Fabrics for Clothes: Synthetic and Natural Fibre
June 23, 2022
39 Insightful Publication
Maths Formulas for Class 10: Download Free PDF
Maths Formulas for Class 10: It is quite a challenging task to memorise formulas in class 10 maths. Students tend to get nervous and forget these formulas easily. These formulae contribute towards building the foundation of mathematics for higher grades, entrance and competitive exams. Formulas in class 10 make it easier for students to solve sums with utmost accuracy. Mathematics formulae can be used in different subjects and fields besides Mathematics. Mastering class 10 math formulae are essential for making every individual’s life easier.
Students can access the chapter-wise class 10 maths formulas to prepare for the board examinations as well. Also, students are advised to download the PDF of these formulas PDF to refer to them in offline mode while preparing for the exams. Scroll down to find everything about Class 10 CBSE Maths formulas.
Maths Formulas for Class 10 (Chapterwise)
Compiling all CBSE Class 10 Maths formulas is not an easy task for the students. However, it is essential to score well in the Class 10 board exams and Maths is one of the compulsory subjects in Class 10 in which students can score well. This exam is out of 100 marks and covers all the basic topics of Mathematics. We at Embibe have covered all the formulas of Maths Class 10 NCERT PDF to help with your exam preparation. This exam is of 3 hours duration and in order to manage this available time well during the examination, you must be aware of all the important concepts and their formulas. Learning Maths s a time-consuming paper because of the need for problem-solving and calculations. To learn these 10th Class Maths formulas, students can use PDFs created by Embibe. Before getting into the list of the formulas, let’s check out the major chapters of Class 10 Maths for which formulas are needed:
Class 10 Maths Formulas for Arithmetic Progression (AP)
If a1, a2, a3, a4….. be the terms of an AP and d be the common difference between each term, then the sequence can be written as: a, a + d, a + 2d, a + 3d, a + 4d…… a + nd. where a is the first term and (a + nd) is the (n – 1) th term. So, the formula to calculate the nth term of AP is given as:
nth term = a + (n-1) d
The sum for the nth term of AP where a is the 1st term, d is a common difference, and l is the last term is given as:
Sn = n/2 [2a + (n-1) d] or Sn = n/2 [a + l]
Download
Class 10 Maths Formulas for Linear Equations
Linear equations in one, two, and three variables have the following forms:
| Linear Equation in one Variable | ax + b=0 | Where a ≠ 0 and a & b are real numbers |
| Linear Equation in Two Variables | ax + by + c = 0 | Where a ≠ 0 & b ≠ 0 and a, b & c are real numbers |
| Linear Equation in Three Variables | ax + by + cz + d = 0 | Where a ≠ 0, b ≠ 0, c ≠ 0 and a, b, c, d 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
Quick Note: Linear equations can also be represented in graphical form.
Trigonometry Formulas for Class 10 Maths
The Trigonometric Formulas for Class 10 cover the basic trigonometric functions for a right-angled triangle i.e. Sine (sin), Cosine (cos), and Tangent (tan) which can be used to derive Cosecant (cos), Secant (sec), and Cotangent (cot).
Let a right-angled triangle ABC is right-angled at point B and have \(\angle \theta\) is one of the other two angles.
sin θ = \(\frac{Side\, opposite\, to\, angle\, \theta}{Hypotenuse}\) = \(\frac{Perpendicular}{Hypotenuse}\) = P/H
cos θ = \(\frac{Adjacent\, side\, to\, angle\, \theta}{Hypotenuse}\) = \(\frac{Adjacent side}{Hypotenuse}\) = B/H
tan θ = \(\frac{Side\, opposite\, to\, angle\, \theta}{Adjacent\, side\, to\, angle\, \theta}\) = P/B
sec θ = \(\frac{1}{cos\, \theta }\)
cot θ = \(\frac{1}{tan\, \theta }\)
cosec θ = \(\frac{1}{sin\, \theta }\)
tan θ = \(\frac{Sin\, \theta }{Cos\, \theta }\)
The Trigonometric Table comprising the values of these trigonometric functions for standard angles is as under:
| Angle | 0° | 30° | 45° | 60° | 90° |
| sinθ | 0 | 1/2 | 1/√2 | √3/2 | 1 |
| cosθ | 1 | √3/2 | 1/√2 | ½ | 0 |
| tanθ | 0 | 1/√3 | 1 | √3 | Undefined |
| cotθ | Undefined | √3 | 1 | 1/√3 | 0 |
| secθ | 1 | 2/√3 | √2 | 2 | Undefined |
| cosecθ | Undefined | 2 | √2 | 2/√3 | 1 |
Some other trigonometric formulas are given below:
- 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 10 Maths Formulas for Algebra & Quadratic Equations
To know the algebra formulas for Class 10, first, you need to get familiar with Quadratic Equations.
| The Quadratic Formula: For a quadratic equation px2 + qx + r = 0, the values of x which are the solutions of the equation are given by: |
\(x=-b\pm\frac{\sqrt{b^2-4ac}}{2a}\)
Now you know the basic quadratic equation.
Let us now go through the list of algebra formulas for Class 10:
- (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]
Quick Note: These formulas will be important in higher classes and various competitive examinations. So, memorise them and understand them well.
Class 10 Maths Formulas for Circle
Circle formulas act as a base for Mensuration. The Class 10 Maths Circle formulas for a circle of radius r are given below:
- 1. Circumference of the circle = 2 π r
- 2. Area of the circle = π r2
- 3. Area of the sector of angle θ = (θ/360) × π r2
- 4. Length of an arc of a sector of angle θ = (θ/360) × 2 π r
Class 10 Maths Formulas for Surface Area & Volume
These formulas are very important for successfully solving mensuration questions. Find below the formulas in a tabulated form for your convenience.
Here, LSA = Lateral Surface Area,
TSA = Total Surface Area.
| Sphere | Diameter: 2r Circumference: 2 π r TSA: 4πr2 Volume: \(\frac{4}{3}\pi r^2\) r = radius |
| Cylinder | Circumference: 2πr LSA: 2πrh TSA: 2πr (r + h) Volume: πr2h r = radius, h = height |
| Cone | Slant height: \(l=\sqrt{h^2+r^2}\) LSA: πrl TSA: πr(r + l) Volume: \(\frac{1}{3}\pi r^2h\) r = radius, l = slant height, h = height |
| Cuboid | LSA: 2h(l + b) TSA: 2(lb + bh + hl) Volume: lbh l = length, b = breadth, h = height |
| Cube | LSA: 4a2 TSA: 6a2 Volume: a3 a = sides of a cube |
Practice 10th CBSE Exam Questions
Class 10 Maths Formulas for Statistics
Statistics in Class 10 is majorly about finding the Mean, Median, and Mode of the given data. The statistic formulas are given below:
(I) The Mean of Grouped Data can be found by 3 methods.
- Direct Method: x̅ = \(\frac{\sum_{i=1}^{n}f_{i}x_{i}}{\sum_{i=1}^{n}f_{i}}\), where fi xi is the sum of observations for i = 1 to n And fi is the number of observations for i = 1 to n
- Assumed Mean Method : x̅ = a+\(\frac{\sum_{i=1}^{n}f_{i}d_{i}}{\sum_{i=1}^{n}f_{i}}\)
- Step Deviation Method : x̅ = a+\(\frac{\sum_{i=1}^{n}f_{i}u_{i}}{\sum_{i=1}^{n}f_{i}}\times h\)
(II) The Mode of Grouped Data: Mode = l +\(\frac{f_{i}-f_{0}}{2f_{1}-f_{0}-f_{2}}\times h\)
(III) The median for a grouped data: Median = l+\(\frac{\frac{n}{2}-cf}{f}\times h\)
Why Should Students Memories all Important Maths Formulas for Class 10?
Mathematical formulas are the basic components needed to solve complicated Math problems and these are highly beneficial in the below-mentioned ways:
- Maths formulas for Class 10 PDF covers all the important formulas of all chapters.
- Using PDF candidates will have easy access to all chapters in one place.
- Formula PDF is prepared in a manner that covers the latest syllabus of CBSE according to chapters.
- With this, students can easily revise all-important things in one place.
FAQs on Maths Formulas for Class 10
Here are some frequently asked questions that students ask regarding Class 10 Maths Formulas.
Q: How can students learn Maths formulas for Class 10?
Ans: For learning Maths formulas, students must take the help of formulas provided in the above segment in this article.
Q: How should students memorise Maths formulas?
Ans: Learning and memorising maths formulas require a lot of effort and practice. Students must be familiar with the chapters and the concepts and then try to understand how a formula is derived.
Q: Is NCERT Syllabus for Class 10 Maths difficult to study?
Ans: The difficulty level of Maths is moderate and topics and in a flow from basic to advanced. The candidate must be acquainted with the formulas for making Maths easy to study and solve.
Q: What are the important topics of NCERT Class 10 Maths syllabus?
Ans: The important topics of NCERT Class 10 Maths syllabus includes statistics & probability, Geometry, and Algebra.
Q: Where can students get the Maths formula for Surface area and volume?
Ans: Students who are looking for the Maths formula for Surface area and volume can find them in this article.
Attempt 10th CBSE Exam Mock Tests
These are some of the important formulas for Class 10 Maths. These Math formulas for Class 10 will prove to be helpful in your learning process. You will find them useful while revising the CBSE Class 10 Maths syllabus.
Solve the free Class 10 Maths questions and refer to these formulas to score better in Class 10 board exams:
If you have any queries regarding this article on Maths formulas for class 10, feel free to ask in the comment section below. We will get back to you at the earliest.
