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By this post you will get most important formula for mathematics.
Along with mind map and notes
Without wasting time let's begin.
PART - 1
1]Angles and its measurement :
• Conversation of degree into radian or radian into degree.
Degree into radian: n°×π/180
Where,n= degree.
Radian into degree: r × 180/π
Where, r= radian
Relationship between degree and radian:
1(radian) = 57.3248°
1°= 0.01745 radian
•Arc length and area of sector
Arc length : S= r.0
Area of sector : A = ½× r.s
A = ½×r.0
2] Trigonometry 1 :
• Basic formula (trigonometry function)
1) Sin 0 = Opposite side/hypoteneous
2) Cos 0 = Adjacent side/hypoteneous
3) tan 0 = opposite side/adjacent side
4) Cosec 0 = 1/ sin 0
5) Sec 0 = 1/ cos 0
6) Cot 0 = 1/ tan 0
Here, 0 (Teta)
• Trigonometry identities
• Trigonometry table
• properties of trigonometry functions in cartesian coordinates( graph).
1) All trigonometry functions are positive in 1st quadrant.
2)In 2nd quadrant only sin and cosec are positive and rest off all are negative.
3) tan and cot are positive in 3th quadrant and other trigonometry functions are negative.
4)In 4th quadrant only cos and sec are positive and rest off are negative.
• polar co-ordinates
3] Trigonometry 2 :
• Compound angle
• Double angle
• Triple angle
• Factorization formula
★formula for conversion of sum or difference into product.
★formula for conversion of product into sum or difference.
• Trigonometry functions of angle in the triangle.
Let, In ∆ABC
4] Determinants and matrices :
• Basic of Determinants
• properties of Determinants
• Types of Matrix
5] Straight line:
•Equation of locus
L= {P|P is a point in the plane and P satisfies given geometrical condition}
E.g..
L is the locus of points in the plane, where A(1,3) and B(2,1) are the points such that PA=PB (where P is equidistant from both point)
Now, equation of locus is "2x-4y+5=0".
•shift of origin
1) x=X+h 2) y=Y+k
Where,
x or y are old co-ordinate,
X or Y are new co-ordinate,
h,k are the value of new origin (h,k)
• Slope of line
m= tan 0 or m= y2 - y1 / x2 - x1
Where,
m is the slope of line
Special case ;
1) If line are perpendicular then there slope be " m1×m2 = -1 "
2) If line are parallel to each other then slope is " m1 = m2 "
Here, m1 is the slope of first line and m2 is of second ones.
• Equation of line in standard form
1) point-Slope form : (y - y1) = m(x - x1)
2) Slope-Intercept form : y = mx + c
3) Two-points form : x-x1/x2-x1 = y-y1/y2-y1
4) Double-Intercept form : x/a+y/b = 1
• General form of equation of a line
Slope of line : - a/b
X- intercept : - c/a
Y- intercept : - c/b
• point of intersection of line
1) Distance of the Origin from a line :
P= | c/√a² +b² |
2) Distance of the point from a line :
P= |ax1+by1+c/√a²+b²|
3) Distance between two parallel lines:
P= |c1 - c2/√a²+b² |
6] Circle
• Standard form : x² + y² = r²
• Diameter form :
(x-x1)(x-x2)+(y-y1)(y-y2)
• Centre-radius form : r² = (x-h)²+(y-k)²
• General equation of a circle :
x²+y²+2gx+2gy+c=0
Where, radius = √g²+f²-c
Centre =(-g,-f)
• parametric form of circle :
x=r cos 0 y= r sin 0
• Equation of tangent to a circle :
xx1+yy1= r²
• Equation of tangent in terms of slope:
y=mx+-√r²m²+r²
• Equation of director circle :
x²+y²=2r²
7] Conic sections
• parabola :
• Ellipse
• Hyperbola
PART - 2
1] Complex Numbers
• Represention of complex numbers
Z = a+ib
Where,
'a' and 'b' are real number,
i is the not real number.
• Properties of complex numbers
1) i=√-1 , i²= -1 , i³= -i , i⁴= 1
2) Z1+Z2= (a1+a2) + (b1+b2) i
Where, Z1 = a1+ib1 and Z2= a2+ib2
3) same for subtraction
• Argand diagram or Complex plane
1) modulus of z : r=|z|=√a²+b²
2) Argument of z : 0 = tan -¹ (b/a)
3) polar form : z = r(cos0 + isin0)
4) Exponential form: z = r e^i0
• Cube roots of unity
1) -1+i√3/2 2) -1-i√3/2
Properties of 1,w,w²
1) w³=1
2) w³-1=0
3) w²+w+1=0
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