For revision purpose.

1. MATHEMATICS FUNDAE

4. Important Chapters??

6. TRIGONOMETRY

10. STRAIGHT LINE Normal Form : x cos α + y sin α = p Parametric Form : x – x 1 x – x 2 r cos θ sin θ

11. Equation of angle bisectors a 1 x + b 1 y +c 1 a 2 x + b 2 y + c 2 √ a 1 2 + b 1 2 √a 2 2 + b 2 2 If c 1 , c 2 > 0, then bisector containing origin is given by +ve sign ACUTE & OBTUSE ANGLE BISECTOR

12. Use of Reflection

14. ax 2 + 2hxy + by 2 + 2gx + 2fy + c = 0 Angle between the two lines : θ = tan -1 2 √(h 2 – ab) │ a + b│ Point of intersection of 2 lines : a h g h b f g f c ax + hy + g = 0 hx + by + f = 0 PAIR OF STRAIGHT LINES

18. The curve y = x 3 – 3x + 2 and x + 3y = 2 intersect in points (x 1 ,y 1 ), (x 2 ,y 2 ) and (x 3 ,y 3 ). Then the point P(A,B) where A = Σ x i and B = Σ y i lies on the line (A) x – 3y = 5 (B) x + y = 1 (C) 3x – 7 = y (D) 2x + y = 2

19. Conic Section ax 2 + 2hxy + by 2 + 2gx + 2fy + c = 0

20. How a conic section is formed

21. PARABOLA Focal Chord t 1 t 2 = -1 Length (PQ) = a*(t 2 – t 1 ) 2 Tangents at P & Q will be perpendicular to each other Length of Latus Rectum : 4 * PS * QS PS + QS

22. Tangents Slope Form : Point of intersection of tangents: ( at 1 t 2 , a(t 1 + t 2 ) ) y = mx + a m Remembering Method : G O A (GOA rule) GM of at 1 2 & at 2 2 , AM of 2at 1 & 2at 2 i.e. at 1 t 2 i.e. a(t 1 + t 2 )

23. Equation of tangent to parabolas of different form :

25. ELLIPSE Tangent in slope form : y = mx + √ (a 2 m 2 + b 2 ) - Normal in slope form : y = mx - m (a 2 – b 2 ) + √ (a 2 + b 2 m 2 )

28. Director Circle : Locus of the points from which perpendicular tangents can be drawn x 2 + y 2 = a 2 + b 2

29. Reflection Property : Ray passing through a focus, passes through the other focus after reflection.

33. DIFFERENTIAL CALCULUS

37. Find the period of y = log Cos(x) Sin(x) Answer : 2 π

44. INTEGRAL CALULUS

48. (A) f(2012) + f(-2012) (B) f(2012) – f(-2012) (C) 0 (D) 2012

51. ALGEBRA

53. Coni Method (Rotation Theorem) z 3 – z 1 OQ ( Cos α + i Sin α ) z 2 – z 1 OP CA . e i α BA │ z 3 – z 1 │ . e i α │ z 2 – z 1 │ or arg z 3 – z 1 α z 2 – z 1

54. Co – Ordinate in terms of Complex Equation of Straight Line : z – z 1 = z – z 1 z 2 – z 1 z 2 – z 1 Circle : zz + az + az + b = 0 , Centre is ‘-a’ radius = √aa - b

55. SEQUENCE & SERIES Identifying whether the sequence is A.P, G.P, H.P If, a – b a A.P b – c a a – b a G.P b – c b a – b a H.P b – c c Arithmetic Mean A = a + b 2 G 2 = AH Geometric Mean G = √ab A > G > H Harmonic Mean H = 2ab a + b

57. If second common difference is in A.P then take the cubic expression as the General Term and solve for constants.

59. QUADRATIC EQUATION ax 2 + bx +c = 0 Conditions For A Common Root : ax 2 + bx + c = 0 , a’x 2 + b’x +c’ = 0 a = b = c a’ b’ c’ Note : To find the common root between the two equations, make the same coefficient of x 2 in both the equations and then subtract the 2 equations.

60. Graph of Quadratic Expression f(x) = ax 2 + bx + c

61. Location Of Roots 1. If both the roots are less than k (i) D >= 0 , (ii) a*f(k) > 0 , (iii) k > -b 2a 2 . If both the roots are greater than k (i) D >= 0 , (ii) a*f(k) > 0 , (iii) k < -b 2a

62. 3. If k lies between the roots (i) D > 0 , (ii) a*f(k) < 0 4 . If one of the roots lie in the interval (k 1 , k 2 ) (i) D > 0 ,(ii) f(k 1 )*f(k 2 ) < 0

63. 5 . If both the roots lie in the interval (k 1 ,k 2 ) (i) D >= 0 6. If k1,k2 lie between the roots (i) D > 0 (ii) a*f(k 1 ) > 0 (iii) a*f(k 2 ) > 0 (iv) k 1 < -b < k 2 2a (iii) a*f(k 2 ) > 0 (ii) a*f(k1) > 0

65. COMBINATION 1. Combination of n different things taking r at a time : n C r 2 . Combination of n different things taking r at a time, when k particular objects occur is: n-k C r-k When k particular objects never occur : n-k C r 3. Combination of n different things selecting at least one of them : n C 1 + n C 2 + n C 3 + …………. + n C n = 2 n – 1 4. If out of (p+q+r+t) things, p are alike of one kind , q are alike of 2 nd kind, r are alike of 3 rd kind, and t are different, then the total number of combinations is : (p+1)(q+1)(r+1)*2 t – 1 5. Number of ways in which n different things can be arranged into r different groups is : n+r-1 P n

67. VECTORS AND 3D GEOMETRY

74. TIPS SECTION

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