2016SHSAT_English

Explanation of correct answersGrade 9 Mathematicsgrade91. (A) First, determine the total number of pets thatthe students own by multiplying the number ofpets owned by the number of students in eachrow of the table. Then add that column to getthe total number of pets.Number ofPets OwnedNumberof StudentsNumber of Pets 3Number of Students0 5 01 7 72 3 63 4 124 0 05 1 5Total: 30Now, calculate the mean by dividing the totalnumber of pets owned by the total number ofstudents:​___3020 ​ 5 1​ 1__2 ​2. (J) Since x is a negative number between 1 and 0,assign a value to x in that range and calculate x 2 .For example, let x 5 2 ​2__3 ​. Then x2 5 ​4__ ​, which9roughly corresponds to point U.3. (C) ​ _____ 2(4/x) ​ 5 ​ __ 32 ​2 • ​x __4 ​ 5 ​ 3 __2 ​2x 5 6x 5 34. (F) Begin by finding a common base for each term.In this case, the common base is 2.4 5 2 28 5 2 3(4 3 )(8 2 ) 5 (2 2 ) 3 (2 3 ) 25 (2 6 )(2 6 )5 2 12So, x 5 12.Alternatively, you could multiply the left side ofthe equation and then factor it:(4 3 )(8 2 ) 5 (4 3 4 3 4)(8 3 8)5 (2 3 2 3 2 3 2 3 2 3 2) (2 3 2 3 2 3 2 3 2 3 2)5 2 125. (B) Each triangle is a right triangle, and theangles formed at point Z are congruentbecause they are vertical angles. Thus, thetwo triangles are similar by definition. Set upthe following proportion between similar sidesto find x:5__3 ​5 __ 6 x​5x 5 18x 5 18 ___5 ​5 3 3__5 ​6. (J) First, calculate the volume of the cylinder:V = πr 2 h 5 π(4) 2 (8) 5 128π cubic inchesThe volume of water in the cube will be thesame as the volume of water in the full cylinder.Use the volume formula of a cube to calculatethe depth (h) of the water in the cube:V 5 lwh128π 5 (8)(8)h128π = 64h2π = h111