12.Practice.Tests.for.the.SAT_2015-2016_1128p

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394 12 Practice Tests for t h e SAT Practice Test Four Answers and Explanations 2. B Difficulty: Low Strategic Advice: Set up a proportion and do t h e arit h metic carefu ll y. Getting to the Answer: s x 2 = 4.4 2x = S( 4.4) = 22 X = 11 3. c Difficulty: Low Strategic Advice: Cross-multiply and then simplify. Getting to the Answer: x_S -y-7 7x =Sy 7x _ _2f Sy - Sy 7x = 1 Sy 4. E Difficulty: Low Strategic Advice: Look for vertical ang l es and straig h t ang l es. Getting to the Answer: Angle FA E is a vertical angle wit h angle BAC, so it is a l so 30°. T h en x = 90 + 30 = 1 20. Angle FA B forms a straig h t ang l e wit h angle BAC, so y= 180. - - 120 + 180 2 2 = lSO 5. A Difficulty: Low Strategic Advice: Add up t h e tota l sc h oo l time and subtract from 2:30 to find t h e starting time. Getting to the Answer: Eac h class period is 1 h r and 20 minutes, or 1tor1- hours, so t h e 4 class periods are a total of 4( 1) = 6 = st h ours. T h e breaks and lunc h add up to S + S + 30 = 40 minutes= cig = t of an h our. So t h e tota l sc h oo l time is st + t = 6 h ours. Six h ours before 2:30 is 8:30. 6. c Difficulty: Medium Strategic Advice: Try using Backso l ving on t h is oneremember t h at a ll t h ree s h ou ld be integers, and x + 4 is t h e median (middl e) num ber. Getting to the Answer: (C) x= 11: 2x -8=2(1 1)-8= 14,x+4= 11 +4=1S, and 3x - 13 = 3(1 1) - 13 = 20. Our t h ree numbers, t h en, are 14, 1 S, and 20-w h ere (x + 4) is the median. C h oice (C) is correct. 7. A Difficulty: Medium Strategic Advice: You want to figure out w h at b has to be in order to get $22S out of t h e net profit equation. Getting to the Answer: P(b) = 2.Sb - 100 = $22S 2.Sb = $32S b= 130 8. A Difficulty: Medium Strategic Advice: FOIL out (x - y)2 and t h en substitute w h at you know. Getting to the Answer: (x - y)2 = (x - y)(x - y) = x2 - xy - xy + y2 =x2 _ 2xy + y2 = (x2 + y2) - 2(xy) = (1 S3) - 2(36) =81 9. E Difficulty: Medium Strategic Advice: Look for specia l triang l es in order to speed up your arit metic. It's rare t h at you' l l have to use t h e Pyt h agorean t h eorem more t h an once on any given question.
12 Practice Tests for t h e SAT I Practice Test Four Answers and Explanations 395 Getting to the Answer: Triang l e BCD is a 45-45-90 triang l e, w h ic h means eac h of t h e l egs h as l engt h 2. So BC = 2. T h en, since h ypotenuse BC is twice l eg AB for t h e l eft triang l e, t h is must b e a 30-60-90 triang l e; y = 30°, so z = 60°. 10. c Difficulty: Medium Strategic Advice: Since t h ey are percentages of t h e same num b er, you can forget a b out t h e "positive num b er." Just t h in k , 20 percent of 30 percent is t h e same as 15 percent of w h at? Getting to the Answer: 200/o of 300/o = 1 50/o of h 0.2(0.3) = 0.15 h 0.06=0.15 h h = 0.4 = 400/o 11. B Difficulty: Medium Strategic Advice: Eac h time t h e square is sp l it, eac h sma l l er square is t t h e size of t h e origina l square. How many suc h sp l its did we make? Getting to the Answer: We made 4 sp l its, so the sma ll est squares are eac h t oft oft oft of t h e l argest square, w h ic h is t x t x t x t = 26 of t h e l argest square. Since two of t h e sma l l est squares are s h a ded, t h ey are 2;6 = 1 is of t h e l argest square. 12. E Difficulty: Medium Strategic Advice: Varia b l es in t h e answer c h oices ma ke t h is a great time to Pick Num b ers. Getting to the answer: Try x = - 1 and y = 2 so t h at -3 < 0 < 2, as required. (A) 0 (B) y = 2 ( l arger t h an (A)) (C) -3x = -3(-1) = 3 ( l arger t h an (8)) (D) -(3x + y) =-(3(-1) + 2) =-(-3 + 2) =-(-1) = 1 (sma l l er t h an (C)) (E) -(3x-y) = -(3(-1) - 2) = -(-3 -2) = - (-5) = 5 ( l arger t h an (C)) So (E) is t h e l argest. 13. D Difficulty: Medium Strategic Advice: Write an expression for eac h d ay's p h ysics pro bl ems, t h en find t h e average. Getting to the Answer: Monday=m Tuesday= 3m Wedesday = 2m 3 Average = m + (3m) + (2m + 3) = 6m + 3 3 3 = 2m + 1 A l so notice you cou l d Pick Num b ers for t h is pro bl em. Picking somet h ing l ike 2 or 3 form makes t h is very quick to so l ve. 14. D Difficulty: Hig h Strategic Advice: In t h e question, t h e reciproca l of t h e expression is equa l to itse l f. W h at num b ers can you t h ink of t h at h ave t h ose properties? Getting to the Answer: Don't l et fractions in t h e exponents t h row you off. T h e first step of any pro bl em l ike t h is is to cross-mu l tip l y. l (a+ br2 (a+ b)- 1 1 i =(a+ br 1 x (a+ br 1 =(a+ b)-1 = (a b) Since t h is fraction is equa l to 1, we know t h e reciproca l is a l so equa l to 1. 1 =(a+b),or (D). Even t h oug h t h ere are answer c h oices wit h varia bl es, t h is is not a good question to try to so l ve b y Picking Num b ers, as it invo l ves comp l icated a l ge b ra. 15. E Difficulty: Hig h Strategic Advice: W h at is t h e x-coordinate at 07 W h at do you know a b out t h e functions at t h at va l ue?
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