Essential Mathematical Formulas

1. Diagonal of a Square = s√2

2. Diagonal of a Cube = s√3

3. Diagonal of a Rectangular Solid = 𝑎2 + 𝑏2 + 𝑐2

4. Whole surface area of a Rectangular Solid = 2(ab×bc×ca)

5. Ratio of sides of a 30/60/90 angle = 1: √3: 2

6. Ratio of sides of a 45/45/90 angle = 1: 1: √2

7. Straight line equation y-y1= 𝑦2−𝑦1

𝑥2−𝑥1 (x-x1) [2 point (x1,y1) & (x2,y2) is given]

8. Straight line equation y = mx + b [m = slope, b= y intercept]

9. Slope = 𝑦2−𝑦1

𝑥2−𝑥1 [

𝑟𝑖𝑠𝑒

𝑟𝑢𝑛 ]

10. Distance between two points = (𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)2

11. Equation of circle = (𝑥 − 𝑎)2 + (𝑦 − 𝑏)2 = 𝑟2 [centre= (a,b) ; radius= r]

12. Sum of the internal angle of a polygon - (n-2)×180o

13. Area of a Triangle = ½ × base × height

= 𝑠(𝑠 − 𝑎)(𝑠 − 𝑏)(𝑠 − 𝑐) [s = 𝑎+𝑏+𝑐

2 ]

= 3

4𝑥2 (equilateral triangle)

14. Area of a Parallelogram = Base × Height (a×h)

= ab sinθ

15. Area of a Rectangle = Length × Width

16. Area of a Rhombus = 1

2 × Diagonal1 × Diagonal2

= Side × Height (a × h)

= a2 sinθ

17. Area of a Trapezoid = 𝐵1+𝐵2 ×𝐻

2

18. Of all quadrilateral/polygon with given perimeter, SQUARE/REGULAR

polygon has the largest area & vice versa

19. Cone -

i) V = 1

3𝜋𝑟2ℎ

ii) S = πr(l + r) [l=length of inclined portion]

20. Sphere –

i) V = 4

3𝜋𝑟3

ii) S = 4𝜋𝑟2

21. Cylinder -

i) V= πr2h

ii) Surface area = 2 πr2 + 2πrh = 2πr(r+h)

Essential Mathematical Formulas

20. Circle -

i) Area = πr2

ii) Circumference = 2πr

iii) Area of a sector = πr2

× 𝑎𝑛𝑔𝑙𝑒 𝑖𝑛 𝑑𝑒𝑔𝑟𝑒𝑒

360

iv) Length of a arc = 2πr × 𝑎𝑛𝑔𝑙𝑒 𝑖𝑛 𝑑𝑒𝑔𝑟𝑒𝑒

360

21. x0

= 1

x-a

= 1

𝑥𝑎

ax .a

y = a

x+y

(ax)

y = a

xy

a

x.b

x = (ab)

x

00=1, 0

1=0

22. 1 is not a prime number

2 is the only even prime number

0 is an integer (not negative or positive integer)

23 . Integers are -1,-2,-3.......0........1,2,3.....

24. Prime factorization:

2|60

2|30

3|15

5

2×2×3×5

25. Factorization:

Small Large

1 60

2 30

3 10

4 15

5 12

6 10

Essential Mathematical Formulas

26. Variance = (S.D)2

27. Weighted avg. = 2

5 180 +

3

5(120) [ avg of 2 out of 5 is 180 & remain 3

is 120]

= 72 + 72

= 144

28. 0,1,1,4|5,6,6,7|7,8,10,12|14,15,18,19

Q1 Q2 Q3

(P25) (P50) (P75)

Q1= 4+5

2= 4.5

Q2= 7+7

2= 7

Q3 = 12+14

2= 13

29. Normal distribution:

+- 1 SD = 68% (34+34)

+- 2 SD = 96% (34+14+34+14)

+- 3SD = 99.9% (34+14+2+34+14+2)

30. Permutation without repetition (normal) nPr =

𝑛!

𝑛−𝑟 !

31. Combination without repetition (normal) nCr =

𝑛 !

𝑟! 𝑛−𝑟 !

32. Permutation with repetition = nr

33. Permutation with same indistinguishable member = 𝑛 !

𝑘!

[Suppose permutation of word SUCCESS = 7!

2!×3! as S is 3 times and C is 2 times]

34. Cyclical permutation = 𝑛 !

𝑟

35.

Essential Mathematical Formulas

36. Arithmetric progressing series:

i) nth

term = a + (n-1)d

ii) sum of the first n term = 𝑛

2 {2a + (n-1)d}

37. Geometric progressing series:

i) nth

term = arn-1

ii) sum of the first n term = 𝑎(1−𝑟𝑛 )

1−𝑟

38. 2 solution of quadratic equation ax2+bx+c= 0 is

−𝑏± b2−4ac

2𝑎

39. Simple Interest V( )= P(1+ 𝑟𝑡

100 )

40. Compound Interest V( )= 𝑃(1 +𝑟

100)𝑡 [Compouded yearly]

41. Compound Interest V( )= 𝑃(1 +𝑟

100𝑛)𝑛𝑡 [Compouded n times yearly]

42. Parabola equation y = ax2+bx+c

i) a +ve hole open upwards

ii) y=0 bosale x er 2 ta intercept paowa jabe jar midpoint

holo vertex er x co ordinate….ekhon equation e ei x er

value bosale y paowa jabe…vertex holo ei (x,y)

43. Prime numbers: 4 4 2 2 3 2 2 3 2 1

44. Probability:

Independent probability :(occurrence of one event doesn’t affect the another)

i) Mutually exclusive means no chance of occurrence simultaneously

(both)…like rolling a die, flipping a coin.

Here, P(A) or P(B) = P(A) + P(B)

P(A) and P(B) = P(A).P(B)

ii) Non mutually exclusive (independent) means chance of occurrence

simultaneously (both can occur at the same time)….like subject

related problems.

Here, P(A) or P(B) = P(A) + P(B) – P(A&B)

P(A) and P(B) = P(A).P(B)

Dependent Probability: (occurrence of one event affects another)

Picking red ball, blue ball from box….3/10 x 2/9

45. Total = nA + nB – n (A&B) + no participation

Essential Mathematical Formulas

46. Miscellaneous:

i) (-3)2

= 9 , -32 = -9

ii) 100 = only 10, not -10

𝑥2 = only +x, not –x

iii) x2 = 16, here x = +4