Important Formulas of Math

7/29/2019 Important Formulas of Math

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GEOMETRY

triangle with sides a,b and c and radius of incircle and circumcircle as r and R respective

hen the relation between them is as follows

= area of triangle/ semiperimeter

= abc/4*ar. of triangle = abc/4*r*semiperimeter

nd in case of right angled triangle with perpendicular as a base as b and hypotenuse as h

hen

= hypotenuse/2

= (perpendicular + base hypotenuse)/2

rea of triangle when an angle is given = 1/2(ab sinC)=1/2(ac sinB)=1/2(bc sin A)

AD is the bisector of angle BAC of triangle ABC then

B/AC=BD/DC

nd in AD is median, then

B2+AC2=2(AD2+BD2 or DC2)

he ratio of area of two similar triangles is equal to the square of the corresponding

medians or altitudes or sides or angle bisector segments.

n right angled triangle ABC, angle B= 900 and BD perpendicular AC, then

D2 = AD*DC

he area eq. triangle described on the side of the square is half the area of eq. triangle

escribed on its diagonals.

n triangle ABC, angle B is obtuse and AD is perpendicular to CB produced, then

C2 = AB2+BC2+2BC*BD

nd, in the case of B being acute angle and AD is perpendicular to BC, then

AC2 = AB2+BC2-2BC*BD

BC is right angled triangle, angle B=900

, and D and E are points on AB and AC, then

E2+CD2=AC2+DE2

nd if D and E are midpoints, then

AE2=4AC2+BC2

CD2=4BC2+AC2

(AE2+CD2)=5AC2=20DE2


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ngle subtended by an arc of a circle at the centre is double the angle subtended by it at

ny point on the remaining part of the circle.

ngle in the same segment are equal.

When two chords AB and AC of circle cuts each other inside or outside the circle, then

P*BP=CP*DP

When chord AB of a circle is produced to a point P, and from that point a tangent is drawn

o the circle, then

T2=PA*PB

When a chord XY is drawn parallel to tangent APB, then angle APX=angle PYX, angle

PY=angle PXY

wo circles with radius r and R, and the distance between them is d, then

Measure of direct tangent = d2 (R-r)2

Measure of transverse tangent = d2 + (R+r)2

Where, R>r

When two circles with equal radius r intersect each other at its center, the length of

ommon chord = r 3

TRIGONOMETRY

sin A + cos A = x, then, sin A cos A = 2 x2

sec A + tan A = x, then, sec A = (x2 + 1)/2x

Maximum value of (sin A*cos A)n =( 1/2)n , therefore sin A*cos A =

n the angle of incidence made by a point on the land to the top of a pole is A and after

ravelling the distance D the angle of incidence become B then, height of the pole

= D/(cot A cot B), where A>B

the angle of depression from top and bottom of a pole with the second pole is A and B

espectively, and the height of the second pole is H, then

eight of the first pole = H sin(A+B)/cos A*cos B

the angle of depression of top and bottom of tree from the top of the pole is A and B

espectively, and height of the tree is h, then the height of the pole, H = h tan A/tan A*tan


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CO-ORDINATE GEOMETRY

he distance measured from origin O along X- axis is called abscissa and along Y- axis is

alled ordinate.

bscissa along Y-axis is 0 and ordinate along X-axis is 0.

he slope or gradient of a line is denoted bym and its intercept is denoted by c

or equation ax+by+c=0, then m = -a/b , and c = -c/b

the vertices of triangle is denoted by (x1,y1),(x2,y2),(x3,y3), then its area is

[x1(y2-y1)+x2(y3-y1)+x3(y1-y2) and its incentre = [ax1+bx2+cx3]/a+b+c ,

ay1+by2+cy3]/a+b+c , and centroid = [x1+x2+x3/3] , [y1+y2+y3/3]

(x1,y1) and (x2,y2) is coordinate of two points on the line then

m= y2-y1/x2-x1

PERCENTAGE

ue to x% increase in a price of commodity a person buys akg less in y rupees then the

ncreased price per kg= xy/100a

nd original price = xy/(100+x)a, and if x is decrease percent akg is more amoun of

ommodity bought in y rupees then

ncreased price per kg = xy/100a, and original price = xy/(100-x)a

ue to increase of x% in price of a commodity a person decreases the consumption to suc

xtent that only y% of expenditure increases, if original consumption is akg then now its

onsumption = a(100+x)/(100+x)

PROFIT AND LOSS

x no. of commodity is bought in Rs y and a commodity is sold for Rs b then

rofit %= [(bx-ay)/ay]100

oss%= [(ay-bx)/ay]100

S.P. of two things are same and one is sold with profit of P% and second is sold for loss

% the loss or profit %

s [{100(P-L)-2PL}/(100+P)(100-L)]

y selling an article for y rupees instead of x rupees, gain% percent becomes n times, the

.P. of article = (nx-y)/(n-1)


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y selling an article for x rupees gain% is n time to the loss% when it is sold in y rupees,

hen C.P. of article = (x+ny)/(n+1)

SIMPLE INTEREST

any sum of money at the rate of S.I. becomes A 1 in t1 years and A2 in t2 years then that

um = A1-{t1(A2-A1)/(t2-t1)}

after t years a sum is to be paid in equal installments at the rate of r%, then each

nstallment = 100x/[100t+{(t-1)+(t-2)+.+(t-t)}r]

COMPOUND INTEREST

the S.I. on a sum is x rupees and C.I. on the same sum is y rupees for 2 years , then rate

%= [2(y-x)/x]*100

um P= x^2/4(y-x)

the S.I. on a sum is x rupees and C.I. on the same sum is y rupees for 2nd year , then rat

%= [(y-x)/x]*100

um P= x^2/(y-x)

he difference of S.I. and C.I. on any sum of money P for 2 years at the rate of r%=Pr2/

100)2

nd for 3 years= Pr2(300+r)/(100)3

the debt of x rupees is to be paid in n equal installments at the rate of r%, of y rupees,

hen x= y/(1+r/100)+y/(1+r/100)2..+y/(1+r/100)n

TIME AND WORK

A and B takes x and y days respectively to finish a work then time taken by A and B

ogether to finish the work

y/x+y

A, B and C takes x, y and z days respectively to finish a work then time taken by A, B and

together to finish the work

yz/xy+yz+zx

(A+B), (B+C) and (C+A) takes x, y and z days respectively to finish a work then time

aken by A, B and C together to finish the work 2xyz/xy+yz+zx

me taken by A alone 2xyz/xy+yz-zx

ime taken by B alone 2xyz/yz+zx-xy

me taken by C alone 2xyz/xy-yz+zx


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A and B together finish a work in x days and A alone finish it in y days then time taken b

to finish it

y/y-x

A finshes a work in x days and after working for t1 days and the remaining work is

nished by B in t2 days then

ime taken by B to finish whole work xt2/x-t1

ime taken by A and B to finish whole work xt2/x-t1+t2

TIME AND SPEED

anything travels two equal distances with x and y km/h then av. Speed= 2xy/x+y

anything travels 3 equal distances with x, y and z km/h then av. Speed= 3xyz/xy+yz+zx

any person run away with x km/h and after t hours it was chased by another person withkm/h then time taken to catch it

t/y-x

an object travels with travels with a/b of its original speed. If it reaches t hours late the

s original speed = (a/b-a)t

it reaches t hours before then its original speed = (a/a-b)t

a person travels with m km/h more than its original speed then it reaches t1 hours befor

nd if travels with n km/h less than its original speed then it reaches t2 hours late.

mn(t1+t2)/mt2-nt1

two trains A and B travelling with x km/h and y km/h and train A starts from P to Q and

rains B starts from Q to P, and after meeting each other reach Q and P after t 1 and t2 hou

^2/y^2 = t2/t1

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Important Formulas of Math