1. Finding the number of bench and students
- 1st condition : n = xb – extra bench X x
- 2nd condition : n = yb + extra students
- Where x = given no. of students in one bench for 1st condition
- Where y = given no. of students in one bench for 2nd condition
2. No. of days to climb
- N = (H-D)/(U-D)
- Where H = Height of the given things, U = Upward climbing and D = Downward
3. Equation for having 2 Legs and 4 Legs
- 1st equation : Total no. of Head = x + y
- 2nd equation : Total no. of Legs = 2x + 4y
4. Series
Arithmetic series Geometric series
nth term = a + (n - 1)d nth term = arn-1
5. Counting the number of squares
- If nxn : no. of squares = n2 + (n-1)2 + (n-2)2 + (n-3)2 +....(n-n)2
- If mxn : no. of squares = n2 + (n-1)2 + (n-2)2 + (n-3)2 +...(n-n)2 + (m-n) (m-1)(m-2)(m-3)....(m-n)
6. Counting the Rectangles
= R(R+1) x C(C+1) x 1/4
7. Counting the triangles
-
No. of triangle = 1
No. of triangle = 2x1/2 = 3
No. of triangle = base line = 4
No. of triangle = base line x 3 = 4x3 = 12
No. of triangle = no. of head x 3 = 2x 3 = 6
No. of triangle = 4n – 3 = 4 x 3 – 3 = 9
8. Addition of natural number = n/2 x (n+1)
9. No. of Shaking hand = n/2 x (n+1)
10. Counting from Right hand side and Left hand side : T = R + L – 1
11. Permutation = n!/(n-r)!
12. Combination = n! / (n-r!)r!
13. Calculation of distance : S = V x T (velocity x time) where V = (V1xV2x2)/(V1+V2)
14. h2 = p2 + b2 (formula of hypotenuse)
15. Simple interest (SI) = PTR/100
16. Compound Interest (CI) = P (1+r)t
17. Area of Rectangle = 2 (l + b)
18. Area of square = 4l
19. Area of four Wall of room = 2h (l x b)
20. Area of Triangle = ½ x b x h
21. Area of Triangle = (s(s-a)(s-b)(s-c))1/2 where s = (a+b+c)/2 and a,b,c = angle of triangle
22. Perimeter of Triangle = a+b+c
23. Equilateral triangle area = 31/3/4 x a2
24. Perimeter of Equilateral triangle area = 3a
25. Area of Parallelogram = b x h
26. Area of Circle =
27. Perimeter of Circle = 2
28. Volume of Cuboids = l x b x h
29. Surface Area of Cuboids = 2 (lb + lh + bh)
30. Volume of Cube = l3
31. Area of surface of Cube = 6l3
32. Volume of Cylinder =
33. Curved surface Area of Cylinder = 2
34. Total surface Area of Cylinder =
35. Volume of Sphere = 4/3
36. Total surface area of sphere = 4
37. Inductive Reasoning = Specific to Generalization
38. Deductive Reasoning = General to Specific
39. Water Images = Turned and Inverted Images
40. Mirror Images = Right hand side is shown in left hand side and vice versa
41. Embedded figure = Contain the same figure in complex figure
42. Directions : Clockwise and Anti-Clockwise
43. Eight Direction : North, South, East, West, North-East, South- East, North-West, South-West
44. Profit and Loss :
- Profit = Sales Value – Cost Price
- Profit % = ( Sales Value – Cost Price ) / Cost Price
- Discount % = ( Marked Value – Sales Value ) / Marked Value
- 1st condition : n = xb – extra bench X x
- 2nd condition : n = yb + extra students
- Where x = given no. of students in one bench for 1st condition
- Where y = given no. of students in one bench for 2nd condition
2. No. of days to climb
- N = (H-D)/(U-D)
- Where H = Height of the given things, U = Upward climbing and D = Downward
3. Equation for having 2 Legs and 4 Legs
- 1st equation : Total no. of Head = x + y
- 2nd equation : Total no. of Legs = 2x + 4y
4. Series
Arithmetic series Geometric series
nth term = a + (n - 1)d nth term = arn-1
5. Counting the number of squares
- If nxn : no. of squares = n2 + (n-1)2 + (n-2)2 + (n-3)2 +....(n-n)2
- If mxn : no. of squares = n2 + (n-1)2 + (n-2)2 + (n-3)2 +...(n-n)2 + (m-n) (m-1)(m-2)(m-3)....(m-n)
6. Counting the Rectangles
= R(R+1) x C(C+1) x 1/4
7. Counting the triangles
-
No. of triangle = 1
No. of triangle = 2x1/2 = 3
No. of triangle = base line = 4
No. of triangle = base line x 3 = 4x3 = 12
No. of triangle = no. of head x 3 = 2x 3 = 6
No. of triangle = 4n – 3 = 4 x 3 – 3 = 9
8. Addition of natural number = n/2 x (n+1)
9. No. of Shaking hand = n/2 x (n+1)
10. Counting from Right hand side and Left hand side : T = R + L – 1
11. Permutation = n!/(n-r)!
12. Combination = n! / (n-r!)r!
13. Calculation of distance : S = V x T (velocity x time) where V = (V1xV2x2)/(V1+V2)
14. h2 = p2 + b2 (formula of hypotenuse)
15. Simple interest (SI) = PTR/100
16. Compound Interest (CI) = P (1+r)t
17. Area of Rectangle = 2 (l + b)
18. Area of square = 4l
19. Area of four Wall of room = 2h (l x b)
20. Area of Triangle = ½ x b x h
21. Area of Triangle = (s(s-a)(s-b)(s-c))1/2 where s = (a+b+c)/2 and a,b,c = angle of triangle
22. Perimeter of Triangle = a+b+c
23. Equilateral triangle area = 31/3/4 x a2
24. Perimeter of Equilateral triangle area = 3a
25. Area of Parallelogram = b x h
26. Area of Circle =
27. Perimeter of Circle = 2
28. Volume of Cuboids = l x b x h
29. Surface Area of Cuboids = 2 (lb + lh + bh)
30. Volume of Cube = l3
31. Area of surface of Cube = 6l3
32. Volume of Cylinder =
33. Curved surface Area of Cylinder = 2
34. Total surface Area of Cylinder =
35. Volume of Sphere = 4/3
36. Total surface area of sphere = 4
37. Inductive Reasoning = Specific to Generalization
38. Deductive Reasoning = General to Specific
39. Water Images = Turned and Inverted Images
40. Mirror Images = Right hand side is shown in left hand side and vice versa
41. Embedded figure = Contain the same figure in complex figure
42. Directions : Clockwise and Anti-Clockwise
43. Eight Direction : North, South, East, West, North-East, South- East, North-West, South-West
44. Profit and Loss :
- Profit = Sales Value – Cost Price
- Profit % = ( Sales Value – Cost Price ) / Cost Price
- Discount % = ( Marked Value – Sales Value ) / Marked Value
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