AP Pre Calc Flash Cards: AP Exam

Even Function over Symmetry

f(x) = f (-x)

Odd Function over symmetry

f(-x) = -f (x)

Even functions are symmetrical over the…

y-axis

Odd functions are symmetrical over the

origin

Numerator > Denominator (N = D+1)

Slant asymptote

Numerator = Denominator

Horizontal Asymptote

Slant asymptote equation

Long division

Horizontal asymptote equation

N leading coef / D leading coef.

Numerator < Denominator

horizontal asymptote = 0

Zero (rational function)

Numerator = 0, Denominator ≠ 0

Holes (rational function)

denominator = 0, denominator and numerator cancel out

vertical asymptote

denominator = 0

csc θ =

1/sinθ

sec θ =

1/cosθ

cot θ =

1/tan θ, cosθ/sinθ

tan θ =

sin θ / cos θ

Trig Identity (Pythagorean) :
1 = …

sin² θ + cos² θ

sec²θ = ?

1 + tan²θ

csc² θ = ?

1 + cot²θ

sin2θ =

2 sinθ cosθ

cos2θ =

cos²θ - sin²θ

cos2θ =

2cos²θ -1

cos2θ =

1 - 2sin²θ

tan2θ =

2tanθ / 1-tan²θ

sin (A + B) =

(sinA cosB) + (cosA sinB)

sin (A - B) =

(sinA cosB) - (cosA sinB)

cos(a + b) =

(cosA cosB) - (sinAsinB)

cos(a - b) =

(cosA cosB) + (sinAsinB)

arithmetic sequence

a_n= a_k + d (n-k)

geometric sequence

g_n= g_k * r^(n-k)