Prerequisites

Question 1

Solve for x: ax + b = c

Answer 1

x = (c - b) / a

Question 2

State the quadratic formula.

Answer 2

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Question 3

Simplify: a^m * a^n

Answer 3

a^(m + n)

Question 4

Simplify: log(ab)

Answer 4

log(a) + log(b)

Question 5

Factor: x^2 - 5x + 6

Answer 5

(x - 2)(x - 3)

Question 6

Simplify: (x+2)(x-3) / (x-3)

Answer 6

x + 2 (x != 3)

Question 7

What is the slope formula?

Answer 7

m = (y2 - y1) / (x2 - x1)

Question 8

What is the distance formula?

Answer 8

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Question 9

What is the equation of a circle?

Answer 9

(x-h)^2 + (y-k)^2 = r^2

Question 10

State the Pythagorean Theorem.

Answer 10

a^2 + b^2 = c^2

Question 11

What is sin(theta) in a right triangle?

Answer 11

sin(theta) = opposite / hypotenuse

Question 12

What is cos(theta) in a right triangle?

Answer 12

cos(theta) = adjacent / hypotenuse

Question 13

What is the Pythagorean identity?

Answer 13

sin^2(theta) + cos^2(theta) = 1

Question 14

What are the sine and cosine values at theta = 0°?

Answer 14

sin(0°) = 0, cos(0°) = 1

Question 15

What is the domain of f(x) = 1/x?

Answer 15

All real numbers except x != 0

Question 16

What is the transformation for f(x + c)?

Answer 16

Horizontal shift left by c units.

Question 17

Solve: ln(e^x)

Answer 17

x

Question 18

What is the limit as x approaches 2 of (x^2 - 4) / (x - 2)?

Answer 18

Limit = 4 (after simplifying to x + 2).

Question 19

What is sin(0°) and cos(0°)?

Answer 19

sin(0°) = 0, cos(0°) = 1

Question 20

What is sin(30°) and cos(30°)?

Answer 20

sin(30°) = 1/2, cos(30°) = sqrt(3)/2

Question 21

What is sin(45°) and cos(45°)?

Answer 21

sin(45°) = sqrt(2)/2, cos(45°) = sqrt(2)/2

Question 22

What is sin(60°) and cos(60°)?

Answer 22

sin(60°) = sqrt(3)/2, cos(60°) = 1/2

Question 23

What is sin(90°) and cos(90°)?

Answer 23

sin(90°) = 1, cos(90°) = 0

Question 24

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

Answer 24

f’(x) = n * x^(n-1)

Question 25

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

Answer 25

f'(x) = cos(x)

Question 26

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

Answer 26

f'(x) = -sin(x)

Question 27

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

Answer 27

f'(x) = e^x

Question 28

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

Answer 28

f'(x) = 1/x

Question 29

What is the integral of f(x) = x^n (n != -1)?

Answer 29

∫ x^n dx = (x^(n+1))/(n+1) + C

Question 30

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

Answer 30

∫ e^x dx = e^x + C

Question 31

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

Answer 31

∫ cos(x) dx = sin(x) + C

Question 32

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

Answer 32

∫ sin(x) dx = -cos(x) + C

Question 33

What is lim(x->0) (sin(x)/x)?

Answer 33

1

Question 34

What is lim(x->∞) (1/x)?

Answer 34

0

Question 35

What is lim(x->∞) (1 + 1/x)^x?

Answer 35

e