# SAT Math Review Course

## Math Basics

### Lesson 1: Operations Basics

- Addition and Subtraction
- Associative Property
- Distributive Property
- Exponents and Roots
- Integers, Decimals, and Fractions
- Multiplication and Division
- Order of Operations

### Lesson 2: Factors and Multiples

- Greatest Common Factor
- Least Common Multiple
- Multiples
- Multiples and Least Common Multiples
- Prime Numbers, Factoring, and Prime Factorization

### Lesson 3: Unit Conversions

## Fractions

### Lesson 1: Fraction Basics

- Changing Mixed Numbers to Improper Fractions
- Converting Improper Fractions to Mixed Numbers
- Fractions of a Whole
- Improper Fractions and Mixed Numbers
- Ordering Fractions

### Lesson 2: Fraction Operations

- Adding and Subtracting Fractions
- Converting Improper Fractions to Mixed Numbers and Decimals
- Converting Mixed Numbers to Decimals and Improper Fractions
- Converting Percentages to Decimals and Fractions
- Multiplying and Dividing Fractions

## Decimals

### Lesson 1: Decimal Basics

### Lesson 2: Decimal Operations

- Adding and Subtracting Decimals
- Changing a Number from Standard Form to Scientific Notation
- Converting Decimals to Fractions and Percentages
- Converting Decimals to Improper Fractions and Mixed Numbers
- Dividing Decimals
- Multiplying Decimals
- Scientific Notation

## Solving Equations

### Lesson 1: Equation Basics

- Absolute Value
- Arithmetic Sequences
- Solving an Equation Using Four Basic Operations
- Solving Equations Using Addition and Subtraction
- Solving Equations Using Multiplication and Division
- Solving Equation with Absolute Value

### Lesson 2: Inequalities

- Equations and Inequalities
- Graphing Solutions to Linear Inequalities
- Linear Inequalities
- Solving Absolute Value Inequalities
- Solving Inequalities Using All four Basic Operations

### Lesson 3: Linear System of Equations

- Comparison of Methods for Solving System of Equations
- Linear Equations Basics
- System of Linear Equations
- System of Equations Basics

### Lesson 4: Graphing of Linear Equations and Functions

- Changing Constants in Graphs of Functions: Linear Functions
- Changing Constants in Graphs of Functions: Quadratic Equations
- Graphing Absolute Value Equations
- Graphing Linear Equations
- Graphing the Inverse of a Function
- Graphs of Functions
- Solutions of a Quadratic Equation on a Graph
- Using a Graph

### Lesson 5: Word Problems

- Right Triangle Word Problems
- Word Problems and Addition
- Word Problems and Division
- Word Problems and Multiplication
- Word Problems and Subtraction

## Geometry

### Lesson 1: Angle Basics

### Lesson 2: Triangles

- Area and Perimeter of a Triangle
- Measurements for Similar Triangles
- Measurements for Similar Triangles – Continued
- Measurements for Similar Triangles – Continued II
- Proof that a Triangle is 180 Degrees
- Similar Triangles

### Lesson 3: Circles

- Area and Circumference of a Circle
- Finding Measurements for Parts of a Circle
- Unit Circles and Standard Position

### Lesson 4: Volume and Surface Area of 3D Shapes

- 3D Geometric Shapes
- Volume and Surface Area of a Cube
- Volume and Surface Area of a Pyramid
- Volume and Surface Area of a Rectangular Solid
- Volume and Surface Area of a Circular Cone
- Volume and Surface Area of a Circular Cylinder
- Volume and Surface Area of a Sphere

## Probability, Statistics, Percentages, Ratios, and Proportions

### Lesson 1: Probability

### Lesson 2: Percentages, Ratios, and Proportions

- Calculation of a Percentage
- Computation with Percentages
- Finding the Percentage Decrease
- Finding the Percentage Increase
- Percentages
- Proportions
- Proportions and Percents
- Proportions in the Real World
- Ratios and Percentages

## SAT Math Review

As reported by recent news, the SAT Math section has received a major makeover—just like the rest of the exam. While this may sound worrying, these changes will actually unfold in your favor. The SAT has been reformatted for the sake of better aligning with what today’s high schoolers are learning across the United States, meaning the material should come a bit more easily to you, or at least seem more familiar in comparison to the old format. In this overview, we’ll go over what you can expect from the SAT Math section—how the new format compares to the old, the types of questions you’ll find, and how you can prepare as thoroughly as possible.

Let’s dive right in!

## How Is the New Math Section Different From Old Version?

The math you’ll encounter on the newest edition of the SAT renders distinct just through presentation alone. The College Board also aims to provide you with math that’s much more “relatable,” and the problems featured on the new Math section align much more with situations you’d be far more likely to face at some point in life.

As such, the Math portion of the SAT has three noteworthy objectives: assessing your capabilities with critical thinking and reading situations, putting various types of math to use based upon the concept of the problem, and knowing how to use and solve math on a rudimentary level.

For the most part, the format of the new Math section is the same as the old. You will be provided with predominantly multiple choice questions. However, much of the exam utilizes “grid-ins,” a new answer format. You can think of this new problem type as a “free answer” question. You may have seen this answer format on other standardized tests. It involves writing out your answer into a boxed space, then shading in bubbles corresponding to the numbers (or symbols, if your answer is a fraction or decimal) just below your written response.

## SAT Math In-Depth

It is worth noting that in addition to the test’s format utilizing “grid-in” questions, you will also be free to and expected to use a calculator—up to a certain point. A little over half of the SAT Math section is calculator-friendly. More specifically, the Math section’s Calculator subsection contains eight questions under the “grid-in” category and 30 multiple choice.

You are more than allowed to bring your own calculator from home for this portion of the SAT Math section. We must clarify, however, that you cannot bring just any calculator on exam day to help you as you take the test. You have to bring a model approved by the College Board. To know what calculators are and are not accepted by the College Board, you can visit the official website and double check whether your calculator fits the bill. A standard calculator should be able to serve your needs throughout the exam, as none of the questions you’ll find on the Calculator section of the SAT exam require intense calculation techniques, like graphing. While it may seem that being able to use your calculator will render this area much easier to complete, you will be granted a total of 55 minutes to work through each question. Be sure to budget your time wisely! Additionally, make sure to remember that just being able to use your calculator does not mean all of the answers will come to you in an instant. You will also have to know what kind of math you should be using and then be able to utilize the calculator properly in order to come to the correct answer.

The No Calculator subsection of the Math section is much shorter. You’ll be allotted 25 minutes to complete this part of the exam, which will span for 20 questions total. Five of them will categorize as “grid-in,” while the remaining 15 are multiple choice.

Now that you know the basics of the Math section’s format, it’s time to brush up on just what subjects you should devote the majority of your study time to. On a general basis, we recommend reviewing Trigonometry, Algebra, Geometry, Statistics, and Arithmetic. All of these subjects will appear on the SAT exam in one form or another. You can also expect to have to use several major formulas under these mathematical subjects. While you will be supplied with these formulas on the exam, we advise you to commit them to memory for the sake of working more efficiently.

To help you prepare as best you can, we will go over how each of these subjects are assessed on the Math section and how you can build an effective study plan for each of them. Three out of four of them—Passport to Advanced Math, Problem Solving and Data Analysis, and Heart of Algebra, to be specific—classify as subscore sections, with your potential grades on each ranging anywhere between 1 and 15.

**Passport to Advanced Math**

You can think of this particular section as an introduction to the complicated mathematical subjects you’ll encounter once you move on to college. Questions falling under this category will thus present more intricate problems for you to solve, and will require you to utilize your knowledge of functions and their notation, polynomials, and quadratic, linear, and exponential equations, among others. When answering Passport to Advanced Math questions, you will be expected to interact with functions in several ways, including interpretation, revision, computation, and production, drawing from the information provided to you by each question. You will also have to draw out the occasional line graph.

**Problem Solving and Data Analysis**

This knowledge category deals specifically with quantitative math and its various applications. You will rely on this form of math the most frequently once you graduate from high school and move on to either higher education or the workforce, hence its heavier emphasis on the new edition of the SAT exam. Questions under this category will be written to conform to various scenarios you may encounter (or have already encountered) in life. To prepare for this exam, we recommend brushing up on the various properties of data sets, as well as how to interpret them. Answering these questions may involve assessing data sets, evaluating percentages and similar types of data, interpreting various types of graphic mathematical data, and working with assorted units of measurement, among similar themes.

**Heart of Algebra**

The Heart of Algebra category is much like what it says on the tin. Questions under this category will require you to flex your knowledge of Algebra. For the most part, this will translate to evaluating inequalities and linear equations, as well as being familiar with all of their properties and applications. Like the Problem Solving and Data Analysis category, you can expect to run into problems of this type later on, as the skills necessary to solve Algebraic equations show up quite frequently in real life. Preparing for this particular knowledge category of the SAT exam math section will require reviewing what you’ve learned about linear equations—both in Algebra I and Algebra II.

**Additional Topics in Math**

Additional Topics in Math will cover more elaborate mathematical subjects than any other part of the Math section. This includes Trigonometry and Geometry, which you’ve likely studied as part of your required curriculum. The good news about this category is that it features the least on the Math section, totaling at a maximum of six questions you’ll have to solve. You will be responsible for knowing how to analyze and solve problems related to shapes—2D and 3D—as well as which formulas to use. You can expect to find problems asking you to utilize and solve for circumference, the Pythagorean theorem, volume, and more. In addition, you should also be familiar with the properties of each major shape, with particular emphasis on circles and triangles. Complex numbers and various trigonometry-related formulas will also appear on this part of the exam. Be sure to brush up on how to read and interpret angles as well, as some problems will involve you measuring angles and inputting their degrees.

We hope this overview will give you a much better picture of what to expect from the new SAT Math section. While the exam won’t necessarily be easier, we hope you will be able to take full advantage of our materials—including our SAT Math practice tests, SAT Math flashcards, and SAT Math study guide—and earn the best score you can. Helping you reach success is why we’ve put together such thorough study tools. Don’t hesitate to explore the rest of our site as you study for this important exam!

Good luck, and work hard!

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*Mometrix Test Preparation*

Last updated: 05/04/2017

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