AP Calculus Formulas

Question 1

VOLUME of a PYRAMID

Answer 1

V=1/3Bh

Question 2

Area of a square

Answer 2

A=s²

Question 3

Area of a parallelogram

Answer 3

A=lw

Question 4

Area of an equilateral triangle

Answer 4

A=(s²√3)/4

Question 5

Volume of a cone

Answer 5

V=1/3πr²h

Question 6

Volume of a sphere

Answer 6

V=4/3πr³

Question 7

Surface area of a cylinder

Answer 7

SA=2πr²+2πrh

Question 8

Surface area of a sphere

Answer 8

SA=4πr²

Question 9

Pythagorean Theorem

Answer 9

a²+b²=c²

Question 10

Distance between two points

Answer 10

d = √(x2-x1)² + (y2-y1)²

Question 11

Slope of a line

Answer 11

m=y2-y1/x2-x1

Question 12

Point-slope form of a line

Answer 12

y-y1=m(x-x1)

Question 13

Quadratic formula

Answer 13

x = -b ± √(b² - 4ac)/2a

Question 14

Area of a rectangle

Answer 14

A=lw

Question 15

Area of a triangle

Answer 15

A=1/2bh

Question 16

Area of a trapezoid

Answer 16

A=1/2(b1+b2)h

Question 17

Area of a circle

Answer 17

A=πr²

Question 18

Circumference of a circle

Answer 18

C=2πr or C=πd

Question 19

Volume of a cylinder

Answer 19

V=πr²h

Question 20

Volume of a rectangular prism

Answer 20

V=lwh

Question 21

x^m (x^n) = ?

Answer 21

x^m+n

Question 22

x^m/x^n = ?

Answer 22

x^m-n

Question 23

(x^m)^n = ?

Answer 23

x^mn

Question 24

(xy)^m = ?

Answer 24

x^m(y^m)

Question 25

(x/y)^m = ?

Answer 25

(x^m)/(y^m)

Question 26

x^-m = ?

Answer 26

1/(x^m)

Question 27

x^(1/m) = ?

Answer 27

m root x

Question 28

Rewrite y = b^x into an equivalent logarithmic equation.

Answer 28

x = log_b(y)

Question 29

Rewrite y = log_b(x) into an equivalent exponential equation

Answer 29

x = b^y

Question 30

log_b(x) + log_b(y) = ?

Answer 30

log_b(xy)

Question 31

log_b(x) - log_b(y) = ?

Answer 31

log_b(x/y)

Question 32

log_b(x^y) = ?

Answer 32

ylog_b(x)

Question 33

One degree equals

Answer 33

π/180 radians

Question 34

One radian equals

Answer 34

80/π degrees

Question 35

csc(theta) = ?

Answer 35

1/sin(theta)

Question 36

When π/2 < theta < π

Answer 36

sin (theta) > 0, cos (theta) < 0, and tan (theta) < 0

Question 37

When π < theta < (3π/2)

Answer 37

sin (theta) < 0, cos (theta) < 0, and tan (theta) > 0

Question 38

When (3π/2) < theta < 2π

Answer 38

sin (theta) < 0, cos (theta) > 0, and tan (theta) < 0

Question 39

tan (theta) = ?

Answer 39

sin (theta)/cos(theta)

Question 40

cot(theta) = ?

Answer 40

cos (theta)/sin (theta)

Question 41

sec (theta) = ?

Answer 41

1/cos(theta)

Question 42

Name one Pythagorean identity

Answer 42

sin²(theta) + cos²(theta) = 1

Question 43

Name another Pythagorean identity

Answer 43

1 + tan²(theta) = sec²(theta)

Question 44

Name the last (of three) Pythagorean identities

Answer 44

1 + cot²(theta) = csc²(theta)

Question 45

sin(a ± b) = ?

Answer 45

sin(a)cos(b) ± cos(a)sin(b)

Question 46

cos(a ± b) = ?

Answer 46

cos(a)cos(b) ± sin(a)sin(b)

Question 47

tan(a ± b) = ?

Answer 47

[tan(a) ± tan(b)] / [1 ± tan(a)tan(b)]

Question 48

sin(2theta) = ?

Answer 48

2sin(theta)cos(theta)

Question 49

cos(2theta) = ?

Answer 49

cos²(theta) - sin²(theta) OR 2cos²(theta) - 1 OR 1 - 2sin²(theta)

Question 50

tan(2theta) = ?

Answer 50

[2tan(theta) ]/ [1 - tan²(theta)]

Question 51

sin²(theta) = ?

Answer 51

[1 -cos(2theta)]/ 2

Question 52

cos²(theta) = ?

Answer 52

[1 + cos(2theta)]/ 2

Question 53

tan²(theta) = ?

Answer 53

[1 -cos (2theta)] / [1 + cos(2theta)]