ultimate sat math study guide
TRANSCRIPT
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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/