1- Choice B is correct
The correct answer is 180∘ The sum of all angles in a quadrilateral is 360 degrees. Let x be the smallest angle in the quadrilateral. Then the angles are: x,2 x,3 x,6 x x + 2 x + 3 x + 6 x=360→12 x=360→x=30 The angles in the quadrilateral are: 30∘,60∘,90∘, and 180∘
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2- Choice B is correct
The correct answer is $1,458 Use simple interest formula: I=prt (I= interest, p= principal, r= rate, t= time) I=(18000) (0.027) (3)=1458
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3- Choice A is correct
The correct answer is 6 x + 32 x2 + 2 x (fg)(x)=f(x)g(x)=6 x + 32 x2 + 2 x
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4- Choice C is correct
The correct answer is 6 √ππ Formula for the area of a circle is: A =π r2 Using 36 for the area of the circle we have: 36=π r2 Let’s solve for the radius (r). 36π=r2→r=√36π=6√π=6√π × √π√π=6 √ππ
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5- Choice A is correct
The correct answer is 12,000 Number of visiting fans: 4 × 3000010=12,000
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6- Choice C is correct
The correct answer is y=8 x − 22 The equation of a line is: y=m x + b, where m is the slope and is the y−intercept. First find the slope: m=y2 − y1x2 − x1=18 − (− 6)5 − 2=243=8 Then, we have: y=8 x + b Choose one point and plug in the values of x and y in the equation to solve for b. Let’s choose the point (2,− 6) y=8 x + b→− 6=8 (2) + b→− 6=16 + b→b=− 22 The equation of the line is: y=8 x − 22
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7- Choice D is correct
The correct answer is 120 degree The angle x and 35 are complementary angles. Therefore: x + 60=180 180∘ − 60∘=120∘
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8- Choice B is correct
The correct answer is √204 sin A=64⇒ Since sin θ=oppositehypotenuse, we have the following right triangle. Then: c=√62 − 42=√36 − 16=√20 cos =√204
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9- Choice E is correct
The correct answer is 90 Length of the rectangle is: 32 × 18=27 perimeter of rectangle is: 2 × (27 + 18)=90
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10- Choice B is correct
The correct answer is 40 First, find the number. Let x be the number. Write the equation and solve for x. 120% of a number is 60, then: 1.2 × x=60⇒x=60 ÷ 1.2=50 80% of 50 is: 0.9 × 50=40
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11- Choice A is correct
The correct answer is 96,000 Three times of 32,000 is 128,000. One sixth of them cancelled their tickets. One sixth of 128,000 equals 32,000 (14 × 128000=32000). 96,000 (128000 – 32000=96000) fans are attending this week
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12- Choice D is correct
The correct answer is 512 cm3 If the length of the box is 32, then the width of the box is one Fourth of it, 8, and the height of the box is 2 (one Fourth of the width). The volume of the box is: V = (length) × (wdth) × (height) =(32) × (8) × (2)=512 cm3
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13- Choice D is correct
The correct answer is 513 tan=oppositeadjacet, and tanx=512, therefore, the opposite side of the angle x is 5 and the adjacent side is 12. Let’s draw the triangle. Using Pythagorean theorem, we have: a2 + b2=c2→52 + 122=c2→25 + 144=c2→c=13 sin x=oppositehypotenuse=513
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14- Choice C is correct
The correct answer is 8.6 × 105 860000=8.6 × 105
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15- Choice A is correct
The correct answer is 1 Plug in the value of each option in the inequality. A. 1 (1 − 3)2 + 2 > 4 (1) − 5→6 >− 1 Bingo! B. 6 (6 − 3)2 + 2 > 4 (6) − 5→11 > 19 No! C. 8 (8 − 3)2 + 2 > 4 (8) − 5→27 > 27 No! D. 3 (3 − 3)2 + 2 > 4 (3) − 5→2 > 7 No! E. 4 (4 − 3)2 + 3 > 4 (4) − 5→4 > 11 No!
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16- Choice C is correct
The correct answer is x ≥ 3 ∪ x ≤− 11 x + 4 ≥ 7→x ≥ 7 − 4→x ≥ 3 Or x + 4 ≤ − 7→x ≤ − 7 − 4→x ≤ − 11 Then, solution is: x ≥ 3 ∪ x ≤ − 11
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17- Choice B is correct
The correct answer is 5 √5 Based on triangle similarity theorem: aa + b=c4→c=4 aa + b=4 √54 √5=1→ area of shaded region is: (c + 42) (b)=52 × 2 √5=5 √5
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18- Choice C is correct
The correct answer is 82% the population is increased by 30% and 40%. 15% increase changes the population to 130% of original population. For the second increase, multiply the result by 140%. (1.30) × (1.40)=1.82=182% 82 percent of the population is increased after two years.
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19- Choice C is correct
The correct answer is 1 − √5 x1,2=− b±√b2 − 4 a c2 a a x2 + b x + c=0 2 x2 − 4 x – 8=0⇒ then: a=1, b=− 2 and c=– 4 x=2 + √− 22 − (4).(1).(− 4)2.1=1 − √5 x=2 − √− 22 − (4).(1).(− 4)2.1=1 + √5
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20- Choice B is correct
The correct answer is x129 (x2)69=x2 × 69=x126=
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21- Choice E is correct
The correct answer is $3 Let x be the cost of one-kilogram orange, then: 4 x + (3 × 6)=30→ 4 x + 18=30→ 4 x=30 − 18→ 4 x=12→x=124=$3
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22- Choice D is correct
The correct answer is 40 Let x be the length of AB, then: 30=x × 22→x=15 The length of AC =√152 + 82=√289=17 The perimeter of △ABC =15 + 8 + 17=40
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23- Choice B is correct
The correct answer is 2 x5 Simplify the expression. √x25 − x225=√5 x225 − x225=√4 x225=√425 x2= √425 × √x2=25 × x=2 x5
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24- Choice D is correct
The correct answer is y25 Solve for x. 5 √x=√y Square both sides of the equation: (5 √x)2=(√y)2 25 x=y x=y25
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25- Choice A is correct
The correct answer is 29 The probability of choosing a Hearts is 1672=29
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26- Choice C is correct
The correct answer is 57.81 average =sum of termsnumber of terms The sum of the weight of all girls is: 23 × 50=1150 kg The sum of the weight of all boys is: 25 × 65=1625 kg The sum of the weight of all students is: 1150 + 1625=2775 kg average =277548=57.81
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27- Choice D is correct
The correct answer is 135 x + 18,000 ≤ 35,000 Let x be the number of shoes the team can purchase. Therefore, the team can purchase 120 x. The team had $35,000 and spent $18000. Now the team can spend on new shoes $17000 at most. Now, write the inequality: 135 x + 18,000 ≤ 35,000
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28- Choice C is correct
The correct answer is − 9 Plug in the value of x and, x=4 and y=2 4 (x + 3 y) − (3 + x)2= 4 (4 + 3 (2)) − (3 + 4)2= 4 (4 + 6) − (7)2=40 − 49=− 9
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29- Choice A is correct
The correct answer is 25 Let x be the smallest number. Then, these are the numbers: x,x + 1,x + 2,x + 3,x + 4 average =sum of termsnumber of terms⇒ 27=x + (x + 1) + (x + 2) + (x + 3) + (x + 4)5⇒ 27=5 x + 105⇒ 135=5 x + 10⇒ 125=5 x⇒x=25
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30- Choice E is correct
The correct answer is 16 x6 y=(− 4 x3)2=(− 4)2 (x3)2=16 x6
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31- Choice B is correct
The correct answer is 8 cm Formula for the Surface area of a cylinder is: SA =2 π r2 + 2 π h→192 π=2 π r2 + 2 π r (4)→r2 + 4 r − 96=0 Factorize and solve for r. (r + 12) (r − 8)=0→r=8 or =− 12 (unacceptable)
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32- Choice D is correct
The correct answer is 27% The question is this: 616.85 is what percent of 845? Use percent formula: part =percent100 × whole 616.85=percent100 × 845⇒ 616.85=percent × 845100⇒ 61685= percent × 845⇒ percent =61685845=73 616.85 is 73% of 845. Therefore, the discount is: 100% – 73%=27%
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33- Choice E is correct
The correct answer is 30 The area of rectangle is: 6 × 3=18 cm2 The area of circle is: π r2=π × (82)2=3 × 16=48 cm2 Difference of areas is: 48 − 18=30
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34- Choice B is correct
The correct answer is 130 miles Use the information provided in the question to draw the shape. Use Pythagorean Theorem: a2 + b2=c2 502 + 1202=c2⇒ 2500 + 14400=c2⇒ 16900=c2⇒c=130
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35- Choice C is correct
The correct answer is − 13 The equation of a line in slope intercept form is: y=m x + b Solve for y. 9 x − 3 y=24⇒ − 3 y=24 − 9 x⇒ y=(24 − 9 x) ÷ (− 3)⇒ y=3 x − 8 The slope is 3. The slope of the line perpendicular to this line is: m1 × m2=− 1⇒ 3 × m2=− 1⇒ m2=− 13
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36- Choice B is correct
The correct answer is x354 − 5 f(g(x))=4 × (x6)3 − 5=4 x3216 − 5=x354 − 5
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37- Choice E is correct
The correct answer is 125 The ratio of boy to girls is 1:5. Therefore, there are 1 boys out of 6 students. To find the answer, first divide the total number of students by 6, then multiply the result by 1. 750 ÷ 6=125⇒125 × 1=125
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38- Choice C is correct
The correct answer is 114 Write the ratio of 7 a to 4 b. 7 a4 b=18 Use cross multiplication and then simplify. 7 a × 8=4 b × 1→56 a=4 b→a=4 b56=b14 Now, find the ratio of a to b. ab=b14b→b14 ÷ b=b14 × 1b=b14 b=114
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39- Choice A is correct
The correct answer is √32 The relationship among all sides of right triangle 30∘ − 60∘ − 90∘ is provided in the following triangle: Sine of 60∘ equals to: oppositehypotenuse=x√32 x=√32
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40- Choice D is correct
The correct answer is 31 Plug in the value of x in the equation and solve for y. 4 y=4 x22 − 4→ 4 y=4 (8)22 − 4→ 4 y=4 (64)2 − 4→ 4 y=128 − 4=124 4 y=124→y=31
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