Question

formulas for class 9 math
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Answer 1

Geometric Figure Area Perimeter

Rectangle A= l × w P = 2 × (l+w )

Triangle A = (1⁄2) × b × h P = a + b + c

Trapezoid A = (1⁄2) × h × (b1+ b2) P = a + b + c + d

Parallelogram A = b × h P = 2 (a+b)

Circle A = π r2 C = 2 π r

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Algebraic Identities For Class 9

(a+b)2=a2+2ab+b2

(a−b)2=a2−2ab+b2

(a+b)(a–b)=a2–b2

(x+a)(x+b)=x2+(a+b)x+ab

(x+a)(x–b)=x2+(a–b)x–ab

(x–a)(x+b)=x2+(b–a)x–ab

(x–a)(x–b)=x2–(a+b)x+ab

(a+b)3=a3+b3+3ab(a+b)

(a–b)3=a3–b3–3ab(a–b)

(x+y+z)2=x2+y2+z2+2xy+2yz+2xz

(x+y–z)2=x2+y2+z2+2xy–2yz–2xz

(x–y+z)2=x2+y2+z2–2xy–2yz+2xz

(x–y–z)2=x2+y2+z2–2xy+2yz–2xz

x3+y3+z3–3xyz=(x+y+z)(x2+y2+z2–xy–yz−xz)

x2+y2=12[(x+y)2+(x–y)2]

(x+a)(x+b)(x+c)=x3+(a+b+c)x2+(ab+bc+ca)x+abc

x3+y3=(x+y)(x2–xy+y2)

x3–y3=(x–y)(x2+xy+y2)

x2+y2+z2−xy–yz–zx=12[(x−y)2+(y−z)2+(z−x)2]

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Shape Surface Area Volume

Cuboid 2(lb + bh +lh)

l= length, b=breadth, h=height

lbh

Cube 6a2 a3

Cylinder 2πr(h+r)

r = radius of circular bases

h = height of cylinder

πr2h

Cone πr(l+r)

r=radius of base

l=slant height  

Also, l2=h2+r2, where h is the height of cone

(1/3)πr2h

Sphere 4πr2 (4/3)πr3

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\(Area ~of~ triangle~ using~ three~ sides =\sqrt{s(s-a)(s-b)(s-c)} \\)

Semi-perimeter, s = (a+b+c)/2

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Polynomial Formula

P(x)=anxn+an−1xn−1−an−2xn−2+……+ax+a0

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Measure of Central Tendency

Mean  Sum of Observation/Total number of observation = ∑ x/n

Median [(n+1)/2]th term [For odd number of observation]

Mean of (n/2)th term and (n/2+1)th term [For even number of observation]

Mode Value which is repeated maximum time in a data set

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mpirical Probability = Number of trials with expected outcome/Total number of Trials