The CBSE Examination for Class 10 Mathematics will be conducted on March 7, 2019. Mathematics is one subject which often gives nightmares to students. While Maths is a little tricky, it is not difficult. It just requires a thorough understanding of concepts, regular practice and a good hold on all important formulas to score high in the Maths subject.
In this article, we have collated all important formulas from all chapters of CBSE Class 10 Maths. We have also put together the important terms and properties which are useful in solving the Class 10 Maths problems.
Important formulas, Terms and properties
1. Real Numbers:
Euclid’s Division Algorithm (lemma): According to Euclid’s Division Lemma 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.)
(i) (a + b)2 = a2 + 2ab + b2
(ii) (a – b)2 = a2 – 2ab + b2
(iii) a2 – b2 = (a + b) (a – b)
(iv) (a + b)3 = a3 + b3 + 3ab(a + b)
(v) (a – b)3 = a3 – b3 – 3ab(a – b)
(vi) a3 + b3 = (a + b) (a2 – ab + b2)
(vii) a3 – b3 = (a – b) (a2 + ab + b2)
(viii) a4 – b4 = (a2)2 – (b2)2 = (a2 + b2) (a2 – b2) = (a2 + b2) (a + b) (a – b)
(ix) (a + b + c) 2 = a2 + b2 + c2 + 2ab + 2bc + 2ac
(x) (a + b – c) 2 = a2 + b2 + c2 + 2ab – 2bc – 2ca
(xi) (a – b + c)2 = a2 + b2 + c2 – 2ab – 2bc + 2ca
(xii) (a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
(xiii) a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)
3. Linear Equations in Two Variables:
For the pair of linear equations
a1 + b1y + c1 = 0 and a2 + b2y + c2 = 0,
the nature of roots (zeroes) or solutions is determined as follows:
(i) If a1/a2 ≠ b1/b2 then we get a unique solution and the pair of linear equations in two variables are consistent. Here, the graph consists of two intersecting lines.
(i) If a1/a2 ≠ b1/b2 ≠ c1/c2, then there exists no solution and the pair of linear equations in two variables are said to be inconsistent. Here, the graph consists of parallel lines.
(iii) If a1/a2 = b1/b2 = c1/c2, then there exists infinitely many solutions and the pair of lines are coincident and therefore, dependent and consistent. Here, the graph consists of coincident lines.
4. Quadratic Equation:
For a quadratic equation, ax2 + bx + c = 0
x2 – (sum of the roots)x + product of the roots = 0
Important Formulas - Boats and Streams
In water, the direction along the stream is called downstream.
In water, the direction against the stream is called upstream.
(iii) Let the speed of a boat in still water be u km/hr and the speed of the stream be v km/hr, then
Speed downstream = (u + v) km/hr
Speed upstream = (u - v) km/hr.
5. Arithmetic Progression:
6. Similarity of Triangles:
7. Coordinate Gemetry:
In a right-angled triangle, the Pythagoras theorem states
(perpendicular )2 + ( base )2 = ( hypotenuse )2
Important trigonometric properties are: (with P = perpendicular, B = base and H = hypotenuse)
Relations between trigonometric identities are given below:
Trigonometric Ratios of Complementary Angles are given as follows:
Values of Trigonometric Ratios of 0° and 90° are tabulated below:
Important properties related to circles:
Equal chord of a circle are equidistant from the centre.
The perpendicular drawn from the centre of a circle, bisects the chord of the circle.
The angle subtended at the centre by an arc = Double the angle at any part of the circumference of the circle.
Angles subtended by the same arc in the same segment are equal.
To a circle, if a tangent is drawn and a chord is drawn from the point of contact, then the angle made between the chord and the tangent is equal to the angle made in the alternate segment.
The sum of opposite angles of a cyclic quadrilateral is always 180o.
Important formulas related to circles:
Here, Area of the segment APB = Area of the sector OAPB – Area of ∆ OAB
Check below the important formulas for areas and volumes of solids:
Understanding the basic concepts and learning all the important formulas is extremely sufficient to pass the Maths exam with flying colours. If you know the formulas very well then it will not take much time for you to solve the questions. So, keep practicing with the list of important formulas given above in this article.