Q. If the true discount on a sum of money is $200 and the rate of interest is 10% per annum for 2 years, what is the present worth?
A.
$800
B.
$1000
C.
$1200
D.
$1500
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Solution
True Discount = Present Worth * Rate * Time / 100. Let Present Worth = x. Then, 200 = x * 10 * 2 / 100. Solving gives x = $1000.
Correct Answer:
B
— $1000
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Q. If the true discount on a sum of money is $250 and the present worth is $1250, what is the time period at 8% per annum?
A.
1 year
B.
2 years
C.
3 years
D.
4 years
Show solution
Solution
True Discount = Present Worth * Rate * Time / 100. 250 = 1250 * 8 * Time / 100. Time = (250 * 100) / (1250 * 8) = 2 years.
Correct Answer:
B
— 2 years
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Q. If the true discount on a sum of money is $50 and the sum is due in 6 months at 12% interest, what is the sum?
A.
$500
B.
$600
C.
$700
D.
$800
Show solution
Solution
True Discount = Sum * Rate / (100 + Rate). Let Sum = x. Then, 50 = x * 12 / (100 + 12/2). Solving gives x = $600.
Correct Answer:
B
— $600
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Q. If today is April 15, what will be the date after 100 days?
A.
July 24
B.
July 25
C.
July 26
D.
July 27
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Solution
April has 15 days left after April 15. 100 - 15 = 85 days left. May has 31 days, June has 30 days, and July has 24 days. 15 + 31 + 30 + 24 = 100. So, the date will be July 25.
Correct Answer:
B
— July 25
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Q. If today is Friday, what day will it be 50 days from now?
A.
Saturday
B.
Sunday
C.
Monday
D.
Tuesday
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Solution
50 days = 7 weeks + 1 day. Therefore, it will be Saturday, which is 1 day after Friday.
Correct Answer:
C
— Monday
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Q. If today is July 4, 2023, what will be the date 200 days from now?
A.
January 20, 2024
B.
January 21, 2024
C.
January 22, 2024
D.
January 23, 2024
Show solution
Solution
From July 4 to July 31 is 27 days. August has 31 days, September has 30 days, October has 31 days, November has 30 days, December has 31 days, and January has 31 days. 27 + 31 + 30 + 31 + 30 + 31 + 20 = 200 days. Thus, it will be January 20, 2024.
Correct Answer:
A
— January 20, 2024
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Q. If today is March 15, 2023, what will be the date after 100 days?
A.
June 23, 2023
B.
June 24, 2023
C.
June 25, 2023
D.
June 26, 2023
Show solution
Solution
March has 31 days, so from March 15 to March 31 is 16 days. April has 30 days, May has 31 days, and June has 30 days. 16 + 30 + 31 + 23 = 100 days. Therefore, the date will be June 24, 2023.
Correct Answer:
B
— June 24, 2023
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Q. If today is October 10, 2023, what will be the date 50 days from now?
A.
November 29, 2023
B.
November 30, 2023
C.
December 1, 2023
D.
December 2, 2023
Show solution
Solution
From October 10 to October 31 is 21 days. November has 30 days. 50 - 21 = 29 days left in November. Thus, it will be November 30, 2023.
Correct Answer:
B
— November 30, 2023
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Q. If today is the 15th of a month, what is the maximum number of days left in that month?
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Solution
The maximum number of days in a month is 31. If today is the 15th, there are 31 - 15 = 16 days left.
Correct Answer:
A
— 14
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Q. If today is the 1st of a month and it has 31 days, what will be the day of the week on the 31st of that month?
A.
Same as today
B.
One day later
C.
Two days later
D.
Three days later
Show solution
Solution
31 days = 4 weeks + 3 days. Therefore, the day on the 31st will be three days later than the 1st.
Correct Answer:
B
— One day later
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Q. If two numbers are in the ratio 3:4 and their H.C.F. is 2, what are the numbers?
A.
6 and 8
B.
4 and 6
C.
8 and 10
D.
10 and 12
Show solution
Solution
The numbers are 3*2 and 4*2, which are 6 and 8.
Correct Answer:
A
— 6 and 8
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Q. If y = (2x + 1)^3, find dy/dx at x = 1.
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Solution
dy/dx = 6(2x + 1)^2. At x = 1, dy/dx = 6(2(1) + 1)^2 = 6(3)^2 = 54.
Correct Answer:
A
— 12
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Q. If y = (2x + 1)^3, find dy/dx.
A.
6(2x + 1)^2
B.
3(2x + 1)^2
C.
2(2x + 1)^2
D.
12(2x + 1)^2
Show solution
Solution
dy/dx = 6(2x + 1)^2 by the chain rule.
Correct Answer:
A
— 6(2x + 1)^2
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Q. If y = (x^2 + 1)^5, find dy/dx at x = 1.
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Solution
dy/dx = 5(x^2 + 1)^4(2x). At x = 1, dy/dx = 5(2)^4(2) = 5(16)(2) = 160.
Correct Answer:
B
— 20
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Q. If y = (x^2 + 1)^5, find dy/dx.
A.
10x(x^2 + 1)^4
B.
5(x^2 + 1)^4
C.
5x(x^2 + 1)^4
D.
20x(x^2 + 1)^3
Show solution
Solution
dy/dx = 10x(x^2 + 1)^4 by the chain rule.
Correct Answer:
A
— 10x(x^2 + 1)^4
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Q. If y = 2^x, find dy/dx at x = 1.
A.
0.693
B.
1.386
C.
2.718
D.
3.141
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Solution
dy/dx = 2^x * ln(2). At x = 1, dy/dx = 2^1 * ln(2) = 2 * 0.693 = 1.386.
Correct Answer:
A
— 0.693
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Q. If y = 3x^2 + 2x, find dy/dx at x = 2.
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Solution
First, find dy/dx = 6x + 2. At x = 2, dy/dx = 6(2) + 2 = 12 + 2 = 14.
Correct Answer:
B
— 18
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Q. If y = 4x^2 + 3x + 2, find dy/dx at x = -1.
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Solution
dy/dx = 8x + 3. At x = -1, dy/dx = 8(-1) + 3 = -8 + 3 = -5.
Correct Answer:
A
— -5
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Q. If y = 4x^3 - 2x + 1, find dy/dx at x = -1.
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Solution
dy/dx = 12x^2 - 2. At x = -1, dy/dx = 12(-1)^2 - 2 = 12 - 2 = 10.
Correct Answer:
C
— -6
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Q. If y = 5x^4 + 3x^2 - x, find dy/dx at x = 1.
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Solution
dy/dx = 20x^3 + 6x - 1. At x = 1, dy/dx = 20(1)^3 + 6(1) - 1 = 20 + 6 - 1 = 25.
Correct Answer:
B
— 22
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Q. If y = 5x^4 - 3x^3 + 2x - 1, find dy/dx at x = 1.
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Solution
dy/dx = 20x^3 - 9x^2 + 2. At x = 1, dy/dx = 20 - 9 + 2 = 13.
Correct Answer:
B
— 16
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Q. If y = cos(5x^2), find dy/dx.
A.
-10xsin(5x^2)
B.
-5xsin(5x^2)
C.
-25xsin(5x^2)
D.
-2xsin(5x^2)
Show solution
Solution
dy/dx = -10xsin(5x^2) by the chain rule.
Correct Answer:
A
— -10xsin(5x^2)
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Q. If y = e^(3x), find dy/dx at x = 0.
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Solution
dy/dx = 3e^(3x). At x = 0, dy/dx = 3e^(0) = 3.
Correct Answer:
A
— 1
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Q. If y = e^(3x), find dy/dx.
A.
3e^(3x)
B.
e^(3x)
C.
9e^(3x)
D.
6e^(3x)
Show solution
Solution
dy/dx = 3e^(3x) by the chain rule.
Correct Answer:
A
— 3e^(3x)
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Q. If y = ln(5x^2 + 3), find dy/dx at x = 1.
A.
5/8
B.
3/8
C.
1/8
D.
1/5
Show solution
Solution
dy/dx = (10x)/(5x^2 + 3). At x = 1, dy/dx = (10)/(5(1) + 3) = 10/8 = 5/4.
Correct Answer:
A
— 5/8
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Q. If y = ln(5x^2 + 3), find dy/dx.
A.
10/(5x^2 + 3)
B.
5/(5x^2 + 3)
C.
2/(5x^2 + 3)
D.
15/(5x^2 + 3)
Show solution
Solution
dy/dx = (10x)/(5x^2 + 3) by the chain rule.
Correct Answer:
A
— 10/(5x^2 + 3)
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Q. If y = sin(2x), find dy/dx at x = π/4.
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Solution
dy/dx = 2cos(2x). At x = π/4, dy/dx = 2cos(π/2) = 2(0) = 0.
Correct Answer:
D
— √2
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Q. If y = sqrt(4x^2 + 1), find dy/dx.
A.
(4x)/(sqrt(4x^2 + 1))
B.
(2x)/(sqrt(4x^2 + 1))
C.
(8x)/(sqrt(4x^2 + 1))
D.
(2)/(sqrt(4x^2 + 1))
Show solution
Solution
Using the chain rule, dy/dx = (4x)/(2sqrt(4x^2 + 1)) = (4x)/(sqrt(4x^2 + 1)).
Correct Answer:
A
— (4x)/(sqrt(4x^2 + 1))
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Q. If y = sqrt(x^2 + 1), find dy/dx at x = 0.
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Solution
dy/dx = (1/2)(x^2 + 1)^(-1/2)(2x). At x = 0, dy/dx = (1/2)(1)^(-1/2)(0) = 0.
Correct Answer:
B
— 1
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Q. If y = tan(3x), find dy/dx at x = π/6.
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Solution
dy/dx = 3sec^2(3x). At x = π/6, dy/dx = 3sec^2(π/2) = 3(∞) = undefined.
Correct Answer:
A
— 3√3
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