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Words 2819

Pages 12

SOME IMPORTANT MATHEMATICAL FORMULAE

Circle

: Area = π r2; Circumference = 2 π r.

Square : Area = x2 ; Perimeter = 4x.

Rectangle: Area = xy ; Perimeter = 2(x+y).

1

Triangle : Area = (base)(height) ; Perimeter = a+b+c.

2

3 2

Area of equilateral triangle = a .

4

4

Sphere : Surface Area = 4 π r2 ; Volume = π r3.

3

2

3

Cube

: Surface Area = 6a ; Volume = a .

1

Cone

: Curved Surface Area = π rl ; Volume = π r2 h

3

π r l + π r2

Total surface area = .

Cuboid : Total surface area = 2 (ab + bh + lh); Volume = lbh.

Cylinder : Curved surface area = 2 π rh; Volume = π r2 h

Total surface area (open) = 2 π rh;

Total surface area (closed) = 2 π rh+2 π r2 .

SOME BASIC ALGEBRAIC FORMULAE:

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

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

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

4. (a - b)3 = a3 - b3 - 3ab(a - b).

2

2

2

2

5.(a + b + c) = a + b + c +2ab+2bc +2ca.

6.(a + b + c)3 = a3 + b3 + c3+3a2b+3a2c + 3b2c +3b2a +3c2a +3c2a+6abc.

7.a2 - b2 = (a + b)(a – b ) .

8.a3 – b3 = (a – b) (a2 + ab + b2 ).

9.a3 + b3 = (a + b) (a2 - ab + b2 ).

10.(a + b)2 + (a - b)2 = 4ab.

11.(a + b)2 - (a - b)2 = 2(a2 + b2 ).

12.If a + b +c =0, then a3 + b3 + c3 = 3 abc .

INDICES AND SURDS m n mn (ab)m = a m b m am 1. am an = am + n 2.

= a m − n . 3. (a ) = a

. 4.

.

an m am

−m = 1

a

5. =

.

6. a 0 = 1, a ≠ 0 .

7. a

. 8. a x = a y ⇒ x = y m am

b

b

9. a x = b x ⇒ a = b 10. a ± 2 b = x ± y , where x + y = a and xy = b.

S B SATHYANARAYANA

M. Sc., M.I.E ., M Phil .

9481477536

2

LOGARITHMS

a x = m ⇒ log m = x (a > 0 and a ≠ 1) a 1. loga mn = logm + logn.

m

2. loga = logm – logn.

n

3. loga mn = n logm. log a

4. logba =

.

log b

5. logaa = 1.

6. loga1 = 0.

1

7. logba =

.

log a b

8. loga1= 0.

9. log (m +n) ≠ logm +logn.

10. e logx = x.

11. logaax = x.

PROGRESSIONS

ARITHMETIC PROGRESSION a, a + d,…...

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