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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) = $\frac{number\ of\ favourable\ outcomes}{total\ number\ of\ outcomes}$

$\frac{a^{m}}{a^{n}}$ = am-n