Let a1,a2,a3,......,an be a set of numbers, average = (a1 + a2 + a3,+......+ an)/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...

...a+b≥x ORa+b≤-x a+b>x OR a+b<x
e.g.
∣2x-1∣≥3=
2x-1≥3 OR 2x-1≤-3
2x≥3+1 2x≤-3+1
2x≥4 2x≤-2
x≥2 x≤-1
Rationalizing
Any fraction involving surds needs to have the denominator rationalised.
Rationalise 23
23 = 23 ×1
=23 ×33 note that33 =1
=233×3
=233
The denominator is rationalised now
Beta
Trigonometry
Basic rules
Hypotenuse
Adjacent
Sin = Opposite/hypotenuse
Cos = Adjacent/hypotenuse
Tan = Opposite/Adjacent
Opposite
Cot = 1/tan
Sec= 1/sin
Csc = 1cos
Special rules
| 300 | 450 | 600 |
Sin | 12 | 12 | 32 |
Cos | 32 | 12 | 12 |
tan | 13 | 1 | 2
2
3
300
600
1
1
3 |
2
450
1
1
Area of triangle
There is an basic formula for finding the area of a triangle A=12BH but I’m going to look at how to find the area of a triangle WITHOUT the base OR the height.
X
Y
Z
As long were are given x,y AND z we can find the area of this triangle without using the base or height. B
A=12×X×Y×sinZ
A
C
c
a
b
AREA=12absinB You can’t find the area if you don’t meet these conditions
AREA=12bcsinA
AREA=12acsinB...

...f(x) = ax2 + bx + c
1.2 Rewrite a quadratic function ax2 + bx + c in the form f(x) = a(x-h)2 + k
and vice versa
1.3 Given a quadratic function, determine:
* highest or lowest point (vertex)
* axis of symmetry
* direction or opening of the graph
1.4 Draw the graph of a quadratic function using the:
* vertex
* axis of symmetry
* direction of opening of the graph
* given points
1.5 Analyze the effects on the graph of changes in a, h and k in
f(x)= a(x-h)2 + k
1.6 Determine the “zeros of a quadratic function” by relating this to “roots of a quadratic equation”
1.7 Find the roots of a quadratic equation by:
* factoring
* quadratic formula
* completing the square
1.8 Derive the quadratic function given:
* zeros of the function
* table of values
* graph
1.9 Solve problems involving quadratic functions and equations
D. Polynomial Functions
1. Demonstrate knowledge and skill related to polynomial functions
1.1 Identify a polynomial function from a given set of relations
1.2 Determine the degree of a given polynomial function
1.3 Find the quotient of polynomials by:
* algorithm
* synthetic division
1.4 Find by synthetic division the quotient and the remainder when p(x) is divided by (x – c)
1.5 State and illustrate the Remainder Theorem
1.6 Find the value of p(x)...

...1
MCR3U
Exam Review
Math Study Guide U.1: Rational Expressions, Exponents, Factoring, Inequalities
1.1 Exponent Rules Rule Product Quotient Power of a power Power of a product Power of a quotient
Description
a m × a n = a m+n a m ÷ a n = a m−n
Example 4 2 × 45 = 47
5 4 ÷ 52 = 52
(a )
a
m n
= a m×n
a a
(3 )
2 4
= 38
2 2 2
(xy) = x y an a = n ,b ≠ 0 b b
a0 = 1 a −m = 1 ,a ≠ 0 am
n
(2 x 3) = 2 x 3 35 3 = 5 4 4
70 = 1 9 −2 =
4 5
Zero as an exponent Negative exponents 1.2 Rational Exponents
1 92
a = a =
n m
power/root m/n
m n
( a)
n
m
m
27 3 = 3 274 =
(
3/2
3
27
)
4
a = a (alphabetical!) Negative Rational Exponents Rational = Fraction Radical = Root 1.3 Solving Exponential Equations e.g. Solve for x.
-m/n m/n n -3/2 3/2 3/2
x = 1/x =1/ √x
(25/4) = (4/25) = (4 )/(25 ) =
3 3
√4 /√25 =8/125
9 x−2 − 8 = 73
Add 8 to both sides. Simplify.
x−2 = 2 x = 2+2 x=4
9 x−2 = 73 + 8 LS and RS are powers of Note 9 x−2 = 81 using the same base. 9 x −2 = 9 2
9, so rewrite them as powers
When the bases are the same, equate the exponents. Solve for x.
LS = 9 x−2 − 8 RS = 73 = 9 4− 2 − 8 = 81 − 8 = 73 = RS
Don’t forget to check your solution!
x = 4 checks
Exponential Growth and Decay Population growth and radioactive decay can be modelled using exponential functions.
2
MCR3U
Decay:
t h
Exam Review
- initial amount t – time...

...The Euler’s Formula
Euler’s formula and Identity: eix = cos(x) + i(sin(x))
The world of math today is one with endless possibilities. It expands into many different and interesting topics, often being incorporated into our everyday lives. Today, I will talk about one of these topics; the most mind-blowing and fascinating formula invented, called the “Euler’s formula”. This formula was created and introduced by mathematician Leonhard Euler. In essence, the formula establishes the deep relationship between trigonometric functions and the complex exponential function.
Euler’s formula: eix=cos(x)+isin(x); x being any real number
Wow -- we're relating an imaginary exponent to sine and cosine! What is even more interesting is that the formula has a special case: when π is substituted for x in the above equation, the result is an amazing identity called the Euler’s identity:
eix=cos(x)+isin(x)
eiπ=cos(π)+isin(π)
eiπ= -1+i(0)
eiπ= -1
Euler’s identity: eiπ= -1
This formula is known to be a “perfect mathematical beauty”. The physicist Richard Feynman called it "one of the most remarkable, almost astounding, formulas in all of mathematics." This is because these three basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation. The identity also links five fundamental...

...
Beauty of Math!1 x 8 + 1 = 912 x 8 + 2 = 98123 x 8 + 3 = 9871234 x 8 + 4 = 987612345 x 8 + 5 = 98765123456 x 8 + 6 = 9876541234567 x 8 + 7 = 987654312345678 x 8 + 8 = 98765432123456789 x 8 + 9 = 9876543211 x 9 + 2 = 1112 x 9 + 3 = 111123 x 9 + 4 = 11111234 x 9 + 5 = 1111112345 x 9 + 6 = 111111123456 x 9 + 7 = 11111111234567 x 9 + 8 = 1111111112345678 x 9 + 9 = 111111111123456789 x 9 +10= 11111111119 x 9 + 7 = 8898 x 9 + 6 = 888987 x 9 + 5 = 88889876 x 9 + 4 = 8888898765 x 9 + 3 = 888888987654 x 9 + 2 = 88888889876543 x 9 + 1 = 8888888898765432 x 9 + 0 = 888888888Brilliant, isn't it?
And look at this symmetry:1 x 1 = 111 x 11 = 121111 x 111 = 123211111 x 1111 = 123432111111 x 11111 = 123454321111111 x 111111 = 123456543211111111 x 1111111 = 123456765432111111111 x 11111111 = 123456787654321111111111 x 111111111=123456789 87654321Now, take a look at this...101%From a strictly mathematical viewpoint:What Equals 100%? What does it mean to give MORE than 100%?Ever wonder about those people who say they are giving more than 100%?We have all been in situations where someone wants you to GIVE OVER 100%.How about ACHIEVING 101%?What equals 100% in life?Here's a little mathematical formula that might help answer these questions:
If:A B C D E F G H I J K L M N O P Q R S T U V W X Y ZIs represented as:1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26. If:H-A-R-D-W-O- R- K8+1+18+4+23+ 15+18+11 = 98%And:K-N-O-W-L-E- D-G-E11+14+15+23+...

...- Politeness formulas in Arabic:
When talking about politeness formulas in Arabic and in English and how they are different, it is crucial to take into account the distinction between propositional content of a formula and its illocutionary force potential. A good example showing the relationship between semantic content or propositional content and illocutionary force illustrates in using congratulations in English and “shukran” in Arabic which is equivalent to “thanks”. Sometimes illocutionary force is not completely predictable, but simply can be learnt by what people agree upon. For instance, there are three expressions in Arabic performing different forces according to the matter of conventions; \baraka-allahu-fik\ “God bless you” is used to perform the act of thanking, whereas \barakafik\ “blessing in yourself” has a different force, addressing the family members and the relatives of the deceased. \mabruuk\ “blesses” is another formula used for congratulations of marriage or success in examinations.
There are many other expressions used by Arabs in one of the earliest means of demonstrating politeness in a second language which are” greetings”. Greetings actually are the first task one should know when learning a new language. In Arabic greetings; for example, one would not restrict themselves to say \ahlan wa sahlan\ “hello” rather they would precede it by \marhaba\ “welcome” and they may...

...CYPOP2-5.3 Evaluate the benefits of different types of formula that are commonly available
Breast milk is a natural form of baby food which is perfect for a baby. But there are some people who for different reasons can’t breastfeed, or have chosen not to, formula milk is the next best thing.
Scientists and medical experts have spent years developing high-quality formula milks that will provide babies with the specific nutrition that they need.
There are many different types of formula feed and there are many different factors to take into account before choosing the right formula feed.
* Health
* Dietary needs
* Age
* Cost and preparation time of different formula milks.
There are three different types of formula:
* Cow’s milk-based formula
* Hydrolysed protein formula
* Soya-based formula
Most babies can have cow’s milk-based formula, however there are some who have a health or dietary reason why they can’t.
The different range of formula milks are described below.
(information obtained from the baby centre website)
Cow’s milk-based formula
Most baby formula milks are based on cow's milk, which is modified to resemble breastmilk as closely as possible. Manufacturers modify cow's milk for babies by adjusting carbohydrate,...

...Marketing Research Project
Pricing strategy for ‘Formula One India Racing Event’ for Retail Customers
Table of Contents
1. Marketing Research Objective: 3
2. Introduction 3
3. Mode of survey 5
4. Survey Questionnaire 6
5. References 8
1. Marketing Research Objective
What should be optimal price for different classes of tickets at ‘Formula One India Racing Event’ for Retail Customers?
1. Introduction
Formula One is the highest class of single seated auto racing authorized by the Fédération Internationale de l'Automobile (FIA). The F1 season consists of a series of races, known as Grand’s Prix held on purpose-built circuits and public roads. The results of each race are combined to determine two annual World Championships, one for the drivers and one for the constructors. The sport is a massive television event and each race is watched by over 600 million people around world.
Europe is Formula One's traditional centre, where all of the teams are based, and where around half of the races take place. However, the sport's scope has expanded significantly in recent years and Formula one event are being organized in several Asian countries including China, Turkey, Singapore, South Korea. More recently, Indian Grand prix has been announced. The first Indian Grand Prix’s race will be held at the Jaypee International Race Circuit in Greater Noida on October 30, 2011. The 5.14 km...