Background Knowledge

Question 1

What is the derivative of a constant function?

Answer 1

0

Question 2

What is the derivative of f(x) = x^n?

Answer 2

f’(x) = n*x^(n-1)

Question 3

What is the integral of f(x) = x^n?

Answer 3

F(x) = (1/(n+1))*x^(n+1) + C, where n ≠ -1

Question 4

True or False: The derivative of e^x is e^x.

Answer 4

True

Question 5

What is the derivative of f(x) = sin(x)?

Answer 5

f’(x) = cos(x)

Question 6

What is the derivative of f(x) = cos(x)?

Answer 6

f’(x) = -sin(x)

Question 7

What is the integral of f(x) = e^x?

Answer 7

F(x) = e^x + C

Question 8

What is the derivative of f(x) = ax^b?

Answer 8

f’(x) = abx^b-1

Question 9

Fill in the blank: The integral of sin(x) is ___

Answer 9

-cos(x) + C

Question 10

What is the integral of cos(x)?

Answer 10

F(x) = sin(x) + C

Question 11

True or False: The integral of a constant k is kx + C.

Answer 11

True

Question 12

What is the derivative of f(x) = x³ + 5x?

Answer 12

f’(x) = 3x² + 5

Question 13

What is the integral of f(x) = 3x²?

Answer 13

F(x) = x³ + C

Question 14

What is the derivative of f(x) = x⁴?

Answer 14

f’(x) = 4x³

Question 15

Fill in the blank: The integral of e^kx is ___

Answer 15

(1/k)e^kx + C

Question 16

What is the derivative of f(x) = 5e^(3x)?

Answer 16

f’(x) = 15e^(3x)

Question 17

What is the integral of f(x) = kx?

Answer 17

F(x) = (k/2)x^2 + C

Question 18

Multiple Choice: What is the derivative of f(x) = x^2 + 2x + 1?
A) 2x + 1 B) 2x + 2 C) 2x

Answer 18

A) 2x + 2

Question 19

What is the integral of f(x) = sin(2x)?

Answer 19

-1/2 cos(2x) + C

Question 20

What is the derivative of f(x) = 3x^5 - 2x + 7?

Answer 20

f’(x) = 15x^4 - 2

Question 21

What is the integral of f(x) = 4x^3?

Answer 21

F(x) = x^4 + C

Question 22

Fill in the blank: The integral of cos(kx) is ___

Answer 22

(1/k)sin(kx) + C

Question 23

True or False: The slope-intercept form of a line is written as y = mx + b.

Answer 23

True.

Question 24

Fill in the blank: The slope of a line is the ratio of the change in y to the change in _____.

Answer 24

x

Question 25

What is the slope of a line that passes through the points (2, 3) and (4, 7)?

Answer 25

2.

Question 26

What is the Cartesian (rectangular) representation of a complex number?

Answer 26

Z = a + bi ## Footnote Here, 'a' is the real part and 'b' is the imaginary part.

Question 27

What does 'A' represent in the sinusoidal function f(t) = A cos(2πft + φ) + B?

Answer 27

Peak amplitude ## Footnote It indicates the maximum value of the function ignoring the offset B

Question 28

What does 'φ' represent in the sinusoidal function f(t) = A cos(2πft + φ) + B?

Answer 28

The phase shift. It determines the horizontal displacement of the wave.

Question 29

What is the period of a sinusoidal function f(t) = A cos(2πft + φ) + B?

Answer 29

T = 1/f | In seconds ## Footnote The period is the time it takes for one complete cycle of the wave.

Question 30

What is the significance of 'B' in the sinusoidal function f(t) = A cos(2ft + φ) + B?

Answer 30

Vertical offset ## Footnote 'B' represents the average value of the signal.

Question 31

What is the relationship between complex exponential and sinusoidal functions? | Euler's Formula

Answer 31

e^(jθ) = cos(θ) + jsin(θ) ## Footnote This is known as Euler's formula.

Question 32

How do you find the angle for z=a+bj?

Answer 32

Θ=atan(b/a) | If a is negative, will need to add π radians.

Question 33

What is the polar representation of a complex number?

Answer 33

z = re^jΘ | r must be a positive number