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The sat math section

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5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 147 – THE SAT MATH SECTION – math section on a past SAT. The distribution of P art 1: Five-Choice Questions questions on your test will vary. 1. 1 8. 2 15. 3 22. 3 The ﬁve-choice questions in the Math section of the 2. 1 9. 3 16. 5 23. 5 SAT will comprise about 80% of your total math score. 3. 1 10. 2 17. 4 24. 5 Five-choice questions test your mathematical reason- 4. 1 11. 3 18. 4 25. 5 ing skills. This means that you will be required to apply 5. 2 12. 3 19. 4 several basic math techniques for each problem. In the 6. 2 13. 3 20. 4 math sections, the problems will be easy at the begin- 7. 1 14. 3 21. 4 ning and will become increasingly difficult as you From this list, you can see how important it is progress. Here are some helpful strategies to help you to complete the ﬁrst ﬁfteen questions before get- improve your math score on the ﬁve-choice questions: ting bogged down in the complex problems that follow. After you are satisﬁed with the ﬁrst ﬁfteen Read the questions carefully and know the ■ questions, skip around the last ten, spending the answer being sought. In many problems, you will most time on the problems you ﬁnd to be easier. be asked to solve an equation and then perform Don’t be afraid to write in your test booklet. an operation with that variable to get an answer. ■ That is what it is for. Mark each question that In this situation, it is easy to solve the equation you don’t answer so that you can easily go back to and feel like you have the answer. Paying special it later. This is a simple strategy that can make a attention to what each question is asking, and lot of difference. It is also helpful to cross out the then double-checking that your solution answers answer choices that you have eliminated. the question, is an important technique for per- Sometimes, it may be best to substitute in an forming well on the SAT. ■ answer. Many times it is quicker to pick an If you do not ﬁnd a solution after 30 seconds, ■ answer and check to see if it is a solution. When move on. You will be given 25 minutes to answer you do this, use the c response. It will be the mid- questions for two of the Math sections, and 20 dle number and you can adjust the outcome to minutes to answer questions in the other section. the problem as needed by choosing b or d next, In all, you will be answering 54 questions in 70 depending on whether you need a larger or minutes! That means you have slightly more than smaller answer. This is also a good strategy when one minute per problem. Your time allotted per you are unfamiliar with the information the question decreases once you realize that you will problem is asking. want some time for checking your answers and When solving word problems, look at each extra time for working on the more difﬁcult prob- ■ phrase individually and write it in math lan- lems. The SAT is designed to be too complex to ﬁn- guage. This is very similar to creating and assign- ish. Therefore, do not waste time on a difﬁcult ing variables, as addressed earlier in the word problem until you have completed the problems problem section. In addition to identifying what you know how to do. The SAT Math problems can is known and unknown, also take time to trans- be rated from 1–5 in levels of difﬁculty, with 1 late operation words into the actual symbols. It is being the easiest and 5 being the most difﬁcult. The best when working with a word problem to repre- following is an example of how questions of vary- sent every part of it, phrase by phrase, in mathe- ing difﬁculty have been distributed throughout a matical language. 147
5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 148 – THE SAT MATH SECTION – Make sure all the units are equal before you cepts, not calculations. If you ﬁnd yourself doing ■ begin. This will save a great deal of time doing a very complex, lengthy calculation—stop! Either conversions. This is a very effective way to save you are not doing the problem correctly or you time. Almost all conversions are easier to make at are missing a much easier way. Use your calcula- the beginning of a problem rather than at the tor sparingly. It will not help you much on this end. Sometimes, a person can get so excited about test. getting an answer that he or she forgets to make Be careful when solving Roman numeral prob- ■ the conversion at all, resulting in an incorrect lems. Roman numeral problems will give you answer. Making the conversion at the start of the several answer possibilities that list a few different problem is deﬁnitely more advantageous for this combinations of solutions. You will have ﬁve reason. options: a, b, c, d, and e. To solve a Roman Draw pictures when solving word problems if numeral problem, treat each Roman numeral as ■ needed. Pictures are always helpful when a word a true or false statement. Mark each Roman problem doesn’t have one, especially when the numeral with a “T” or “F,” then select the answer problem is dealing with a geometric ﬁgure or that matches your “Ts” and “Fs.” location. Many students are also better at solving problems when they see a visual representation. These strategies will help you to do well on the Do not make the drawings too elaborate; unfor- ﬁve-choice questions, but simply reading them will tunately, the SAT does not give points for artistic not. You must practice, practice, and practice. That is ﬂair. A simple drawing, labeled correctly, is usu- why there are 40 problems for you to solve in the next ally all it takes. section. Keep in mind that on the SAT, you will have Avoid lengthy calculations. It is seldom, if ever, fewer questions at a time. By doing 40 problems now, ■ necessary to spend a great deal of time doing cal- it will seem easy to do smaller sets on the SAT. Good culations. The SAT is a test of mathematical con- luck! 148
5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 149 – THE SAT MATH SECTION – 4 0 Practice Five-Choice Questions All numbers in the problems are real numbers. ■ You may use a calculator. ■ Figures that accompany questions are intended to provide information useful in answering the questions. ■ Unless otherwise indicated, all ﬁgures lie in a plane. Unless a note states that a ﬁgure is drawn to scale, you should NOT solve these problems by estimating or by measurement, but by using your knowledge of mathematics. Solve each problem. Then, decide which of the answer choices is best, and ﬁll in the corresponding oval on the answer sheet below. ANSWER SHEET 1. a b c d e 16. a b c d e 31. a b c d e 2. a b c d e 17. a b c d e 32. a b c d e 3. a b c d e 18. a b c d e 33. a b c d e 4. a b c d e 19. a b c d e 34. a b c d e 5. a b c d e 20. a b c d e 35. a b c d e 6. a b c d e 21. a b c d e 36. a b c d e 7. a b c d e 22. a b c d e 37. a b c d e 8. a b c d e 23. a b c d e 38. a b c d e 9. a b c d e 24. a b c d e 39. a b c d e 10. a b c d e 25. a b c d e 40. a b c d e 11. a b c d e 26. a b c d e 12. a b c d e 27. a b c d e 13. a b c d e 28. a b c d e 14. a b c d e 29. a b c d e 15. a b c d e 30. a b c d e 149
5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 150
5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 151 – THE SAT MATH SECTION – REFERENCE SHEET • The sum of the interior angles of a triangle is 180˚. • The measure of a straight angle is 180˚. • There are 360 degrees of arc in a circle. 60˚ 45˚ 2x 2s x s h 30˚ 45˚ b ¯¯¯¯¯ s 3x A = 1 bh Special Right Triangles 2 l r h r w h w l A = πr2 V = πr2h V = lwh A = lw C = 2πr 3. In right triangle ABC, m∠C = 3y – 10, m∠B = y 1. Three times as many robins as cardinals visited a + 40, and m∠A = 90. What type of right triangle bird feeder. If a total of 20 robins and cardinals visited the feeder, how many were robins? is triangle ABC? a. 5 a. scalene b. 10 b. isosceles c. 15 c. equilateral d. 20 d. obtuse e. 25 e. obscure 2. One of the factors of 4x2 – 9 is 4. If x > 0, what is the expression ( x)( 2x) a. (x + 3). equivalent to? b. (2x + 3). a. 2x c. (4x – 3). b. 2x c. x2 2 d. (x – 3). e. (3x + 5). d. x 2 e. x – 2 151
5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 152 – THE SAT MATH SECTION – 5. At a school fair, the spinner represented in the 8. Given the statement: “If two sides of a triangle accompanying diagram is spun twice. are congruent, then the angles opposite these sides are congruent.” Given the converse of the statement: “If two R G angles of a triangle are congruent, then the sides opposite these angles are congruent.” B What is true about this statement and its What is the probability that it will land in section converse? G the ﬁrst time and then in section B the second a. Both the statement and its converse are true. time? b. Neither the statement nor its converse is true. c. The statement is true, but its converse is false. 1 a. 2 d. The statement is false, but its converse is true. 1 b. e. There is not enough information given to 4 1 determine an answer. c. 8 1 d. 16 9. Which equation could represent the relationship 3 e. between the x and y values shown below? 8 x y 6. If a and b are integers, which equation is always 0 2 true? 1 3 a b a. b = a 2 6 b. a + 2b = b + 2a 3 11 c. a – b = b – a 4 18 d. a + b = b + a e. a – b a. y = x + 2 b. y = x2 + 2 x2 + 2x 7. If x ≠ 0, the expression is equivalent to c. y = x2 x a. x + 2. d. y = 2x b. 2. e. y2 c. 3x. d. 4. 10. If bx – 2 = K, then x equals K e. 5. a. b + 2. K–2 b. b. 2–K c. b. K+2 d. b. e. k – 2. 152

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