Download SAT Math

SAT Math Tips
Types of Math Questions:
 Multiple Choice (A, B, C, D, or E)
o A wrong answer to a multiple-choice question costs you 1 of the value of the
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question, so 4 wrong answers cancel out one right answer.

Student-Produced Response (grid-in)
o The answer in the boxes will NOT be scored. Only the answer marked in the
ovals in the grid will be scored.
o Fractions do not need to be reduced unless they do not fit in the grid.
o You cannot grid in a mixed number. Use improper fractions. For example grid in
5 ½ as 11/2 or 5.5.
o For repeating decimals, enter the most accurate value the grid will accommodate.
For example, grid in 0.6666… as .666 or .667, not .66 or .67.
o Do not grid in a leading zero for a decimal that is less than 1. Grid in .5, not 0.5.
o No question has a negative answer.
o If the answer is a percent, disregard the % symbol.
o There is no penalty for a wrong answer to a student-produced response
question. Attempt to answer all student-produced response questions.
Math Sections:
Section
1
2
3
Number and Type of Questions
20 Multiple Choice
8 Multiple Choice and 10 Student-Produced Response (grid-in)
16 Multiple Choice
Total number of questions: 54
Total time: 70 min
Range of scores in Math: 200 to 800
Note: Sections 1 & 2 may be reversed.
Time Allowed
25 min
25 min
20 min
Math Categories:
 Arithmetic – Numbers and Operations (20%)
 Algebra and Functions (35-40%)
 Geometry and Measurement (25-30%)
 Number Patterns, Probability, Statistics, and Data Analysis (10-15%)
Note: The math covers Algebra I, Algebra II, and Geometry.
You only have a little bit over a minute per math question. The
questions are in the order of easy, medium, and hard. Do not attempt
the last 2-3 questions in a math section unless you are absolutely
certain of the answer.
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SAT Math Tips
Math Test-Taking Strategies
General Strategies
1. Take a calculator with good batteries in it with you and know how to use your calculator.
2. Become familiar with the directions ahead of time.
3. Pace yourself. Have a watch with you to help monitor your time.
4. Practice everyday.
5. Keep track of your place on the answer sheet.
6. Do not assume that your answer is correct just because it appears among the choices.
7. Remember that all correct answers are equal in point value.
8. Be aware that incorrect answers are not equal in point value. A wrong answer to a multiplechoice question costs you 1 of the value of the question, so 4 wrong answers cancel out one
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right answer.
9. Do not engage in wild guessing.
Specific Strategies
1. Sub-in.
2. Backfill.
3. Always scan answers.
4. Do not waste time doing complex arithmetic or lengthy algebraic solutions.
5. Fill in what is known to help you find what is unknown.
6. Recognize “Figure not drawn to scale” as a warning.
7. Test the extremes.
8. Find a pattern.
9. Do not be misled by generic answers.
a. “None of the above”
b. “It cannot be determined from the information given”
c. All of the above”
10. Do the math.
Multiple-Choice Questions
As you work through the multiple-choice math questions, you'll be given reference information
(formulas and facts), but you'll need to know how to use them. You're allowed to use a calculator,
but it won't help you unless you know how to approach the problems. If you're stuck, try
substituting numbers for variables. You can also try plugging in numbers from the answer choices.
Start with the middle number. That way, if it doesn't work, you can strategically choose one that's
higher or lower.
Grid-Ins
These questions are not multiple-choice - you come up with an answer and fill it into a grid. The grid
does not contain a minus sign, so there is no way to indicate that a value is less than zero. That
means that an answer can't be a negative number. Unlike the multiple-choice questions, you won't
be penalized for wrong answers, so make your best guess even if you're not sure. You can't
grid mixed numbers, so if you get a mixed number as an answer, you'll have to convert it to an
improper fraction or a decimal.
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SAT Math Tips
Reference Information
This is the reference information that you are
given at the beginning of each math section. Use
it when you need it. Familiarize yourself with it
ahead of time.
c
2x
60
b
45
x
s
r
30
x 3
a
c2  a 2  b2
s 2
45
s
A  r 2
C  2r
Special Right Triangles
l
r
w
h
h
w
b
A  lw
A
h
l
1
bh
2
V  lwh
V  r 2 h
 The measure of a straight angle is 180 .
 The sum of the measures of the interior angles
in a triangle is 180 .
 The total number of degrees in a circle is 360 .
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SAT Math Tips
Arithmetic
You will have problems on the following arithmetic areas:
1. Integers (Basic Integer Operations, Exponents and Roots, Missing-Digit Questions,
and Word Problems)
2. Number Theory (Odd and Even Integers, Positive and Negative Integers,
Consecutive Integers, Prime Numbers, Multiples, Factors, and Divisibility)
3. Fractions; Decimals; Percents (Basic Operations: Fractions, Fraction Word
Problems, Decimals, Percents, Percent Word Problems)
4. Ratio; Proportion; Rate (Ratio and Proportion, Rate, Measurements)
5. Number Lines
6. Sets, Set Notation, Unions, and Intersections
7. Mixed Word Problems (Business, Logic, and Motion)
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1
1
x
x2
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1
1
x
x3
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Common Squares and Square Roots
2 3 4 5
6
7
8
9 10
11
12
15
20
25
30
4 9 16 25 36 49 64 81 100 121 144 225 400 625 900
Common Cubes and Cube Roots
2 3
4
5
8 27 64 125
Ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9
Consecutive Integers: n, n  1, n  2, n  3,...
Consecutive Odd/Even Integers: n, n  2, n  4, n  6,...
Prime Numbers - numbers divisible by 1 and itself; Examples: 2, 3, 5, 7, 11,
13, 17, 19, 23, …
Composite Numbers – whole numbers greater than 1 that are not prime
numbers; a factor tree can be used to factor a composite number into
primes
Percent Increase/Decrease: the difference__
the original amount
The intersection of two sets consists of the elements they have in common.
The symbol is  .
The union of two sets consists of all the elements of both sets with no
common elements listed more than once. The symbol is  .
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SAT Math Tips
Algebra and Functions
You will have problems on the following algebra areas:
1. Algebraic Expressions (Simplifying and Evaluating Algebraic Expressions,
Exponents and Roots)
2. Equations (Solving Linear Equations, Solving an Equation with Several Variables,
Systems of Equations: Linear and Nonlinear Systems, Absolute Value Equations,
Quadratics (Factor/FOIL), Rational Expressions and Equations, Radical Equations,
and Inequalities: Linear, Absolute Value, Radical, and Rational)
3. Word Problems (Translating Words into Algebra, Word Problems with Numerical
Solutions, Direct and Inverse Variations, Word Problems with Literal Solutions)
4. Functions (Function Notation and Evaluation)
5. Parabolas and Graphic Behavior (Quadratic Function, Vertex, Axis of Symmetry,
Direction of Opening, Domain, Range, Transformations, Finding
Zeros/Solutions/Roots/X-intercepts by Factoring, Quadratic Formula and
Discriminant, Graphing (Calculate Zero or Intersection))

Exponent Rules:
Operation
Rule
a a  a m n
am
 a m n
n
a
Multiplication
m n
Division
ca h a
m n
Power to a Power

1
an
Negative Exponent
a n 
Zero Exponent
babcg 1
0
1
Fractional Power

mn
m
a n  n a or a n 
da i
n
m
Solve systems of equations by graphing (calculate the intersection), substitution,
elimination, or using matrices (matrix equation or augmented matrix (RREF))
You can solve equations using a graph by typing in the left side as Y1 and the right side as
Y2 , then calculate the intersection.

Quadratics
o Use FOIL (first, outer, inner, last) to multiply binomials
o Use the distributive property for all other polynomial products
o Quadratics often seen on the SAT are

ba  bg ba  bgba  bg a
ba  bg ba  bgba  bg a
ba  bgba  bg a  b
2
2
 2ab  b 2
2
2
 2ab  b 2
2
2
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SAT Math Tips
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The domain of a function is the set all possible x-values.
The range of a function is the set of possible y-values.
Review transformations: translations, reflections, and dilations (stretches
and compressions)
Review quadratic equations: graphing, axis of symmetry, and vertex
Finding roots of Quadratic Equations
o Graphing – look for x-intercepts
o Factoring and Zero-Product Property
b  b 2  4ac
o Quadratic Formula x 
2a
2
o Discriminant, b  4ac , tells you the nature and number of roots
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SAT Math Tips
Geometry
Formulas/Properties
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Complementary angles have a sum of 90 .
Supplementary angles have a sum of 180 .
Review parallel lines: corresponding angles, alternate interior angles,
alternate exterior angles, same-side inter angles, vertical angles
Review triangles: interior angles, largest angle is opposite the longest side,
smallest angle is opposite the shortest side, exterior angle equals the sum of
the measures of the two nonadjacent angles
The sum of any two sides of a triangle must be greater than the third side.
The difference of any two sides of a triangle is less than the third side.
Pythagorean Triples you should know are
o 3, 4, 5
5, 12, 13
7, 24, 25
8, 15, 17
Review the special right triangles: 45-45-90 and 30-60-90
Right Triangle Trigonometry (SOHCAHTOA)
Opp
Adj
Opp
o Sin 
Cos 
Tan 
Hyp
Hyp
Adj
sin A
sin B
cos A  sin B tan A 
tan B 
o sin A  cos B
cos A
cos B
Draw a diagram to fit the facts of the problem if a diagram has not been
given.
Examine the diagram for clues. Fill in any additional information you can
determine.
Draw additional lines or circles if needed.
Use formulas and relationships wherever necessary.
Review Similarity (setting up proportions)
y  y1
Slope = 2
x2  x1
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SAT Math Tips
Number Patterns, Probability, Statistics, and Data Analysis
You will have problems on the following areas:
1. Special Symbols – a rule is usually given using variables, and you are
asked to apply the rule to numbers.
a. Example 1 p = 2p when p is odd
p = 3p when p is even
Find 3 + 4 x 2 .
= 6 + 12 x 6 = 78
b. Example 2
b g
For all number x and y, let x Φ y = x  y . What is
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the value of 2 Φ 3?
b g
2 Φ 3 = 2  3  52  25
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2. Pattern Recognition – to determine the next term in a sequence, you
need to find the rule.
a. Arithmetic Sequences: an  a1  (n  1)d where a n is the nth term,
a1 is the 1st term and d is the constant difference
Example: 3, 7, 11, 15, 19
b. Geometric Sequences: an  a1r n 1 where a n is the nth term, a1 is the
1st term and r is the constant ratio
Example
48, 24, 12, 6, 3
c. Exponential Growth and Decay
b g
i. Growth (appreciates)
A  P 1  r where A is the final
amount, P is the initial amount, r is the rate (convert % to a
decimal), and t is the time
t
ii. Decay (depreciates)
A  P 1 r
t
b g
d. Compound Interest
rI
F
G
H nJ
K
i. N times per year: A  P 1 
nt
ii. Continuously: A  Pert
3. Probability
4. Data Analysis
a. Average (Mean), Median, and Mode
b. Bar Graphs, Charts, Pie Graphs, Line Graphs, and Scatter-plots
(Line of best fit)
c. Data Charts and Matrices
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