2016SHSAT_English
2016SHSAT_English 2016SHSAT_English
Explanation of correct answersGrade 9 Mathematics9grade7. (B) If the coordinates of a point labeled R are (a, b),then a 908 counterclockwise rotation aboutthe origin would make the coordinates of pointR9 ( 2 b, a). A 908 clockwise rotation about theorigin would make the coordinates of R9 (b, 2 a).In the question, P is (3, 5) and P9 is (5, 2 3).Using the rule stated above, P9 is the imageafter point P is rotated 908 clockwise.Alternatively, it may help to make a sketchof this problem. Place the two points onthe coordinate grid: Point P is in the firstquadrant, and point P9 is in the fourthquadrant. Draw a line from each point to theorigin. The angle formed at the origin shouldresemble a right angle, which is option B (908).yP (3, 5)xP9(5, – 3)8. (H) In order to add or subtract two numbers inscientific notation, the exponent on the 10 mustbe the same. Since the question asks for thevalue of k 3 10 19 , change both terms into thissame power of 10:12.6 × 10 18 5 (1.26 3 10) 3 10 18 5 1.26 3 10 191.1 × 10 17 5 (0.011 3 10 2 ) 3 10 17 5 0.011 3 10 19Now, perform the subtraction:(1.26 × 10 19 ) 2 (0.011 3 10 19 )5 (1.26 2 0.011) 3 10 195 1.249 3 10 19Thus, k 5 1.2499. (C) At the beginning (hour 0), the pool is empty.After 5 hours, the pool holds 2,000 gallons.Thus, the rate of change (or slope of the line)2,000 − 0is _________5 − 0 5 ______ 2,000 5 400 gallons per hour.5To find the number of gallons after 20 hours,multiply the rate by the number of hours:400 3 20 5 8,000 gallons.10. (G) Using the translation equation given in thequestion, set up two small equations to findn and r:For n:x 1 10 5 100x 5 90For r:y – 10 5 100y 5 110So, (n, r) 5 (90, 110)11. (A) Because both triangles are right triangles thatshare a vertex, they are similar. To find x, setup a proportion using the two known sides ofeach triangle:________ (4 1 x)1.0 5 ____ 40.8 0.8 (4 x) 5 1.0 (4)4 1 x 5 5x 5 112. (H) An x-intercept of 3 means the point (3, 0) is online k. Using (3, 0) and (2 3, 4), calculate theslope (m) of the line:(420)m 5 _______( 2 323) 5 4__6 5 2__3 The equation of line k must contain slope 2__3 ,so only Options G and H are potentially correct.Next, find which of the two equations is true forthe point (3, 0). To solve, substitute 3 for x ineach equation and find the one in which y 5 0.112
Explanation of correct answersGrade 9 Mathematics9gradeOption G: y 5 2__3 (3) − 3 5 2 2 2 3 5 2 5Option H: y 5 2__3 (3) 1 2 5 2 2 1 2 5 0Option H is the correct answer.13. (B) Since P is on the x-axis, we know its y-valuemust equal 0. Use that in the equation tosolve for x:y 5 15x – 450 5 15x – 4545 5 15x3 5 xSo, the coordinates for P are (3, 0).14. (G) The question asks for the second integer, so letn be the second integer. Then, the sum of the 7integers is:(n – 1) 1 n 1 (n 1 1) 1 (n 1 2) 1 (n 1 3) 1(n 1 4) 1 (n 1 5) 5 7k7n 1 14 5 7k7(n 1 2) 5 7kn 1 2 5 kn 5 k – 215. (B) A rational number is a number that can bewritten as a fraction. Since p 5 q, then __p q 5 1,___ p 25 1, and p 2 q 5 0, all of which are2qrational. That leaves two expressions to test:1p 1 q 5 ____Ï 1 ____ 12 Ï 2 5 ____ 2Ï 2(irrational because Ï __ 2 is irrational)p 2 1 q 2 5 (1 ____Ï __ 2 ) 2 1 (1____Ï 2) 2 5 1__2 1 1__2 5 1 (rational)Thus, p 1 q is not a rational expression.16. (G) Since the number of red flashes is known (15),G calculate where the robot would be after the15 red flashes. For each red flash,(x, y) (x – 1, y 1 4). So, after 15 red flashes:(1 2 [1 3 15], 2 2 1 [4 3 15]) 5 ( 2 14, 58)Next, use the point ( 2 14, 58) to calculate wherethe robot will be after n blue flashes. For eachblue flash, (x, y) (x 1 4, y 2 5). So, after nblue flashes: ( 2 14 1 4n, 58 2 5n)The question states that the robot’s finalposition is on the line y 5 x, which means thex- and y-coordinates will have the same value.To find n, set the two coordinates above asequal and solve for n:2 14 1 4n 5 58 – 5n9n 5 72n 5 817. (C) First, determine which integer values of xwould make each inequality true:|x – 1| , 3 can also be written as2 3 , x – 1 , 3Adding 1 to each term results in2 2 , x , 4Since these are only “less than” and not “lessthan or equal to,” the possible values of x forthis inequality are 2 1, 0, 1, 2, and 3.Similarly, |x 1 2| , 4 can also be written as2 4 , x 1 2 , 4Subtracting 2 from each term results in2 2 , x , 2The possible values of x in this inequality are2 1, 0, and 1.The possible x values in common betweenthe two inequalities are 2 1, 0, and 1, so theanswer is 3.Answer Key for Grade 9 Mathematics1. A2. J3. C4. F5. B6. J7. B8. H9. C10. G11. A12. H13. B14. G15. B16. G17. C113
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Explanation of correct answersGrade 9 Mathematics9gradeOption G: y 5 2__3 (3) − 3 5 2 2 2 3 5 2 5Option H: y 5 2__3 (3) 1 2 5 2 2 1 2 5 0Option H is the correct answer.13. (B) Since P is on the x-axis, we know its y-valuemust equal 0. Use that in the equation tosolve for x:y 5 15x – 450 5 15x – 4545 5 15x3 5 xSo, the coordinates for P are (3, 0).14. (G) The question asks for the second integer, so letn be the second integer. Then, the sum of the 7integers is:(n – 1) 1 n 1 (n 1 1) 1 (n 1 2) 1 (n 1 3) 1(n 1 4) 1 (n 1 5) 5 7k7n 1 14 5 7k7(n 1 2) 5 7kn 1 2 5 kn 5 k – 215. (B) A rational number is a number that can bewritten as a fraction. Since p 5 q, then __p q 5 1,___ p 25 1, and p 2 q 5 0, all of which are2qrational. That leaves two expressions to test:1p 1 q 5 ____Ï 1 ____ 12 Ï 2 5 ____ 2Ï 2(irrational because Ï __ 2 is irrational)p 2 1 q 2 5 (1 ____Ï __ 2 ) 2 1 (1____Ï 2) 2 5 1__2 1 1__2 5 1 (rational)Thus, p 1 q is not a rational expression.16. (G) Since the number of red flashes is known (15),G calculate where the robot would be after the15 red flashes. For each red flash,(x, y) (x – 1, y 1 4). So, after 15 red flashes:(1 2 [1 3 15], 2 2 1 [4 3 15]) 5 ( 2 14, 58)Next, use the point ( 2 14, 58) to calculate wherethe robot will be after n blue flashes. For eachblue flash, (x, y) (x 1 4, y 2 5). So, after nblue flashes: ( 2 14 1 4n, 58 2 5n)The question states that the robot’s finalposition is on the line y 5 x, which means thex- and y-coordinates will have the same value.To find n, set the two coordinates above asequal and solve for n:2 14 1 4n 5 58 – 5n9n 5 72n 5 817. (C) First, determine which integer values of xwould make each inequality true:|x – 1| , 3 can also be written as2 3 , x – 1 , 3Adding 1 to each term results in2 2 , x , 4Since these are only “less than” and not “lessthan or equal to,” the possible values of x forthis inequality are 2 1, 0, 1, 2, and 3.Similarly, |x 1 2| , 4 can also be written as2 4 , x 1 2 , 4Subtracting 2 from each term results in2 2 , x , 2The possible values of x in this inequality are2 1, 0, and 1.The possible x values in common betweenthe two inequalities are 2 1, 0, and 1, so theanswer is 3.Answer Key for Grade 9 Mathematics1. A2. J3. C4. F5. B6. J7. B8. H9. C10. G11. A12. H13. B14. G15. B16. G17. C113
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