write all formuals of class 10 maths-2 ssc board english medium
Answers
Answer:
Class 10 Maths Formulas For Arithmetic Progression (AP)
If a1, a2, a3, a4….. be the terms of an AP and d be the common difference between each term, then the sequence can be written as: a, a + d, a + 2d, a + 3d, a + 4d…… a + nd. where a is the first term and (a + nd) is the (n – 1) th term. So, the formula to calculate the nth term of AP is given as:
nth term = a + (n-1) d
The sum for the nth term of AP where a is the 1st term, d is the common difference, and l is the last term is given as:
Sn = n/2 [2a + (n-1) d] or Sn = n/2 [a + l]
Class 10 Maths Formulas
Download
Algebra Formulas For Class 10
Class 10 Maths Formulas For Linear Equations
Linear equations in one, two, and three variables have the following forms:
Linear Equation in one Variable ax + b=0 Where a ≠ 0 and a & b are real numbers
Linear Equation in Two Variables ax + by + c = 0 Where a ≠ 0 & b ≠ 0 and a, b & c are real numbers
Linear Equation in Three Variables ax + by + cz + d = 0 Where a ≠ 0, b ≠ 0, c ≠ 0 and a, b, c, d are real numbers
The pair of linear equations in two variables are given as:
a1x+b1+c1=0 and a2x+b2+c2=0
Where a1, b1, c1, & a2, b2, c2 are real numbers & a12+b12 ≠ 0 & a22 + b22 ≠ 0
Quick Note: Linear equations can also be represented in graphical form.
Trigonometry Formulas For Class 10 Maths
The Trigonometric Formulas for Class 10 covers the basic trigonometric functions for a right-angled triangle i.e. Sine (sin), Cosine (cos), and Tangent (tan) which can be used to derive Cosecant (cos), Secant (sec), and Cotangent (cot).
Let a right-angled triangle ABC is right-angled at point B and have \(\angle \theta\) is one of the other two angles.
sin θ = \(\frac{Side\, opposite\, to\, angle\, \theta}{Hypotenuse}\) = \(\frac{Perpendicular}{Hypotenuse}\) = P/H
cos θ = \(\frac{Adjacent\, side\, to\, angle\, \theta}{Hypotenuse}\) = \(\frac{Adjacent side}{Hypotenuse}\) = B/H
tan θ = \(\frac{Side\, opposite\, to\, angle\, \theta}{Adjacent\, side\, to\, angle\, \theta}\) = P/B
sec θ = \(\frac{1}{cos\, \theta }\)
cot θ = \(\frac{1}{tan\, \theta }\)
cosec θ = \(\frac{1}{sin\, \theta }\)
tan θ = \(\frac{Sin\, \theta }{Cos\, \theta }\)
The Trigonometric Table comprising the values of these trigonometric functions for standard angles is as under:
Angle 0° 30° 45° 60° 90°
sinθ 0 1/2 1/√2 √3/2 1
cosθ 1 √3/2 1/√2 ½ 0
tanθ 0 1/√3 1 √3 Undefined
cotθ Undefined √3 1 1/√3 0
secθ 1 2/√3 √2 2 Undefined
cosecθ Undefined 2 √2 2/√3 1
Some other trigonometric formulas are given below:
sin (90° – θ) = cos θ
cos (90° – θ) = sin θ
tan (90° – θ) = cot θ
cot (90° – θ) = tan θ
sec (90° – θ) = cosecθ
cosec (90° – θ) = secθ
sin2θ + cos2 θ = 1
sec2 θ = 1 + tan2θ for 0° ≤ θ < 90°
Cosec2 θ = 1 + cot2 θ for 0° ≤ θ ≤ 90°
Class 10 Maths Formulas
Class 10 Maths Formulas For Algebra & Quadratic Equations
To know the algebra formulas for Class 10, first, you need to get familiar with Quadratic Equations.
The Quadratic Formula: For a quadratic equation px2 + qx + r = 0, the values of x which are the solutions of the equation are given by:
\(x=-b\pm\frac{\sqrt{b^2-4ac}}{2a}\)
Now you know the basic quadratic equation.
Let us now go through the list of algebra formulas for Class 10:
(a+b)2 = a2 + b2 + 2ab
(a-b)2 = a2 + b2 – 2ab
(a+b) (a-b) = a2 – b2
(x + a)(x + b) = x2 + (a + b)x + ab
(x + a)(x – b) = x2 + (a – b)x – ab
(a + b)3 = a3 + b3 + 3ab(a + b)
(a – b)3 = a3 – b3 – 3ab(a – b)
(x – a)(x + b) = x2 + (b – a)x – ab
(x – a)(x – b) = x2 – (a + b)x + ab
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
(x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
(x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
(x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz -xz)
x2 + y2 =½ [(x + y)2 + (x – y)2]
(x + a) (x + b) (x + c) = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc
x3 + y3= (x + y) (x2 – xy + y2)
x3 – y3 = (x – y) (x2 + xy + y2)
x2 + y2 + z2 -xy – yz – zx = ½ [(x-y)2 + (y-z)2 + (z-x)2]
Quick Note: These formulas will be important in higher classes and various comeptitive examninations. So, memorize them and understand them well.
Class 10 Maths Formulas For Circle
Circle formulas act as a base for Mensuration. The Class 10 Maths Circle formulas for a circle of radius r are given below:
1. Circumference of the circle = 2 π r
2. Area of the circle = π r2
3. Area of the sector of angle θ = (θ/360) × π r2
4. Length of an arc of a sector of angle θ = (θ/360) × 2 π r