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# General Maths Formula Sheet

General Maths Formula Sheet:

A list of  mathematical  general formula is given in pdf  for student reference which helps in solving  problems.

Commercial Mathematics:

Profit = S.P -C.P
Profit% = $\frac{profit}{C.P}$*100%
Loss  = C.P - S.P
Loss% = $\frac{loss}{C.P}$*100%
Simple interest = $\frac{PTR}{100}$
P = principal,T = time ,R = rate of interest,S.P = selling price,C.P = cost price

Geometric Formula:

Cylinder:

V = πr2h
Lateral surface area A = 2πrh
Total surface area = 2πr2+2πrh

Sphere:

V = $\frac{4}{3}$ πr3 A = 4πr2

Cone:

V = $\frac{1}{3}$ πr2h Lateral surface area = πrs          Total surface area = πrs + πr2

Square- based Prism:

V = $\frac{1}{3}$ b2h Total area = 2bs + b2

Distance Formula:

Distance between two points P(x1,y1) and Q(x2,y2) is
PQ = $\sqrt{(x_1-x_2)^{2}+(y_1-y_2)^{2}}$
Equation of straight line through (x1,y1) is y = m x+c
m is gradient, b is y-intercept
Angle between two straight line
$\tan \theta = \left | \frac{m_1-m_2}{1+m_1m_2} \right |$
two lines are parallel if m= m2
two lines are perpendicular if, m1m2 = -1

Circles:

General equation of circles  = x+ y+ 2gx + 2fy + c = 0
Radius of general equation of circle is $\sqrt{g^{2}+f^{2}-c}$
Center of a general equation of  a circle is (-g,-f)

Quadratic Equation: x = -b ± $\frac{\sqrt{b^{2}-4ac}}{2a}$
Sum of roots of equation = - $\frac{b}{a}$
Product of roots = $\frac{c}{a}$

Permutation and  Combination:

The number of permutation of n different things taken r at a time is nPr = $\frac{n!}{(n-r)!}$

The number of combination of n different things taken r at a time is nCr = $\frac{n!}{r!(n-r)!}$

Differential Formula

Derivative of a constant: $\frac{dc}{dx}$ = 0

Derivative of sum: $\frac{d(u+v)}{dx}=\frac{du}{dx}+\frac{dv}{dx}$

Derivative of Difference: $\frac{d(u-v)}{dx}=\frac{du}{dx}-\frac{dv}{dx}$

Product rule: $\frac{d(uv)}{dx}=u\frac{dv}{dx}+v\frac{du}{dx}$

Chain rule: $\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}$

Quotient rule: $\frac{d}{dx}\frac{u}{v}=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^{2}}$

1. $\frac{d}{dx}$ k = 0     $\frac{d}{dx}$ k.f(x) = kf'(x)

2. $\frac{d}{dx}$ f(x)+g(x) = f'(x)+g'(x)      $\frac{d}{dx}$ f(g(x)) = f'(g(x)) .g'(x)

3. $\frac{d}{dx}$ xn = nxn-1        $\frac{d}{dx}$ sin x = cos x

4. $\frac{d}{dx}$ cos x = -sin x $\frac{d}{dx}$ tan x = sec2x

5. $\frac{d}{dx}$ cot x = -csc2x $\frac{d}{dx}$ sec x = sec x tan x

6. $\frac{d}{dx}$ csc x = -csc x cot x     $\frac{d}{dx}$ ax – ax loga

7. $\frac{d}{dx}$ ex = ex       $\frac{d}{dx}$ log x = $\frac{1}{x}$

8. $\frac{d}{dx}$ sin-1x = $\frac{1}{\sqrt{1-x^{2}}}$       $\frac{d}{dx}$ cos-1x = $\frac{-1}{\sqrt{1-x^{2}}}$

9. $\frac{d}{dx}$ tan-1x = $\frac{1}{x^{2}+1}$    $\frac{d}{dx}$ cot-1x = $\frac{-1}{x^{2}+1}$

10. $\frac{d}{dx}$ sec-1x = $\frac{1}{\left | x \right |\sqrt{x^{2}-1}}$    $\frac{d}{dx}$ csc-1x = $\frac{-1}{\left | x \right |\sqrt{x^{2}-1}}$

Trigonometry Formula:

sin A = $\frac{opposite(BC)}{hypotenuse(AC)}$  cos =  $\frac{adjacent(AB)}{hypotenuse(AC)}$

tan A = $\frac{opposite(BC)}{adjacent(AB)}$   cot A =   $\frac{adjacent(AB)}{opposite(BC)}$

sec A = $\frac{hypotenuse(AC)}{opposite(BC)}$     cosec A =   $\frac{hypotenuse(AC)}{adjacent(AB)}$

Trigonometric Ratio/Angle Table:

 θ 0º 30º 45º 60º 90º sinθ 0 $\frac{1}{2}$ $\frac{1}{\sqrt{2}}$ $\frac{\sqrt{3}}{2}$ 1 cosθ 1 $\frac{\sqrt{3}}{2}$ $\frac{1}{\sqrt{2}}$ $\frac{1}{2}$ 0 tanθ 0 $\frac{1}{\sqrt{3}}$ 1 $\sqrt{3}$ Not Defined cotθ Not Defined $\sqrt{3}$ 1 $\frac{1}{\sqrt{3}}$ 0 secθ 1 $\frac{2}{\sqrt{3}}$ $\sqrt{2}$ 2 Not Defined cosecθ Not Defined 2 $\sqrt{2}$ $\frac{2}{\sqrt{3}}$ 1

a)  sin2A + cos2A  = 1
b)  sec2A - tan2A  = 1
c)  cosec2A - cot2A = 1

Relation Between Trigonometric Ratio:

a) sin A =  $\frac{1}{cosecA}$

b) cos A =  $\frac{1}{secA}$

c) tan A =  $\frac{1}{cotA}$

d) tan A =  $\frac{sinA}{cosA}$

e) cot A =  $\frac{cosA}{sinA}$

Probability of an Event

The probability of an event where outcomes are equally likely is given by:
p(n) = $\frac{number\ of\ favourable\ outcomes}{total\ number\ of\ outcomes}$

amxan = am+n
$\frac{a^{m}}{a^{n}}$ = am-n
(am)n  = amn
(ambn)p =   ampbnp
a0 = 1

From Wikipedia

Worksheet

A worksheet is a sheet of paper, or on a computer, on which problems are worked out or solved and answers recorded.

## Education

Students in a school may have 'fill-in-the-blank' sheets of questions, diagrams, or maps to help them with their exercises. Students will often use worksheets to review what has been taught in class. A worksheet generator is a software program that generates problems, particularly in mathematics or numeracy. Such software is often used by teachers to make classroom materials and tests.

## Accounting

In accounting a worksheet often refers to a loose leaf piece of stationery from a columnar pad, as opposed to one that has been bound into a physical ledger book. From this, the term was extended to designate a single, two-dimensional array of data within a computerized spreadsheet program. Common types of worksheets used in business include financial statements, such as profit and loss reports. Analysts, investors, and accountants track a company's financial statements, balance sheets, and other data on worksheets.

In the Microsoft spreadsheet program Excel, a single document is known as a 'workbook' and by default each workbook contains three arrays or 'worksheets'. One advantage of such programs is that they can contain formulae so that if one cell value is changed, the entire document is automatically updated, based on those formulae.

Question:if i want to know the factorial of 13,i want to multiply1,2,3,4,5,6,7,8,9,10,11,12,13.it is a lengthy process. so i need a short cut formula for finding the factorials.

Answers:1. there is no shortcut if you have to multiply i.e. you do not have a factorial function on calculator 2. what you can do then is to gradually build up a table. suppose you have built up a table upto 10! and are asked to compute 12! 12! = 10!*11*12 and when you have computed thus, enlarge your table upto 12! P.S. ----- for very large numbers you could try stirling's approximation, (see source cited) but i dnt think that's what u want

Question:i need to find a link to a pdf file of the EDEXCEL MATHS A LEVEL formula sheets. please don't bother sending me links to the edexcel site itself cos i cant get on there. thank you. :)

Answers:It doesn't seem to have a formula sheet but a formula BOOK (40 pages). I'm not sure whether this is the right one (don't be daunted by the 40 pages - most are blank or contents). Here's a link to the PDF (unfortunately it is from the edexcel site but hopefully you will be able to access it in PDF format): http://www.edexcel.com/migrationdocuments/GCE%20Curriculum%202000/219797_Formulae_book_Revised_Specification.pdf Good luck.

Question:ive been trying to find a complete sheet of formulas on the internet, but so far i haven't been able to find one, the ones i have found seem to be incomplete, missing formulas.. anyone have one that is standard for math 10, in canada?

Answers:ya i have but i m putup in INDIA...so....sory i cant help

Question:Im taking the ACT tomorrow and I didn't know if I should study my formulas for the math part or if they give you one? does anybody know?

Answers:REMEMBER THEM YOU WILL NEED THEM GOOD LUCK !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! =)=)