2016SHSAT_English
2016SHSAT_English 2016SHSAT_English
Sample Test – MathematicsExplanations of Correct AnswersBForm90. (H) The left side of the given equation(xy 1 xz 5 100) must be rearranged to look likex __ (3y 1 3z) 1 10 to get the answer.5First, factor out the x: x (y 1 z) 5 100Next, multiply both sides of the equation by 3:3x (y 1 z) 5 3(100) x (3y 1 3z) 5 300Then, divide both sides by 5:1 __5 x (3y 1 3z) 5 ____ 3005 x __ (3y 1 3z) 5 605Finally, add 10 to both sides:x __ (3y 1 3z) 1 10 5 705Now that the left side looks like the expressionin the question, the answer is the number onthe right side (70).91. (D) The volume of the container is10 10 10 1,000 cubic feet. Since it isalready half full at 9:00 a.m., it will beginto overflow after 500 cubic feet of water isadded to it.7 cubic feet of water are being added perminute, but 2 cubic feet of water leak out perminute. That means 7 – 2 5 cubic feet ofwater are being added to the tank each minute.500 cubic feet 5 cubic feet per minute 100 minutes100 minutes is equal to 1 hour 40 minutes.1 hour 40 minutes after 9:00 a.m. is 10:40 a.m.92. (G) Angle PQR and the marked 40° angle arevertical angles and thus are congruent, soangle PQR is 40°. Similarly, angle QRP is45° because it is a vertical angle with the onemarked 45°. Given those two angles, calculatethe third angle of triangle PQR (angle RPQ):40 1 45 1 RPQ 5 180RPQ 5 95Angle RPQ and angle x are supplementary,which means they sum to 180, sox 5 180 2 95 5 85.Similarly, angle y and angle QRP aresupplementary, so y 5 180 2 45 5 135.Thus, the value of y 2 x 5 135 2 85 5 5093. (A) Each chair costs Arnold $150 to make, and hesells the chair for $275. His profit is found bysubtracting the cost from the price:$275 $150 $125 per chairIf Arnold makes and sells 25 chairs in a week,his initial profit is 25 • $125 $3,125. However,Arnold has additional fixed expensesof $1,250 per week, so this cost must also besubtracted. Thus, his final profit is:$3,125 $1,250 $1,87594. (H) First, calculate the area of the entire lot:75 3 100 5 7,500 sq ftThere are 12 equal-sized squares, so eachsquare is equal to 7,500 ÷ 12 = 625 sq ft.From the figure, it appears the building(shaded region) covers 1 full square, 1 halfsquare,and 2 quarter-squares, for a total of2 full squares (1 1 1__2 1 2( 1__ ) 5 2). Two full4squares are equal to 625 1 625 5 1,250 sq ft.To find the area that is not shaded, subtractthe area of the building from the area of theentire lot: 7,500 – 1,250 = 6,250 sq ft, whichrounds to 6,000 sq ft.Remember that the question asks you to findout about how many square feet and notexactly how many square feet.95. (B) To find the mean salary for all 12 employees,find the sum for each group. Thus, 4 peopleearned a total of $272,000 and 8 people earneda total of $376,000. Use the mean formula:648,000272,000 376,000 5 ________ $54,00012106
Sample Test – MathematicsExplanations of Correct AnswersBForm96. (J) Madison’s car travels 27 miles one way to work,so it travels a total of 54 miles per day. In 5days, it travels 5 3 54 5 270 miles. Her cartravels 30 miles on each gallon of gas, so it uses____ 270 5 9 gallons of gas per week. To find the30total savings, multiply the number of gallonsby the savings per gallon:9 gallons • $0.05 5 $0.4597. (E) Let m 5 Marta’s age now, and k 5 Kim’s agenow. Then 5 years ago, Marta’s age wasm 2 5, and Kim’s age was k 2 5. Using theinformation in the question, set up theequation to solve for k:k 2 5 5 2(m 2 5)k 5 2(m 2 5) 1 598. (G) Using the counting principle, the first digithas 6 possible values (1 through 6). Thesecond digit then has 5 possible values, andthe third digit has 4 possible values. So thetotal number of possible different ID numbersis 6 3 5 3 4 5 120.99. (E) Since the floor measurement is in feet and thetile measurement is in inches, change inchesinto feet:88 in. ___12 2__3 ftThe floor is 12 ft wide. To find the number oftiles needed along the width of the floor, dividethe width by the size of a tile:12 ft 2__3 12 • 3__ 18 tiles2The floor is 16 ft long. Find the number oftiles needed along the length of the floor:16 ft 2__ 24 tiles3To find the total number of tiles needed, multiplythe number needed along the width by thenumber needed along the length:18 • 24 432 tilesTo find the total cost, multiply the total tilesby the cost per tile: 432 tiles • $8 $3,456100. (F) First, find the prime factorization of 5,355:5,355 5 5 • 1,071 5 5 • 9 • 119 5 3 2 • 5 • 7 • 17The greatest prime factor is 17.Answer Key for Sample Form BParagraph 1R U Q S TParagraph 2T S U R QParagraph 3U S T R QParagraph 4Q S R U TParagraph 5S U T Q R11. C12. F13. D14. J15. A16. H17. B18. K19. A20. K21. B22. F23. C24. J25. B26. K27. D28. H29. B30. J31. B32. F33. D34. K35. D36. J37. A38. G39. D40. K41. B42. G43. A44. H45. A46. K47. A48. H49. A50. G51. E52. K53. D54. F55. A56. J57. B58. H59. C60. F61. B62. G63. A64. K65. B66. J67. C68. F69. D70. H71. C72. K73. A74. J75. C76. K77. B78. G79. B80. G81. D82. J83. B84. F85. B86. J87. C88. G89. A90. H91. D92. G93. A94. H95. B96. J97. E98. G99. E100. F107
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Sample Test – MathematicsExplanations of Correct AnswersBForm96. (J) Madison’s car travels 27 miles one way to work,so it travels a total of 54 miles per day. In 5days, it travels 5 3 54 5 270 miles. Her cartravels 30 miles on each gallon of gas, so it uses____ 270 5 9 gallons of gas per week. To find the30total savings, multiply the number of gallonsby the savings per gallon:9 gallons • $0.05 5 $0.4597. (E) Let m 5 Marta’s age now, and k 5 Kim’s agenow. Then 5 years ago, Marta’s age wasm 2 5, and Kim’s age was k 2 5. Using theinformation in the question, set up theequation to solve for k:k 2 5 5 2(m 2 5)k 5 2(m 2 5) 1 598. (G) Using the counting principle, the first digithas 6 possible values (1 through 6). Thesecond digit then has 5 possible values, andthe third digit has 4 possible values. So thetotal number of possible different ID numbersis 6 3 5 3 4 5 120.99. (E) Since the floor measurement is in feet and thetile measurement is in inches, change inchesinto feet:88 in. ___12 2__3 ftThe floor is 12 ft wide. To find the number oftiles needed along the width of the floor, dividethe width by the size of a tile:12 ft 2__3 12 • 3__ 18 tiles2The floor is 16 ft long. Find the number oftiles needed along the length of the floor:16 ft 2__ 24 tiles3To find the total number of tiles needed, multiplythe number needed along the width by thenumber needed along the length:18 • 24 432 tilesTo find the total cost, multiply the total tilesby the cost per tile: 432 tiles • $8 $3,456100. (F) First, find the prime factorization of 5,355:5,355 5 5 • 1,071 5 5 • 9 • 119 5 3 2 • 5 • 7 • 17The greatest prime factor is 17.Answer Key for Sample Form BParagraph 1R U Q S TParagraph 2T S U R QParagraph 3U S T R QParagraph 4Q S R U TParagraph 5S U T Q R11. C12. F13. D14. J15. A16. H17. B18. K19. A20. K21. B22. F23. C24. J25. B26. K27. D28. H29. B30. J31. B32. F33. D34. K35. D36. J37. A38. G39. D40. K41. B42. G43. A44. H45. A46. K47. A48. H49. A50. G51. E52. K53. D54. F55. A56. J57. B58. H59. C60. F61. B62. G63. A64. K65. B66. J67. C68. F69. D70. H71. C72. K73. A74. J75. C76. K77. B78. G79. B80. G81. D82. J83. B84. F85. B86. J87. C88. G89. A90. H91. D92. G93. A94. H95. B96. J97. E98. G99. E100. F107
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