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Charlotte Vilkus

Combinations and Permutations

Slide Duration:Table of Contents

I. Basic Math

Signed Numbers

18m 58s

- Intro0:00
- The Basics: Signed Numbers0:13
- How to Think of Negative Numbers0:39
- Signed Numbers on the Number Line2:16
- Signed Numbers: Addition and Subtraction3:07
- Subtracting a Negative8:35
- The Loss of a Negative is the Addition of a Positive8:43
- Flip the sign!11:16
- Addition and Subtraction Examples12:19
- Signed Numbers: Multiplication and Division13:45
- Quick Rules15:08
- Multiplication and Division Examples17:02

I. Basic Algebra

Exponents and Roots

24m 44s

- Intro0:00
- The Basics: Exponents0:09
- Base and Exponent0:42
- Squared Terms1:23
- Cubed Terms2:26
- Exponent Rules3:40
- Multiplying Terms with the Same Base5:51
- Dividing Terms with the Same Base6:48
- Exponent Term Raised to a Power8:32
- Product of Different Bases to the Same Power10:14
- Quotient of Different Bases to the Same Power11:57
- The Basics: Radicals17:24
- Square Roots19:39

Divisibility

16m 45s

- Intro0:00
- The Basics: Divisibility0:12
- Divisibility Tricks3:07
- The Rules3:44
- Examples of Quickly Determing what a Number is Divisibly by9:44

Prime Factorization

10m 1s

- Intro0:00
- Prime Numbers and Prime Factorization0:22
- How to: Prime Factorization2:27
- Bigger Divisors5:10
- Finding all Factors of 28 and 2105:52

Powers of 10

8m 56s

- Intro0:00
- The Basics: Powers of 100:15
- Multiplying and Dividing by Powers of 102:59
- Dealing with Multiplication3:37
- Dealing with Division5:16
- Example Set6:05

Fractions

12m 50s

- Intro0:00
- The Basics: Fractions0:09
- Fractions as Part of a Whole0:46
- Equivalent Fractions1:10
- Fractions: Addition and Subtraction4:11
- Finding the Common Denominator5:25
- Fractions: Multiplication and Division7:27
- Division: Multiplying the Reciprocal (Flip It)8:53
- Fractions: Comparing Fractions10:36
- Determining the relationship between fractions11:54

Algebraic Expression

17m 39s

- Intro0:00
- The Basics: Algebraic Expressions0:11
- Algebraic Expression Definitions1:54
- Simplifying Algebraic Expressions5:12
- Identifying Like Terms5:23
- Using Coefficients to Add and Subtract Like Terms6:14
- Combining Like Terms8:00
- Multiplication of Algebraic Expressions9:24
- Multiplying Two Terms: Coefficients and Variables9:38
- Combining Like Variables in Multiplication10:15
- Multiplying Expressions by a Term12:08
- Example 1: Multiplying Out and Simplifying13:45
- Example 2: Multiplying Out and Simplifying15:18

Equations

6m 7s

- Intro0:00
- The Basics: Equations0:10
- Valid Operations on an Equation0:26
- Isolate the Variable3:24

Function Evaluation

10m 50s

- Intro0:00
- The Basics: Function Evaluation0:10
- Function Definition and Notation2:23
- Function Evaluation Examples4:55
- Function Evaluation Mistakes to Avoid8:47
- Evaluation of Multiple Functions9:20

II. Geometric Concepts

Geometric Terms and Notation

8m 36s

- Intro0:00
- The Basics: Geometric Terms and Notation0:15
- Geometric Notation6:01

Angles

18m 46s

- Intro0:00
- The Basics: Angles0:09
- Classifying Angles1:40
- Acute Angles1:55
- Right Angles2:21
- Obtuse Angles2:54
- Straight Angles3:46
- Angle Relationships4:13
- Complementary Angles4:28
- Supplementary Angles5:25
- Bisected Angles6:20
- Angles at Intersections7:14
- Parallel Lines and Angles9:50
- Drawing Two Intersections to Determine Equal Angles10:31
- Angle Rules11:20
- Shapes and Angles14:48
- Angles in a Triangle15:23
- Angles in a Quadrilateral15:40
- Determining the Number of Angles is Larger Shapes16:58

Triangles

21m 25s

- Intro0:00
- Triangle Basics0:12
- Special Triangles: Isosceles and Equilateral5:29
- Special Triangles: Right Triangles11:33
- Special Triangles: 45, 45, 90 Triangles18:49

Circles

16m 34s

- Intro0:00
- The Basics: Parts of the Circle0:11
- The Diameter1:04
- The Radius2:08
- Arcs and Sectors3:41
- Arc3:47
- Sector6:41
- Using Fractional Weights7:32
- Tangent and Concentric8:39
- Lines that are Tangent to Circles8:47
- Tangent Circles10:02
- Concentric Circles11:02
- Angles in a Circle11:55
- Half Circles and Quarter Circles12:19
- Proportional Areas and Circumferences for Circle Parts13:29
- Inscribed angles14:37

Volume and Surface Area

10m 53s

- Intro0:00
- The Basics: Volume0:17
- Volume Equations1:52
- Equation for the Volume of a Cube2:30
- Equation for the Volume of a Cylinder3:26
- Finding other Volumes4:14
- The Basics: Surface Area5:26
- Surface Area of a Cube6:30
- Surface Area of a Cylinder8:15

III. Advanced Algebra

Foil

11m 2s

- Intro0:00
- The Basics: Foil0:16
- Foil Examples2:34
- Skip Foil: Memorize These6:22

Factoring

28m 35s

- Intro0:00
- The Basics: Factoring0:12
- Factoring: Pull out the GCF1:07
- Example of Pulling Out the Greatest Common Factor3:41
- Factoring: Difference of Squares5:30
- Examples with Difference of Squares Factorizations6:16
- Factoring: General Quadratic Equations9:35
- Zooming in on C10:12
- Factoring Given Quadratic Equations12:30
- Factoring: Special Quadratic Expressions17:39
- How to Decide if You Need a + or -19:37
- Using Factoring in Rational Expressions21:43
- Steps: Take out the GCF, Factor, and Cancel22:15
- Factoring in Rational Expressions: Examples23:48

Systems of Equations

28m 57s

- Intro0:00
- The Basics: Systems of Equations0:19
- Equations with Infinite Solutions0:44
- Number of Equations Should Match the Number of Unknowns2:41
- Why Manipulation and Combination is Often the Best Method4:34
- Why Addition and Subtraction of Equations is Valid7:23
- The Most Important Step--The Common Coefficient10:41
- Manipulation and Combination: Steps13:50
- Substitution15:49
- Which Method Should Be Used?20:13
- How to Solve Problems with Three Equations and Three Unkowns22:58
- Three Equation Example24:22

Distance Between Two Points

11m 55s

- Intro0:00
- The Basics: Finding the Distance0:13
- Breaking Apart X and Y Cooridinates0:48
- Using Pythagorean Theorom2:53
- The Distance Formula4:26
- Example 1: Plugging into the Formula6:18
- Example 2: Using the Given Length to Find a Missing Coordinate8:20

Intercepts

6m 32s

- Intro0:00
- The Basics: Intercepts0:11
- The x-intercept0:43
- The y-intercept1:44
- Determing the Intercepts3:05
- The Special Case: b4:37

IV. Statistics

Average

13m 28s

- Intro0:00
- The Basics: Averages0:11
- Finding the Average2:26
- Rearraning the Average Equation2:59
- Average Examples3:48
- Finding the Missing Value4:32
- The Basics: Weighted Averages6:25
- Fractional Weight Method6:54
- Sum and Retake Method7:48
- Weighted Average Examples8:30
- Example Using the Sum and Retake Method10:50

Median, Mode and Range

10m 8s

- Intro0:00
- The Basics: Median0:23
- How to Find the Median1:01
- Quick Median Examples1:23
- The Basics: Mode5:10
- How to Find the Mode5:16
- Quick Mode Examples5:28
- The Basics: Range7:20
- How to Find the Range8:06
- Quick Range Example8:28

V. The Rest

Rates

17m 49s

- Intro0:00
- The Basics: Rates0:11
- Using Units in Rate Problems1:18
- The Classic Rate Problems, d=rt2:13
- Dealing with Time in Rates2:47
- Changing Minutes to Seconds and Vice Versa3:40
- Changing Hours to Minutes and Vice Versa4:41
- The Big One: Seconds to Hours5:19
- Combining Multiple Rates6:31
- Which Questions to Ask7:14
- Set Up Two Equations8:59
- Solving Rates9:32
- Quick Example: Using d=rt10:03
- Solving Multiple Rates12:29

Sequences

10m

- Intro0:00
- The Basics: Sequences0:11
- When Sequences Are Just Patterns1:14
- Arithmetic Sequences2:24
- Using the Arithmetic Sequence Equation3:11
- Geometric Sequences5:24
- Using the Geometric Sequence Equation6:08
- Geometric Series that Alternate Between Negative and Positive Elements8:02

Sets

10m 21s

- Intro0:00
- The Basics: Sets0:08
- How to Represent Sets0:25
- The Union of Sets--Joining the Two Together1:33
- The Intersection of Sets--Where the Two Meet, What they Share2:25
- Sets: Intersection and Union3:56
- Venn Diagrams6:21
- Representing Two Sets6:27
- Representing the Union7:17
- Representing the Intersection7:55
- Box in Numbers Outside of the Set8:16

Probability

8m 52s

- Intro0:00
- The Basics Probability0:10
- The Scale of Probability0:34
- How to Calculate Probability1:42
- How to Solve Probability Problems2:52
- A Probability Example4:51

Combinations and Permutations

7m 22s

- Intro0:00
- The Basics: Combinations0:11
- Combination Equation1:49
- The Basics: Permutations4:16
- Permutation Equation6:18

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For more information, please see full course syllabus of GRE/ACT/PSAT Math

For more information, please see full course syllabus of GRE/ACT/PSAT Math

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