Algebra, Logs, and Quadratics Key Concepts (Flashcards)

Flashcards cover factoring, exponent rules, radicals, logarithms, triangle and distance concepts, quadratic forms, and conic sections. Fill in the blank prompts students to recall the missing result or definition from the lecture notes.

ab + ac = a( ).

b + c

x^2 − y^2 = (x + y)().

x − y

x^3 − y^3 = (x − y)().

x^2 + xy + y^2

x^3 + y^3 = (x + y)().

x^2 − xy + y^2

x^3 − 3x^2y + 3xy^2 − y^3 = (x − y)().

x^2 − 2xy + y^2

x^n + y^n = (x + y)().

x^{n−1} − x^{n−2} y + x^{n−3} y^2 … − y^{n−1}

x^{2n} − y^{2n} = (x^n − y^n)().

x^n + y^n

If n is odd then x^n − y^n = (x − y)().

x^{n−1} + x^{n−2} y + … + y^{n−1}

logb (xy) = ___.

logb x + logb y

logb (x^k) = _ log_b x.

k

logb (x/y) = _.

logb x − logb y

log_b b = __.

1

Natural logarithm is written as ln and equals log base ____ of x.

e

Common logarithm uses base .

10

√[n]{x} = x^{____}.

1/n

√[n]{xy} = .

√[n]{x} √[n]{y}

If n is odd, √[n]{x^n} = .

x

If n is even, √[n]{x^n} = .

|x|

d(PA, PB) = sqrt( (x2 − x1)^2 + (y2 − y1)^2 ).

sqrt[(x2 − x1)^2 + (y2 − y1)^2]

Natural Numbers are the set {}.

1, 2, 3, 4, 5, …

Real Numbers R are numbers that are either or .

rational, irrational

Real Numbers R are numbers that are either rational or irrational.

(Used for context; answer is two categories: rational and irrational)

Circle equation: (x − h)^2 + (y − k)^2 = r^2; the center is at (____, _____).

h, k

Ellipse center: (____).

h, k

Hyperbola centered at (____) with axes a, b (horizontal form): (x − h)^2 / a^2 − (y − k)^2 / b^2 = 1.

h, k

Asymptotes: y = ± (b/a)(x − h) + k. The slope of the asymptotes is .

± b/a

In a right triangle, a^2 + b^2 = c^2. The value to be equated is .

c^2

Quadratic Formula: x = (−b ± √(b^2 − 4ac)) / (2a).

(-b ± sqrt(b^2 - 4ac)) / (2a)

Discriminant D = .

b^2 − 4ac

If b^2 − 4ac > 0, there are real solutions.

two

If b^2 − 4ac = 0, there is real solution.

one

If b^2 − 4ac < 0, there are real solutions.

no

A = P (1 + r/n)^{nt} is the formula for interest.

compound

A = P e^{rt} is for interest.

continuously compounded