# Advanced Placement Calculus Final Exam Sample Test!

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Questions: 10 | Attempts: 259

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Hey, all of you young mathematicians, welcome to this short and essential Advanced Placement Calculus sample quiz! Here you are going to face ten most important questions on the same topic for which you shall be judged how much you have learned in your math classes. So, let's get started.

• 1.
• A.

1/2

• B.

2

• C.

3

• D.

-0.5

C. 3
Explanation
The correct answer is 3 because it is the only whole number among the given options. The other options, 1/2, 2, and -0.5, are not whole numbers.

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• 2.
• A.

-6

• B.

-7

• C.

-8

• D.

-9

D. -9
• 3.
• A.

0

• B.
• C.

-1

• D.

1

A. 0
• 4.
C.
• 5.

D.
• 6.

### Compute the derivative of    4 sec(x) - 3 csc(x)

• A.

4 csc(x) + 3 sec(x)

• B.

4 sec(x)tan(x) + 3 csc(x)cot(x)

• C.

4(csc(x))^2 + 3(sec(x))^2

• D.

4 csc(x)tan(x) - 3 csc(x)cot(x)

B. 4 sec(x)tan(x) + 3 csc(x)cot(x)
Explanation
The given expression is a combination of two trigonometric functions, sec(x) and csc(x). To find the derivative of this expression, we can use the rules of differentiation for trigonometric functions. The derivative of sec(x) is sec(x)tan(x), and the derivative of csc(x) is -csc(x)cot(x). Therefore, the derivative of 4 sec(x) - 3 csc(x) is 4 sec(x)tan(x) + 3 csc(x)cot(x).

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• 7.

### Compute

• A.

-pi

• B.

2pi

• C.

0

• D.

Pi

D. Pi
Explanation
The given question asks for the result of the computation of -pi. The negative sign in front of pi indicates that the value of pi should be multiplied by -1. Therefore, the correct answer is -pi.

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• 8.
D.
• 9.

B.
• 10.

### Determine the concavity of the graph of  f(x) = 2 sin(x) + 3(cos(x))^2  at x = pi.

• A.

6

• B.

-7

• C.

3

• D.

-6

D. -6
Explanation
To determine the concavity of the graph of f(x) at x = pi, we need to find the second derivative of f(x) and evaluate it at x = pi. The first derivative of f(x) is f'(x) = 2cos(x) - 6sin(x)cos(x), and the second derivative is f''(x) = -2sin(x) - 6sin^2(x) + 6cos^2(x). Evaluating f''(pi) gives us -2sin(pi) - 6sin^2(pi) + 6cos^2(pi) = 0 - 0 + 6(1) = 6. Since the second derivative is positive at x = pi, the graph is concave up at that point. Therefore, the given answer of -6 is incorrect.

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