Transcript AP Calculus

AP Calculus
Summer Work Notes
Undefined slope
Zero slope
equal
Opposite multiplicative inverses (aka opposite reciprocals)
rate of change
m
(𝑥1 , 𝑦1 )
y = mx + b
b
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 )
m
point
slope
𝐴𝑥 + 𝐵𝑦 = 𝐶
Notecards from Section 1.1: Rules for Rounding
ALL DECIMAL PLACES NEED TO BE
ROUNDED OR TRUNCATED TO
THE THOUSANDTHS PLACE
(THAT’S 3 DECIMAL PLACES!!!!!)
Notecards from Section 1.2: Odd/Even Functions
EVEN: Symmetric about the Y-AXIS
f(-x) = f(x)
ODD: Symmetric about the ORIGIN
f(-x) = -f(x)
𝐿𝐸𝐹𝑇 𝑐
𝐻𝑂𝑅𝐼𝑍
STRETCH/COMP
BY FAC𝑇𝑂𝑅 𝑂𝐹 𝑏
𝑅𝐼𝐺𝐻𝑇 𝑐
𝑈𝑃 𝑑
𝐷𝑂𝑊𝑁 𝑑
VERT
𝑅𝐸𝐹𝐿𝐸𝐶𝑇𝐼𝑂𝑁
𝑂𝑉𝐸𝑅 𝑌 − 𝐴𝑋𝐼𝑆
STRETCH/COMP
BY FAC𝑇𝑂𝑅 𝑂𝐹 𝑎
𝑅𝐸𝐹𝐿𝐸𝐶𝑇𝐼𝑂𝑁
OVER X-AXIS
Notecards from Parent Functions and Transformations:
Transformations (Parent Functions)
Know the following parent graphs without a calculator:
Notecards from Section 1.5: Inverse Functions
THINGS TO KNOW ABOUT THE INVERSE
OF A FUNCTION:
(1) Switch x and y: this is the
inverse…oftentimes we solve if for y
so that we can write y as a function
of x.
(2) Inverses are reflection over y = x
(3) (𝑓 𝑓 −1 𝑥 = 𝑓 −1 (𝑓 𝑥 = x
I would put these on a notecard also…
NOTECARD WORTHY: Unit Circle…memorize the sine and cosine of 30, 45, 60 and 90 degree angles and their multiples.
0
𝑠𝑖𝑛𝜃
𝑐𝑜𝑠𝜃
𝑡𝑎𝑛𝜃
𝑠𝑒𝑐𝜃
𝑐𝑠𝑐𝜃
𝑐𝑜𝑡𝜃
𝜋
6
𝜋
4
𝜋
3
𝜋
2
Notecards from Section 1.6: Trigonometric Identities
𝑠𝑖𝑛2 𝑥 + 𝑐𝑜𝑠 2 𝑥 = 1
1 + 𝑐𝑜𝑡 2 𝑥 = 𝑐𝑠𝑐 2 𝑥
𝑡𝑎𝑛2 𝑥 + 1 = 𝑠𝑒𝑐 2 𝑥