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Simplification problems
1. If a : b = c : d = 1 : 6, then what is the value of a2+c2b2+d2 ?
Options
A. 1/600
B. 1/60
C. 1/36
D. 1/360
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Correct Answer: 1/36
2. For x > 0, what is the minimum value of x + x+22x ?
Options
A. 1
B. 2
C. 2.5
D. 1.5
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Correct Answer: 2.5
3. If 1/3(12x/5 - 1/2) + 6/5 = 7/6, then what is the value of x?
Options
A. 1/6
B. -1/6
C. 1/5
D. -1/5
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Correct Answer: 1/6
4. If a - b = 10 and ab =-21, then what is the value of a3-b3 ?
Options
A. 316
B. 370
C. 185
D. 158
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Correct Answer: 370
5. What is the reflection of the point (5, -2) in the line y = -1?
Options
A. (-7 , -2)
B. (-5 , 0)
C. (5 , 0)
D. (-7 , 2)
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Correct Answer: (5 , 0)
6. ax + 3y = 6 has slope -2/3. What is the value of a?
Options
A. -2
B. 2
C. 3
D. -3
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Correct Answer: 2
7. What is the value of Sin 30° + 2 Cos 30° ?
Options
A. (2?2 + 3)/?6
B. (9 + 2?3)/9
C. (1 + 2?3)/2
D. (2?6 + 1)/?3
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Correct Answer: (1 + 2?3)/2
8. ? XYZ is right angled at Y. If m?Z = 60°, what is the length of YZ (in cm), if ZX = 3?3 cm?
Options
A. 3?3/2
B. 3?3
C. 9
D. 6
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Correct Answer: 3?3/2
9. If Sec ? = 13/12, then Cot ? = ?
Options
A. 12/5
B. 13/5
C. 5/13
D. 5/12
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Correct Answer: 12/5
10. If 7x - (3/2) * (4x - 9) = 6.5, then the value of x is?
Options
A. 7
B. 20
C. -7
D. -20
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Correct Answer: -7
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