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Mark Zegarelli. SAT Math For Dummies with Online Practice
SAT® Math For Dummies® To view this book's Cheat Sheet, simply go to www.dummies.com and search for “SAT Math For Dummies Cheat Sheet” in the Search box. Table of Contents
List of Tables
List of Illustrations
Guide
Pages
Introduction
About This Book
Foolish Assumptions
Icons Used in This Book
Beyond the Book
Where to Go from Here
Getting Started with SAT Math
Welcome to SAT Math
SAT Math Basics
Using the Reference list of formulas
Filling answers into the grid
Overview of SAT Math Topics
Heart of Algebra
Problem Solving and Data Analysis
Passport to Advanced Math (and Other Topics)
SAT Math Strategy
Isn’t there some way to get a good SAT Math score without actually knowing math?
Is there a penalty for guessing?
Are some questions harder than others?
Do I have to answer every question?
So, how many questions should I answer?
Clearing 500
Breaking solidly beyond 600
Reaching 700 and beyond
When’s the latest I can take the SAT and still get into school?
Hey wait — do I even have to take the SAT to go to college?
Three SAT Success Stories
Jay’s story — clearing 500
Shaun’s story — breaking solidly beyond 600
Amy’s story — reaching 700 and beyond
Review of Pre-Algebra
Sets of Numbers
Natural numbers
Integers
Rational numbers
Real numbers
Complex numbers
Fractions, Ratios, Decimals, and Percentages
Review of fractions and ratios
Converting between improper fractions and mixed numbers
Finding simplified and increased forms of fractions
Adding and subtracting fractions
Multiplying and dividing fractions
Connecting fractions and ratios
Review of decimals and percentages
Converting decimals to percentages
Changing percentages to decimals
Absolute Value
Radicals
Understanding radicals
Multiplying and dividing radicals
Simplifying radicals
Adding and subtracting radicals
Rationalizing radicals in the denominator
Understanding Algebra Terminology
Algebra and arithmetic
Equations, identities, and inequalities
Expressions
Variable and constant terms
Breaking terms into coefficient and variable
Polynomial basics
Understanding the degree of a polynomial
Counting the terms of a polynomial
Graphing on the xy-Plane
Understanding the axes, the origin, and the quadrants
Plotting coordinates on the xy-plane
Plotting equations on the xy-plane
Choosing and Using a Calculator
Knowing which calculators to avoid on the SAT
No cellphone calculators allowed!
No fancy inputs, power cords, or paper tape
Choosing a calculator
Nice, normal calculators are fine
Considering a graphing calculator
Knowing some basic calculator moves
Getting familiar with a few advanced calculator moves
Conquering the Heart of Algebra
Algebra I Reboot Part 1: Expressions
Evaluating Expressions
Simplifying Expressions
Combining like terms
Distributing to remove parentheses
FOILing to multiply the contents of parentheses
FOILing a pair of binomials
FOILing with larger polynomials
Factoring Expressions
GCF Factoring
Difference of squares
Sum and difference of cubes
Factoring quadratic trinomials
Easy quadratic factoring: When the leading coefficient is 1
Difficult quadratic factoring: When the leading coefficient isn’t 1
Factoring cubic expressions
Algebra I Reboot Part 2: Equations and Inequalities
Solving Simple and Intermediate Algebra Equations
Solving basic algebra equations
Working with equations that have more than one variable
Isolating a specific variable
Factoring to solve for a variable
Solving for an expression that contains more than one variable
Solving More Difficult Equations
Solving quadratic equations
Solving two-term quadratic equations
SOLVING
SOLVING
Solving three-term quadratic equations
FACTORING TO SOLVE QUADRATICS
USING THE QUADRATIC FORMULA
Solving rational equations
Multiplying by the denominator
Cross-multiplying
Getting a common denominator
Solving rational equations that become quadratics
Solving Inequalities
Using equation-solving skills with inequalities
Knowing when to flip the inequality sign
Lining up inequalities to solve systems
Linear Functions
Interpreting Linear Functions as Words, Tables, Graphs, and Equations
Understanding linear functions in four complementary ways
Making words count
Tabling your progress
Graphing the results
Creating an equation (or function)
Answering SAT questions about linear functions
Linear Function Basics
Slope-intercept form
b is the y-intercept
m is the slope
x is the input value
y is the output value
Standard form
Changing standard form to slope-intercept form
Converting slope-intercept form to standard form
Finding the intercepts of a standard-form linear equation
Graphing a linear equation in standard form
Using Two Formulas to Find the Slope
Measuring the slope of a graph
Measuring slope using two points
Solving Linear Function Problems
Finding the equation when you have two pieces of information
Finding the equation when you know the slope and the y-intercept
Answering point-slope questions
Finding the equation when you have the y-intercept and another point
Solving two-point problems
Understanding problems with parallel and perpendicular lines
Answering parallel line questions
Using perpendicular lines to solve problems
Solving Word Problems
Angela’s flowers
Peter’s autos
Jacqueline’s ascent
Systems of Equations
Systems of Linear Equations
Solving systems of linear equations
Substitution
Elimination
Looking for a fast solution
Solving word problems with a system of linear equations
For students who love charts
For students who hate charts
Working with Problematic Systems of Equations
Understanding systems with one solution
Troubleshooting problematic systems
Systems with no solutions
Systems with infinite solutions
Understanding what makes a system problematic
Answering SAT questions about problematic systems
Systems of Linear Inequalities
Setting up systems of linear inequalities to solve word problems
Graphs with linear inequalities
Systems of Non-Linear Equations
Tackling Problem Solving and Data Analysis
Ratios, Proportions, and Percentages
Understanding Ratios and Proportions
Understanding ratios
Creating proportional equations
Using Ratios and Proportions to Solve SAT Word Problems
Solving unit conversion problems
Using population density in a proportional equation
Answering questions involving similar triangles
Understanding direct proportionality
Using Percentages to Answer SAT Questions
Setting up equations to solve percentage problems
Solving percent increase and percent decrease problems
Finding percent increase and decrease in two steps
Finding the multiplier to calculate percent increase and decrease
Identifying percent increase and decrease
Solving tricky reverse percent increase and decrease problems with algebra
Statistics and Probability
Statistics
Statistical calculations
Ordering a data set
Finding the minimum, maximum, and range
Calculating the mean and median of a data set
Understanding outliers
Knowing about normal distribution of data sets
Understanding the standard deviation
Collecting data and interpreting statistics
Understanding sample bias
Keeping an eye on sample size
Accounting for margin of error
Probability
Understanding the probability formula
Answering SAT probability questions
Simple probability
Compound probability
Conditional probability
Answering table-based SAT probability questions
Finding probability
Working out compound probability
Calculating conditional probability
Understanding Data and Information from Tables and Graphs
Reading Information from Tables
Understanding Bar Graphs, Histograms, and Dot Plots
Bar graphs
Histograms
Dot plots
Working with Line Graphs and Scatterplots
Mapping time with line graphs
Understanding scatterplots
Your Passport to Advanced Math
Functions
Understanding Function Notation
Evaluating a function by plugging in a number
Evaluating a function plus or minus a value
Evaluating a function times or divided by a value
Evaluating a function by plugging in a variable or an expression
Working with Function Notation
Combining functions
Combining functions using standard notation
Combining functions using special notation
Compositions of functions
Inverse functions
Using the Vertical Line Test for Functions
Knowing Some Key Parent Functions
Polynomial functions
Linear functions
Quadratic functions
Cubic functions
Quartic functions
Other important parent functions
Absolute value functions
Exponential functions
Radical functions
Rational functions
Trigonometric functions
SINE FUNCTION
COSINE FUNCTION
Transforming Functions
Clarifying vertical and horizontal transformations
Vertical transformations
Horizontal transformations
Distinguishing vertical and horizontal transformations
Combining vertical and horizontal transformations
Understanding stretch-compress-flip transformations
When a is positive
When a is negative
Working with all three types of transformations
Polynomials
Knowing Polynomial Basics
Looking at the leading term
Identifying the degree of a polynomial
Positive and negative polynomials
Using the constant term to find the y-intercept
Identifying Odd and Even Polynomials
Identifying odd and even functions
Spotting end behavior as x approaches
Finding the x-Intercepts of Polynomials
Knowing a few names for x-intercepts
Finding the x-intercepts of a polynomial in factored form
Finding the x-intercepts of a polynomial in standard form
Sketching the Graph of a Polynomial
Sketching a polynomial from its factored form
Sketching “bounce” x-intercepts
Sketching a polynomial from its standard form
Equivalent Polynomials
Recalling Synthetic Division for Polynomials
Quadratic Functions
The Quadratic Function in Standard Form
Understanding standard-form quadratic functions
Identifying concavity
Plotting the y-intercept
Calculating the axis of symmetry
Finding the vertex
Sketching a parabola from standard form
The Quadratic Function in Vertex Form
Understanding vertex form quadratic functions
Vertical and horizontal transformations with k and h
THE VERTICAL TRANSFORMATION WITH VARIABLE K
THE HORIZONTAL TRANSFORMATION WITH VARIABLE H
COMBINING VERTICAL AND HORIZONTAL TRANSFORMATIONS
Stretch-compress-reflect transformations with variable a
THE STRETCH-COMPRESS TRANSFORMATION WITH VARIABLE A
THE REFLECTION TRANSFORMATION WHEN VARIABLE A IS NEGATIVE
Sketching a parabola from vertex form
Connecting Standard and Vertex Forms
Changing vertex form to standard form
Changing standard form to vertex form
Changing to vertex form without completing the square
Completing the square
UNDERSTANDING SQUARES OF BINOMIALS
COMPLETING THE SQUARE FOR QUADRATICS WHEN A IS 1
COMPLETING THE SQUARE WHEN A ISN’T 1
Finding the Roots of a Quadratic Function
Distinguishing quadratic functions from quadratic equations
Identifying quadratic functions with 2, 1, and no x-intercepts
Using the discriminant to count x-intercepts
Finding the roots of a quadratic function
Using quadratic equations to solve word problems about projectiles
Exponential and Radical Equations
Solving Exponential Equations
Using exponential identities
Solving exponential equations
Answering SAT Math Questions Using Exponential Functions
Understanding exponential growth
Working with exponential decay
Graphing Exponential Functions
Radical Equations and Functions
Solving radical equations
Graphing radical functions
Geometry and Trigonometry
Geometry
Geometric formulas for success
Knowing the angles
Vertical angles are equal, and linear pairs add up to
Corresponding angles are equal
The three angles in a triangle add up to
Isosceles triangles
Similar triangles
Working with right triangles
Right triangles and the Pythagorean Theorem
Knowing the most common Pythagorean Triples
Looking at the two special right triangles
Trigonometry
Using SOH-CAH-TOA to understand sines, cosines, and tangents
Building a triangle from a single trig ratio
Applying trig ratios to special right triangles
Remembering the most important SAT identity
Radian measure and arc length
Understanding radian measure for angles
Measuring arc length using radians
Additional SAT Math Topics
Imaginary and Complex Numbers
The imaginary number i
Imagining and defining i
Calculating with i
ADDING AND SUBTRACTING WITH I
MULTIPLYING WITH I
RAISING I TO AN EXPONENT
Complex numbers
Adding and subtracting complex numbers
Multiplying complex numbers
Dividing complex numbers
FINDING THE COMPLEX CONJUGATE
USING THE COMPLEX CONJUGATE TO DIVIDE
Circles on the xy-Plane
Circles in center-radius form
Circles centered at the origin
Circles centered at any point on the xy-plane
Plotting points on a circle on the xy-plane
Identifying interior and exterior points on a circle
Completing the square to solve difficult circle problems
Practice Makes Perfect: SAT Math Section Practice Tests
Practice SAT Math Test 1
Answer Sheet for Practice SAT Math Test 1
Section 3
Section 4
Section 3 — No Calculator
Section 4 — Calculator
Answers and Explanations for Practice SAT Math Test 1
Section 3 — No Calculator
Section 4 — Calculator
Practice SAT Math Test 2
Answer Sheet for Practice SAT Math Test 2
Section 3
Section 4
Section 3 — No Calculator
Section 4 — Calculator
Answers to Practice SAT Math Test 2
Section 3 — No Calculator
Section 4 — Calculator
The Part of Tens
Ten Things You Will Almost Definitely See on Your SAT Math Test
Linear Functions
Systems of Linear Equations
Quadratic Functions
Percentages
Ratio/Proportion Problems
The Mean and the Median
The Trig Identity
The Quadratic Formula
The Imaginary Number i
Circles on the Graph
Ten Tips to Improve Your SAT Math Score
Study Diligently in Your Math Classes
Get Good at Doing Basic Calculations in Your Head
Get Good at Using Your Calculator
Study SAT-Specific Math Skills
Get Comfortable Turning Words into Numbers
Take Timed Practice Tests
When Taking Practice Tests, Budget Your Time to Maximize Your Score
Study from Your Timed Practice Tests
Retake Your Timed Practice Tests
Take the SAT More than Once
Ten Tips to Be at Your Best on the SAT
Do Something Fun the Day Before the Test
Don’t Study for More than 20 Minutes the Night Before the Test
Pack Everything You Need the Night Before
Do Something Relaxing Before Bed
Get a Good Night’s Sleep
Wear Several Layers of Clothing
Arrive at the Test Site Extra Early
Spend Your Time Just Before the Test However You Please
Remember to Breathe
Skip Over Any Questions That Throw You
Index. A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
About the Author
Dedication
Author’s Acknowledgments
WILEY END USER LICENSE AGREEMENT
