Question 1

A ramp is inclined at an angle $$	heta to $$the horizontal. Which trigonometric function best describes the ratio of the vertical height to the hypotenuse of the ramp?

Accepted Answer

$$\sin	heta$$

Question 2

A car travels along a straight road. The position $$x as a $$function of time $$t is $$given by $$x(t) = 5t^2$. What is the instantaneous velocity at t = 2$ s?

Accepted Answer

$$20 m/s$$

Question 3

Which of the following best describes the meaning of the slope in a position vs. time graph?

Accepted Answer

The rate of change of position with respect to time

Question 4

Evaluate $$\sin(60^\circ).$$

Accepted Answer

$$\frac{\sqrt{3}}{2}$$

Question 5

A ball moves at a constant speed of $$3 m/s $$for $$2$$ seconds. Using integration, what is the total distance traveled?

Accepted Answer

$$6 m$$

Question 6

Find the derivative of $$y = \sin x$$ with respect to $$x.$$

Accepted Answer

$$\cos x$$

Question 7

Which of the following is the correct derivative of $$y = x^n$$?

Accepted Answer

$$n x$$^{n-1}$$

Question 8

A function $$y = 2x^4$ - 3x^2$ + 5$$ models the height of a projectile at time $$x. $$What is the velocity function $$y'$$?

Accepted Answer

$$8x^3 - 6x$

Question 9

Find $$\int 5x^4$ dx.$$

Accepted Answer

$$x^5 + C$

Question 10

Which trigonometric function is associated with the horizontal component in a right triangle?

Accepted Answer

$$\cos	heta$$

Question 11

Find the derivative of $$y = \ln x.$$

Accepted Answer

$$\frac{1}{x}$$

Question 12

If $$y = e^x$$, what is $$\frac{dy}{dx}$$?

Accepted Answer

$$e^x$$

Question 13

Find the definite integral $$\int_{0}^{1} 3x^2$ dx.$$

Accepted Answer

$$1$$

Question 14

A function $$y = \frac{x}{x^2$ + 1}$$ models the concentration of a drug in the bloodstream over time $$x. $$What is the rate of change of concentration with respect to time?

Accepted Answer

$$\frac{1 \cdot (x^2$ + 1) - x \cdot 2x}{(x^2$ + 1)^2$}$$

Question 15

Find the derivative of $$y = 	an x.$$

Accepted Answer

$$\sec^2$ x$$

Question 16

Which operation is most closely related to finding the area under a curve?

Accepted Answer

Integration

Question 17

Find $$\int x dx.$$

Accepted Answer

$$\frac{1}{2} x^2$ + C$$

Question 18

A function $$y = 4x^2$ - 3x - 1$$ describes the displacement of a spring. What is the total displacement after integrating from $$x = 0 to$$ $$x = 2$$?

Accepted Answer

$$\frac{4}{3} (2^3$) - \frac{3}{2} (2^2$) - 2$$

Question 19

Find the derivative of $$y = 5x^2$.

Accepted Answer

$$10x$$

CH.0 - Physics with Calculus: Trigonometry, Limits, Differentiation, and Integration Study Guide

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