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CBSE 10th Exam 2020: Maths Important Formulas & Theorems

PUBLISH DATE 14th January 2020

The Central Board of Secondary Education (CBSE) will conduct the annual board examinations of class 10th from February 26, 2020, to March 18, 2020.

The 10th Mathematics examination will be held on March 12, 2020. The students now have about two months to prepare for the Mathematics examination. In these two months, the students need to give full focus to their studies to secure maximum marks in Mathematics subject.

Starting from this year, the CBSE Board has introduced two options in 10th Mathematics paper - Standard Mathematics and Basic Mathematics. Students who want to study Mathematics in higher classes can opt for Standard Mathematics exam while those who find the subject difficult and don't want to study this subject in higher classes can choose Basic Mathematics exam.

Though the books, syllabus and exam pattern for both options are same but there will be difference in the difficulty level of the papers. Basic Maths paper will be set easier compared to the standard one. But Mathematics is an important subject for overall development of a child. Hence, all the students are advised to complete their Mathematics syllabus and practice as many questions as possible.

To help students in their Mathematics exam preparation, we have provided below some of the important formulas and properties:

Real Numbers

Euclid’s Division: If we have two positive integers a and b, then there exist unique integers q and r such that a = bq + r, where 0 = r = b. (Here, a = dividend, b = divisor, q = quotient and r = remainder.)

Polynomials

(i) (a + b) 2 = a 2 + 2ab + b 2

(ii) (a – b) 2 = a 2 – 2ab + b 2

(iii) a 2 – b 2 = (a + b) (a – b)

(iv) (a + b) 3 = a 3 + b 3 + 3ab(a + b)

(v) (a – b) 3 = a 3 – b 3 – 3ab(a – b)

(vi) a 3 + b 3 = (a + b) (a 2 – ab + b 2)

(vii) a 3 – b 3 = (a – b) (a 2 + ab + b 2)

(viii) a 4 – b 4 = (a 2) 2 – (b 2) 2 = (a 2 + b 2) (a 2 – b 2) = (a 2 + b 2) (a + b) (a – b)

(ix) (a + b + c) 2 = a 2 + b 2 + c 2 + 2ab + 2bc + 2ac

(x) (a + b – c) 2 = a 2 + b 2 + c 2 + 2ab – 2bc – 2ca

(xi) (a – b + c) 2 = a 2 + b 2 + c 2 – 2ab – 2bc + 2ca

(xii) (a – b – c) 2 = a 2 + b 2 + c 2 – 2ab + 2bc – 2ca

(xiii) a 3 + b 3 + c 3 – 3abc = (a + b + c)(a 2 + b 2 + c 2 – ab – bc – ca)

Linear Equations in Two Variables

An equation that can be put in the form ax + by + c = 0, where a, b and c are real numbers and a, b not equal to zero is called a linear equation in two variables namely x and y.

Quadratic Equation

For a quadratic equation, ax 2 + bx + c = 0


Arithmetic Progression

a n = a + (n−1)×d

Where,

a n = the nth term in the sequence
a 1 = the first term in the sequence
d = the common difference between terms

Similarity of Triangles
If two triangles are similar then ratio of their sides are equal.


Coordinate Geometry

Distance Formulae:
Section Formula

Mid Point Formula :

Area of a Triangle

Trigonometry

In a right-angled triangle, the Pythagoras theorem states

(perpendicular ) 2 + ( base ) 2 = ( hypotenuse ) 2

Important trigonometric properties: (with P = perpendicular, B = base and H = hypotenuse)

  1. SinA = P / H
  2. CosA = B / H
  3. TanA = P / B
  4. CotA = B / P
  5. CosecA = H / P
  6. SecA = H/B

Trigonometric Identities:

  1. sin2A + cos2A=1
  2. tan2A +1 = sec2A
  3. cot2A + 1= cosec2A

Relations between trigonometric identities are given below:

Trigonometric Ratios of Complementary Angles are given as follows:

  1. sin (90° – A) = cos A
  2. cos (90° – A) = sin A
  3. tan (90° – A) = cot A
  4. cot (90° – A) = tan A
  5. sec (90° – A) = cosec A
  6. cosec (90° – A) = sec A

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