SAT Math Tips

Types of Math Questions: . Multiple Choice (A, B, C, D, or E) 1 o A wrong answer to a multiple-choice question costs you of the value of the 4 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 20 Multiple Choice 25 min 2 8 Multiple Choice and 10 Student-Produced Response (grid-in) 25 min 3 16 Multiple Choice 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.

1 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 multiple- 1 choice question costs you of the value of the question, so 4 wrong answers cancel out one 4 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

2 SAT Math Tips 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. 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 45 s 2

b x s r 30 45 a x 3 s 2 2 2 2 c  a  b Special Right Triangles A  r C  2r

l r w h h

w h b l 1 A  lw A  bh V  lwh V  r 2h 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 .

3 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)

 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 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  .

4 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 Multiplication aman  amn am Division  amn an m n mn Power to a Power ca h a

n 1 Negative Exponent a  an 0 Zero Exponent babcg 1 m 1 m or n n Fractional Power a n  n a a  da i  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

5 SAT Math Tips

ba  bg2  ba  bgba  bg a2  2ab  b2 . ba  bg2  ba  bgba  bg a2  2ab  b2 ba  bgba  bg a2  b2  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  b2  4ac o Quadratic Formula x  2a o Discriminant, b2  4ac , tells you the nature and number of roots

6 SAT Math Tips

Geometry

Formulas/Properties  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 o sin A  cosB cosA  sin B tan A  tan 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)

y2  y1  Slope = x2  x1

7 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

2 b. Example 2 For all number x and y, let x Φ y =bx  yg. What is the value of 2 Φ 3? 2 2 Φ 3 = b2  3g 52  25

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 an is the nth term, st a1 is the 1 term and d is the constant difference Example: 3, 7, 11, 15, 19 n1 b. Geometric Sequences: an  a1r 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 t i. Growth (appreciates) A  Pb1 rg 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  Pb1 rg d. Compound Interest F r Int i. N times per year: A  PG1 J H nK ii. Continuously: A  Pert 3. Probability 4. Data Analysis a. Average (Mean), Median, and Mode

8 SAT Math Tips b. Bar Graphs, Charts, Pie Graphs, Line Graphs, and Scatter-plots (Line of best fit) c. Data Charts and Matrices

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