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

QUADRATIC EQUATIONS
MATH10
ALGEBRA
Quadratic Equations (Algebra and Trigonometry, Young 2nd Edition, page 113-135)
GENERAL
OBJECTIVE
Week 3 Day
3
At the end of the lesson the students are
expected to:
Solve quadratic equations using different methods,
Sol

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

SYSTEMS OF INEQUALITIES
MATH10
ALGEBRA
Systems of Equations(Algebra and Trigonometry, Young 2nd Edition, page 917- 943)
Week 7 Day 1
GENERAL OBJECTIVE
At the end of the chapter the students are expected to:
Solve a system of linear inequalities by findin

RELATIONS FUNCTIONS AND GRAPHS
MATH10
ALGEBRA
Functions and Their Graphs(Algebra and Trigonometry, Young 2nd Edition, page 225-322)
Week 8 Day 1
GENERAL OBJECTIVE
At the end of the chapter the students are expected to:
Determine whether a relation is a fu

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

BINOMIAL THEOREM
OBJECTIVES
Recognize patterns in binomial expansions.
Evaluate a binomial coefficient.
Expand a binomial raised to a power.
Find a particular term in a binomial expansion
Understand the principle of mathematical induction.
Prove statement

TRIGONOMETRIC
EQUATIONS
DEFINITION:
TRIGONOMETRIC
EQUATIONS
Equations that involve the trigonometric
functions
are
called
trigonometric
equations.
Solving a trigonometric equation means the
same thing as solving an algebraic equation,
like finding the val

INVERSE
TRIGONOMETRIC
FUNCTIONS
DEFINITION: If
is a one-to-one function
f
1
with domain A and range B, then its inverse
f
is the function with domain B and
range A defined by
f 1 x y
f y x
For a function to have an inverse, it must
be one-to-one. Since t

OBLIQUE TRIANGLES
DERIVATION OF LAW OF SINES
Let ABC be an oblique triangle with sides a,
b, and c opposite their respective angles as
shown in the figure below. If an altitude h is
drawn to the base, we can write the following
relationship:
C
b
A
h
c
h
s

Lesson 4: GRAPHS OF
TRIGONOMETRIC
FUNCTIONS
Math 12
Plane and Spherical Trigonometry
OBJECTIVES
At the end of the lesson the students are expected to:
Develop the properties of trigonometric functions.
Find the amplitude, period, phase shift and vertical

SPHERICAL
TRIGONOMETRY
DEFINITION OF
TERMS:
Spherical Trigonometry is a branch of
trigonometry that concerns with triangles extracted
from the surface of the sphere.
Great Circle is a circle obtained by passing a
section through the center of the sphere

EXPONENTIAL AND
LOGARITHMIC
FUNCTIONS
EXPONENTIAL FUNCTION
If x and b are real numbers such that b > 0
and b 1, then f(x) = bx is an exponential
function with base b.
Examples of exponential functions:
a) y = 3x
b) f(x) = 6x
c) y
= 2x
Example: Evaluate th

QUADRATIC EQUATIONS
MATH10
ALGEBRA
Quadratic Equations (Algebra and Trigonometry, Young 2nd Edition, page 113-135)
GENERAL
OBJECTIVE
Week 3 Day
3
At the end of the chapter the students are expected to:
Solve quadratic equations using different methods,
S

LINEAR EQUATIONS
MATH10
ALGEBRA
Week 1 Day 1 Linear Equations (Algebra and Trigonometry, Young 2nd Edition, page 90-99)
GENERAL
OBJECTIVE
Week 1 Day 1
At the end of the lesson the students are
expected to:
Classify equations as linear, fractional, or rat

LINEAR EQUATIONS
MATH10
ALGEBRA
Week 1 Day 1 Linear Equations (Algebra and Trigonometry, Young 2nd Edition, page 90-99)
Week 1 Day 1
GENERAL
OBJECTIVE
At the end of the lesson the students are
expected to:
Classify equations as linear, fractional, or rati

THE INDEFINITE INTEGRAL AND THE
BASIC INTEGRATION FORMULAS
OBJECTIVES:
know the relationship between
differentiation
and integration;
identify and explain the different
parts of the
integral operation; and
EFINITION: ANTIDERIVATIVE (INTEGRAL)
The inverse

GENERALIZED POWER FORMULA
(Integration by Simple Substitution)
OBJECTIVES:
identify an integrand that can be
integrated using
simple substitution;
perform integration using the
generalized power
formula;
relate integration by power
formula to the
NTEGRATI

THE DEFINITE INTEGRAL
OBJECTIVES:
define and interpret definite
integral,
identify and distinguish the
different properties of
the definite integrals; and
evaluate definite integrals
HE DEFINITE INTEGRAL
If F(x) is the integral of f(x)dx, that is, F(x) =

Transformation of Trigo Fcns
Power of Sine and Cosine
example
example
example
example
Product of Sine and Cosine
example
Powers of Tangent, Secant, Cotangent, and Cosecant
example
example
example
example

Chapter 1
SETS AND THE REAL NUMBER SYSTEM
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 most
important sets in algebra is the se

Chapter 2
ALGEBRAIC EXPRESSIONS
Every day, we encounter situations or phenomena that we need to study and analyze.
Expressing this mathematically will simplify the whole process of analysis. The mathematical
expressions used to model situations may involv

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

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

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

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

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

Sequences and Series
OBJECTIVES
Define sequences and identify the different kinds of
sequences.
Find the nth term or the general term of a sequence for
which some initial terms are given.
Find the common difference of an arithmetic sequence.
Find the comm