PLUGGING IN PLUGGING IN READING College Board makes a big deal about the diﬀerences between Heart of Algebra WRITING AND questions and Passport to Advanced Math questions, but those diﬀerences don’t LANGUAGE matter too much to us. If there are variables in a question, turn it into an arithme- tic question by plugging in numbers. 9. Which of the following is equivalent to the expression x2 – 4x + 11 ? A) (x + 2)2 – 7 B) (x + 2)2 + 7 C) (x – 2)2 + 7 D) (x – 2)2 – 7 MATH PLUGGING IN BASIC APPROACH 1. Identify the variable(s). 2. Plug in a number for the variable(s). 3. Work the steps of the problem. 4. Circle the Target Value. 5. Plug into all four answers, eliminating any that do not match the Target Value. 6k2 +11k 3k +1 11. The expression above can be rewritten as which of the following? A) 2k 3 3 1 3k 3 B) 2k 3k 1 C) 2k + 11 D) 2k |© TPR Education IP Holdings, LLC 375

SAT MANUAL READING WHAT TO PLUG IN Why would it be a bad idea to plug in x = 37 on question 9? What happens if you plug in a number that results in a denominator of 0 on question 11? Choose num- bers that make the arithmetic as straightforward as possible. WRITING AND What’s a good number to 8. Which of the following must be true if w 4 ? LANGUAGE plug in for w? w 3v 13 A) w = 12 v 17 B) v = 4 w 3 MATH C) v = 3 w 4 D) w 4 vw PLUGGING IN TIPS • If the question is about a relationship between numbers, plug in! The question may contain variables, fractions, equivalent expressions, or the phrase “in terms of.” • Try numbers that make the math as straightforward as possible, especially when calculator use is not allowed. Numbers like 2, 3, 5, and 10 work great, and 100 is good for percent questions. • As long as your numbers ﬁt the requirements of the problem, your numbers will be good, viable numbers to use. Even a weird target number will probably only match one answer choice. • Check all four answer choices if they have variables. If two of them work, plug in again! |376 © TPR Education IP Holdings, LLC

PLUGGING IN 23. If r r s t, where r is a positive integer and s is a negative integer, READING thesn which of the following must be true? A) t = 0 WRITING AND B) t = −5 LANGUAGE C) The value of t is negative. D) The value of t is positive. Sometimes you’ll plug in values from a chart or graph, rather than your own numbers. MATH Metric versus U.S. measurements 2 Liters (2,000 milliliters) 67.63 ounces 591.47 milliliters 20 ounces 3,785.41 milliliters 1 gallon (128 ounces) 473.81 milliliters 1 pint (16 ounces) 22. The table above shows the conversion between metric and U.S. measurements of common beverage sizes. If m milliliters is equal to o ounces, which best represents the relationship between m and o ? A) m = 29.57o B) o = 29.57m C) m = 0.034o D) mo = 0.034 |© TPR Education IP Holdings, LLC 377

SAT MANUAL READING Plugging In can be a great tool for word problems too. Are there variables? 28. If the average (arithmetic mean) of 8 and q is a, the average of 12 and Plug in! 1 1 2 q is b, and the average of 16 and 3 q is c, what is the average of a, b, WRITING AND and c, in terms of q ? LANGUAGE A) 11 q + 36 6 B) 11 q + 18 12 MATH C) 11 q + 9 24 D) 11 q + 6 36 HIDDEN PLUG-INS Plugging In is not just for questions with variables in the answer choices—be on the lookout for questions that ask about changes to values but don’t provide the actual values. Instead of trying to imagine how the numbers behave, plug in num- bers and see what happens. 13. Pyramid Q has a rectangular base and a volume of 96 cubic inches. Pyramid R has a rectangular base that is one-half the base area of pyramid Q and a height that is 3 times the height of pyramid Q. What is the volume of pyramid R? A) 64 B) 144 C) 288 D) 432 |378 © TPR Education IP Holdings, LLC

PLUGGING IN 31. A person’s height H, in centimeters, can be estimated based on the READING length of the femur bone f, in centimeters, using the formula H = 2.71f + 45.86. According to the model, for every increase of 5 centimeters in the length of the femur, by how many centimeters will the person’s estimated height increase? (Round your answer to the nearest tenth.) WRITING AND LANGUAGE MATH PLUG AND PLAY On occasion, a question will contain a variable or an unknown quantity, but it is not clear exactly what to plug in. When that happens, play around with the num- bers until you find one that works. 2x2y = 162 17. If the equation above is true for some positive integer values of x, what is one possible value of y ? |© TPR Education IP Holdings, LLC 379

READINGSAT MANUAL PLUGGING IN DRILL Time: 8 minutes Unless you are aiming for a top score, don’t try all the questions! Use your POOD to choose the best ones for you. WRITING AND 9 20 LANGUAGE If y = (cd)2, x = c2 – d2, and c ≠ d, which of the following is equivalent to xy ? v m2 6m 9 0 c−d m A) c3d2 + c2d3 3 m 3 3 B) 2c2d2 MATH C) d2 – c2 If the equation above is true, and the variable m ≠ 3, D) c3d2 – c2d3 then what is the value of constant v ? |380 © TPR Education IP Holdings, LLC

PLUGGING IN 10 27 READING A marble rolls down a track at an average speed of P S SF s centimeters per second, where s = 3 p . Which p A tennis league uses the formula above to WRITING AND determine a player’s first serve practice score, P, of the following gives the distance traveled by the LANGUAGE based on the number of successful first serves, S, and the faults on first serves, F. Which of the marble, in centimeters, over p seconds? following expresses the number of successful serves, in terms of F and P ? A) p 3p A) S FP B) p 1 P B) S FP C) 3 p MATH P 1 C) S F D) p P 1 D) S F 1 P 21 29 11x + 5 = 9x + p 11y + 5 = 9y + q The intensity of light, I, is inversely proportional to In the equations above, p and q are constants. If the square of the distance, d, from the light source, p = q + 4, which of the following is true? iass5gitvimenesbyasthfaerefqruomatiothneIl1i(gdh1)t2s=ouI2r(cde2)a2s. If Viewer A Viewer B, A) x = y – 2 the intensity of light seen by Viewer A is what B) x = y + 2 fraction of the intensity of light seen by Viewer B? C) x = y + 4 D) x = y + 8 A) 1 25 B) 1 5 C) 5 1 D) 25 1 |© TPR Education IP Holdings, LLC 381

SAT MANUAL Summary • What are the advantages of Plugging In? ______________________________________ ______________________________________ • What are some clues that you can Plug In? ______________________________________ ______________________________________ ______________________________________ ______________________________________ • What are the steps for Plugging In? ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ • What are some good numbers to use when Plugging In to make the math more convenient? ______________________________________ • I have accomplished ______ of the 3 goals stated at the beginning of this chapter. |382 © TPR Education IP Holdings, LLC

PLUGGING IN THE ANSWERS The most dangerous phrase is “We’ve always done it that way.” –Grace Hopper 395

SAT MANUAL READING GOALS REVIEW WRITING AND At the conclusion of this chapter, you will be able to accomplish the following: LANGUAGE • Identify when Plugging In the Answers is possible • Follow the steps of PITA to accurately and efficiently solve problems • Explain why PITA is such a powerful technique MATH |396 © TPR Education IP Holdings, LLC

PLUGGING IN THE ANSWERS PLUGGING IN THE ANSWERS (PITA) READING When the question asks for a speciﬁc amount and the answer choices are presented in numerical order, Plug In the Answers. 10. Which of the following is a possible solution to the equation 20 18 WRITING AND a -1 - a 1 2? LANGUAGE A) 4 MATH B) 5 C) 6 D) 7 PITA BASIC APPROACH 1. Label the answer choices—what do the answers represent? 2. If the question asks for the greatest or smallest value, start there. Otherwise, start with one of the answers in the middle. 3. Use Bite-Sized Pieces to work the steps of the problem. 4. Eliminate answers that are too big or small. 5. When one of the answers works, STOP. 9. If 3 2 y , then which of the following is a possible value of 2 – y ? RTFQ! What do the 2 y answer choices represent? What does A) 3 that mean about y? B) 3 C) 2 + 3 D) 9 |© TPR Education IP Holdings, LLC 397

SAT MANUAL READING By plugging in the answers, you can avoid doing time-consuming algebra and fall- ing for trap answers. Why can you eliminate 21. If x2 7x 10 and x > 0, what is the value of x ? (A) immediately? 6 6 WRITING AND A) –5 LANGUAGE B) 2 C) 12 D) 24 MATH 2 y 1 x 3 y+4=x Plug the points into the 4. Which of the following ordered pairs (x, y) is the solution to the system simpler equation first. of equations above? A) (1, –3) B) (2, –6) C) (5, 1) D) (13, –21) 8. What is the solution set to the equation a 5 7 3a 10 ? A) {–3, –1, 2} B) {–3, 2} C) {–3} D) {2} |398 © TPR Education IP Holdings, LLC

PLUGGING IN THE ANSWERS 16. If 8x2 – 14x – 15 = 0, then which of the following is the least value of x ? When the question asks READING for the greatest number A) - 5 or the maximum value, 2 plug in that answer choice first. B) 3 - 4 C) 3 WRITING AND 4 LANGUAGE D) 5 2 CLUES THAT YOU CAN USE PITA MATH • The question asks for a specific amount—“how much,” “how many,” or “what is the value of…?” • You get the urge to write your own equation. • All the answer choices are numbers. PITA often works for word problems too! 18. A car begins at rest 200 meters from the finish line of a straight segment of track. If the car accelerates from rest at a constant rate of 4 meters per second each second, its distance from the finish line, x, is given by the equation x = 200 – 2t2, where 0 ≤ t ≤ 10. After how many seconds has the car travelled 72 meters? A) 2 B) 6 C) 8 D) 12 11. A preschool teacher gave out a total of 65 cookies to her class during snack time. She allowed each of her 25 students to choose either 3 small cookies or 2 large cookies. Assuming all the children in the class chose one of these two options at snack time, how many of the students in her class chose to have 3 small cookies? A) 10 B) 15 C) 18 D) 20 |© TPR Education IP Holdings, LLC 399

READINGSAT MANUAL PLUGGING IN THE ANSWERS DRILL Time: 8 minutes Unless you are aiming for a top score, don’t try all the questions! Use your POOD to choose the best ones for you. WRITING AND 4 6 LANGUAGE If the expression n2 – 2n – 8 represents the net profit 4 2 on the sale of n units of a product, which of the a 5 3a following values represents the number of units MATH sold for which the net profit equals 0 dollars? Given the equation above, what is the value of 3a ? A) 9 A) 2 B) 4 B) 3 C) 6 D) 8 C) 1 D) 1 3 |400 © TPR Education IP Holdings, LLC

PLUGGING IN THE ANSWERS 7 15 READING –5 < –2x + 4y If 3 13 10x, then x could equal which of the WRITING AND Which of the following ordered pairs satisfies the x LANGUAGE inequality above? following? I. (2, 3) II. (4, 2) A) 0.2 III. (6, 1) B) 0.5 C) 0.6 D) 1.5 A) I only MATH B) III only C) I and II only 25 D) II and III only A leader of a scouting troop is planning to decorate 11 vests for the members of the troop. If he buys x The Eiffel Tower was constructed for the Exposition beads to divide among the vests, he can put 4 beads on each and still have 4 beads left over. If Universelle, a world’s fair held in Paris in 1889. Four he misplaces 12 beads, however, he can only put 3 years later, the first Ferris Wheel was constructed beads on each vest and will have 9 beads left over. for the World’s Columbian Exhibition in Chicago, How many vests is the troop leader planning to Illinois. The combined total height of these two decorate? structures was 1,248 feet. If the Eiffel Tower is 720 feet taller than the Ferris Wheel was, how tall was A) 12 the Ferris Wheel? B) 13 A) 264 C) 17 B) 528 D) 22 C) 678 D) 980 |© TPR Education IP Holdings, LLC 401

SAT MANUAL Summary • What are the advantages of Plugging In the Answers? ______________________________________ ______________________________________ • What are some clues that you can PITA? ______________________________________ ______________________________________ ______________________________________ ______________________________________ • What are the steps for PITA? ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ • I have accomplished ______ of the 3 goals stated at the beginning of this chapter. |402 © TPR Education IP Holdings, LLC

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