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This includes a ton of stuff you must remember for the AP Test. It includes equations, theories, rules, derivatives, integrals, and more. I only recommend using these as flashcards or multiple choice only.

Calculus

Differential Equations

AP Calculus BC

Unit 1: Limits and Continuity

AP

Calculus BC

Review

Final

Images

Everything!

Everything

Equations

Theorems

Theories

Rules

Derivatives

Integrals

Slope

Distance

Displacement

Polar

Parametric

Cartesian

Average Value Theorem

Mean Value Theorem

Extreme Value Theorem

Continuity

Final Review

AP Test

11th

1

L'Hôpital's Rule

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2

Slope of a Parametric equation

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3

Euler’s Method

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4

Polar Area

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5

Polar Slope

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6

Integration by parts

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7

Integral of logarithms

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8

Ratio Test

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9

sin(2x)

2sin(x)cos(x)

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10

cos(2x)

cos^2(x) - sin^2(x)

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11

cos(2x)

1 - 2sin^2(x)

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12

cos^2(x)

1/2(1+cos(2x))

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13

sin^2(x)

1/2(1-cos(2x))

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14

sin^2(x) + cos^2(x)

1

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15

1+tan^2(x)

sec^2(x)

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16

cot^2(x) + 1

csc^2(x)

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17

sin(-x)

-sin(x)

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18

cos(-x)

cos(x)

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19

Taylor Series

f(x) = f(a) + f’(a)(x-a) + [f’’(a)(x-a)^2 / 2!] + [f’’’(a)(x-a)^3 / 3!] + …

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20

Lagrange Error Bound

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21

Maclaurin Series

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22

Alternating Series Error Bound

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23

Geometric Series

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24

sin(0)

0

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25

cos(0)

1

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26

tan(0)

0

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27

sin(pi/6)

1/2

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28

cos(pi/6)

root3/2

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29

sin(pi/4)

root2/2

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30

cos(pi/4)

root2/2

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31

sin(pi/3)

root3/2

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32

cos(pi/3)

1/2

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33

sin(pi/2)

1

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34

cos(pi/2)

0

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35

Chain Rule

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36

Product Rule

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37

Quotient Rule

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38

Trapezoidal Rule

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39

NEVER FORGET (for integrals)

+C

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40

Average Value

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41

d/dx sin(x)

cos(x)

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42

d/dx cos(x)

-sin(x)

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43

d/dx tan(x)

sec^2(x)

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44

d/dx cot(x)

-csc^2(x)

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45

d/dx sec(x)

sec(x)tan(x)

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46

d/dx csc(x)

-csc(x)cot(x)

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47

d/dx ln(u)

1/u

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48

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49

Solid Disk Method

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50

Solid Washer Method

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51

Cartesian Arc Length

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52

Polar Arc Length

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53

Parametric Arc Length

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54

Intermediate Value Theorem

If the function f(x) is continuous on [a,b], then f(x) achieves every value between f(a) and f(b) in the open interval (a,b).

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55

Mean Value Theorem

If the function f(x) continuous on [a,b], and the first derivative exists on the interval (a,b), then there is at least one number x = c in (a,b) such that f’(c) = [ f(b)-f(a) ] / (b-a).

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56

Rolle’s Theorem

Same as mean value theorem but if f(a) = f(b), then there is at least one number x = c in (a,b) such that f’(c) = 0.

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57

d/dx loga(x)

1/xln(a)

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58

Displacement

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59

Speed

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60

Distance

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