AP Precalculus Flashcards

Key vocabulary and concepts from AP Precalculus notes.

Average Rate of Change (AROC)

The slope of the secant line between two points (a, f(a)) and (b, f(b)) on a function's graph. AROC = (f(b) - f(a)) / (b - a)

Secant Line

A line formed between two points 'a' and 'b' on a curve, whose slope is calculated using the Average Rate of Change formula.

Concave Up

A curve where the rate of change is increasing.

Concave Down

A curve where the rate of change is decreasing.

Point of Inflection

A point on a curve where the rate of change changes from increasing to decreasing or vice versa.

Odd Function

A function where f(-x) = -f(x). Its graph passes through the origin.

Even Function

A function where f(-x) = f(x). Its graph reflects over the y-axis.

Zeros, Multiplicity and Factors

x-intercept(s): Let y=0. y-intercept: Let x=0

Complex Conjugate

If a + bi is a factor, then a - bi is also a factor.

Limit Notation

lim (x→c) f(x) = L

Odd Degree Polynomial

End behaviors are opposites.

Even Degree Polynomial

End behaviors are the same.

Vertical reflection

across x-axis for a < 0

Horizontal dilation

by factor of 1/b

Pascal’s Triangle

Used for Binomial Expansion

Arithmetic sequence

Have the same differences between terms (add): d = a2 − a1, a3 − a2 , . . . d = common difference between consecutive terms. Linear.

Geometric sequences

Have common ratios between consecutive terms. Exponential.

Reciprocal Identities

csc (𝑥𝑥) = 1 / sin(𝑥𝑥), sec 𝑥𝑥 = 1 / cos(𝑥𝑥), cot 𝑥𝑥 = 1 / tan(𝑥𝑥)

Pythagorean Trig Identities

𝑠𝑠𝑠𝑠𝑛𝑛2𝑥𝑥 + 𝑐𝑐𝑐𝑐𝑠𝑠2𝑥𝑥 = 1, 1 + 𝑡𝑡𝑡𝑡𝑛𝑛2𝑥𝑥 = sec2(𝑥𝑥), 𝑐𝑐𝑐𝑐𝑡𝑡2𝑥𝑥 + 1 = csc2(𝑥𝑥)

Double Angle Trig Identities

𝑠𝑠𝑠𝑠𝑠𝑠 2𝑥𝑥 = 2 sin 𝑥𝑥 cos(𝑥𝑥), 𝑐𝑐𝑐𝑐𝑐𝑐 2𝑥𝑥 = cos2 𝑥𝑥 − sin2(𝑥𝑥) = 2 cos2 𝑥𝑥 − 1 = 1 − 2 sin2(𝑥𝑥)

Transformations of Sinusoidal Functions

y = A sin (B (x + C)) + D ; y = A cos(B(x+C)) + D ; A = Amplitude ; Period = 2pi / B; Phase shift is opposite sign of C; D = Vertical Shift (midline)

Polar to Rectangular Coordinates

x = r cos θ, y = r sin θ

Rectangular to Polar Coordinates

x^2 + y^2 = r^2, tan θ = y / x (x ≠ 0)