2016SHSAT_English

Explanation of correct answersGrade 9 Mathematics9grade7. (B) If the coordinates of a point labeled R are (a, b),then a 908 counterclockwise rotation aboutthe origin would make the coordinates of pointR9 ( 2 b, a). A 908 clockwise rotation about theorigin would make the coordinates of R9 (b, 2 a).In the question, P is (3, 5) and P9 is (5, 2 3).Using the rule stated above, P9 is the imageafter point P is rotated 908 clockwise.Alternatively, it may help to make a sketchof this problem. Place the two points onthe coordinate grid: Point P is in the firstquadrant, and point P9 is in the fourthquadrant. Draw a line from each point to theorigin. The angle formed at the origin shouldresemble a right angle, which is option B (908).yP (3, 5)xP9(5, – 3)8. (H) In order to add or subtract two numbers inscientific notation, the exponent on the 10 mustbe the same. Since the question asks for thevalue of k 3 10 19 , change both terms into thissame power of 10:12.6 × 10 18 5 (1.26 3 10) 3 10 18 5 1.26 3 10 191.1 × 10 17 5 (0.011 3 10 2 ) 3 10 17 5 0.011 3 10 19Now, perform the subtraction:(1.26 × 10 19 ) 2 (0.011 3 10 19 )5 (1.26 2 0.011) 3 10 195 1.249 3 10 19Thus, k 5 1.2499. (C) At the beginning (hour 0), the pool is empty.After 5 hours, the pool holds 2,000 gallons.Thus, the rate of change (or slope of the line)2,000 − 0is ​ _________5 − 0 ​ 5 ​ ______ 2,000​ 5 400 gallons per hour.5To find the number of gallons after 20 hours,multiply the rate by the number of hours:400 3 20 5 8,000 gallons.10. (G) Using the translation equation given in thequestion, set up two small equations to findn and r:For n:x 1 10 5 100x 5 90For r:y – 10 5 100y 5 110So, (n, r) 5 (90, 110)11. (A) Because both triangles are right triangles thatshare a vertex, they are similar. To find x, setup a proportion using the two known sides ofeach triangle:________ (4 1 x)1.0 ​5 ____ ​ 40.8 ​0.8 (4 x) 5 1.0 (4)4 1 x 5 5x 5 112. (H) An x-intercept of 3 means the point (3, 0) is online k. Using (3, 0) and (2 3, 4), calculate theslope (m) of the line:(420)m 5 ​ _______( 2 323) ​ 5 ​ 4__6 ​ 5 ​2__3 ​The equation of line k must contain slope ​2__3 ​ ,so only Options G and H are potentially correct.Next, find which of the two equations is true forthe point (3, 0). To solve, substitute 3 for x ineach equation and find the one in which y 5 0.112