# SAT: Mathematics Exponents on the SAT

Section 1: Basic Math: Lecture 5 | 9:32 min

Lecture Description

In this lesson our professor Charlotte Vilkus shows students what sort of exponent topics they can expect to encounter on the SAT and then goes through a few exponent examples.

Charlotte Vilkus

Exponents on the SAT

Slide Duration:Table of Contents

Section 1: Basic Math

SAT Properties of Integers

6m 40s

- Intro0:00
- How Properties of Integers are Tested0:12
- Learn by Example: Prime Factors4:38

Fractions on the SAT

8m 50s

- Intro0:00
- How Fractions are Tested on the SAT0:11
- Learn by Example: Evaluation with Fractions3:16
- Learn by Example: Word Problem with Fractions6:32

Percent on the SAT

22m 16s

- Intro0:00
- How the SAT Tests Percent0:10
- Percent Increase and Decrease3:24
- Percent More Than, Percent Less Than7:53
- Learn by Example: Percent Translation9:29
- Learn by Example: Percent More Than13:38
- Learn by Example: Dealing with Tax and Tip16:31

Number Lines on the SAT

8m 31s

- Intro0:00
- How Number Lines are Tested on the SAT0:08
- How to Solve SAT Number Line Problems0:54
- Learn by Example: Number Line Coordinates4:52
- Learn by Example: Representing and Inequality with a Number Line6:33

Exponents on the SAT

9m 32s

- Intro0:00
- How Exponents are Tested on the SAT0:09
- Consider Plugging in on Exponent Problems0:21
- Learn by Example: Exponents in Simultaneous Equations1:03
- Learn by Example: Exponent Analysis6:15

Absolute Value on the SAT

12m 36s

- Intro0:00
- How Absolute Value is Tested on the SAT0:11
- Learn by Example: Absolute Value3:07
- Learn by Example: Absolute Value and Inequalities7:09

Section 2: Proportions, Rates and Variations

Proportions on the SAT

11m 15s

- Intro0:00
- How Proportions are Tested on the SAT0:11
- Learn by Example: Map Scaling2:07
- Learn by Example: Medium to Hard Unit Conversion4:40
- Learn by Example: Where the SAT Really Tries to Trip You Up on Units8:24

Rates on the SAT

12m 39s

- Intro0:00
- How Rates are Tested on the SAT0:12
- Learn by Example: Videos Processed per Hour2:50
- Learn by Example: Multiple Rates7:27

Variations on the SAT

7m 59s

- Intro0:00
- How Variations are Tested on the SAT0:13
- Learn by Example: Direct Variation2:22
- Learn by Example: Variations4:12
- Learn by Example: Inverse Variation7:04

Section 3: Geometry

Area and Perimeter on the SAT

16m 59s

- Intro0:00
- SAT Problems on Area and Perimeter0:11
- Learn by Example: Perimeter of a Quarter Circle2:50
- Learn by Example: Area of the Unshaded Region4:26
- Learn by Example: Perimeter of a Square Inscribed in a Circle10:03
- Learn by Example: Using Pythagorean to Get Side Lengths13:23

Angles on the SAT

12m 11s

- Intro0:00
- How Angles are Tested on the SAT0:11
- What You Need to Know About Angles1:13
- Lean by Example: Angles (1)2:48
- Lean by Example: Angles (2)5:45

Triangles on the SAT

15m 25s

- Intro0:00
- What Sort of Triangles Will I see on the SAT?0:11
- Learn by Example: Triangle Basics5:09
- Learn by Example: Special Triangles10:14
- Learn by Example: Triangles with other Shapes12:12

Quadrilaterals on the SAT

13m 34s

- Intro0:00
- How Quadrilaterals are Tested on the SAT0:12
- Learn by Example: Squares1:50
- Learn by Example: Rectangle with Triangles6:29
- Learn by Example: Angles in a Quadrilateral Problem11:17

Circles on the SAT

16m 40s

- Intro0:00
- How Circles are Tested on the SAT0:11
- But Don't Bother with Any of This1:40
- How to Deal with Sections of a Circle1:55
- College Board Expects Mistakes Here4:04
- Circumference=Perimeter4:47
- Learn by Example: How Circle Problems Are Presented5:18
- Three Tangential Circles5:48
- Learn by Example: Concentric Circles8:56
- Learn by Example: Shaded Area with Combination Circles and Squares11:53

Section 4: Graphing

SAT Coordinate Geometry

14m 38s

- Intro0:00
- How the SAT Test Coordinate Geometry0:17
- Learn by Example: Midpoint and Distance3:08
- Distance Example: the Length of the Square5:39
- Example: Figures in the Coordinate Plane9:34

SAT Translation

10m 6s

- Intro0:00
- How the SAT Tests Graph Translation0:11
- Shifting the Graph in the Y: f(x)+a1:01
- Shifting the Graph in the X: f(x+a)1:50
- Multiplying the Graph af(x)2:59
- Multiplying the Graph f(ax)5:07
- How the SAT Tests Rotations and Reflections6:19
- Learn by Example: Rotations and Reflections7:52

Lines on the SAT

6m 15s

- Intro0:00
- How Lines are Tested on the SAT0:09
- Learn by Example: Finding the Intercept1:48
- Learn by Example: Perpendicular Lines3:42

Line Slope on the SAT

10m 46s

- Intro0:00
- How Line Slope is Tested on the SAT0:10
- Definition of Slope0:25
- Slope Equation1:12
- Classifying Slopes: Steep, Flat, Negative1:50
- Determining the Slope in Problems3:41
- Learn by Example: Line Slope (I)4:43
- Learn by Example: Line Slope (2)8:04

Section 5: Advanced Algebra

SAT Quadratic Equations

6m 46s

- Intro0:00
- How the SAT Tests Quadratic Equations0:11
- Required Knowledge for Quadratic Equations2:52
- Learn by Example: Quadratic Equations5:02

Expressions on the SAT

10m 20s

- Intro0:00
- How Expression are Tested on the SAT0:10
- Learn by Example: Expression Evaluation--Signed Numbers and Exponents1:17
- Learn by Example: Expression Evaluation of Arithmetic Overload6:16

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
- Manipulation and Combination4:34
- Manipulation and Combination: Really?7:23
- Manipulation and Combination: Coefficients10:41
- Manipulation and Combination: Steps13:50
- Substitution15:49
- Which Method Should Be Used?20:13
- Oh No, Three Equations?22:58
- Three Equation Example24:22

Inequalities on the SAT

13m 8s

- Intro0:00
- How Inequalities are Tested on the SAT0:11
- What to Know: Inequalities3:12
- Learn by Example: Solving an Inequality for a Variable7:12
- Learn by Example: Inequalities with Parameters9:02

Special Functions on the SAT

8m 16s

- Intro0:00
- 'Special Functions' on the SAT0:09
- Treating Special Functions like General Function Evaluation *Same Idea (Implies)1:24
- Learn by Example: Special Functions (1)3:40
- Learn by Example Special Functions: (2)4:40

Section 5: Statistics, Combinations and Probability

Averages on the SAT

10m 20s

- Intro0:00
- How Averages are Tested on the SAT0:10
- Important Quantities: Average, Sum and Number of Values0:36
- Rearranging the Average Equation to be of Maximum Use1:36
- Learn by Example: Averages (1)3:16
- Learn by Example: Averages (2)7:17

Median and Mode on the SAT

8m 31s

- Intro0:00
- How the SAT Test Median and Mode0:32
- Learn by Example: Using a Table to find the Median1:46
- Learn by Example: Finding the Median with an Unknown4:41
- Learn by Example: Mode6:35

Data Analysis on the SAT

18m

- Intro0:00
- How Data Analysis is Tested on the SAT0:11
- Tables1:16
- Using Table Totals2:08
- Pie Charts3:50
- Pie Charts Examples5:56
- Creating Pie Charts7:00
- Bar Graphs9:35
- Comparing Pie Charts and Bar Graphs11:22
- Scatter Plot Graphs12:45
- Example of a Scatter Plot13:48
- Line Graphs15:12
- Line Chart Example15:32

Probability on the SAT

9m 37s

- Introduction0:00
- How the SAT Tests Probability0:10
- Probability Definition0:54
- Probability of A or B occurring1:56
- Probability of A and B both occurring3:16
- Learn by Example: Probability (1)4:12
- Learn by Example: Probability (2)6:07

Combinations and Permutations on the SAT

10m 10s

- Intro0:00
- How Combinations and Permutations are Tested on the SAT0:14
- Using 'Blank Space' Representors1:32
- Learn by Example: Combinations2:44
- Writing Out the Possibilities3:53
- Learn by Example: Permutations5:14
- Writing Out the Possibilities7:04

Logical Reasoning on the SAT

9m 18s

- Intro0:00
- How Logical Reasoning is Tested on the SAT0:11
- Learn by Example: Logic Questions and Using Differences0:54
- Learn by Example: Logic Questions with Inequalities5:32

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For more information, please see full course syllabus of SAT: Mathematics

For more information, please see full course syllabus of SAT: Mathematics

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0 answers

Post by Nada Al Bedwawi on December 23, 2013

I am confused about how x which is -0.5 is greater than 0??

0 answers

Post by Jeffrey Tao on October 22, 2013

For the first example, b isn't an integer. I think the problem should be "given that NUMBERS a,b, and c..." instead of "given that INTEGERS a, b, and c..."

1 answer

Last reply by: Professor Vilkus

Wed Apr 17, 2013 11:02 AM

Post by Rajendran Rajaram on March 12, 2013

for the last ex, isn't -1/2 greater than -1. I am confused.

1 answer

Last reply by: Professor Vilkus

Tue Jan 29, 2013 8:13 PM

Post by Kevin Song on January 26, 2013

For the last example problem, isn't the -(1/2) less than 0?