving for.

ALGEBRA
Math 10-3
LESSON 6
EQUATIONS
EQUATIONS
An equation is a statement about the equality of two
expressions.
If either of the expressions contains a variable, the equation may
be a true statement for some values of the variable and a false
statement f

ALGEBRA
Math 10-3
LESSON 8
INEQUALITIES
INTERVAL NOTATION
INTERVAL NOTATION
The graph of cfw_x | x > 2 is shown in Figure P.2. The set is the
real numbers greater than 2.
Figure P.2
The parenthesis at 2 indicates that 2 is not included in the set.
Rather

ALGEBRA
Math 10-3
LESSON 2
POLYNOMIALS
ALGEBRAIC EXPRESSIONS
ALGEBRAIC EXPRESSIONS
Mathematical statements use two types of quantities: constants
and variables.
A constant is a symbol whose value does not change .
Examples: 26, -6, 2.71828, 2 ,
2
5
A vari

(TRUE OR FALSE)
1. Linear equations only have variables to the first power.
2. The values of the unknown that make the equation true are called roots of the equation.
3. An inconsistent equation is an equation that is not true even for one real number.
4.

SYSTEMS OF EQUATIONS
MATH10
ALGEBRA
Systems of Equations(Algebra and Trigonometry, Young 2nd Edition, page 874-904)
GENERAL OBJECTIVE
Week 6 Day 1
At the end of the chapter the students are expected to:
Solve systems of equations in two variables with th

OBJECTIVES
Identify a polynomial function.
Distinguish a polynomial function from among
different types of functions.
Determine the degree of a polynomial function.
Determine the value of the function with the use of
the Remainder Theorem.
Use the Factor

RATIO, VARIATION AND
PROPORTION
MATH10
ALGEBRA
Week 3 Day 1 Ratio, Variation and Proportion (Algebra and Trigonometry, Young 2nd Edition, page 304-313)
TODAYS OBJECTIVE
Week 3 Day 1
At the end of the lesson the students are expected to:
Use ratio and pro

INEQUALITIES
MATH10
ALGEBRA
Inequalities (Algebra and Trigonometry, Young 2nd Edition, page 136-170)
GENERAL OBJECTIVE
Week 5 Day 1
At the end of the chapter the students are expected to:
Use interval notation.
Solve linear inequalities.
TODAYS OBJECTIVE