Class X Maths Formulas

Oct 19 • Board Sample Papers • 201904 Views • 635 Comments on Class X Maths Formulas

Introduction
Here is a quick review of class X maths formulas chapter wise for all those students of class X. It will help the students to memories the formulas very quickly. The ppt given below will help the students to remember the formulas quickly.

• Real number
• Polynomials
• Remainder theorem
• Linear equations in two variables
• 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)

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.

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.

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374. MUKESH says:

10th

375. Anonymous says:
376. Anonymous says:

10nt

10nt

10nt

10nt

10nt

10nt

10nt

10nt

10nt

10nt

10nt

10nt

389. Ajay kumar says:

Ba part2

390. sss says:

Formulae for trigonometry

391. Anonymous says:
392. Dipu Ranjan Nayak says:

10+2

393. Anonymous says:
394. Maya says:
395. Maya says:
396. Maya says:
397. Maya says:
398. Maya says:
399. Anonymous says:
400. Anonymous says:
401. Anonymous says:
402. kailash says:
403. ABGNHI says:
404. ABGNHI says:
405. Anonymous says:
406. Anonymous says:
407. Ghulam abbas says:

m.phil

408. m.bharathi says:

10 class triganamitry basics

409. Anonymous says:

10 class triganamitry basics

410. Anonymous says:

10 class triganamitry basics

411. harsh chaudhary says:

Learning

412. harsh chaudhary says:
413. abid khan says:

Formulas of all chapters

414. Anonymous says:
415. Anonymous says:
416. Deepak says:
417. Santhosh says:

Formula

418. Anonymous says:
419. Anonymous says:
421. Yunuseyusff says:

Formula

422. Maruthi kindidoddi says:

All formula

423. Maruthi kindidoddi says:
424. Ravi Anil Phate says:

No

425. Anonymous says:
426. Anonymous says:
427. p says:
428. sk das says:

no

429. Anonymous says:
430. Anonymous says:
431. Shruti Awasthi says:

No

432. Anonymous says:
433. saurabh kumar says:

math

434. saurabh kumar says:
435. nandu kumar baiwa says:
436. nandu kumar baiwa says:
437. Anonymous says:
438. Anonymous says:
439. Nandkumar says:

Refraction through glass prism

440. Nandkumar says:
441. Nandkumar says:
442. Anonymous says:
443. Manisha says:

Maths geometry doubts

444. manisha says:
445. pawan says:

maths

446. pawan says:

maths

447. pawan says:

maths

448. Honey says:

Maths formulae ch 1
Class 10 Ncert

449. Honey says:
450. Honey says:
451. Honey says:
452. Honey says:
453. Honey says:
454. ARVIND KUMAR says:

deploma polytechnic

455. ARVIND KUMAR says:

deploma polytechnic

456. Anonymous says:
457. Anonymous says:
458. Ansarkhan says:

Cbse class10

459. megha says:

Maths

460. megha says:

Maths

461. megha says:
462. Athira Mohan says:
463. Anonymous says:
464. Devi santoshi matha says:
465. Devi santoshi matha says:
466. Devi santoshi matha says:
467. Devi santoshi matha says:
468. Devi santoshi matha says:
469. Devi santoshi matha says:
470. Devi santoshi matha says:
471. Devi santoshi matha says:
472. Devi santoshi matha says:
473. Devi santoshi matha says:
474. Rishi raj kurmi says:

Studying in 10 class

475. Anonymous says:
477. sai vinay says:
478. Anonymous says:
480. Anonymous says:
481. N. GOWRI SHANKAR says:

10th maths formulae

482. Anonymous says:
483. Kohinoor says:

10th class

484. Piyush Patidar says:

All formulaes of class 10

485. Piyush Patidar says:

All formulaes of class 10

486. Piyush Patidar says:

All formulaes of class 10

487. Piyush Patidar says:

All formulaes of class 10

488. Piyush Patidar says:

All formulaes of class 10

489. Piyush Patidar says:

All formulaes of class 10

490. Piyush Patidar says:

All formulaes of class 10

491. Diya says:

Trigonometry proving questions

492. Diya says:
493. Diya says:
494. Monu kumar says:

Matihani

495. Anonymous says:
496. manish kumar says:
497. saurav sheakhar says:

Formula ex papare board papaer

498. saurav sheakhar says:

Formula ex papare board papaer

Studay

Studay

Studay

Studay

Studay

Studay

Studay

506. Anonymous says:
507. Anonymous says:
508. Akhand says:

Trigonometry formula

509. Akhand says:
510. Akhand says:
511. Anonymous says:

Maths formulas for class 10

514. Anonymous says:
515. Anonymous says:
516. Jagannath sahu says:

Math Pollynomia

517. Jagannath sahu says:

Math Pollynomia

518. Jagannath sahu says:

Math Pollynomia

519. Anonymous says:
520. Anonymous says:
521. Anonymous says:
522. Atraj says:
523. Atraj says:
524. Atraj says:
525. Atraj says:
526. Anonymous says:
527. Anonymous says:
528. Anonymous says:
529. saksham says:

all formulas

530. saksham says:

all formulas

531. saksham says:
532. saksham says:
533. haider says:

534. Shivam Banchhod says:

Nothing

535. Shivam Banchhod says:

Nothing

536. Shivam Banchhod says:
537. sabir nawab says:
538. sabir nawab says:
539. pravindra says:

10th class

540. Anonymous says:
541. himanshu raj says:

No

542. himanshu raj says:

No

543. himanshu raj says:

No

544. himanshu raj says:
545. himanshu raj says:
546. Anonymous says:
547. Anonymous says:
548. tavneet singh says:

Formulas

549. ankitwarsi says:

A

550. ankitwarsi says:

A

551. ankitwarsi says:
552. Ravi ranjan Kumar says:

matric

553. Anonymous says:
554. gagan says:

Maths

555. gagan says:

Maths

556. gagan says:
557. gagan says:
558. gagan says:
559. gagan says:
560. gagan says:
561. Anonymous says:
562. Anonymous says:
563. Anonymous says:

Democraxy

Democraxy

567. harishchandra says:

12

568. harishchandra says:
569. harishchandra says:
570. shankar oraon says:
571. khushi Rajput says:
572. Anjana kumari says:
573. Gurjit Singh says:

Math

574. SAM JOSHUA says:

no

575. SAM JOSHUA says:
576. alina ansari says:

10th class

577. Divyansh gupta says:

Enter your any educational query or doubt from subhash chandra bose

578. Anonymous says:
579. birbal dass says:

10+2

580. birbal dass says:

10+2

581. birbal dass says:

10+2

582. birbal dass says:

10+2

583. birbal dass says:

10+2

584. birbal dass says:

10+2

585. amar sharma says:

Short tricks for maths

586. amolakdeep singh says:

knowledge or formulas used in 10th class

587. amolakdeep singh says:

knowledge or formulas used in 10th class

588. Prashant verma says:

Not

589. Prashant verma says:

Not

590. Prashant verma says:

Not

591. Prashant verma says:
592. shanoaf says:

593. shanoaf says:
594. Anonymous says:
595. Anonymous says:
596. Rahul says:

I hectare is equal to how many metre

597. Rahul says:

I hectare is equal to how many metre

598. Anonymous says:
599. Altaf khan says:
600. Anonymous says:
601. Harsh Gupta says:

W

602. Harsh Gupta says:

No

603. Harsh Gupta says:

No

604. Harsh Gupta says:
605. Nehru says:
606. Nehru says:
607. Anonymous says:
608. Komal kumari says:

10

609. Komal kumari says:
610. dj says:

a list of all the basic farmulas , defenations and thearmes of maths of class10

611. Anonymous says:

Enter your any educational query or doubtmy doubt in trignomentry

612. abdussalam says:

11th class from bokaro ispat senior secondry school 2/c

613. DILPREET KAUR says:
614. aayush kumar says:

i want all the mathematical formulas for class 10 chapterwise

615. AASTHA SINGH says:

I have so much problem in trigonometryof class 10th

616. Archishman Satpathy says:

Prepare a formula chart based on mathematics class 10 chapter wise systematically of ncert book

617. jnahvi bhalla says:

pleasegive me polynomiallvformulas of al-pha and beta v

618. himanshu says:

maths formulae
full SST especially history civics and maps

619. arvind says:

in ditanceword pro. where we have to do add or sub.

620. S.Priyansi Priti Rani says:

I want to know all the formula related to class 10 chapters of sa 2 course

621. Harsh Sawaitul says:

i want all formulas of class 10 geometry to download on net

622. Vishvanath Patil says:

Hi All,
Do anyone here has chapterwise formulas of Science, Algebra & Geometry for Std VIII, IX & X (SSC)

623. Vijay Kumar says:

want to have all maths formulas for class X of cbse

Thanx for that formula
But in that formula some formulas are not there

625. varun somani says:

can you help me
give me class 10 cbse chapterwise formula list
cna you send by a mail
mail id : kumawathimanshu25@gmail.com

626. anitha s r says:

list of maths formulas for 10th standard english medium students of karnataka state syllabus

627. pravina deshmukh says:

required Formula chart for algebra, geometra, physics , chemistry
of 10th class stste board maharashtra

628. SANDEEP THALI says:

SSC AND HSC-SCIENCE NOTES (MAHARASHTRA BOARD) FOR KIDS

629. kshitija says:

I am in 10th & very weak at maths so need help right from basics

630. akku says:

can you please suggest me some ideas to make a stunning and mind-blowing chart on maths for class 10

631. sunandita deb gupta says:

i want formulas of all chapters in class 10 for second upto

632. kaushik sagar says:

i have doubt in trigonometry and tangents and secants

633. arati says:

i want all the important theorems of 2016 in boards point of view

634. M.A.Aashima shirin says:

i can’t remember the trigonometric formulas. is there any easy tricks?

635. Arun Jyothi says:

I need Maths formulas for 10th Standard Maharastra Board