2016SHSAT_English

​​​Sample Test – mathematicsExplanations of Correct Answers AForm62. (G) The scale is 1 foot 0.25 inch. Since the restof the question is in inches, change the scaleconversion into inches: 1 foot is equal to12 inches, so 12 inches 0.25 inch.Next, set up a proportion, where x representsthe scale inches for a distance of 36 inches:_____ 120.25 ​ 5 ​ ___ 36x ​12x 36(0.25)12x 9x ​ ___ 912 ​ 5 ​ __ 3​ 5 0.75 in.463. (D) First, find the prime factorization of eachnumber:2,205 3 • 3 • 5 • 7 • 73,675 3 • 5 • 5 • 7 • 7Now, determine what each prime factorizationhas in common, and multiply those:2,205 3 • (3 • 5 • 7 • 7) 3 • 7353,675 5 • (3 • 5 • 7 • 7) 5 • 735The greatest common factor is 735.64. (H) List in order the prime numbers between 6and 36: 7, 11, 13, 17, 19, 23, 29, and 31. Sincethere are 8 numbers, find the middle two andcalculate the mean to find the median of allthe numbers. The middle two are 17 and 19.The mean is ​________17 19​ 18.265. (D) The car gets between 20 and 22 miles per gallon.Ms. Grant would use the most gas if thecar gets only 20 miles per gallon, so use thisvalue. Then, use $4.50 (the highest possibleprice per gallon) to determine the greatestamount of money she will spend:200 miles 4 20 miles per gallon 5 10 gallons of gas10 gallons • $4.50 5 $45.0067. (C) To eliminate the decimals in this equation,multiply the numerators and denominators by100:_____ 0.21(0.33 ​ ____ 100)(100 ​ ) 5 _____ x(​1.10 ​ ____ 100)(100 ​ )___ 2133 ​ 5 ​ _____ 100x110 ​x 5 ____ 110(100 ​ ___ 21)(33 ​ ) 5 ​ _____ 70100 ​ 5 0.7068. (J) Let x be the number of seventh grade studentsthat must join to meet the president’s wishes.There are 65 students currently in the club.The percentage of seventh graders is calculatedby dividing the number of seventh gradersby the total number of students in the club.Using the president’s desired percentage of40% (0.40), the equation is:_______ 20 x65 x ​ 0.4020 x (0.40)(65 x)20 x 26 0.40x0.60x 6x 1069. (E) First, find the length of ___​ PR​: 4 – ( 5) 5 9 unitsPoint Q is located ​__1 ​of the way from R to P, so3calculate where that point would be:9 3 ​1__ ​5 3 units3So, point Q is located at 4 2 3 5 1. Finally,calculate the midpoint of ___​ PQ​:Midpoint PQ = ​ ______ 5 1 12 ​ 5 270. (H) The two-digit numbers must be even, so theonly possible two-digit numbers must endin 8, since 8 is the only even digit given inthe problem. Since the numbers cannot berepeated, the only possibilities for two-digiteven numbers are 78 and 98. Thus, theanswer is two possible two-digit numbers.66. (K) The climbers started at 125 feet below sealevel, which can be expressed as 125. Theystopped at 5,348 feet above sea level, which isexpressed as a positive number. The elevationgain for the day is 5,348 – ( 125) = 5,473 feet.65