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# SAT Class 1 Demo 2

## Description: SAT_Ultimate_Class_1_Lessons_2020-01-07

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 vw 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 SF 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

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