Algebra II Theory Study Guide

Flashcards on Algebra II Theory

What is the factored form of the sum of two cubes: (a³ + b³)

(a + b)(a² − ab + b²)

What is the factored form of the difference of two cubes: (a³ - b³)

(a - b)(a² + ab + b²)

How can you express the root of x as an exponent?

x^(power/root)

What condition makes a function even?

f(-x) = f(x) and it has y axis symmetry

What condition makes a function odd?

f(-x) = -f(x) and it has symmetry through the origin

How do you calculate P(A or B)?

P(A) + P(B) - P(A and B)

What is the formula for conditional probability P(A|B)?

P(A and B) / P(B)

How do you test for independence?

P(A|B) = P(A) or P(A)*P(B) = P(A and B)

What function on a calculator calculates proportion (probability) under the normal curve?

normalcdf(lower,upper,mean, standard deviation)

What is the margin of error at 95% confidence?

2 standard deviations

What type of transformation is f(x-c)?

right shift

What type of transformation is -f(x)?

Reflection over x-axis (Flipped upside down)

In vertex form of a quadratic, y = a(x-h)² + k, what represents the vertex?

(h, k)

What is the compound interest formula?

A = P(1 + r/n)^(nt)

What is the formula for compounding continuously?

A = Pe^(rt)

What is the solution to a system of equations graphically?

Solution to a system represents an intersection point(s) for two functions.

What command solves a 3x3 system of equations using matrices?

rref([A])

What is the explicit formula for an arithmetic sequence?

an = a1 + (n - 1)d

What is the explicit formula for a geometric sequence?

an = a1 * r^(n-1)

What is the recursive formula for an arithmetic sequence?

an = a(n-1) + d

What is the recursive formula for a geometric sequence?

an = a(n-1) * r

What is the formula for the sum of a geometric series?

S = a_1(1 - r^n) / (1 - r)

sin θ =

opposite / hypotenuse

cos θ =

adjacent / hypotenuse

tan θ =

opposite / adjacent

Period =

2π / b

Vertex form

Y = a(x-h)² + k

Focus-Directrix Form

(X-h)² = 4p(y-k)