MATHS Xth Formulas

 THE SIDDIQUI ACADEMY

(POWERED BY EXTRAMARKS)

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 a 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 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 cover 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 ∠θ$\mathrm{\angle }\theta$ is one of the other two angles.

sin θ = SideoppositetoangleθHypotenuse$\frac{Sideoppositetoangle\theta }{Hypotenuse}$ = PerpendicularHypotenuse$\frac{Perpendicular}{Hypotenuse}$ = P/H

cos θ = AdjacentsidetoangleθHypotenuse$\frac{Adjacentsidetoangle\theta }{Hypotenuse}$ = AdjacentsideHypotenuse$\frac{Adjacentside}{Hypotenuse}$ = B/H

tan θ = SideoppositetoangleθAdjacentsidetoangleθ$\frac{Sideoppositetoangle\theta }{Adjacentsidetoangle\theta }$ = P/B

sec θ = 1cosθ$\frac{\mathrm{<br>}}{}$

cot θ = 1tanθ$\frac{\mathrm{<br>}}{}$

cosec θ = 1sinθ$\frac{\mathrm{<br>}}{}$

tan θ = SinθCosθ

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:

1. sin (90° – θ) = cos θ
2. cos (90° – θ) = sin θ
3. tan (90° – θ) = cot θ
4. cot (90° – θ) = tan θ
5. sec (90° – θ) = cosecθ
6. cosec (90° – θ) = secθ
7. sin2θ + cos2 θ = 1
8. sec2 θ = 1 + tan2θ for 0° ≤ θ < 90°
9. Cosec2 θ = 1 + cot2 θ for 0° ≤ θ ≤ 90°

Class 10 Maths Formulas for Algebra And 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±b2−4ac√2a$x=-b\pm \frac{\sqrt{b^2-4ac}}{2a}$

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 competitive examinations. So, memorise them and understand them well.

Class 10 Maths Formulas for Surface Area and Volume

These formulas are very important for successfully solving mensuration questions. Find below the formulas in a tabulated form for your convenience.

Here, LSA = Lateral Surface Area,

TSA = Total Surface Area.

Sphere	Diameter: 2r Circumference: 2 π r TSA: 4πr2  Volume: 43πr2$\frac{4}{3}\pi r^2$ r = radius
Cylinder	Circumference: 2πr LSA: 2πrh TSA: 2πr (r + h) Volume: πr2h r = radius, h = height
Cone	Slant height: l=h2+r2−−−−−−√$l=\sqrt{h^2+r^2}$ LSA: πrl TSA: πr(r + l) Volume:  13πr2h$\frac{1}{3}\pi r^{2}h$  r = radius, l = slant height, h = height
Cuboid	LSA: 2h(l + b) TSA: 2(lb + bh + hl) Volume: lbh l = length, b = breadth, h = height
Cube	LSA: 4a2 TSA: 6a2 Volume: a3 a = sides of a cube

Class 10 Maths Formulas for Statistics

Statistics in Class 10 is mostly about finding the given data’s Mean, Median, and Mode. The statistic formulas are given below:

(I) The Mean of Grouped Data can be found by 3 methods.

• Direct Method: x̅ = ∑ni=1fixi∑ni=1fi$\frac{\underset{\mathrm{}}{\overset{}{}}{}_{}{}_{}}{\underset{\mathrm{}}{\overset{}{}}{}_{}}$ where fi xi is the sum of observations for i = 1 to n And fi is the number of observations for i = 1 to n
• Assumed Mean Method : x̅ = a+∑ni=1fidi∑ni=1fi$\frac{\underset{\mathrm{}}{\overset{}{}}{}_{}{}_{}}{\underset{\mathrm{}}{\overset{}{}}{}_{}}$
• Step Deviation Method : x̅ = a+∑ni=1fiui∑ni=1fi×h$\frac{\underset{}{\overset{}{<br>}}}{}$

(II) The Mode of Grouped Data: Mode = l +fi−f02f1−f0−f2×h$\frac{{\mathrm{<br>}}_{}}{}$

(III) The median for a grouped data: Median = l+n2−cff×h