ultimate sat math study guide

8/10/2019 Ultimate SAT Math Study Guide

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reasonprep.com -- [email protected] -- 1

SAT Math Study Guide 2.2

Begin with the Math Diagnostic Test. Use the test to direct you to the videos that target your

weaknesses in content and/or application.

This study guide is for use with the SAT Math Bootcamp video series & the introduction

videos of the SAT Math Tactics series. You can find these videos in the Math section of

reasonprep.com.

SAT Math BootcampCovers the CONTENTtested on the SAT. Check the lines after youwatch the video.

___ #1 Properties of Integers

___ #2 Number Lines

___ #3 Squares and Square Roots

___ #4 Fractions

___ #5 Reciprocals

___ #6 Decimals

___ #7 Factors

___ #8 Remainders

___ #9 Multiples

___ #10 Prime Numbers

___ #11 Ratios and Proportions

___ #12 Percents; Fractions & Decimals Revisited

___ #13 Sequences

___ #14 Sets

___ #15 Counting Problems

___ #16 Algebra Basics

___ #17 Factoring Expressions

___ #18 Exponents and Exponent Rules

___ #19 Exponent and Radical Equations

___ #20 Solving SAT Equations

___ #21 Absolute Value

___ #22 Translating Word Problems into Eqns.

___ #23 Inequalities

___ #24 Systems of Equations

___ #25 Solving Quadratic Equations

___ #26 Rational Equations

___ #27 Direct & Inverse Variation

___ #28 Functions

___ #29 Special or Symbolic Functions

___ #30 Transformations

___ #31 Geometry Basics

___ #32 Angles

___ #33 Triangle Basics

___ #34 Special Triangles

___ #35 Congruence and Similarity

___ #36 Triangle Inequality___ #37 Quadrilaterals

___ #38 Area and Perimeter

___ #39 Polygons

___ #40 Circles


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___ #41 Solids

___ #42 Lines & Slopes

___ #43 Miscellaneous Formulas

___ #44 Geometric Transformations

___ #45 Charts & Graphs

___ #46 Mean, Median, Mode

___ #47 Probability

___ #48 Geometric Probability


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#1 - Properties of Integers (for practice problems, see SAT Math Tactics: Arithmetic videos)

Integer: any positive or negative whole number, including 0. NOT a decimal or fraction.

Consecutive Integers: Integers follow each other in order

four consecutive integers

five consecutive even integers

four largest consecutive negative odd integers

Odd & Even Integers

even -

odd -

even + even =

even + odd =

odd + odd =

even x even =

even x odd =

odd x odd =

Additive Identity:

Multiplicative Identity:

Zero Property of Multiplication:

NOTES & QUESTIONS:


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#2 - Number Lines (for practice problems, see SAT Math Tactics: Number Line videos)

Estimating unlabeled points

Operations with points

x - y =

|x| - |y|=

Finding the "jumps"

NOTES & QUESTIONS:


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#3 - Squares and Square Roots (for practice problems, see SAT Math Tactics: Radicals videos)

x =

x2=

y =

y2=

x =

x =

Inverse Operations

Squaring Fractions

Cubing Fractions and Beyond

Memorize the rules and/or reproduce them on demand.

NOTES & QUESTIONS:


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#4 - Fractions (for practice problems, see SAT Math Tactics: Fractions videos)

An elementary school topic....remember the properties...know how to work them by hand...don't

just rely on calculator...

Adding & Subtracting Fractions

Simplifying Fractions

Mixed Numbers & Improper Fractions


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Multiplying & Dividing Fractions

Nested Fractions

NOTES & QUESTIONS:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#5 - Reciprocals

Negative Reciprocal


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#6 - Decimals

Rounding

Adding & Subtracting Decimals

Multiplying & Dividing Decimals

Repeating Decimals & Grid-Ins

Scientific Notation

NOTES & QUESTIONS:


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#7 - Factors (for practice problems, see SAT Math Tactics: Factors videos)

Factor: number that divides into another number without remainder (a.k.a. equally)

Prime Factorization

Greatest Common Factor (GCF)

NOTES & QUESTIONS:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#8 - Remainders (for practice problems, see SAT Math Tactics: Remainder videos)

What's left over after you've divided as much as you can?


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#9 - Multiples (for practice problems, see SAT Math Tactics: Arithmetic videos)

Multiples of a number nare numbers that n is a factor of

orjust multiply your number nx 1, x 2, x 3, ...

Least Common Multiple (Denominator)

NOTES & QUESTIONS:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#10 - Prime Numbers (for practice problems, see SAT Math Tactics: Arithmetic videos)

Prime number: number that is divisible by one and itself ONLY

NOTES & QUESTIONS:


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#11 - Ratios and Proportions (for practice problems, see SAT Math Tactics: Ratio, Proportions videos)

Ratio: relative size of two quantities (their relationship)

Ratios vary by common multiples up and down, yielding...

Proportions:

100 tea bags contain 8 oz. of tea. How much do 3 bags of tea weigh?

Ratio Box

In science class, there are two boys for every five girls. If there are 35 total students in the class, how

many are boys?

Rates & Speed:

NOTES & QUESTIONS:


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#12 - Percents, Fractions, Decimals (for practice problems, see SAT Math Tactics: Percents, Fractions

videos)

Percent:out of 100

Percent Fraction Decimal

25%9/200

.45

Percent to Fraction

Percent to Decimal

Fraction to Percent

Fraction to Decimal

Decimal to Percent

Decimal to Fraction

Translating Words to Equations With Percents

What is 25% of 50?


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Translation rules:

What, a number (variable)

is, is equal to =

% decimal form

of multiply

32 is what percent of 96?

Real SAT Grid-in: If a + 2b is equal to 125% of 4b, what is a/b?

If 20% of m is 40, what is 15% of m?

For more example problems from real SATs, see SAT Math Tactics.

NOTES & QUESTIONS:


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#13 - Sequences (for practice problems, see SAT Math Tactics: Sequences videos)

Find the Rule & Extrapolate

Given the Rule, then Extrapolate

The first term of a sequence is 5. Each term after the first is three times the previous term. What is

the 4th term of this sequence?

Plenty of examples in SAT Math Tactics, including those questions that seem "impossible," e.g. ask

for the 122nd term.

NOTES & QUESTIONS:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#14 - Sets (for practice problems, see SAT Math Tactics: Sets videos)

Set: a collection of things; made up of members or elements


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Venn Diagrams

See SAT Math Tactics for example problems.

NOTES & QUESTIONS:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#15 - Counting Problems (for practice problems, see SAT Math Tactics: Counting Problems videos)

How many ways can we arrange things in orders or groups?

Ex.You have five shirts and four pairs of jeans. How many different outfits can you make?

Ex. Twelve ice skaters are competing in the final match. How many different ways could you award

gold, silver, and bronze medals to skaters in this group if you only have one of each medal?

Ex.There are ten dancers in your group. You need to arrange them into pairs for the competition.

How many different pairs of dancers could you create?


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#16 - Algebra Basics (for practice problems, see SAT Math Tactics: Algebra videos)

Adding/Subtracting v. Multiplying Dividing

Solving for x

Two rules:

1) Get x by itself

2) Whatever you do to one side, you must do to the other (can't target individual terms)

NOTES & QUESTIONS:


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#17 - Factoring Expressions (for practice problems, see SAT Math Tactics: Algebra videos)

1) Difference of two perfect squares

2) Finding common factors

3) FOIL

(x + y)2

(x - y)2

NOTES & QUESTIONS:


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#18 - Exponents & Exponent Rules (for practice problems, see SAT Math Tactics: Exponents videos)

Definitions

Exponent Rules

1)

2)

3)

NOTES & QUESTIONS:


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#19 - Exponent and Radical Equations (for practice problems, see SAT Math Tactics: Exponents,

Radicals videos)

Check out SAT Math Tactics: Exponents for actual problems.

NOTES & QUESTIONS:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#20 - Solving SAT Equations (for practice problems, see SAT Math Tactics: Algebra videos)

The SAT knows you will approach algebra problems like you were taught in high school algebra, so

sometimes you'll need to think outside the box.


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Solving for a variable in terms of another:

If 4x+2y = z, what is x in terms of y and z?

The best way to learn: real practice problems. See SAT Math Tactics: Algebra.

NOTES & QUESTIONS:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#21 - Absolute Value (for practice problems, see SAT Math Tactics: Absolute Value videos)

Definition:

Example:

NOTES & QUESTIONS:


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#22 - Translating Word Problems (for practice problems, see SAT Math Tactics: Algebra videos)

3 times the quantity (4x+6)

A number y decreased by 60

Five less than k

x less than y

20 divided by y, quotient

20 divided into a number n

is, is equal to, was, equals, has

more than, sum, greater than [five more than x]

less than, difference, fewer than [the difference of a and b]

of, product

NOTES & QUESTIONS:


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#23 - Inequalities (for practice problems, see SAT Math Tactics: Inequalities videos)

Definitions:

Examples:

NOTES & QUESTIONS:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#24 - Systems of Equations (for practice problems, see SAT Math Tactics: Algebra videos)

NOTES & QUESTIONS:


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#25 - Solving Quadratic Equations (for practice problems, see SAT Math Tactics: Parabolas videos)

No quadratic formula needed...just find the roots

Axis of Symmetry:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#26 - Rational Equations (for practice problems, see SAT Math Tactics: Algebra videos)

Polynomial in numerator and denominator...

NOTES & QUESTIONS:


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#27 - Direct and Inverse Variation (for practice problems, see SAT Math Tactics: Direct and Inverse

Variation videos)

Directly proportional...varies directly

A is directly proportional to B. If A = 10 when B = 2, then what does A equal when B is 6?

Inversely proportional...varies inversely

When x = 12, y = 10. If x varies inversely with y, what does y equal when x is 30?

NOTES & QUESTIONS:


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#28 - Functions (for practice problems, see SAT Math Tactics: Functions videos)

Input --> Output

SAT: Know when to look for input vs. output

Graphing Functions


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#29 - Symbolic Functions (for practice problems, see SAT Math Tactics: Symbolic Functions videos)

Input vs. Output

Let a$b = (a+b)/(a-b). What does 3$5 equal?

If a$3 = 3, what does a equal?

NOTES & QUESTIONS:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#30 - Transformations (for practice problems, see SAT Math Tactics: Transformations videos)

Function Notation


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Negatives

Absolute Value

NOTES & QUESTIONS:


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#31 - Geometry Basics

#32 - Angles (for practice problems, see SAT Math Tactics: Angles videos)

NOTES & QUESTIONS:


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#33 - Triangle Basics (for practice problems, see SAT Math Tactics: Triangles videos)

#34 - Special Triangles (for practice problems, see SAT Math Tactics: Triangles videos)

Pythagorean Triples

45-45-90

30-60-90


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#35 - Congruence & Similarity (for practice problems, see SAT Math Tactics: Similar Triangles videos)

Corresponding Sides & Angles: Two congruent triangles will have equivalent pairs of sides and

angles. (Fancy: Corresponding sides and angles occupy the same relative position.)

Similar Triangles:

#36 - Triangle Inequality (for practice problems, see SAT Math Tactics: Triangles, Miscellaneous videos)

NOTES & QUESTIONS:


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#37 - Quadrilaterals (for practice problems, see SAT Math Tactics: Area, Perimeter videos)

Angles in quadrilateral add to 360

Parallelogram: opposite sides are parallel and congruent; opposite angles are equal

Rectangle:

Square:

#38 - Area and Perimeter (for practice problems, see SAT Math Tactics: Area, Perimeter videos)

Perimeter: Sum of all sides

Area: Formulas at front of each math section


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#39 - Polygons (for practice problems, see SAT Math Tactics: Polygons videos)

Shapes with more than four sides:

5 - pentagon

6 - hexagon

8 - octagon

Regular polygon: equal sides and angles

Sum of Angles:

Measure of one angle in n-sided regular polygon:

NOTES & QUESTIONS:


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#40 - Circles (for practice problems, see SAT Math Tactics: Circles videos)

radius

diameter

circumference

area

arc

sector

central angle

tangent

NOTES & QUESTIONS


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#41 - Solid Geometry (for practice problems, see SAT Math Tactics: Solid Geometry videos)

Cube:

Rectangular solid/rectangular prism:

Cylinder:

Other Solids:

Surface area: sum of areas of faces

NOTES & QUESTIONS:


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#42 - Lines and Slopes (for practice problems, see SAT Math Tactics: Lines videos)

Slope:

"Rise over run"

Slope-intercept formula

Parallel lines: slopes of lines are equal

Perpendicular lines: slopes of lines are negative reciprocals

NOTES & QUESTIONS


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#43 - Miscellaneous Formulas

Midpoint formula:

Distance formula:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#44 - Geometric Transformations (for practice problems, see SAT Math Tactics: Spatial Reasoning,

Transformations videos)

Translation:

Dilation:

Rotation:

Reflection:

Symmetry:


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#45 - Charts & Graphs (for practice problems, see SAT Math Tactics: Charts & Graphs videos)

Pie chart/circle graph:

See Math Tactics!

Line graph:

Bar Graph:

Pictograph:

Table:

Scatterplots:


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#46 - Mean, Median, Mode (for practice problems, see SAT Math Tactics: Mean, Median, Mode videos)

Median: middle number of ordered list

Mode: number that appears the most

Average/Arithmetic mean:

See Math Tactics for arithmetic mean tricks, especially "finding the total"

NOTES & QUESTIONS:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#47 - Probability (for practice problems, see SAT Math Tactics: Probability videos)

Chance that some event will occur.


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#48 - Geometric Probability (for practice problems, see SAT Math Tactics: Miscellaneous videos)

Estimate:

NOTES & QUESTIONS:


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SAT Math TacticsCovers theAPPLICATION of SAT content to real SAT problems

Videos #1-7 are located on reasonprep.com for free. The rest of the videos, listed in this table of

contents, are in the Members Area. Learn more about the Members Area at reasonprep.com/enroll/

___ #1 Introduction

___ #2 Math Section Basics

___ #3 Pacing and Guessing

___ #4 Math Myths

___ #5 Core Strategy

___ #6 General Strategies

___ #7 How to Get an 800

___ALGEBRA

___ Solve the Equation

___ Substitutions

___ Test the Answers

___ Translate Words into Equation

___ Translate the Real into Equation___ Multiple Equations___ Stack Em___ Plug In

___ Shortcuts___ Cross Multiply___ Use the Rules___ Distributive Property___ Finding Constants

___ Equal Parts

___ FUNCTIONS

___ Input v. Output___ Tables___ Graphs___ Plug In Values___ Exponentials

___ Translation & Constants

___ Nested Functions

___ CHARTS & GRAPHS

___ Read Carefully!___ Fill in the Blanks___ Must Be True

___ Combined With Other Topics

___ARITHMETIC

___ Basic Operations___ Prime Numbers

___ Evens & Odds___ Ordering___ Must or Could Be True___ New Definitions___ Digits

___ Multiples

___ANGLES

___ The Angle Game___ Parallel Lines___ Triangles

___ Plugging In

___ LINES

___ Finding the Equatino___ Slope___ Rise Over Run

___ Parallel & Perpendicular

___ Best Fit Line

___TRIANGLES

___ Sides___ Using the Pythagorean Theorem___ Special Triangles___ Equilateral & Isosceles___ Overlapping Shapes


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___ CIRCLES

___ Get the Radius___ Circle Logics___ Circumference___ Overlapping Shapes___ Central Angles

___ Area

___ SEQUENCES

___ Find the Rule___ Using Expressions

___ Extrapolate

___ EXPONENTS

___ Know the Rules___ Fractional and Negative Exponents___ Exponent Equations

___ MEAN, MEDIAN, MODE

___ Find the Total___ Plug In Values___ Test the Answers

___ Understand the Median

___AREA

___ Use the Equation___ Divide Figures Into Shapes___ Use Triangles___ Shaded Area

___ Properties of Squares

___ PERCENTS

___ Translate Into Equation___ Circle Graphs

___ INEQUALITIES

___ Test Different Values___ Create Inequalities

___ LOGIC

___ Brainteaser Problems___ Must/Could Be True

___ FRACTIONS

___ Know Fraction Properties___ Basic Operations___ Translate Into Equation

___ COUNTING PROBLEMS

___ Use the Lines Method___ Do Restrictions First___ Brute Force

___ Eliminate Extra Pairs

___ Be Systematic

___ SOLID GEOMETRY

___ Volume

___ CubesFind Edges___ Enclosed Shapes

___ Use Triangles

___ Sketch the Problem

___ Surface Area___ Cylinders

___ Other Solids

___ PARABOLAS

___ Understanding Roots

___ Symmetry

___ PERIMETER

___ SETS

___ Union and Intersection___ Venn Diagrams

___ SYMBOLIC FUNCTIONS


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___ NUMBER LINE

___ Interpolate Values

___ Absolute Value

___ Getting the Tick Marks

___ With Exponents

___ABSOLUTE VALUE

___ Inequalities

___ Coordinate Geometry

___ Equations & Ranges

___ PROBABILITY

___ COORDINATE GEOMETRY

___ Strategies___ Midpoints

___ SPATIAL REASONING

___ Strategies

___ Move Around Shapes

___ RATIO

___ Strategies

___ Geometric Ratios

___ LINE SEGMENTS

___ Strategies

___ Logics

___ PROPORTIONS

___TRANSFORMATIONS

___ Strategies

___ Geometric Transformations

___ RADICALS

___ POLYGONS

___ REMAINDER

___ DIRECT & INDIRECT VARIATION

___ FACTORS

___ SIMILAR TRIANGLES

___ SCIENTIFIC NOTATION

___ MISCELLANEOUS

___ Geometric Probability

___ Percent Change

___ Triangle Inequality___ Tangents


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#1 - Introduction, SAT Math Tactics

In this video:

What does SAT Math Tactics cover?

How to use the videos

How to practice

SAT Math Bootcamp: ________________________________

SAT Math Tactics: __________________________________

SAT Math Tactics videos are:

in order of importance

dedicated to one topic, but can cover multiple topics

intended to teach you problem solving FLEXIBILITY

How to Use the Videos

1. Download the SAT Math Study Guide & 4 Practice Tests

2. Watch the videos & take notes

3.

Do practice problems before I do

4. Rewatch videos as necessary

How to Practice (see my video on Youtube titled: "Don't Take Practice SATs"

1. Untimed questions

2.

Untimed sections

3. Timed sections

4. Full tests

When practicing, make sure you:

check answers and make sure you go over ALL questions

find different ways to solve questions you got right

figure out what went wrong on incorrect questions

struggle with problems that you got wrong or omitted

ask me for further help when necessary


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#2 - Math Section Basics, SAT Math Tactics

_______ Sections

_______ Q ________ minutes

_______ Q ________ minutes

_______ Q ________ minutes

How the Math Section is Scored:

Right ______ Omit ______ Wrong ______


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Order of Difficulty:


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Section Instructions:

Other More or Less Important Math Formulas:


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#3 - Pacing and Guessing, SAT Math Tactics

Your most limited resource: ___________________________

How many questions should I do?

600: _________________________________________________

>700: _________________________________________________

Omitting vs. Guessing


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#4 - SAT Math Myths, SAT Math Tactics

Myth #1: The SAT tests advanced math.

Myth #2: SAT solutions are complicated.

Myth #3: The SAT is like a high school math test.

Myth #4: If you know all the math content, you'll get an 800.

Myth #5: SAT math is just math.


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#5 - Core Strategy, SAT Math Tactics

Approach SAT math problems as "puzzles" or "brainteasers."

1. Read each question piece by piece.

2. Stop and write down/sketch out each piece of information.

3. Circle what the problem is asking for.

4. Solve the problem; seek the 30 Second Solution.

5. If you get stuck, reread the question.

6. Keep moving - mark questions and return later.

7. If time permits, review your answers.


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#6 - General Strategies, SAT Math Tactics

1. Break questions into pieces - whole questions are indigestible!

2. Think with your pencil - write everything down & draw, draw, draw.

3. Don't do everything in your head.

4. Use all the information given.

5. Take advantage of multiple choice - test the answers.

6. "Figure not drawn to scale" and "it cannot be determined from the information given"...

7. Eliminate choices when you can and guess if necessary.

8. Use your calculator effectively.

9. Use brute force when necessary!

10. Don't get bogged down - keep moving. Mark problems for future review.

11. Is your answer reasonable?

12. Be systematic with I, II, III problems.

13. Pay attention to "must be true" and "could be true."

14. If the answer choices contain variables, plug in your own numbers.

#7 - How to Get an 800, SAT Math Tactics

1. Master all content.

2. Practice - get in your repetitions, especially hard questions.

3. Flexibility - practice multiple ways of answering Qs

4. Check your work as you go - constantly review & revise

5. Most important: use time at the end of each section to check answers.


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Congrats on making it to the end of the study guide! There are hundreds more SAT Math

Tactics videos and practice problems waiting for you in the Members Area of Reason Prep.

To find out more about the Members Area, go to reasonprep.com/enroll/

ultimate sat math study guide

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