2016SHSAT_English

Sample Test – mathematicsExplanations of Correct Answers AForm90. (G) Because the volume of the tent is calculatedusing the area of the cross-section 3 depth(d), you can also use this formula to find d.The pattern shows the largest possible value ofthe expression is 1, which occurs when x 5 0.94. (H) This problem can be solved by creating aVenn diagram:StudentsStudents withwith 3 dogscatsxy5The circle on the left indicates the studentswith cats, and the circle on the right indicatesstudents with dogs. The number outside bothcircles (5) is the number of students withoutcats or dogs. The number inside the intersectionof the two circles (3) indicates the numberof students who have both cats and dogs.Calculate x and y using the given information:There are 20 students who have cats, and ofthose 20 students, 3 have cats and dogs. Thus,x = 20 – 3 = 17. There are 23 students whohave dogs, and of those 23 students, 3 havecats and dogs. Thus, y = 23 – 3 = 20.To find the total number of students surveyed,add the numbers in the diagram:3 1 5 1 x 1 y 5 8 1 17 1 20 5 4595. (E) The question says that an equal number (x) ofeach type of space was purchased. To find thenumber of each type of space that was purchased,multiply the price per type by x andset it equal to the total amount spent:200x 350x 600x 11,5001,150x 11,500x 10x 1 – x 2Thus, the store purchased 10 units of each 2 type of space. To find the total amount of3page space purchased, multiply each type of 1 0space by 10 and add:0 1(10 • ​1__1 04 ​ page) (10 • ​1__2 ​ page) (10 • 1 page)2 3The area of the cross-section is the sum of theareas of the two triangles and the rectangle.The two triangles have the same base length(2 ft) and height (6 ft), so the area of one of thetriangles is:A 5 ​1__ ​ 3 2 3 6 5 6 sq ft2The area of the center rectangle is:A 5 4 3 6 5 24 sq ftSo the total area of the cross-section is:A 5 6 1 6 1 24 5 36 sq ftUse that to calculate the depth of the tent:V 5 36d216 5 36d6 5 d91. (A) After Ang gives Julia ​__1 ​of his money (which3can be expressed as ​__1 3 ​x or ​x __ ​), Julia has3y ​x__3 ​ in her account. If she spends ​1 __ ​of that4amount, the expression is now:​1 __4 ​ y ​x__3 ​ ​y__4 ​ ​ ___ x12 ​92. (K) The integers that are included in Set R butnot in Set T are 10 through 81. (Note that 82is included in Set T.) To calculate the numberof integers between 10 and 81, inclusive,subtract the two endpoints and add 1. (Onemust be added because the endpoints are bothcounted in the total) 81 – 10 1 7293. (C) To answer this question, assign several positiveand negative values to x and determinewhat the value of the expression will be: 2​1__2 ​ 5 10 17​ 1__2 ​ pages68