SAT Math Tips

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Types of Math Questions: § Multiple Choice (A, B, C, D, or E)

o A wrong answer to a multiple-choice question costs you 14

of the value of the

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 Number and Type of Questions Time Allowed 1 2 3

20 Multiple Choice 8 Multiple Choice and 10 Student-Produced Response (grid-in) 16 Multiple Choice

25 min 25 min

20 min Total number of questions: 54

Total time: 70 min Range of scores in Math: 200 to 800

Note: Sections 1 & 2 may be reversed. 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.

SAT Math Tips

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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

multiple-choice question costs you 14

of the value of the question, so 4 wrong answers

cancel out one 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.

SAT Math Tips

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Formulas & 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° 45° s 2 r b x s a 30° 45°

c a b2 2 2= + x 3 s A r= π 2 Special Right Triangles C r= 2π l r w h h

w h b l

A lw= A bh=12 V lwh= V r h= π 2

§ 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° .

Below are additional facts that you should know, which are not provided on the test.

Standard Symbols

= means “is equal to” < means “is less than” < means “is less than or equal to”

≠means “is not equal to” > means “is greater than” > means “is greater than or equal to”

⊥means “is perpendicular to” || means “is parallel to” |n| means “absolute value of n” ~ means “is similar to” ≅ means “congruent to”

Formulas Distance = Rate x Time Interest = Principal x Rate x Time

Average = Sum of all the parts__ Total number of parts

SAT Math Tips

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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) • Common Squares and Square Roots

x 1 2 3 4 5 6 7 8 9 10 11 12 15 20 25 30 x2 1 4 9 16 25 36 49 64 81 100 121 144 225 400 625 900

• Common Cubes and Cube Roots

x 1 2 3 4 5 x3 1 8 27 64 125

• Ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 • Consecutive Integers: n n n n, , , ,...+ + +1 2 3 • Consecutive Odd/Even Integers: n n n n, , , ,...+ + +2 4 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 ∪ .

SAT Math Tips

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Algebra and Functions

You will have problems on the following algebraic 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) • Algebraic Relationships

o Distributive Law: a(x + y) = ax + ay a(x – y) = ax – ay

o Exponents: a a am n m n= + aa

am

nm n= − a am n mnc h= a

an

n− =

1

abcb g0 1= a an n1= a a

mn n

m=d i

o Radicals: a b ab× = xy

xy

=

• Solve systems of equations by graphing (calculate the intersection), substitution, elimination, or using matrices (matrix equation or augmented matrix (RREF))

• You can solve several equations using a graph by typing in the left side as Y1 and the right side asY2 , and 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

§ a b a b a b a ab b

a b a b a b a ab b

a b a b a b

+ = + + = + +

− = − − = − +

+ − = −

b g b gb gb g b gb gb gb g

2 2 2

2 2 2

2 2

2

2

• The domain of a function is the set all possible x-values. • The range of a function is the set of possible y-values.

SAT Math Tips

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Geometry You will have problems on the following geometrical areas:

1. Angles and Lines 2. Figures (Triangles, Special Right Triangles, Right Triangle Trigonometry,

Polygons, and Circles and Tangent Lines) 3. Perimeter; Area; Volume 4. Coordinate Geometry (Points and Lines and Slopes) 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))

Formulas/Properties

• Complementary angles = 90° and Supplementary angles =180° . • Review parallel lines: corresponding angles, alternate interior angles,

alternate exterior angles, same-side interior 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: 3, 4, 5 5, 12, 13 7, 24, 25 8, 15, 17 B • Review the special right triangles: 45 45 90°− °− °and 30 60 90°− °− °

o Right Triangle Trigonometry (SOHCAHTOA) c a o Sin Opp

Hyp= Cos Adj

Hyp= Tan Opp

Adj=

o sin cos∠ = ∠A B cos sin∠ = ∠A B A b C o tan sin

cos∠ =

∠

∠A A

A tan sin

cos∠ =

∠

∠B B

B

• Draw a diagram to fit the facts of the problem if one 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 and solving proportions) • Review Lines: Slope, m = y y

x x2 1

2 1

−

−; y = mx + b; vertical, horizontal, parallel,

and perpendicular

SAT Math Tips

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• Midpoint = x x y y1 2 1 2

2 2+ +FHG IKJ, ; Distance = x x y y2 1

22 1

2− + −b g b g

• Review transformations: translations, reflections, and dilations (stretches and compressions)

• Review quadratic equations: graphing, axis of symmetry, and vertex • Review finding roots (or zeros) of Quadratic Equations

o Graphing – look for x-intercepts o Factoring and Zero-Product Property

o Quadratic Formula x b b aca

=− ± −2 4

2

o Discriminant, b ac2 4− , tells you the nature and number of roots

SAT Math Tips

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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 For all number x and y, let x Φ y = x y+b g2 . What is the value of 2 Φ 3?

2 Φ 3 = 2 3 52 2+ = =b g 25

2. Pattern Recognition – to determine the next term in a sequence, you need to find the rule.

a. Arithmetic Sequences: a a n dn = + −1 1( ) where an is the nth term, a1 is the 1st term and d is the constant difference

Example: 3, 7, 11, 15, 19 b. Geometric Sequences: a a rn

n= −1

1 where an 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

i. Growth (appreciates) A P r t= +1b g where A is the final

amount, P is the initial amount, r is the rate (convert % to a decimal), and t is the time

ii. Decay (depreciates) A P r t= −1b g

d. Compound Interest

i. N times per year: A P rn

nt

= +FHG IKJ1

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