SYMYC Pre-Cal

<

less than

>

greater than

≤

less than or equal to

≥

greater than or equal to

≠

not equal to

Order of Operation

PEMAS

Mean

Arithmetic numerical average of a list of numbers

Median

The middle number when the list of numbers or ordered

Mode

The number that occurs most often in a list; sometimes its more than one

Commutative Property of Addition

a+b=b+a

Commutative Property of Multiplication

ab=ba

Associative Property of Addition

(a+b)+c = a+(b+c)

Associative Property of Multiplication

(ab)c = a(bc)

Identity Property of Addition

a+0 = 0+a

Identity Property of Multiplication

a*1 = 1*a

Inverse Property of Addition

a+-a = -a+a

Inverse Property of Multiplication

a*1/2 = 1

Distributive Property

a(b+c) = ab+ac

1^2

1

2^2

4

3^2

9

4^2

16

5^2

25

6^2

36

7^2

49

8^2

64

9^2

81

10^2

100

11^2

121

12^2

144

1^3

1

2^3

8

3^3

27

4^3

64

5^3

125

Complimentary angles add up to

90 degrees

Supplimentary angles add up to

180 angles

Square Area Formula

A = s^2

Triangle Area Formula

A = 1/2bh

Circle Area Formula

A = πr^2

Parallelogram Area Formula

A = b*h

Rectangle Area Formula

Av= l*w

Trapezoid Area Formula

A = 1/2h(b1+b2)

Pythagorean Theroem

a^2 + b^2 = c^2

a/b = c/d

ad = bc

Domain

Set of all input values; independent variable

Range

Set of all output values; dependent variable

Function

Relationship for which each element of the domain corresponds to exactly one value of the range

Standard Form of Linear

Ax+By = C

Slope-Intercept Form of Linear

y = mx+b

Point-Slope Form of Linear

y-y∨1 = m(x-x∨1)

Slope Formula

(y2-y1)/(x2-x1)

Parallel Slope

m

Perpendicular Slope

-1/m

h(x) = f(x) +/- k

Down/Up k units

h(x) = f(x +/- h)

Right or left h units(Is always opposite sign)

h(x) = -f(x)

Reflect over x-axis

h(x) = f(-x)

Reflect over y-axis

h(x) = af(x)

Vertical stretch or compression

h(x) = f(bx)

Horizontal stretch or compression

a^0 =

1

a^1 =

a

(ab)^n =

(a^n)(b^n)

a^m*a^n =

a^m+n

(a^m)/(a^n) =

a^m-n

(ab^m)^n =

ab^mn

(a/b)^n =

(a^n)/(b^n)

a^-n =

1/a^n

Standard Form of Quadratics

y = a(x-h)^2+k

Do you know quadratic formula?

I can sing the song!

a^2 - b^2 =

(a-b)(a+b)

a^2 + 2ab + b^2 =

(a+b)^2

a^2 - 2ab +b^2

(a-b)^2

Distance Formula

√(x2-x1)^2 + (y2-y1)^2

0!

1

1!

1

2!

2

3!

6

4!

24

5!

120

Circle Formula

(x-h)^2 + (y-k)^2 = r^2

Perimeter of Square

P = 4s

Perimeter of Rectangle

P = 2l + 2w

Circumference of Circle

C = 2πr

Volume of Cube

A = s^3

Volume of Cylinder

A = (πr^2)(h)

Volume of Cone

A = 1/3(πr^2)(h)

Volume of Prism

A = B*h

Volume of Pyramid

A = 1/3(B*h)

Volume of Sphere

A = 4/3πr^3

Triangle Interior Angle Sum

180 degrees

Quadrilateral Interior Angle Sum

360

Regular Polygon Interior Angle Sum

180(n-2)

Apothem

Line from center of regular polygon at right angles to any of its sides

Trigonometry

SOH CAH TOA