Prerequisites Flashcards
Solve for x: ax + b = c
x = (c - b) / a
State the quadratic formula.
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Simplify: a^m * a^n
a^(m + n)
Simplify: log(ab)
log(a) + log(b)
Factor: x^2 - 5x + 6
(x - 2)(x - 3)
Simplify: (x+2)(x-3) / (x-3)
x + 2 (x != 3)
What is the slope formula?
m = (y2 - y1) / (x2 - x1)
What is the distance formula?
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
What is the equation of a circle?
(x-h)^2 + (y-k)^2 = r^2
State the Pythagorean Theorem.
a^2 + b^2 = c^2
What is sin(theta) in a right triangle?
sin(theta) = opposite / hypotenuse
What is cos(theta) in a right triangle?
cos(theta) = adjacent / hypotenuse
What is the Pythagorean identity?
sin^2(theta) + cos^2(theta) = 1
What are the sine and cosine values at theta = 0°?
sin(0°) = 0, cos(0°) = 1
What is the domain of f(x) = 1/x?
All real numbers except x != 0
What is the transformation for f(x + c)?
Horizontal shift left by c units.
Solve: ln(e^x)
x
What is the limit as x approaches 2 of (x^2 - 4) / (x - 2)?
Limit = 4 (after simplifying to x + 2).
What is sin(0°) and cos(0°)?
sin(0°) = 0, cos(0°) = 1
What is sin(30°) and cos(30°)?
sin(30°) = 1/2, cos(30°) = sqrt(3)/2
What is sin(45°) and cos(45°)?
sin(45°) = sqrt(2)/2, cos(45°) = sqrt(2)/2
What is sin(60°) and cos(60°)?
sin(60°) = sqrt(3)/2, cos(60°) = 1/2
What is sin(90°) and cos(90°)?
sin(90°) = 1, cos(90°) = 0
What is the derivative of f(x) = x^n?
f’(x) = n * x^(n-1)
What is the derivative of f(x) = sin(x)?
f’(x) = cos(x)
What is the derivative of f(x) = cos(x)?
f’(x) = -sin(x)
What is the derivative of f(x) = e^x?
f’(x) = e^x
What is the derivative of f(x) = ln(x)?
f’(x) = 1/x
What is the integral of f(x) = x^n (n != -1)?
∫ x^n dx = (x^(n+1))/(n+1) + C
What is the integral of f(x) = e^x?
∫ e^x dx = e^x + C
What is the integral of f(x) = cos(x)?
∫ cos(x) dx = sin(x) + C
What is the integral of f(x) = sin(x)?
∫ sin(x) dx = -cos(x) + C
What is lim(x->0) (sin(x)/x)?
1
What is lim(x->∞) (1/x)?
0
What is lim(x->∞) (1 + 1/x)^x?
e
