NCERT Class 10 Maths Important Formulas Pdf, CBSE Maths important formulas: All students preparing for 10th board examination are perfectly aware that when it comes to Mathematics the most effective way to score high marks are by keeping all the important maths formulas on their tips. all formulas of maths class 10th ncert But one must also understand that class 10th maths formulas are the base on which higher study maths theories are build on hence, having a clear concept of these formulas is quite significant. Even most of the competitive exams covers, high school mathematics in their aptitude syllabus which is why it is crucial to emphasize on these all formulas of maths class 10th.
Here we have discussed NCERT Class 10th Maths Formulas chapter wise, in order to make it easier for you to understand. The list of all the important formulas of class 10th that is presented below will surly help the students in solving all types of difficult questions. You can go thorough these formulas before your examination weather it a board examination or for any aptitude test that you’re preparing for. Also check out the links provided below related to CBSE class 10th for your assistance.
NCERT 10th Class Important Maths Formulas Pdf : Over-view
As discussed above here we are focusing on the Class 10th Important Formulas Pdf which are being provided here for the students who are preparing for their board exams. The chapters that we’re going to examine in this post are mentioned below. This will give you an over-view of what all is included in this article.
1) Algebra and Quadratic Equation Formulas
2) Pair of Linear Equation in Two Variables Formulas
3) Arithmetic Progression Formulas
4) Trigonometry Formulas
5) Circle Formulas
6) Surface Area and Volume Formulas
7) Statistics Formulas
Important Algebra And Quadratic Equation Formulas
Before getting into the various algebraic formulas you must know the quadratic formula. Take a look at it.
|The Quadratic Formula: For a quadratic equation ax2 + bx + c = 0, the values of x which are the solutions of the equation are given by:|
Now check out the list of algebraic formulas.
- (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]
Quadratic Equation Formula
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.
Important Linear Equation Formulas
Linear Equation in one Variable is given by : ax + b=0 (Where a ≠ 0 and a & b 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)
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.
Arithmetic Progression (AP) Formulas
An arithmetic progression is a sequence of numbers such that the difference d between each consecutive term is constant. The sequence is represented as : a, a + d, a + 2d, a + 3d, a + 4d…… a + nd. Here a is the first term whereas (a+nd) is the (n-1)th term.
Formula for calculating the nth term = a + (n-1) d
Formula for calculating the sum of n terms = Sn = n/2 [2a + (n-1) d]
Sn = n/2 [a + l]
NOTE : Here a is the first term, d is the common difference, l is the last term and n is the number of terms.
Important Trigonometric Formulas
The values of the trigonometric functions are as per the trigonometric table provided beneath.
Remember these formulas :
- sin (90° – θ) = cos θ
- cos (90° – θ) = sin θ
- tan (90° – θ) = cot θ
- cot (90° – θ) = tan θ
- sec (90° – θ) = cosecθ
- cosec (90° – θ) = secθ
- sin2θ + cos2 θ = 1
- sec2 θ = 1 + tan2θ for 0° ≤ θ < 90°
- Cosec2 θ = 1 + cot2 θ for 0° ≤ θ ≤ 90°
Class 10th Important Circle Formulas
Formulas for a circle of radius r is given below:
- Circumference of the circle (also the perimeter) = 2 π r
- Area of the circle = π r2
- Area of the sector of angle θ = (θ/360) × π r2
- Length of an arc of a sector of angle θ = (θ/360) × 2 π r
- Area of ring = π (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.
Important Surface Areas and Volume Formulas
For solving any mensuration question quickly one must remember these formulas by heart. In the table given below we have presented all formulas used for various shapes such as cube, cuboid, cylinder, sphere etc.
NOTE : LSA means Lateral Surface Area and TSA means Total surface Area.
|Cube with a = sides of a cube)||4a2||6a2||a3|
|Cuboid with l = length,
b = breadth,
h = height
|2h(l + b)||2(lb + bh + hl)||lbh|
|Cylinder with radius r and height h||2πrh||2πr (r + h)||πr2h|
|Sphere with radius r||4πr2||4πr2||4/3 πr3|
|Cone with l = length,
b = breadth,
h = height
|πrl||πr(r + l)||1/3 πr2 h|
|Hemisphere with radius r||2πr2||3πr2||2/3πr3|
Important Statistics Formulas
(I) The Mean of Grouped Data can be found by 3 methods.
- Direct Method formula: This method can be very calculation intensive if the values of f and x are large.We have big calculations and chance of making mistake is quite high.
2. Assumed mean method formula: Where a= Assumed mean and di = xi –a
This method is quite useful when the values of f and x are large. It makes the calculation easiar.In this method we take some assumed mean and calculate the deviation from it and then calculate mean using below given formula.
3. Step deviation Method Formula: Where a= Assumed mean and ui => (xi –a)/h
This method is quite useful when the values of f and x are large. It makes the calculation further easiar by dividing the deviation from common factor.
(II) The Mode of Grouped Data: The class interval having highest frequency is called the modal class and Mode is obtained using the modal class. Mode formula is given as
NOTE : Where
l = lower limit of the modal class,
h = size of the class interval (assuming all class sizes to be equal),
f1 = frequency of the modal class,
f0 = frequency of the class preceding the modal class,
f2 = frequency of the class succeeding the modal class.
(III) The median for a grouped data: The formula for finding a median of a given data is
l = lower limit of median class,
n = number of observations,
cf = cumulative frequency of class preceding the median class,
f = frequency of median class,
h = class size (assuming class size to be equal)
These were all the formulas that are quite necessary to remember. Don’t just start mugging these formulas but rather understand there concepts and it will become easier then. We have tried our best to narrow down the important formulas of class 10th.
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