2016SHSAT_English
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2016SHSAT_English

2016SHSAT_English 2016SHSAT_English

akilbello
30.07.2015 Views

​​​Sample Test – MathematicsExplanations of Correct AnswersBForm51. (E) ____ 4.5 ​ 3 0.22 5 45 3 0.22 5 9.90.152. (K) First, find the ratio of red to green to bluepencils: 480:240:160 5 6:3:2Since 6 1 3 1 2 5 11, multiply each value by2 (because 2 3 11 5 22) to get the number ofeach color pencil in a set of 22 randomlychosen pencils: 12 red, 6 green, 4 blue57. (B) Write 0.75 as a fraction in lowest terms to find75the least value of x: 0.75 5 ​ ____100 ​ 5 ​ 3__4 ​So, the least possible positive integer valueof x 5 3.(58. (H)​ ___________ 51)( 51)17 • 17 • 17 ​ ​ _________ ( 3)( 3)​ ​ ____ 917 17 ​53. (D) The quickest solution is to first “round up” from46 hours to 48 hours, because 48 hours is2 full days. Thus, 48 hours after 9:30 p.m. onFriday would be 9:30 p.m. on Sunday. Sincethe question asks for 46 hours, subtract 2 hoursfrom 9:30 p.m. Sunday to get 7:30 p.m. Sunday.54. (F) The cost for one child’s supplies is:$1.09 1 2($0.59) 5 $2.27Divide the total money available ($15) by thecost for one child’s supplies ($2.27) to get thenumber of children that can be provided withthe supplies: $15 4 $2.27 5 6.6…You do not need to complete the division,because the number of children must be awhole number. Six children can be providedwith the complete requirement of supplies.55. (A) First, simplify the inequality:x 1 7 < 23x < 16The positive integers that satisfy the inequalityare 1, 2, 3, …, 14, 15. (We cannot include 16because x must be less than 16.) 15 positiveintegers satisfy this inequality.56. (J) The area of triangle MPR is equal to half thearea of rectangle MNQP. So, the area of MPRis also equal to the area of triangles MNP 1RPQ. Point P is the midpoint of side ____​ NQ​, sotriangle MNP is equal in area to triangle RQP.Thus, triangle MPR 5 2(RQP). The area of theunshaded region is the sum of the areas of trianglesMPR and MNP.MNP 5 RQP 5 24 sq cmMPQ 5 2(RQP) 5 48 sq cmThus, the area of the unshaded region is24 1 48 5 72 sq cm59. (C) To find the average, multiply each number ofsongs by the number of radio stations. Thenadd those products and divide by the totalnumber of radio stations:_____________________________________________(14 • 8) 1 (15 • 4) 1 (16 • 4) 1 (17 • 5) 1 (18 • 9)305 ​ __________________________112 1 60 1 64 1 85 1 162​305 16.160. (F) |190 – 210| |19 – 21| x 100| 20 | | 2 | x 10020 2 x 100x 7861. (B) Use proportions to make the conversions:​ ​ ​ ​Lorgs to dollars____ 140x 5 __ 717x 5 140 x 5 $20Dalts to dollars___ 16x 5 ____ 0.510.5x 5 16 x 5 $32Total dollars 5 20 1 32 5 $5262. (G) The question asks for the number of childrenwith blond hair or brown eyes, but not both.According to the chart, 18 children have blondhair and blue eyes, and 15 children have browneyes and black hair. 18 15 33 childrenwith blond hair or brown eyes, but not both.63. (A) The only item on the chart that is priced above$75 is the rain coat. Only one rain coat waspurchased. Calculate the sales tax on theprice of that rain coat:$102 3 0.06 5 $6.12102

​​​​​Sample Test – MathematicsExplanations of Correct AnswersBForm64. (K) The values in the problem can be grouped into 68. (F) It may be easier to see the order of the3 terms that each contain a positive and negativevalue: ( 2, 4), ( 6, 8), ( fractions by changing them to mixed22, 24). Arrangenumbers or decimals:the terms into 2 rows to determine the patternand find the missing terms:3 ​ 5 3​ 2__ ​5 3.666…___ 113 2 6 … 22___ 2574 8 … 24​ 5 3​ 4__ ​5 3.57…7___ 18The values in the top row are decreasing by5 ​ 5 3​ 3__ ​5 3.654, while the values in the bottom row areThe smallest fraction is ​___25 ​, followed by ​18 ___7 5increasing by 4. Fill in the remaining values:​,and finally ​___113 2 6 10 14 18 ​.224 8 12 16 20 2469. (D) First, find the sale price of the dress. If it is onTo find the sum, combine the terms as follows:( 2 1 4) 1 ( 6 1 8) 1 ( 10 1 12) 1 … 1 ( 22 1 24)sale for ​__1 ​off the original price, the sale price3Note that each pair of parentheses sums to 2.is ​2__3 ​of the original price: $450 3 ​ 2__3 ​ 5 $300Count the number of pairs of parentheses (6)and multiply to find the final answer:Alia has a 10% discount on the sale price. 10%of $300 is $30, so the discounted price will be:2 1 2 1 2 1 … 1 2 5 6(2) 5 12$300 2 $30 = $270Next, calculate the sales tax on the discounted65. (B) The pitcher originally contained 44 ouncesprice: $270 3 0.06 5 $16.20of juice (32 12). If x ounces of grapefruitjuice is added, the pitcher now containsSo, the total cost that Alia pays for the dress is:44 x ounces of juice. 12 x ounces of that$270 1 $16.20 5 $286.20is grapefruit juice, which makes up ​__1 ​of the3entire juice mix. Use that information to setup a proportion to solve for x:70. (H) The tallest tree (T) goes in the middle, so thereis only 1 possible location for that tree. The_______ 12 x44 x ​ ​ __ 13 ​next two tallest trees (call them a and b) goon either side of the tallest tree, so there are 23(12 x) 44 xpossible options (aTb and bTa). The final two36 3x 44 xtrees (c and d) go on either side of the set2x 8(caTbd, daTbc, cbTad, dbTac). So, there are 4different ways to arrange the trees.x 4 ouncesYou could also use the counting principle to66. (J) To find the median, first count the number ofsolve this: 1 3 2 3 2 5 4tests (Xs) in the figure, which is 17. The medianis the middle value. The middle value of 17is 9. Counting from the left, find the ninth X in 71. (C) The question asks for integers that are notthe figure to determine the median score (80).divisible by 2 or 3. Since all even numbers aredivisible by 2, begin by listing the odd integersin this set:67. (C) If the ratio is 5 ounces of gasoline to 6 ounces ofoil, then gasoline makes up ​___513, 15, 17, 19, 21, 23, 25, 27, 29​ of the fuel mix.11Use a proportion to calculate the number ofThen, eliminate those integers that are multiplesof 3. The remaining integers are:ounces of gasoline (x) in 33 ounces of mix:13, 17, 19, 23, 25, 29___ x33 ​ ​ ___ 511 ​ x 15 ounce The answer is 6.103

​​​​​Sample Test – MathematicsExplanations of Correct AnswersBForm64. (K) The values in the problem can be grouped into 68. (F) It may be easier to see the order of the3 terms that each contain a positive and negativevalue: ( 2, 4), ( 6, 8), ( fractions by changing them to mixed22, 24). Arrangenumbers or decimals:the terms into 2 rows to determine the patternand find the missing terms:3 ​ 5 3​ 2__ ​5 3.666…___ 113 2 6 … 22___ 2574 8 … 24​ 5 3​ 4__ ​5 3.57…7___ 18The values in the top row are decreasing by5 ​ 5 3​ 3__ ​5 3.654, while the values in the bottom row areThe smallest fraction is ​___25 ​, followed by ​18 ___7 5increasing by 4. Fill in the remaining values:​,and finally ​___113 2 6 10 14 18 ​.224 8 12 16 20 2469. (D) First, find the sale price of the dress. If it is onTo find the sum, combine the terms as follows:( 2 1 4) 1 ( 6 1 8) 1 ( 10 1 12) 1 … 1 ( 22 1 24)sale for ​__1 ​off the original price, the sale price3Note that each pair of parentheses sums to 2.is ​2__3 ​of the original price: $450 3 ​ 2__3 ​ 5 $300Count the number of pairs of parentheses (6)and multiply to find the final answer:Alia has a 10% discount on the sale price. 10%of $300 is $30, so the discounted price will be:2 1 2 1 2 1 … 1 2 5 6(2) 5 12$300 2 $30 = $270Next, calculate the sales tax on the discounted65. (B) The pitcher originally contained 44 ouncesprice: $270 3 0.06 5 $16.20of juice (32 12). If x ounces of grapefruitjuice is added, the pitcher now containsSo, the total cost that Alia pays for the dress is:44 x ounces of juice. 12 x ounces of that$270 1 $16.20 5 $286.20is grapefruit juice, which makes up ​__1 ​of the3entire juice mix. Use that information to setup a proportion to solve for x:70. (H) The tallest tree (T) goes in the middle, so thereis only 1 possible location for that tree. The_______ 12 x44 x ​ ​ __ 13 ​next two tallest trees (call them a and b) goon either side of the tallest tree, so there are 23(12 x) 44 xpossible options (aTb and bTa). The final two36 3x 44 xtrees (c and d) go on either side of the set2x 8(caTbd, daTbc, cbTad, dbTac). So, there are 4different ways to arrange the trees.x 4 ouncesYou could also use the counting principle to66. (J) To find the median, first count the number ofsolve this: 1 3 2 3 2 5 4tests (Xs) in the figure, which is 17. The medianis the middle value. The middle value of 17is 9. Counting from the left, find the ninth X in 71. (C) The question asks for integers that are notthe figure to determine the median score (80).divisible by 2 or 3. Since all even numbers aredivisible by 2, begin by listing the odd integersin this set:67. (C) If the ratio is 5 ounces of gasoline to 6 ounces ofoil, then gasoline makes up ​___513, 15, 17, 19, 21, 23, 25, 27, 29​ of the fuel mix.11Use a proportion to calculate the number ofThen, eliminate those integers that are multiplesof 3. The remaining integers are:ounces of gasoline (x) in 33 ounces of mix:13, 17, 19, 23, 25, 29___ x33 ​ ​ ___ 511 ​ x 15 ounce The answer is 6.103

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