Part 1: Five-Choice Questions The five-choice questions in the Math section of the SAT will comprise about 80% of your total math score. Five-choice questions test your mathematical reason- ing skills. This means that you will be required to apply several basic math techniques for each problem. In the math sections, the problems will be easy at the begin- ning and will become increasingly difficult as you progress. Here are some helpful strategies to help you improve your math score on the five-choice questions: ■ Read the questions carefully and know the answer being sought. In many problems, you will be asked to solve an equation and then perform an operation with that variable to get an answer. In this situation, it is easy to solve the equation and feel like you have the answer. Paying special attention to what each question is asking, and then double-checking that your solution answers the question, is an important technique for per- forming well on the SAT. ■ If you do not find a solution after 30 seconds, move on. You will be given 25 minutes to answer questions for two of the Math sections, and 20 minutes to answer questions in the other section. In all, you will be answering 54 questions in 70 minutes! That means you have slightly more than one minute per problem. Your time allotted per question decreases once you realize that you will want some time for checking your answers and extra time for working on the more difficult prob- lems. The SAT is designed to be too complex to fin- ish. Therefore, do not waste time on a difficult problem until you have completed the problems you know how to do. The SAT Math problems can be rated from 1–5 in levels of difficulty, with 1 being the easiest and 5 being the most difficult. The following is an example of how questions of vary- ing difficulty have been distributed throughout a math section on a past SAT. The distribution of questions on your test will vary. 1. 1 8. 2 15. 3 22. 3 2. 1 9. 3 16. 5 23. 5 3. 1 10. 2 17. 4 24. 5 4. 1 11. 3 18. 4 25. 5 5. 2 12. 3 19. 4 6. 2 13. 3 20. 4 7. 1 14. 3 21. 4 From this list, you can see how important it is to complete the first fifteen questions before get- ting bogged down in the complex problems that follow. After you are satisfied with the first fifteen questions, skip around the last ten, spending the most time on the problems you find to be easier. ■ Don’t be afraid to write in your test booklet. That is what it is for. Mark each question that you don’t answer so that you can easily go back to it later. This is a simple strategy that can make a lot of difference. It is also helpful to cross out the answer choices that you have eliminated. ■ Sometimes, it may be best to substitute in an answer. Many times it is quicker to pick an answer and check to see if it is a solution. When you do this, use the c response. It will be the mid- dle number and you can adjust the outcome to the problem as needed by choosing b or d next, depending on whether you need a larger or smaller answer. This is also a good strategy when you are unfamiliar with the information the problem is asking. ■ When solving word problems, look at each phrase individually and write it in math lan- guage. This is very similar to creating and assign- ing variables, as addressed earlier in the word problem section. In addition to identifying what is known and unknown, also take time to trans- late operation words into the actual symbols. It is best when working with a word problem to repre- sent every part of it, phrase by phrase, in mathe- matical language. –THE SAT MATH SECTION– 147 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 147 ■ Make sure all the units are equal before you begin. This will save a great deal of time doing conversions. This is a very effective way to save time. Almost all conversions are easier to make at the beginning of a problem rather than at the end. Sometimes, a person can get so excited about getting an answer that he or she forgets to make the conversion at all, resulting in an incorrect answer. Making the conversion at the start of the problem is definitely more advantageous for this reason. ■ Draw pictures when solving word problems if needed. Pictures are always helpful when a word problem doesn’t have one, especially when the problem is dealing with a geometric figure or location. Many students are also better at solving problems when they see a visual representation. Do not make the drawings too elaborate; unfor- tunately, the SAT does not give points for artistic flair. A simple drawing, labeled correctly, is usu- ally all it takes. ■ Avoid lengthy calculations. It is seldom, if ever, necessary to spend a great deal of time doing cal- culations. The SAT is a test of mathematical con- cepts, not calculations. If you find yourself doing a very complex, lengthy calculation—stop! Either you are not doing the problem correctly or you are missing a much easier way. Use your calcula- tor sparingly. It will not help you much on this test. ■ Be careful when solving Roman numeral prob- lems. Roman numeral problems will give you several answer possibilities that list a few different combinations of solutions. You will have five options: a, b, c, d, and e. To solve a Roman numeral problem, treat each Roman numeral as a true or false statement. Mark each Roman numeral with a “T” or “F,” then select the answer that matches your “Ts” and “Fs.” These strategies will help you to do well on the five-choice questions, but simply reading them will not. You must practice, practice, and practice. That is why there are 40 problems for you to solve in the next section. Keep in mind that on the SAT, you will have fewer questions at a time. By doing 40 problems now, it will seem easy to do smaller sets on the SAT. Good luck! –THE SAT MATH SECTION– 148 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 148 40 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. –THE SAT MATH SECTION– 149 1.abcde 2.abcde 3.abcde 4.abcde 5.abcde 6.abcde 7.abcde 8.abcde 9.abcde 10.abcde 11.abcde 12.abcde 13.abcde 14.abcde 15.abcde 16.abcde 17.abcde 18.abcde 19.abcde 20.abcde 21.abcde 22.abcde 23.abcde 24.abcde 25.abcde 26.abcde 27.abcde 28.abcde 29.abcde 30.abcde 31.abcde 32.abcde 33.abcde 34.abcde 35.abcde 36.abcde 37.abcde 38.abcde 39.abcde 40.abcde ANSWER SHEET 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 149 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 150 1. Three times as many robins as cardinals visited a bird feeder. If a total of 20 robins and cardinals visited the feeder, how many were robins? a. 5 b. 10 c. 15 d. 20 e. 25 2. One of the factors of 4x 2 – 9 is a. (x + 3). b. (2x + 3). c. (4x – 3). d. (x – 3). e. (3x + 5). 3. In right triangle ABC,m∠C = 3y – 10, m∠B = y + 40, and m∠A = 90. What type of right triangle is triangle ABC? a. scalene b. isosceles c. equilateral d. obtuse e. obscure 4. If x > 0, what is the expression (͙x ෆ )(͙2x ෆ ) equivalent to? a. ͙2x ෆ b. 2x c. x 2 ͙2 ෆ d. x͙2 ෆ e. x – 2 –THE SAT MATH SECTION– 151 REFERENCE SHEET 45˚ 45˚ s s 2s Ί ¯¯¯¯¯ 3x 60˚ 30˚ x 2x h b A = 1 2 bh l w h l w r A = πr 2 C = 2πr r V = πr 2 h h Special Right Triangles V = lwh A = lw • 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. Ί 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 151 5. At a school fair, the spinner represented in the accompanying diagram is spun twice. What is the probability that it will land in section G the first time and then in section B the second time? a. ᎏ 1 2 ᎏ b. ᎏ 1 4 ᎏ c. ᎏ 1 8 ᎏ d. ᎏ 1 1 6 ᎏ e. ᎏ 3 8 ᎏ 6. If a and b are integers, which equation is always true? a. ᎏ a b ᎏ = ᎏ a b ᎏ b. a + 2b = b + 2a c. a – b = b – a d. a + b = b + a e. a – b 7. If x ≠ 0, the expression ᎏ x 2 + x 2x ᎏ is equivalent to a. x + 2. b. 2. c. 3x. d. 4. e. 5. 8. Given the statement: “If two sides of a triangle are congruent, then the angles opposite these sides are congruent.” Given the converse of the statement: “If two angles of a triangle are congruent, then the sides opposite these angles are congruent.” What is true about this statement and its converse? a. Both the statement and its converse are true. b. Neither the statement nor its converse is true. c. The statement is true, but its converse is false. d. The statement is false, but its converse is true. e. There is not enough information given to determine an answer. 9. Which equation could represent the relationship between the x and y values shown below? xy 02 13 26 311 418 a. y = x + 2 b. y = x 2 + 2 c. y = x 2 d. y = 2 x e. y 2 10. If bx – 2 = K, then x equals a. ᎏ K b ᎏ + 2. b. ᎏ K b –2 ᎏ . c. ᎏ 2– b K ᎏ . d. ᎏ K b +2 ᎏ . e. k – 2. RG B –THE SAT MATH SECTION– 152 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 152 . 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. THE SAT MATH SECTION 149 1.abcde 2.abcde 3.abcde 4.abcde 5.abcde 6.abcde 7.abcde 8.abcde 9.abcde 10.abcde 11.abcde 12.abcde 13.abcde 14.abcde 15.abcde 16.abcde 17.abcde 18.abcde 19.abcde 20.abcde 21.abcde 22.abcde 23.abcde 24.abcde 25.abcde 26.abcde 27.abcde 28.abcde 29.abcde 30.abcde 31.abcde 32.abcde 33.abcde 34.abcde 35.abcde 36.abcde 37.abcde 38.abcde 39.abcde 40.abcde ANSWER. 1: Five-Choice Questions The five-choice questions in the Math section of the SAT will comprise about 80% of your total math score. Five-choice questions test your mathematical reason- ing skills to do smaller sets on the SAT. Good luck! THE SAT MATH SECTION 148 5658 SAT2 006[04](fin).qx 11/21/05 6:44 PM Page 148 40 Practice Five-Choice Questions ■ All numbers in the problems are real