Charlotte Vilkus

Charlotte Vilkus

Combinations and Permutations

Slide Duration:

Table of Contents

Section 1: Basic Math
Signed Numbers

18m 58s

Intro
0:00
The Basics: Signed Numbers
0:13
How to Think of Negative Numbers
0:39
Signed Numbers on the Number Line
2:16
Signed Numbers: Addition and Subtraction
3:07
Subtracting a Negative
8:35
The Loss of a Negative is the Addition of a Positive
8:43
Flip the sign!
11:16
Addition and Subtraction Examples
12:19
Signed Numbers: Multiplication and Division
13:45
Quick Rules
15:08
Multiplication and Division Examples
17:02
Section 1: Basic Algebra
Exponents and Roots

24m 44s

Intro
0:00
The Basics: Exponents
0:09
Base and Exponent
0:42
Squared Terms
1:23
Cubed Terms
2:26
Exponent Rules
3:40
Multiplying Terms with the Same Base
5:51
Dividing Terms with the Same Base
6:48
Exponent Term Raised to a Power
8:32
Product of Different Bases to the Same Power
10:14
Quotient of Different Bases to the Same Power
11:57
The Basics: Radicals
17:24
Square Roots
19:39
Divisibility

16m 45s

Intro
0:00
The Basics: Divisibility
0:12
Divisibility Tricks
3:07
The Rules
3:44
Examples of Quickly Determing what a Number is Divisibly by
9:44
Prime Factorization

10m 1s

Intro
0:00
Prime Numbers and Prime Factorization
0:22
How to: Prime Factorization
2:27
Bigger Divisors
5:10
Finding all Factors of 28 and 210
5:52
Powers of 10

8m 56s

Intro
0:00
The Basics: Powers of 10
0:15
Multiplying and Dividing by Powers of 10
2:59
Dealing with Multiplication
3:37
Dealing with Division
5:16
Example Set
6:05
Fractions

12m 50s

Intro
0:00
The Basics: Fractions
0:09
Fractions as Part of a Whole
0:46
Equivalent Fractions
1:10
Fractions: Addition and Subtraction
4:11
Finding the Common Denominator
5:25
Fractions: Multiplication and Division
7:27
Division: Multiplying the Reciprocal (Flip It)
8:53
Fractions: Comparing Fractions
10:36
Determining the relationship between fractions
11:54
Algebraic Expression

17m 39s

Intro
0:00
The Basics: Algebraic Expressions
0:11
Algebraic Expression Definitions
1:54
Simplifying Algebraic Expressions
5:12
Identifying Like Terms
5:23
Using Coefficients to Add and Subtract Like Terms
6:14
Combining Like Terms
8:00
Multiplication of Algebraic Expressions
9:24
Multiplying Two Terms: Coefficients and Variables
9:38
Combining Like Variables in Multiplication
10:15
Multiplying Expressions by a Term
12:08
Example 1: Multiplying Out and Simplifying
13:45
Example 2: Multiplying Out and Simplifying
15:18
Equations

6m 7s

Intro
0:00
The Basics: Equations
0:10
Valid Operations on an Equation
0:26
Isolate the Variable
3:24
Function Evaluation

10m 50s

Intro
0:00
The Basics: Function Evaluation
0:10
Function Definition and Notation
2:23
Function Evaluation Examples
4:55
Function Evaluation Mistakes to Avoid
8:47
Evaluation of Multiple Functions
9:20
Section 2: Geometric Concepts
Geometric Terms and Notation

8m 36s

Intro
0:00
The Basics: Geometric Terms and Notation
0:15
Geometric Notation
6:01
Angles

18m 46s

Intro
0:00
The Basics: Angles
0:09
Classifying Angles
1:40
Acute Angles
1:55
Right Angles
2:21
Obtuse Angles
2:54
Straight Angles
3:46
Angle Relationships
4:13
Complementary Angles
4:28
Supplementary Angles
5:25
Bisected Angles
6:20
Angles at Intersections
7:14
Parallel Lines and Angles
9:50
Drawing Two Intersections to Determine Equal Angles
10:31
Angle Rules
11:20
Shapes and Angles
14:48
Angles in a Triangle
15:23
Angles in a Quadrilateral
15:40
Determining the Number of Angles is Larger Shapes
16:58
Triangles

21m 25s

Intro
0:00
Triangle Basics
0:12
Special Triangles: Isosceles and Equilateral
5:29
Special Triangles: Right Triangles
11:33
Special Triangles: 45, 45, 90 Triangles
18:49
Circles

16m 34s

Intro
0:00
The Basics: Parts of the Circle
0:11
The Diameter
1:04
The Radius
2:08
Arcs and Sectors
3:41
Arc
3:47
Sector
6:41
Using Fractional Weights
7:32
Tangent and Concentric
8:39
Lines that are Tangent to Circles
8:47
Tangent Circles
10:02
Concentric Circles
11:02
Angles in a Circle
11:55
Half Circles and Quarter Circles
12:19
Proportional Areas and Circumferences for Circle Parts
13:29
Inscribed angles
14:37
Volume and Surface Area

10m 53s

Intro
0:00
The Basics: Volume
0:17
Volume Equations
1:52
Equation for the Volume of a Cube
2:30
Equation for the Volume of a Cylinder
3:26
Finding other Volumes
4:14
The Basics: Surface Area
5:26
Surface Area of a Cube
6:30
Surface Area of a Cylinder
8:15
Section 3: Advanced Algebra
Foil

11m 2s

Intro
0:00
The Basics: Foil
0:16
Foil Examples
2:34
Skip Foil: Memorize These
6:22
Factoring

28m 35s

Intro
0:00
The Basics: Factoring
0:12
Factoring: Pull out the GCF
1:07
Example of Pulling Out the Greatest Common Factor
3:41
Factoring: Difference of Squares
5:30
Examples with Difference of Squares Factorizations
6:16
Factoring: General Quadratic Equations
9:35
Zooming in on C
10:12
Factoring Given Quadratic Equations
12:30
Factoring: Special Quadratic Expressions
17:39
How to Decide if You Need a + or -
19:37
Using Factoring in Rational Expressions
21:43
Steps: Take out the GCF, Factor, and Cancel
22:15
Factoring in Rational Expressions: Examples
23:48
Systems of Equations

28m 57s

Intro
0:00
The Basics: Systems of Equations
0:19
Equations with Infinite Solutions
0:44
Number of Equations Should Match the Number of Unknowns
2:41
Why Manipulation and Combination is Often the Best Method
4:34
Why Addition and Subtraction of Equations is Valid
7:23
The Most Important Step--The Common Coefficient
10:41
Manipulation and Combination: Steps
13:50
Substitution
15:49
Which Method Should Be Used?
20:13
How to Solve Problems with Three Equations and Three Unkowns
22:58
Three Equation Example
24:22
Distance Between Two Points

11m 55s

Intro
0:00
The Basics: Finding the Distance
0:13
Breaking Apart X and Y Cooridinates
0:48
Using Pythagorean Theorom
2:53
The Distance Formula
4:26
Example 1: Plugging into the Formula
6:18
Example 2: Using the Given Length to Find a Missing Coordinate
8:20
Intercepts

6m 32s

Intro
0:00
The Basics: Intercepts
0:11
The x-intercept
0:43
The y-intercept
1:44
Determing the Intercepts
3:05
The Special Case: b
4:37
Section 4: Statistics
Average

13m 28s

Intro
0:00
The Basics: Averages
0:11
Finding the Average
2:26
Rearraning the Average Equation
2:59
Average Examples
3:48
Finding the Missing Value
4:32
The Basics: Weighted Averages
6:25
Fractional Weight Method
6:54
Sum and Retake Method
7:48
Weighted Average Examples
8:30
Example Using the Sum and Retake Method
10:50
Median, Mode and Range

10m 8s

Intro
0:00
The Basics: Median
0:23
How to Find the Median
1:01
Quick Median Examples
1:23
The Basics: Mode
5:10
How to Find the Mode
5:16
Quick Mode Examples
5:28
The Basics: Range
7:20
How to Find the Range
8:06
Quick Range Example
8:28
Section 5: The Rest
Rates

17m 49s

Intro
0:00
The Basics: Rates
0:11
Using Units in Rate Problems
1:18
The Classic Rate Problems, d=rt
2:13
Dealing with Time in Rates
2:47
Changing Minutes to Seconds and Vice Versa
3:40
Changing Hours to Minutes and Vice Versa
4:41
The Big One: Seconds to Hours
5:19
Combining Multiple Rates
6:31
Which Questions to Ask
7:14
Set Up Two Equations
8:59
Solving Rates
9:32
Quick Example: Using d=rt
10:03
Solving Multiple Rates
12:29
Sequences

10m

Intro
0:00
The Basics: Sequences
0:11
When Sequences Are Just Patterns
1:14
Arithmetic Sequences
2:24
Using the Arithmetic Sequence Equation
3:11
Geometric Sequences
5:24
Using the Geometric Sequence Equation
6:08
Geometric Series that Alternate Between Negative and Positive Elements
8:02
Sets

10m 21s

Intro
0:00
The Basics: Sets
0:08
How to Represent Sets
0:25
The Union of Sets--Joining the Two Together
1:33
The Intersection of Sets--Where the Two Meet, What they Share
2:25
Sets: Intersection and Union
3:56
Venn Diagrams
6:21
Representing Two Sets
6:27
Representing the Union
7:17
Representing the Intersection
7:55
Box in Numbers Outside of the Set
8:16
Probability

8m 52s

Intro
0:00
The Basics Probability
0:10
The Scale of Probability
0:34
How to Calculate Probability
1:42
How to Solve Probability Problems
2:52
A Probability Example
4:51
Combinations and Permutations

7m 22s

Intro
0:00
The Basics: Combinations
0:11
Combination Equation
1:49
The Basics: Permutations
4:16
Permutation Equation
6:18
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Combinations and Permutations

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  • Intro 0:00
  • The Basics: Combinations 0:11
  • Combination Equation 1:49
  • The Basics: Permutations 4:16
  • Permutation Equation 6:18
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