2. Table of contents
01 Analytic Geometry
Lesson 1.1: Introduction to Conic Sections
and Circle
Lesson 1.2: Parabolas
Lesson 1.3: Ellipses
Lesson 1.4: Hyperbolas
Lesson 1.5: More Problems on Conic
Sections
Lesson 1.6: Systems of Nonlinear
Equations
4. Table of contents
03 Trigonometry
Lesson 3.1: Angles in a Unit Circle
Lesson 3.2: Circular Functions
Lesson 3.3: Graphs of Circular Functions
and Situational Problems
Lesson 3.4: Fundamental Trigonometric
Identities
Lesson 3.5: Sum and Differences
Identities
Lesson 3.6: Double-Angle and Half-Angle
Identities
5. Table of contents
03 Trigonometry
Lesson 3.7: Inverse Trigonometric
Functions
Lesson 3.8: Trigonometric Equations
Lesson 3.9: Polar Coordinate System
7. Lesson Objectives
At the end of the lesson, the student is able to:
1. illustrate the different types of conic sections:
parabola ellipse, circle, hyperbola, and degenerate
cases;
2. define a circle;
3. determine the standard form of equation of a circle;
4. graph a circle in a rectangular coordinate system; and
5. solve situational problems involving conic sections
(circles).
8. Conic Sections
A conic section, also called conic in
geometry is formed when a plane
intersects a cone at different angles and
positions. It can be
a circle, ellipse, parabola,
or hyperbola according to the varied
angles of intersection.
13. Parabola
It formed when a
plane cuts a cone
parallel to its slant
height. The slant
height is also
considered the
generator line as it is
the outer surface of a
15. Degenerate Conic Sections
A degenerate conic results when a plane
intersects the double cone and passes
through the apex. Depending on the
angle of the plane, three types of
degenerate conic sections are possible: a
point, a line, or two intersecting lines.
21. The slide title goes here!
Do you know what helps you make your point
crystal clear? Lists like this one:
● They’re simple
● You can organize your ideas clearly
● You’ll never forget to buy milk!
And the most important thing: the audience
won’t miss the point of your presentation
22. Key concepts in pre-calculus
Mars is actually a very
cold planet
Venus has extremely
high temperatures
Jupiter is the biggest
planet of them all
Saturn is a gas giant and
has several rings
Functions
and relations
Rational
functions
Trigonometri
c basics
Exponents
and
logarithms
23. Venus has extremely
high temperatures
Neptune is the farthest
planet from the Sun
Mars is actually a very
cold planet
Mercury is the closest
planet to the Sun
Saturn is a gas giant
and has several rings
Jupiter is the biggest
planet of them all
Mars Venus Neptune
Mercury Saturn Jupiter
Review the concepts
29. Jupiter’s rotation period
9h 55m 23s
333,000
The Sun’s mass compared to Earth’s
386,000 km
Distance between Earth and the Moon
30. Let’s use some percentages
Mercury is the closest
planet to the Sun and a
very small object
Mercury
Venus has a beautiful
name and is the second
planet from the Sun
Venus
Despite being red, Mars
is actually a cold place.
It’s full of iron oxide
dust
Mars
50% 75%
25%
31. Computer
mockup
You can replace the image on the screen
with your own work. Just right-click on it
and select “Replace image”
32. Phone mockup
You can replace the image on the screen
with your own work. Just right-click on it
and select “Replace image”
33. Venus
Mars
Mercury
This is a map
Venus is the second
planet from the Sun
Despite being red,
Mars is a very cold
planet
Mercury is the closest
planet to the Sun
34. A timeline always works well
Introduction
Venus is the second
planet from the Sun
Trigonometr
y
Mercury is the closest
planet to the Sun
Geometry
Despite being red,
Mars is a very cold
planet
Polynomials
Jupiter is the biggest
planet of them all
1 3
2 4
36. Use tables to represent data
Team A Team B Team C Team D
Mercury 0.06 0.53 0.38 0.38
Mars 0.11 9.4 0.53 0.78
Saturn 95.2 1.16 9.4 1.16
37. Percentage values
Follow the link in the graph to modify its data and then paste the new one here. For more info, click here
Financial planning
Mercury is quite a small planet
Investment
growth
Venus has very high temperatures
60%
40%
38. Rubric
Category Insufficien
t
Basic Proficient Advanced
Fundamental
Concepts
Fails to
demonstrate an
understanding of
basic concepts
Partially
comprehends
some basic
concepts with
significant errors
Demonstrates a
solid
understanding of
fundamental
concepts
Exhibits an
exceptional
understanding of
fundamental
concepts
Equation
Solving
Unable to solve
trigonometric
equations
Solves algebraic
equations with
limited success
Effectively solves
trigonometric
equations
Exceptionally
solves algebraic
equations
Attitude and
Participation
Displays a negative
attitude towards
the subject
Displays a neutral
attitude
participates
Demonstrates a
positive attitude
and participates
constructively
An exceptionally
positive attitude,
actively
participates
39. Multiple choice questions
Question 1:
If f(x) = 2x^2 - 3x + 1,
what is the value of f(3)?
a) 16
b) 10
c) 4
d) 14
Question 2:
Solve the trigonometric
equation: sin(x) = 0.5
a) x = π/6
b) x = π/4
c) x = π/3
d) x = π/2
Question 3:
Find the value of the
definite integral (2x^2
∫
+ 3x) dx from x = 1 to x =
5
a) 37
b) 43
c) 45
d) 51
40. Short answer questions
Problem
:
If one number
is 5 times
greater than
another
number, and
their sum is 24,
what are the
two numbers?
Step 1: Let's call the first number "x" and the second number "y"
Step 2: Translate the first part of the problem into an equation:
"One number is 5 times greater than another number" translates
to X =5y
Step 3: Translate the second part of the problem into an
equation: "The sum of both is 24" translates to X+Y=24
Step 4: Now, you have a system of two equations:
X = 5Y
X + Y = 24
You can solve this system of equations to find the values of x and
y
Solution:
41. Group discussion
Pre-Calculus group activity: "problem
solving"
Team
formation
In-class
presentatio
n
Problem
selection
Discussion /
feedback
Problem
solving
Assessment
42. Practical application
Practical exercise: finding the Intersection point of two
lines
Objective: Apply pre-calculus concepts to find the intersection point of two
lines on a cartesian plane
Graph paper Ruler
Colored
pencils
1 2 3
Materials needed:
43. Essay
1. Functions in pre-calculus: explore the concept of functions in mathematics and
their importance in pre-calculus
2. Intersection of lines: describe how the points of intersection between two lines
are found on a Cartesian plane
3. Slope of lines: explain the slope of a line, its calculation, and its relevance in pre-
calculus
4. Solving systems of equations: discuss how systems of linear equations are
solved and their application in pre-calculus
5. Quadratic functions: explore the characteristics of quadratic functions and their
application in real-world situations
44. Preparing for advanced
mathematic
● STEM readiness: Pre-calculus is
essential for students planning
to pursue degrees in science,
technology, engineering, and
mathematics (STEM)
● Career opportunities:
Proficiency in pre-calculus
opens doors to careers in fields
like engineering, data science,
and research
● Pre-calculus foundation: Pre-
calculus provides a strong
mathematical foundation,
ensuring students are well-
prepared for more advanced
courses
● Transition to calculus: It acts
as a bridge to calculus,
introducing fundamental
concepts such as limits,
continuity, and functions
45. Practical pre-Calculus
applications
Solving everyday
problems
Pre-calculus aids in budgeting, distance calculations, and
economic analysis
Design and
engineering
Essential for sizing and modeling in important design and
engineering projects
Sciences and
data
Used in biology, physics, and data science for important
evidence-based decisions
Economics and
finance:
Key to understanding interest rates and financial analysis
University
preparation
Preps for future calculus and science careers
46. Kaliyah Harris
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Our teachers
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“Despite being red,
Mars is actually a
very cold place”
“Mercury is the
smallest planet in
the Solar System”
“Neptune is the
farthest planet from
the Sun”
“Saturn is a gas
giant and has
several rings”
“Venus is the
second planet from
the Sun and is
terribly hot”
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68. “Despite being red,
Mars is actually a
very cold place”
“Jupiter is the
biggest planet in the
entire Solar System”
“Saturn is a gas
giant and has
several rings”
75%
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“Mercury is the
smallest planet in the
Solar System”
TITLE 1
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