  # Quest for Calculus Trivia Quiz

### This quiz will cover your knowledge of basic differential and integral calculus. Drop me a line if you like this quiz!

A multiple-choice quiz by Diamondlance. Estimated time: 4 mins.

Author
Diamondlance
Time
4 mins
Type
Multiple Choice
Quiz #
127,041
Updated
Dec 03 21
# Qns
10
Difficulty
Tough
Avg Score
6 / 10
Plays
5709
Awards
Top 35% Quiz
Last 3 plays: Guest 149 (2/10), Guest 147 (8/10), Guest 122 (2/10).
1. Find f'(x) (the derivative of f(x)) if f(x) = 7x^3 - 2x^2 + 4x - 5. Hint

21x^2 - 4x + 4 - 5
21x^2 - 4x + 4 - 5/x
21x^2 - 4x + 4 + C
21x^2 - 4x + 4

#### NEXT>

2. The integral of 3x^2 - 4x + 1 equals x^3 - 2x^2 + x. Is this always correct?

Yes
No

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3. Find dy/dx if y = e^a and a is constant. Hint

1
ln a
e^a
0

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4. If f(x) = x (ln x), find f'(x). Hint

1 + ln x
e^(x + 1)
(ln x)^2 + x
1 + e^x

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5. If the velocity of a particle at time t is represented by the equation v(t) = 8t + 2, find the position of the particle at time 3 if the position at time 0 is 0. Hint

42
26
8
0

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6. An object is in freefall. It remains in freefall for 5 seconds before it hits the ground. How high was the object when it first started falling if its starting velocity was 0? (Acceleration due to gravity is -9.8 meters/second^2). Hint

49 meters
245 meters
122.5 meters
15 meters

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7. Okay, an easier one. If f(x) = (sin x)/x, what is the limit of the function as x approaches zero? Hint

1
undefined
0

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8. Find the area of the region bounded by the graphs of y = x^2; x = 0; x = 2; and the x axis. Hint

3
10/3
7/3
8/3

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9. If f(x) = e^x, the integral of f(x) always equals the derivative of f(x).

Yes
No

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10. If f(x) = x^3 - 2x^2 + 4x + 1, how many inflection points does this graph have? Hint

1
2
0
3

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Quiz Answer Key and Fun Facts
1. Find f'(x) (the derivative of f(x)) if f(x) = 7x^3 - 2x^2 + 4x - 5.

Answer: 21x^2 - 4x + 4

The derivative of a polynomial equation can be found by multiplying the exponent of the variable by the coefficient of each term, then by reducing the exponent of the variable by one.
2. The integral of 3x^2 - 4x + 1 equals x^3 - 2x^2 + x. Is this always correct?

The correct answer is x^3 - 2x^2 + x + C. Here, C equals the "constant of integration", because, since integration is the same as antidifferentiation, without more information, it is impossible to know what, if any, constant the antiderivative had in its equation.
3. Find dy/dx if y = e^a and a is constant.

Since there is no x-dependence in the equation, y is equal to a constant. Therefore, the derivative equals zero.
4. If f(x) = x (ln x), find f'(x).

The rule for the derivative of a product is the first term times the derivative of the second term, plus the second term times the derivative of the first term.
5. If the velocity of a particle at time t is represented by the equation v(t) = 8t + 2, find the position of the particle at time 3 if the position at time 0 is 0.

The position function can be found by integrating the velocity funcion, which is 4t^2 + 2t + C. I said that the position at time 0 is 0, so 4(0) + 2(0) + C=0, which makes C = 0. Therefore, when t = 3, the position equals 4(9) + 2(3) = 36 + 6 = 42.
6. An object is in freefall. It remains in freefall for 5 seconds before it hits the ground. How high was the object when it first started falling if its starting velocity was 0? (Acceleration due to gravity is -9.8 meters/second^2).

a(t) = -9.8 since acceleration due to gravity is -9.8 meters/second^2. The velocity function is found by integrating the acceleration function. v(t) = -9.8t + C. Since the velocity at time 0 is 0, C = 0. Integrating this gives the position function, x(t) = -4.9t^2 + C. When t = 5, the position is zero. So, -4.9(25) + C = 0 and C = 122.5, which is the original height of the object.
7. Okay, an easier one. If f(x) = (sin x)/x, what is the limit of the function as x approaches zero?

L'h�pital's rule can be used to solve this one. If the limit evaluates to 0/0 (or infinity over infinity), then the limit equals the limit of the derivatives of each side of the fraction.
8. Find the area of the region bounded by the graphs of y = x^2; x = 0; x = 2; and the x axis.

This can be found by integrating the equation y = x^2 from 0 to 2. 8/3 - 0/3 = 8/3.
9. If f(x) = e^x, the integral of f(x) always equals the derivative of f(x).

The derivative is e^x, and the integral is e^x + C.
10. If f(x) = x^3 - 2x^2 + 4x + 1, how many inflection points does this graph have?

It has one at x = 2/3, where the second derivative equals zero. The point is indeed an inflection point because the second derivative, 6x - 4, changes signs at x = 2/3 and thus the graph changes concavity.
Source: Author Diamondlance

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