Most standardized exams require similar skills and test on similar types of problems, especially when it comes to the math sections. The GRE, ACT, and PSAT have more in common than you realize. Professor Charlotte Vilkus teaches Educatorâ€™s Standardized Math course specializing in the GRE/ACT/PSAT, and will show you all of her tricks and everything you need to know in order to get the highest score possible. In addition, Charlotte has worked with students across the most popular prep books for all the major exams. Using her experience, she creates an all-inclusive course which begins with a basic overview of math concepts, then covers the types of problems you should expect on test day, and finally guides you through the best ways to approach math questions on standardized tests. Professor Vilkus obtained her BA in civil engineering with a math minor from Loyola Marymount University.

expand all   collapse all

## I. Basic Math

Signed Numbers 18:58
Intro 00:00
The Basics: Signed Numbers 00:13
How to Think of Negative Numbers 00:39
Signed Numbers on the Number Line 02:16
Signed Numbers: Addition and Subtraction 03:07
Subtracting a Negative 08:35
The Loss of a Negative is the Addition of a Positive 08:43
Flip the sign! 11:16
Signed Numbers: Multiplication and Division 13:45
Quick Rules 15:08
Multiplication and Division Examples 17:02

## I. Basic Algebra

Exponents and Roots 24:44
Intro 00:00
The Basics: Exponents 00:09
Base and Exponent 00:42
Squared Terms 01:23
Cubed Terms 02:26
Exponent Rules 03:40
Multiplying Terms with the Same Base 05:51
Dividing Terms with the Same Base 06:48
Exponent Term Raised to a Power 08:32
Product of Different Bases to the Same Power 10:14
Quotient of Different Bases to the Same Power 11:57
Square Roots 19:39
Divisibility 16:45
Intro 00:00
The Basics: Divisibility 00:12
Divisibility Tricks 03:07
The Rules 03:44
Examples of Quickly Determing what a Number is Divisibly by 09:44
Prime Factorization 10:01
Intro 00:00
Prime Numbers and Prime Factorization 00:22
How to: Prime Factorization 02:27
Bigger Divisors 05:10
Finding all Factors of 28 and 210 05:52
Powers of 10 8:56
Intro 00:00
The Basics: Powers of 10 00:15
Multiplying and Dividing by Powers of 10 02:59
Dealing with Multiplication 03:37
Dealing with Division 05:16
Example Set 06:05
Fractions 12:50
Intro 00:00
The Basics: Fractions 00:09
Fractions as Part of a Whole 00:46
Equivalent Fractions 01:10
Finding the Common Denominator 05:25
Fractions: Multiplication and Division 07:27
Division: Multiplying the Reciprocal (Flip It) 08:53
Fractions: Comparing Fractions 10:36
Determining the relationship between fractions 11:54
Algebraic Expression 17:39
Intro 00:00
The Basics: Algebraic Expressions 00:11
Algebraic Expression Definitions 01:54
Simplifying Algebraic Expressions 05:12
Identifying Like Terms 05:23
Using Coefficients to Add and Subtract Like Terms 06:14
Combining Like Terms 08:00
Multiplication of Algebraic Expressions 09:24
Multiplying Two Terms: Coefficients and Variables 09:38
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 6:07
Intro 00:00
The Basics: Equations 00:10
Valid Operations on an Equation 00:26
Isolate the Variable 03:24
Function Evaluation 10:50
Intro 00:00
The Basics: Function Evaluation 00:10
Function Definition and Notation 02:23
Function Evaluation Examples 04:55
Function Evaluation Mistakes to Avoid 08:47
Evaluation of Multiple Functions 09:20

## II. Geometric Concepts

Geometric Terms and Notation 8:36
Intro 00:00
The Basics: Geometric Terms and Notation 00:15
Geometric Notation 06:01
Angles 18:46
Intro 00:00
The Basics: Angles 00:09
Classifying Angles 01:40
Acute Angles 01:55
Right Angles 02:21
Obtuse Angles 02:54
Straight Angles 03:46
Angle Relationships 04:13
Complementary Angles 04:28
Supplementary Angles 05:25
Bisected Angles 06:20
Angles at Intersections 07:14
Parallel Lines and Angles 09:50
Drawing Two Intersections to Determine Equal Angles 10:31
Angle Rules 11:20
Shapes and Angles 14:48
Angles in a Triangle 15:23
Determining the Number of Angles is Larger Shapes 16:58
Triangles 21:25
Intro 00:00
Triangle Basics 00:12
Special Triangles: Isosceles and Equilateral 05:29
Special Triangles: Right Triangles 11:33
Special Triangles: 45, 45, 90 Triangles 18:49
Circles 16:34
Intro 00:00
The Basics: Parts of the Circle 00:11
The Diameter 01:04
Arcs and Sectors 03:41
Arc 03:47
Sector 06:41
Using Fractional Weights 07:32
Tangent and Concentric 08:39
Lines that are Tangent to Circles 08:47
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 10:53
Intro 00:00
The Basics: Volume 00:17
Volume Equations 01:52
Equation for the Volume of a Cube 02:30
Equation for the Volume of a Cylinder 03:26
Finding other Volumes 04:14
The Basics: Surface Area 05:26
Surface Area of a Cube 06:30
Surface Area of a Cylinder 08:15

Foil 11:02
Intro 00:00
The Basics: Foil 00:16
Foil Examples 02:34
Skip Foil: Memorize These 06:22
Factoring 28:35
Intro 00:00
The Basics: Factoring 00:12
Factoring: Pull out the GCF 01:07
Example of Pulling Out the Greatest Common Factor 03:41
Factoring: Difference of Squares 05:30
Examples with Difference of Squares Factorizations 06:16
Zooming in on C 10:12
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 28:57
Intro 00:00
The Basics: Systems of Equations 00:19
Equations with Infinite Solutions 00:44
Number of Equations Should Match the Number of Unknowns 02:41
Why Manipulation and Combination is Often the Best Method 04:34
Why Addition and Subtraction of Equations is Valid 07:23
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 11:55
Intro 00:00
The Basics: Finding the Distance 00:13
Breaking Apart X and Y Cooridinates 00:48
Using Pythagorean Theorom 02:53
The Distance Formula 04:26
Example 1: Plugging into the Formula 06:18
Example 2: Using the Given Length to Find a Missing Coordinate 08:20
Intercepts 6:32
Intro 00:00
The Basics: Intercepts 00:11
The x-intercept 00:43
The y-intercept 01:44
Determing the Intercepts 03:05
The Special Case: b 04:37

## IV. Statistics

Average 13:28
Intro 00:00
The Basics: Averages 00:11
Finding the Average 02:26
Rearraning the Average Equation 02:59
Average Examples 03:48
Finding the Missing Value 04:32
The Basics: Weighted Averages 06:25
Fractional Weight Method 06:54
Sum and Retake Method 07:48
Weighted Average Examples 08:30
Example Using the Sum and Retake Method 10:50
Median, Mode and Range 10:08
Intro 00:00
The Basics: Median 00:23
How to Find the Median 01:01
Quick Median Examples 01:23
The Basics: Mode 05:10
How to Find the Mode 05:16
Quick Mode Examples 05:28
The Basics: Range 07:20
How to Find the Range 08:06
Quick Range Example 08:28

## V. The Rest

Rates 17:49
Intro 00:00
The Basics: Rates 00:11
Using Units in Rate Problems 01:18
The Classic Rate Problems, d=rt 02:13
Dealing with Time in Rates 02:47
Changing Minutes to Seconds and Vice Versa 03:40
Changing Hours to Minutes and Vice Versa 04:41
The Big One: Seconds to Hours 05:19
Combining Multiple Rates 06:31
Set Up Two Equations 08:59
Solving Rates 09:32
Quick Example: Using d=rt 10:03
Solving Multiple Rates 12:29
Sequences 10:00
Intro 00:00
The Basics: Sequences 00:11
When Sequences Are Just Patterns 01:14
Arithmetic Sequences 02:24
Using the Arithmetic Sequence Equation 03:11
Geometric Sequences 05:24
Using the Geometric Sequence Equation 06:08
Geometric Series that Alternate Between Negative and Positive Elements 08:02
Sets 10:21
Intro 00:00
The Basics: Sets 00:08
How to Represent Sets 00:25
The Union of Sets--Joining the Two Together 01:33
The Intersection of Sets--Where the Two Meet, What they Share 02:25
Sets: Intersection and Union 03:56
Venn Diagrams 06:21
Representing Two Sets 06:27
Representing the Union 07:17
Representing the Intersection 07:55
Box in Numbers Outside of the Set 08:16
Probability 8:52
Intro 00:00
The Basics Probability 00:10
The Scale of Probability 00:34
How to Calculate Probability 01:42
How to Solve Probability Problems 02:52
A Probability Example 04:51
Combinations and Permutations 7:22
Intro 00:00
The Basics: Combinations 00:11
Combination Equation 01:49
The Basics: Permutations 04:16
Permutation Equation 06:18
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}