2016SHSAT_English

​Sample Test – mathematicsExplanations of Correct Answers AForm71. (B) First, change the improper fractions intomixed numbers:​5__2 ​ 2​ 1__ ​ and ​20 ___2 3 ​ 6​ 2__3 ​The integers between these two values are 3,4, 5, and 6. So, there are 4 integers between​5__2 ​ and ​ ___ 203 ​ .72. (G) Angle LKN 75° because vertical anglesare congruent. The interior angles ofquadrilateral KLPN sum to 360°. So,angle LPN 360 – (120 120 75) 45°.Angle LPN and angle QPR are vertical angles,so x 45.73. (C) Let x be the number of bundles needed forthe roof’s area of 416 square feet. Set up aproportion to find x:____ x416 ​ ​ ___ 396 ​ x 416 3(___96 ​ ) 1374. (G) All 6 of the smaller rectangles are congruent.Let the shorter side of one of these small rectanglesbe x. Based on the figure, the longerside is then 4x, because the shorter side offour rectangles stacked together is the samelength as the longer side of one rectangle.Using this information, you can now figureout the length and width of WXYZ:Width of WXYZ 4xLength of WXYZ x 1 4x 1 x 5 6xUse the area of WXYZ to calculate x:(4x)(6x) 5 5424x 2 5 54x 2 5 ​__9 4 ​x ​3__2 ​Now that x is known, use that to find thelength and width of WXYZ:Width of WXYZ 5 4(​3__2 ​) 5 6Length of WXYZ 6x 5 6(​3__2 ​) 5 9So, the perimeter of WXYZ 5 2(6) 1 2(9)5 12 1 18 5 30 cm75. (D) Let x equal the number of gallons needed todrive m miles. Set up a proportion to solve for x:​ ___m x ​5 ​ ___ 365 ​ x 5 ____ 3m65 ​76. (G) To find when the two flashes occur at the sametime, find the least common multiple of 12 and18, which is 36. Every 36 minutes, the lightsflash at the same time. The first time is 8:00a.m. The next 6 times would be 8:36, 9:12,9:48, 10:24, 11:00, and 11:36. Only 2 of thosetimes are listed (9:12 a.m. and 10:24 a.m.).77. (D) First, find the amount of the tax charged onthe sale price:$1.89 • 0.06 $0.1134 $0.11 (rounded tothe nearest cent)Then, subtract the original tax from the tax onthe sale price calculated above:$0.15 $0.11 $0.0478. (H) First, add the percentage of cars containing3 people, 4 people, and 5 or more people:15% 1 7% 1 3% 5 25%Thus, 25% of the cars contained at least 3 people,so use that to calculate the number of cars:420 3 25% 5 105 cars79. (E) Roberto began his first 5 hour watch at6:00 p.m. Since he had 5 hours off before hebegan his second watch, the second watchbegan 10 hours after the first watch began.Thus, his third watch began 20 hours after hisfirst watch began. 20 hours after 6:00 p.m. is2:00 p.m. the next day.80. (G) Let c be Crystal’s age:3c 1 2 5 m3c 5 m 2 2c 5 ​ _______ m 2 2​366