Class X Maths Formulas

Last Updated: Dec 9, 2025

Oct 12 • Board Sample Papers • 202590 Views • 635 Comments on Class X Maths Formulas

Introduction

Here’s a quick chapter-wise review of Class X Maths formulas designed for students to memorize efficiently. The PPT provided below serves as a handy reference, helping students quickly recall important formulas and revise effectively. Regular practice along with this formula sheet can boost problem-solving speed and accuracy. This guide ensures that students are well-prepared for exams and confident in tackling any question.

• Real number
• Polynomials
• Remainder theorem
• Linear equations in two variables
• Quadratic equations
• Ratio and proportion
• Similarity
• Distance and section formulae
• Equation of a line
• Circle and tangents
• Circumference and area of a circle
• Solids
• Trigonometric identities
• Graphical representation
• Measures of central tendency
• probability

Class X Maths Formulas

Real number

Euclid’s division algorithm (lemma): Given positive integers ‘a’ and ‘b’, there exists unique integers q and r such that a= b.q+r, where 0 <=r< b ( where a= dividend, b= divisor, q= quotient, and r= remainder.

Polynomials

In step 1 : Factorize the given polynomials,

a)  Either by splitting the terms, ( OR )

b)  Using these identities :

1. (a+b)^2 = a*a + 2ab+b*b
2. (a-b)^2 = a*a – 2ab +b*b
3. a*a – b*b = (a+b)( a-b)
4. a^4 – b^4 = (a^2)^2 –( b^2)^2= (a*a+ b*b)(a*a – b*b) = (a*a + b*b)(a-b)(a+b)
5. (a+b)^3 = a^3 + b^3 + 3ab(a+b)
6. a^3 + b^3 =( a+b)(a*a +ab + b*b)
7. (a-b)^3 = a^3- b^3 – 3ab (a-b)
8. a^3- b^3= (a-b) (a*a+ ab +b*b)
9. (a+b+c)^2 = a*a + b*b +c*c + 2ab+2bc+2ca
10. a^3+b^3+c^3- 3abc = (a+b+c)(a*a + b*b + c*c –ab – bc- ac)

Formulas for Class X Mathematics by oureducation.in

Trial and error method

In step 2 : take a product of ‘ Common terms’ as their HCF.

In step3 : Take the product of All the terms, Omit the HCF value which gives you the value of LCM.

Product of  LCM* HCF=Product of the two polynomials

Note: If cubical expression is given, it may be factorized by using ‘trial and error’ method.

 

Remainder theorem

If (x-2) is a factor of the given expression, then take x-2 = 0 , therefore x = 2 , then substitute this value in p(x) = 5 x*x + 3 x-6

P(2) : 5(2*2) + 3(2)-6 =0 (here taking = 0 is very important. If not taken, answer can’t be found)

If (x-2) leaves a remainder of 4

P(2) : 5(2*2) + 3 (2)-6 =4 ( Here taking = 4 is very important. If not taken, answer can’t be found)

Linear equations in two variables

If pair of linear equation is : a1 + b1y +c1 =0  and a2x + b2 y + c2=0

Then nature of roots/zeroes/solutions :

i.  If a1/a2 is not equal to b1/b2 then, system has unique solution, is consistent OR graph is two intersecting lines

ii.  If a1/a2 = b1/b2 is not equal to c1/c2 , then system has no solution, is inconsistent OR graph is parallel lines.

iii.  If a1/a2=b1/b2=c1/c2, then system has infinite solution, is consistent OR graph are coincident lines.

Quadratic Equations

Note: To find the value of ‘x’ you may adopt either ‘splitting the middle term’ or ‘formula method’.

X=( -b +-(D)^.5)/2a (where D= b*b – 4ac) Hence x= (-b+- (b*b- 4ac)^.5)/2a

• Sum of the roots = -b/a & Product of roots= c/a
• If roots of an equation are given, then :

Quadratic equation : x*x – (Sum of roots).x + (product of the roots) =0

If Discriminant > 0, then the roots are Real & unequal or unique, lines are intersecting.

Discriminant = 0, then the roots are real & equal , lines are coincident.

Discriminant< 0 , then the roots are imaginary (not real), parallel lines.

 

Ratio & proportion

•  Duplicate ratio of a : b is a*a : b*b (Incase of Sub-duplicate ratio you have to take ‘Square root’)
• Triplicate ratio of a: b is a^3 : b^3 (Incase of Sub-triplicate ratio you have to take ‘cube root’)
• Proportion a:b =c:d, continued proportion a :b = b : c, (Middle value is repeated)
• Product of ‘Means’( Middle values)= Product of ‘Extremes’ (Either end values)
• If a/b= c/d is given then Componendo & dividend is (a+b)/ (a-b) = (c+d) / (c-d)

Note : “Where to take “K” method ? “ You may adopt it in the following situations.

If a/b = c/d = e/f are given , then you may assume as a/b= c/d= e/f =k

Therefore a = b.k, c= d.k, e= f.k, then substitute the values of ‘a’ ‘b’ and c’c’ in the given problem.

Incase of continued proportion : a/b = b/c = k , hence , a=bk, b= ck therefore putting the value of b we can get a= c k*k & b= ck.( putting these values equation can be solved)

Similarity

•  If two triangles are similar then, ratio of their sides are equal.

i.e if triangle ABC~ triangle PQR then AB/PQ = BC/QR = AC/PR

• If triangle ABC ~ triangle PQR then (Area of triangle ABC)/ Area of triangle PQR) = (side*side) /(side*side) = ( AB*AB) /( PQ*PQ) =( BC*BC)/( QR*QR) = (AC*AC)/ (PR*PR)

Distance and section formulae

• Distance =(( x2- x1 )^2 + y2-y1)^2))^.5  ( The same formula is to be used to find the length of line segment, sides of a triangle , square , rectangle, parallelogram etc.)
• To prove co-linearity of the given three points A,B and C, you have to find length of  AB, BC, AC then use the condition AB + BC = AC .OR use this condition to solve the question easily :

Area of triangle formed by these points : 0.5 [x1 ( y2-y3)+ x2(y3 – y1) + x3(y1- y2)]=0

• Section formula : point (x,y)=[ ( m1x2 + m2x1)/( m1 + m2) , (m1y2 + m2y1)/ (m1 + m2)]
• Mid-point =[( x1 + x2 )/2 ,( y1 +y2 )/2 ]
• Centroid of a triangle=[( x1+x2+x3)/3 ,( y1+y2+y3)/3]
• If line is trisected then take m:n ratio as 1:2 and find co- ordinates of point p(x,y).

Equation of a line

• If two points are given, then Slope (m) = (y2-y1)/(x2-x1)
• If a point , and slope are given , then Slope (m)= (y-y1)/(x-x1)
• If two lines are ‘Parallel’ to each other then their slopes are equal i.e m1=m2.
• If two lines are ‘Perpendicular’ to each other then product of their slopes is -1 i.e m1 *m2 = -1
• Depending upon the question You may have to use equation of straight line as

a)      Y=mx + c, where ‘c’ is the y- intercept. OR    b) (y-y1)= m.( x-x1)

Circles and Tangents

• Equal chords of a circle are equidistant from the centre .( Chord Property)
• The perpendicular drawn from the centre of a circle, bisects the chord of the circle. (Chord Property)
• The angle subtended at the centre by an arc= Double the angle at any part of the circumference of the circle .(Angle Property)
• Angles subtended by the same arc in the same segment are equal.(Angle property)
• To a circle, if a tangent is drawn and a chord is drawn from the point of contact , then angle made between the chord and the tangent = angle made in the alternate segment(Tangent property)
• The sum of opposite angles of a cyclic quadrilateral is always 180 degree.

Circumference and area of a circle

• Area of a circle = pi(r*r)
• Perimeter of a circle = 2*pi*r
• Area of sector = theta/360 ( pi*r*r)
• Length of an arc = theta / 360 (2*pi*r)
• Area of ring = pi (R*R- r*r)
• Distance moved by a wheel in one revolution = Circumference of the wheel.
• Number of revolutions=Total distance moved/Circumference of the wheel.

Note: While solving ‘Mensuration’ problems, take care of the following.

1. If diameter of a circle is given , then find the radius first

2. Check the units of the entire data. If the units are different , then convert them to the same units.

Solids

 Cylinder  : Volume of a cylinder= pi* r*r *h

Curved surface area = 2*pi*r*h

Total surface area = 2*pi*r*h + 2*pi*r*r = 2*pi*r ( h+r)

Volume of hollow cylinder = pi * R*R*h- pi*r*r*h= pi(R*R-r*r) h

TSA of hollow cylinder = Outer CSA + Inner CSA+ 2. Area of ring .

 

Cone: Volume  of a cone =1/3  pi*r*r*h

CSA of a cone = pi*r*l( here ‘l’ refers to ‘slant height’) [where l= [(h*h + r*r)]^.5

TSA of a cone = pi*r*l + pi*r*r = pi*r (l+r)

Sphere  :  Surface area of a sphere = 4*pi*r*r( Incase of sphere , CSA=TSA i.e they are same)

Volume of hemisphere = 2/3 pi*r*r*r [take half the volume of a sphere]

CSA of hemisphere = 2*pi*r*r [Take half the SA of a sphere]

TSA of hemisphere= 2*pi*r*r+pi*r*r = 3*pi*r*r

Volume of a sphere = 4/3 pi*r*r*r

Volume of spherical shell= Outer volume-Inner volume = 4/3*pi*(R^3-r^3)

Trigonometric identities

 Wherever ‘square’ appears think of using the identities

•  sin^2(x) + cos^2(x) = 1
• tan^2(x) + 1 = sec^2(x)
• cot^2(x) + 1 = csc^2(x)
• tan(x y) = (tan x tan y) / (1 tan x tan y)
• sin(2x) = 2 sin x cos x
• cos(2x) = cos^{^2}(x) – sin^{^2}(x) = 2 cos^{^2}(x) – 1 = 1 – 2 sin^{^2}(x)
• tan(2x) = 2 tan(x) / (1 – tan^{^2}(x))
• sin^{^2}(x) = 1/2 – 1/2 cos(2x)
• cos^{^2}(x) = 1/2 + 1/2 cos(2x)
• sin x – sin y = 2 sin( (x – y)/2 ) cos( (x + y)/2 )
• cos x – cos y = -2 sin( (x – y)/2 ) sin( (x + y)/2 )

Measures of Central tendency

For un-grouped data

• Arithmatic Mean = Sum of observations/ no. of observations
• Mode = the most frequently occurred value of the raw data
• To find the Median first of all arrange the data in ‘Ascending’ or ‘Descending’ order, then

Median= N+1)/2 term value of the given data, in case of the data is having odd no of observations.

Median= (N/2) +(N+1)/2]/2 term value of the given data, in case of the datais having even number of observation.

Probability

Probability of an event : P(event)= Number of favourable outcomes/ Total number of outcomes

If probability of happening an event is x then probability of not happening that event is (1-x).

(Spades in black colour ) having A,2,3,4,5,6,7,8,9,10,J,K and Q total 13 cards

(Clubs in black colour) having A,2,3,4,5,6,7,8,9,10,J,K and Q total 13 cards.

(Hearts in red colour) having A,2,3,4,5,6,7,8,9,10,J,K and Q total 13 cards.

(Diamond in red colour) having A,2,3,4,5,6,7,8,9,10,J,K and Q total 13 cards.

 

• Jack , king and queen are known as face cards.
• If one coin is tossed the total number of outcomes are 2 either a head or a tail.
• If two coins are tossed the total number of outcomes are 2*2 = 4
• If three coins are tossed the total number of outcomes are 2*2*2 = 8
• Similarly for dice, in a single roll total number of outcomes are 6
• If two Dices are rolled , total number of outcomes are 6*6 = 36.

 

You may also like to visit :-

• Maths Sample paper class X Andhra Pradesh Board
• Class X English Sample Paper for Karnataka Board
• BSER English Sample Paper Class X
• Chemistry Sample Paper class X Andhra Pradesh Board
• Class X Science Sample Paper Karnataka Board

For more Board Sample Papers Click here

Users can give their views in comment box so as to improve the article

chapterwise class x maths formulasclass x maths formulasmaths formulas

« RACE SSC Coaching Hyderabad Reviews ISRO Scientist/Engineer SC Syllabus , Eligibility , Exam Pattern Imp Dates »