Number Sequence Tutorial

Below is the series on Number Sequence Tutorial. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 1: ASEQ01 Introduction to Number Sequence
Lesson 2: ASEQ02 Introduction to Arithmetic Sequence
Lesson 3: ASEQ03 Arithmetic Sequence Sample Problem (Finding the nth Term)
Lesson 4: ASEQ04 Arithmetic Sequence Sample Problems (Finding the nth Term)
Lesson 5: ASEQ05 Arithmetic Sequence Sample Problem (Finding the First Term)
Lesson 6: ASEQ06 Arithmetic Sequence Sample Problem (Finding the Common Difference)
Lesson 7: ASEQ07 Arithmetic Sequence Sample Problem (Finding the Number of Terms)
Lesson 8: ASEQ08 Arithmetic Mean of Two Numbers
Lesson 9: ASEQ09 Inserting Arithmetic Means in Arithmetic Sequence
Lesson 10: ASEQ10 Arithmetic Sequence Sample Problem (2 Equations in 2 Unknowns)
Lesson 11: ASEQ11 Sum of Arithmetic Sequence: Gauss’ Trick
Lesson 12: ASEQ12 Derivation of the Formula for the Sum of Arithmetic Sequence
Lesson 13: ASEQ13 Sum of the Arithmetic Sequence: Sample Problems


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Slope Tutorial

Below is the series on Slope Tutorial. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

SLOPE01 Definition of Slope and the Slope Formula
SLOPE02 Finding the Slope of a Line
SLOPE03 Positive and Negative Slopes of a Line
SLOPE04 Zero and Undefined Slopes
SLOPE07 How to Find the Slope of a Line from the Equation Part 1
SLOPE08 How to Find the Slope of a Line from the Equation Part 2


You might also want to learn about Calculus click here:

Calculus Series – Part I
Calculus Series – Part II
Calculus Series – Part III

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Calculus Series – Part III

Below is the series on Calculus – Part III. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 93: Calculus 3.00 Introduction to Chapter 3
Lesson 94: Calculus 3.01 Formulas for Finding the Derivative of Trigonometric Functions
Lesson 95: Calculus 3.02 Derivative of Trigonometric Functions – Worked Examples 1
Lesson 96: Calculus 3.03 Derivative of Trigonometric Functions – Worked Examples 2
Lesson 97: Calculus 3.04 Derivative of Trigonometric Functions – Worked Examples 3
Lesson 98: Calculus 3.07 Introduction to Chain Rule
Lesson 99: Calculus 3.08 Chain Rule – Worked Examples 1
Lesson 100: Calculus 3.09 Chain Rule – Worked Examples 2
Lesson 101: Calculus 3.10 Chain Rule – Worked Examples 4 (Negative Exponents and Radicals)
Lesson 102: Calculus 3.11 Chain Rule – ‘Derivation’ of The General Power Rule

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Calculus Series – Part II

Below is the series on Calculus – Part II. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 51: Calculus 1.50 Definition of Continuity of a Function at a Number
Lesson 52: Calculus 1.51 Understanding the Definition of Continuity
Lesson 53: Calculus 1.52 Continuity at a Point Sample Problem 1 (Removable Discontinuity)
Lesson 54: Calculus 1.53 Sample Problem on Continuity Part 2 (Infinite Discontinuity)
Lesson 55: Calculus 1.54 Sample Problem on Continuity Part 3
Lesson 56: Calculus 1.55 Sample Problem on Continuity Part 4
Lesson 57: Calculus 1.56 Continuous and Discontinuous Functions – Summary
Lesson 58: Calculus 2.00 The Concept and Definition of Derivative
Lesson 59: Calculus 2.01 Finding the Slope of a Line Tangent to a Curve at Any Point
Lesson 60: Calculus 2.02 Finding the Slope of a Line Tangent to a Curve at a Particular Point

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Calculus Series – Part I

Below is the series on Calculus – Part I. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 1: Calculus 1.00 Overview of the Calculus Video Series
Lesson 2: Calculus 1.01 The Origins of Calculus
Lesson 3: Calculus 1.02 The Tangent Problem
Lesson 4: Calculus 1.03 The Area Problem
Lesson 5: Calculus 1.04 Finding the Slope of a Tangent Line Part 1
Lesson 6: Calculus 1.05 Finding the Slope of a Tangent Line Part 2
Lesson 7: Calculus 1.06 Finding the Slope of a Tangent Line Part 3
Lesson 8: Calculus 1.07 Finding the Slope of a Tangent Line Part 4
Lesson 9:: Calculus 1.08 Summary of the Tangent Problem
Lesson 10: Calculus 1.09 Another Notation for Slope of a Tangent Line

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Inscribe Angle Theorem

Below are the tutorials on Inscribe Angle Theorem. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 1: INSA1 Introduction to the Inscribed Angle Theorem Series

Lesson 2: INSA2 Inscribed and Central Angles Intercepting the Same Arc

Lesson 3: INSA3 Proof of the Inscribed Angle Theorem (Case 1)

Lesson 4: INSA4 Proof of the Inscribed Angle Theorem (Case 2)

Lesson 5: INSA5 Proof of the Inscribed Angle Theorem (Case 3)

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Precalculus Tutorials for Senior High School and College Students

Below are the tutorials on Precalculus Tutorials for Senior High School and College Students. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 1.00: Introduction to Precalculus for Senior High School
Lesson 1.01: A Brief Review of the Cartesian Plane
Lesson 1.02: The Conic Sections – Circle, Ellipse, Parabola, Hyperbola
Lesson 1.03: Equation of a Circle with Center at the Origin – Practice Exercises
Lesson 1.04: Equation of a Circle with Center (h,k)
Lesson 1.05: Equation of a Circle with Center at the Origin and Radius
Lesson 1.06: Writing the Equation of a Circle with Center (h,k) and the Radius
Lesson 1.07: Finding the Center and Radius of a Circle Given its Equation
Lesson 1.08: Standard and General Forms of the Equation of a Circle
Lesson 1.09: Converting Equations of a Circle From Standard Form to General
Form

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Operations on Polynomial Expressions

Below are the tutorials on Operations on Polynomial Expressions. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

PE01 Introduction to Polynomial Expressions
PE02 Like Terms and Unlike Terms
PE03 Addition of Polynomial Expressions Part 1
PE04 Addition of Polynomial Expressions Part 2
PE05 Addition of Polynomial Expressions Part 3
PE06 Subtraction of Polynomial Expressions Part 1
PE07 Subtraction of Polynomial Expressions Part 2
PE08 Multiplication of Polynomial Expressions Part 1
PE09 Multiplication of Polynomial Expressions Part 2
PE10 Multiplication of Polynomial Expressions Part 3
PE11 Multiplication of Polynomial Expressions Part 4
PE12 Division of Polynomial Expressions Part 1
PE13 Division of Polynomial Expressions Part 2
PE14 Division of Polynomial Expressions Part 3
PE15 Division of Polynomial Expressions Part 4
PE16 Division of Polynomial Expressions Part 5
PE17 Division of Polynomial Expressions Part 6

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Factoring Tutorial Series

Below are the tutorials on Factoring. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 1: Basic Concepts of Factoring
Lesson 2: Factoring Polynomials with Common Monomial Factor
Lesson 3: Factoring Polynomials by Grouping Part 1
Lesson 4: Factoring Polynomials by Grouping Part 2
Lesson 5: Factoring Perfect Square Trinomials
Lesson 6: Factoring General Trinomials Part 1
Lesson 7: Factoring General Trinomials Part 2
Lesson 8: Factoring General Trinomials Part 3
Lesson 9: Factoring Difference of Two Squares
Lesson 10: Factoring Sum and Difference of Two Cubes
Lesson 11: Factoring Polynomials with More than 2 Factors

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Clock Word Problem Solving Series

Below are the tutorials on Clock Word Problem Series. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 1: Introduction to the Clock Problems Tutorial Series
Lesson 2: Clock Problems: Formula for the Amount of Rotation of the Hour Hand
Lesson 3: DERIVATION of the Amount of Rotation of the Hour Hand Given the Time
Lesson 4: Derivation of the Formula for the Amount of Rotation of the Minute Hand
Lesson 5: Derivation of the Formula for Calculating the Angle Between the Hands of the Clock
Lesson 6: Applying the Clock Angle Problem Formulas

to be continued…

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Angle Sum Tutorial Series

Below are the tutorials on Angle Sum Theorem. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 1: A Brief Review of the Concept of Angles
Lesson 2: Proof that The Sum of the Interior Angles of Triangles is 180 degrees
Lesson 3: Proof that The Sum of the Interior Angles of a Quadrilateral is 360 degrees
Lesson 4: Proof that The Sum of the Interior Angles of a Pentagon is 540 degrees
Lesson 5: Sum of the Interior Angles of Any Polygon (Derivation)

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REX05 Reducing Rational Expressions to Lowest Terms Part 1

In the previous video, we have learned about domain of rational functions. In this video, we are going to learn about how to reduce rational expressions particularly fractions to lowest terms.  Watch the Tagalog math tutorial video above and then answer the exercises below. The complete video playlist of the Sipnayan tutorials on Rational Expressions can be found here.

Practice Exercise

Reduce the following to lowest terms.

1.) \dfrac{8}{12}

2.) \dfrac{15}{25}.

3.) \dfrac{9}{27}.

4.) \dfrac{6}{24}.

5.) $latex  \dfrac{10}{22}$.

Answers

1.) \dfrac{2}{3}

2.) \dfrac{3}{5}.

3.) \dfrac{1}{3}.

4.) \dfrac{1}{4}.

5.) $latex  \dfrac{5}{11}$.
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REX04 Domain of Rational Functions

In the previous video, we have learned to rule out values of a variable in a rational expression. In this video, we are going to learn to find the domain of a rational function. This is very similar to the concept of ruling out values of rational expressions.  Watch the Tagalog math tutorial video above and then answer the exercises below. The complete video playlist of the Sipnayan tutorials on Rational Expressions can be found here.

Practice Exercise

Find the domain of the following rational functions.

1.) f(x) = \dfrac{x - 9}{x - 3}

2.) f(x) = \dfrac{2x + 1}{x^2 + 3x + 2}.

3.) g(x) = \dfrac{x^2 - 1}{x}.

4.) h(x) = \dfrac{x^2 + 2x}{x^2 - 9}.

5.) j(x) = \dfrac{x + 6}{3 - x}.

Answers

1. \{x|x \neq 3\}

2. \{x|x \neq -2, x \neq -1\}

3. \{x|x \neq 0 \}

4. \{ x|x \neq 3, x \neq -3 \}

5. \{ x \neq 3 \}

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REX03 Ruling Out the Values of the Variable

In the previous video, we have learned how to evaluate rational expressions. In this video, we are going to learn how to rule out the values of the variable in rational expressions. This concept is important because it is connected to the domain of rational functions  Watch the Tagalog math tutorial video above and then answer the exercises below. The complete video playlist of the Sipnayan tutorials on Rational Expressions can be found here.

Practice Exercise

Rule out the values of the variable of the following rational expressions.

1.) \dfrac{x + 4}{x}

2.) \dfrac{2x - 1}{x + 2}.

3.) \dfrac{x^2 - 1}{2x + 5}.

4.) \dfrac{x^2 + 2x}{x^2 - 9}.

5.) \dfrac{x - 9}{x^2 - 5x + 4}.

Answers

1. x \neq 0

2. x \neq -2

3. x \neq -\frac{5}{2}

4. x \neq 3, x \neq -3

5. x \neq 1, x \neq 4

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REX02 Evaluating Rational Expressions

In the previous video, we have learned about rational expressions. In this video, we learn how to evaluate rational expressions .  Watch the Tagalog math tutorial video above and then answer the exercises below. The complete video playlist of the Sipnayan tutorials on Rational Expressions can be found here.

Practice Exercise

Evaluate the following rational expressions.

1.)  If x = -2, find the value of

\dfrac{3x - 1}{x - 4}

2.) If y = 3, find the value of

\dfrac{y^2 + 5y - 6}{5y + 1}.

3.) The function f(x) = \frac{2x + 5}{-x + 7} is a rational function. Find f(0).

4.) If p = -4, q = 3, and r = 1, what is the value of

\dfrac{p^2 - qr + q^2}{p - r}

5.) If x = \frac{1}{2}, what is the value of

\dfrac{4x - 1}{2x^2 + 1}

Answers

1.  7/6
2. – 3/4
3. 5/7
4. – 22/5
5. 7/4

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REX01 Introduction to Rational Expressions

In this video, we learn the definition of rational numbers, rational expressions, and rational functions .  Watch the Tagalog math tutorial video above and then answer the exercises below. The complete video playlist of the Sipnayan tutorials on Rational Expressions can be found here.

Practice Exercise

True or False

1.)  The fraction \frac{\pi}{3} is a rational number.

2.) The fraction \frac{2x - 1}{5x + 1} is a rational expression.

3.) The fraction \frac{\sqrt{x} + 3}{x^2 + 3} is a rational expression.

4.) The function f(x) = \frac{1}{x} is a rational function.

5.) The fraction \frac{3}{8} is a rational number.

Answers

1.False. The numerator and denominator of a rational number must be integers.
2. True
3. False. \sqrt{x} + 3 is not a polynomial expression.
4. True
5. True

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