SETS

Definition

What is a set? Well, simply put, it's a collection.

First you specify a common property among "things" (this word will be defined later) and then you gather up all the "things" that have this common property.

For example, the items you wear: these would include shoes, socks, hat, shirt, pants, and so on. I'm sure you could come up with at least a hundred. This is known as a set.

Or another example would be types of fingers. This set would include index, middle, ring, and pinky.

So it is just things grouped together with a certain property in common.

Notation

There is a fairly simple notation for sets. You simply list each element, separated by a comma, and then put some curly brackets around the whole thing.

The curly brackets { } are sometimes called "set brackets" or "braces".

This is the notation for the two previous examples:

{socks, shoes, watches, shirts, ...}
{index, middle, ring, pinky}

Average formula: 
Let a₁,a₂,a₃,......,a_n be a set of numbers, average = (a₁ + a₂ + a₃,+......+ a_n)/n

Fractions formulas: 












Converting a mixed number to an improper fraction:




Converting an improper fraction to a mixed number:




Formula for a proportion: 




In a proportion, the product of the extremes (ad) equal the product of the means(bc), 

Thus, ad = bc

Percent: 
Percent to fraction: x% = x/100

Percentage formula: Rate/100 = Percentage/base

Rate: The percent. 
Base: The amount you are taking the percent of.
Percentage: The answer obtained by multiplying the base by the rate

Consumer math formulas: 

Discount = list price × discount rate

Sale price = list price − discount

Discount rate = discount ÷ list price

Sales tax = price of item × tax rate

Interest = principal × rate of interest × time

Tips = cost of meals × tip rate

Commission = cost of service × commission rate

Geometry formulas: 
Perimeter:

Perimeter of a square: s + s + s + s 
s:length of one side

Perimeter of a rectangle: l + w + l + w
l: length
w: width

Perimeter of a triangle: a + b + c
a, b, and c: lengths of the 3 sides

Area:

Area of a square: s × s 
s: length of one side

Area of a rectangle: l × w
l: length
w: width

Area of a triangle: (b × h)/2
b: length of base
h: length of height

Area of a trapezoid: (b₁ + b₂) × h/2
b₁ and b₂: parallel sides or the bases
h: length of height

volume:

Volume of a cube: s × s × s 
s: length of one side

Volume of a box: l × w × h
l: length
w: width
h: height

Volume of a sphere: (4/3) × pi × r³
pi: 3.14
r: radius of sphere

Volume of a triangular prism: area of triangle × Height = (1/2 base × height) × Height
base: length of the base of the triangle
height: height of the triangle
Height: height of the triangular prism

Volume of a cylinder:pi × r² × Height
pi: 3.14
r: radius of the circle of the base
Height: height of the cylinder

MATH SHAPE FORMULA

Shapes	Formula
	Rectangle: Area = Length X Width A = lw Perimeter = 2 X Lengths + 2 X Widths P = 2l + 2w
	Parallelogram Area = Base X Height a = bh
	TriangleArea = 1/2 of the base X the height a = 1/2 bh Perimeter = a + b + c (add the length of the three sides)

	Trapezoid Perimeter = area + b1 + b2 + c P = a + b1 + b2 + c
	Circle Try the Online tool. The distance around the circle is a circumference. The distance across the circle is the diameter (d). The radius (r) is the distance from the center to a point on the circle. (Pi = 3.14) More about circles. d = 2r c = pd = 2 pr A = pr2 (p=3.14)
	Rectangular Solid Volume = Length X Width X Height V = lwh Surface = 2lw + 2lh + 2wh
	Prisms Volume = Base X Height v=bh Surface = 2b + Ph (b is the area of the base P is the perimeter of the base)
	Cylinder Volume = pr2 x height V = pr2 h Surface = 2p radius x height S = 2prh + 2pr2
	Pyramid V = 1/3 bh b is the area of the base Surface Area: Add the area of the base to the sum of the areas of all of the triangular faces. The areas of the triangular faces will have different formulas for different shaped bases.
	ConesVolume = 1/3 pr2 x heightV= 1/3 pr2h  Surface = pr2 + prsS = pr2 + prs  =pr2 + pr
	SphereVolume = 4/3 pr3V = 4/3 pr3 Surface = 4pr2S = 4pr2

BASIC MATH SYMBOLS

Symbol	Symbol Name	Meaning / definition	Example
=	equals sign	equality	5 = 2+3
≠	not equal sign	inequality	5 ≠ 4
>	strict inequality	greater than	5 > 4
<	strict inequality	less than	4 < 5
≥	inequality	greater than or equal to	5 ≥ 4
≤	inequality	less than or equal to	4 ≤ 5
( )	parentheses	calculate expression inside first	2 × (3+5) = 16
[ ]	brackets	calculate expression inside first	[(1+2)*(1+5)] = 18
+	plus sign	addition	1 + 1 = 2
−	minus sign	subtraction	2 − 1 = 1
±	plus - minus	both plus and minus operations	3 ± 5 = 8 and -2
∓	minus - plus	both minus and plus operations	3 ∓ 5 = -2 and 8
*	asterisk	multiplication	2 * 3 = 6
×	times sign	multiplication	2 × 3 = 6
∙	multiplication dot	multiplication	2 ∙ 3 = 6
÷	division sign / obelus	division	6 ÷ 2 = 3
/	division slash	division	6 / 2 = 3
–	horizontal line	division / fraction
mod	modulo	remainder calculation	7 mod 2 = 1
.	period	decimal point, decimal separator	2.56 = 2+56/100
a b	power	exponent	23 = 8
a^b	caret	exponent	2 ^ 3 = 8
√a	square root	√a · √a  = a	√9 = ±3
3√a	cube root		3√8 = 2
4√a	forth root		4√16 = ±2
n√a	n-th root (radical)		for n=3, n√8 = 2
%	percent	1% = 1/100	10% × 30 = 3
‰	per-mille	1‰ = 1/1000 = 0.1%	10‰ × 30 = 0.3
ppm	per-million	1ppm = 1/1000000	10ppm × 30 = 0.0003
ppb	per-billion	1ppb = 1/1000000000	10ppb × 30 = 3×10-7
ppt	per-trillion	1ppb = 10-12	10ppb × 30 = 3×10-10

FORM 4 MATH TOPICS

Standard Form  Quadratic Expressions and Equations  Sets  Mathematical Reasoning  The Straight Line  Statistics  Probability I  Circles III  Trigonometry  II  Angles of Elevation and Depression  Lines and Planes in 3-Dimensions

MATH FACTS

• The word 'mathematics' comes from the Greek máthēma, which means learning, study, science.

• What comes after a million, billion and trillion? A quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion and undecillion.

• Different names for the number 0 include zero, nought, naught, nil, zilch and zip.

• Zero ( 0 ) is the only number which can not be represented by Roman numerals.

• The name 'zero' derives from the Arabic word sifr which also gave us the English word 'cipher' meaning 'a secret way of writing' .

• Do you know the magic of no. nine (9)? Multiply any number with nine (9 ) and then sum all individual digits of the result (product) to make it single digit, the sum of all these individual digits would always be nine (9).

• Here is an interesting trick to check divisibility of any number by number 3.A number is divisible by three if the sum of its digits is divisible by three (3).

• The = sign ("equals sign") was invented by 16th Century Welsh mathematician Robert Recorde, who was fed up with writing "is equal to" in his equations.

MATH JOKES

Halloween

Q: What do you get if you divide the circumference of a jack-o-lantern by its diameter?
A: Pumpkin Pi

Mathematicians at the beach

Q: Why do you rarely find mathematicians spending time at the beach?
A: Because they have sine and cosine to get a tan and don't need the sun

Zero said to eight

Q: What does the zero say to the the eight?
A: Nice belt!

Fear

Q. Why is the number six scared of seven?
A. Because seven eight nine (7 ate 9)!