**Maths Formulas for Class 10 **

People are math-phobic and they think that they could not master the math formulas at all. This negative attitude affects their progress and they are nervous during their exams too. To get rid of this situation, students should have a stronghold on the basics of this subject. With a depth understanding of mathematical formulas, this is possible to score maximum marks in the exam and crack the most difficult mathematics problems too.

#### Class 10 Polynomials Formulas

\[(a+b)^{2}=a^2+2ab+b^{2}\] |

\[(a-b)^{2}=a^{2}-2ab+b^{2}\] |

\[\left (a + b \right ) \left (a – b \right ) = a^{2} – b^{2}\] |

\[\left (x + a \right )\left (x + b \right ) = x^{2} + \left (a + b \right )x + ab\] |

\[\left (x + a \right )\left (x – b \right ) = x^{2} + \left (a – b \right )x – ab\] |

\[\left (x – a \right )\left (x + b \right ) = x^{2} + \left (b – a \right )x – ab\] |

\[\left (x – a \right )\left (x – b \right ) = x^{2} – \left (a + b \right )x + ab\] |

\[\left (a + b \right )^{3} = a^{3} + b^{3} + 3ab\left (a + b \right )\] |

\[\left (a – b \right )^{3} = a^{3} – b^{3} – 3ab\left (a – b \right )\] |

\[ (x + y + z)^{2} = x^{2} + y^{2} + z^{2} + 2xy + 2yz + 2xz\] |

\[ (x + y – z)^{2} = x^{2} + y^{2} + z^{2} + 2xy – 2yz – 2xz\] |

\[ (x – y + z)^{2} = x^{2} + y^{2} + z^{2} – 2xy – 2yz + 2xz\] |

\[ (x – y – z)^{2} = x^{2} + y^{2} + z^{2} – 2xy + 2yz – 2xz\] |

\[ x^{3} + y^{3} + z^{3} – 3xyz = (x + y + z)(x^{2} + y^{2} + z^{2} – xy – yz -xz\] |

\[ x^{2} + y^{2} = \frac{1}{2} \left [(x + y)^{2} + (x – y)^{2} \right ]\] |

\[ (x + a) (x + b) (x + c) = x^{3} + (a + b +c)x^{2} + (ab + bc + ca)x + abc\] |

\[ x^{3} + y^{3} = (x + y) (x^{2} – xy + y^{2})\] |

\[ x^{3} – y^{3} = (x – y) (x^{2} + xy + y^{2})\] |

\[ x^{2} + y^{2} + z^{2} -xy – yz – zx = \frac{1}{2} [(x-y)^{2} + (y-z)^{2} + (z-x)^{2}]\] |

#### Class 10 Quadratic Equations Formulas

\(x^2+bx+c=0 \;where\; a ≠ 0\) |

\(x=-b\pm\frac{\sqrt{b^2-4ac}}{2a}\) |

#### Class 10 Arithmetic Progressions Formulas

n^{th} Term of an Arithmetic Progression |

\( {a_n = a + (n – 1) \times d} \) |

Sum of 1^{st} n Terms of an Arithmetic Progression |

\( {S_n = \frac{n}{2}\left[ {2a + \left( {n – 1} \right)d} \right]} \) |

#### Class 10 Triangles Formulas

\[Area\;of\;Isoscele\;Triangle =\frac{1}{2}bh\] |

\[Altitude\;of\;an\;Isosceles\;Triangle=\sqrt{a^{2}-\frac{b^{2}}{4}}\] |

\[ Perimeter\;of\;Isosceles\;Triangle,P=2\,a+b\] |

Where, b = Base , h = Height, a = length of the two equal sides |

\[ Area \;of \;an \;Right\;Triangle = \frac{\sqrt{1}}{2}bh\] |

\[ Perimeter \;of \;an \;Right \;Triangle = a+b+c\] |

\[ semi\;Perimeter \;of \;an \;Right \;Triangle = \frac{a+b+c}{2}\] |

where:; b:Base, h:Hypotenuse a: Hight |

\[\ Area\;of\;Scalene\;Triangle = \sqrt{s(s-a)(s-b)(s-c)} \] |

\[\ Perimeter\;of\;Scalene\;Triangle = a+b+c \] |

Where: a, b, c are Side of Scalene Triangle |

\[ Area \;of \;an \;Equilateral \;Triangle = \frac{\sqrt{3}}{4}a^{2}\] |

\[ Perimeter \;of \;an \;Equilateral \;Triangle = 3a\] |

\[ Semi \;Perimeter \;of \;an \;Equilateral \;Triangle = \frac{3a}{2}\] |

\[ Height \;of \;an \;Equilateral \;Triangle = \frac{\sqrt{3}}{2}a\] |

Where, a:side, h: altitude |

#### Class 10 Coordinate Geometry Formulas

Distance Formula |

\( {AB = \sqrt {\left( {x_2 – x_1 } \right)^2 + \left( {y_2 – y_1 } \right)^2 } } \) |

Section Formula |

\( {\left( {\frac{{mx_2 + nx_1 }}{{m + n}},\frac{{my_2 + ny_1 }}{{m + n}}} \right)}\) |

Mid-point Formula |

\( {\left( {\frac{{x_1 + x_2 }}{2},\;\frac{{y_1 + y_2 }}{2}} \right)} \) |

Area of Triangle |

\( \text{ar}(\Delta A B C)=\frac{1}{2} \times \begin{bmatrix}x_{1}(y_{2}-y_{3})+\\x_{2}(y_{3}-y_{1})+\\x_{3}(y_{1}-y_{2})\end{bmatrix} \) |

#### Class 10 Trigonometry Formulas

Trigonometric Identities |

\( \sin ^2 A + \cos ^2 A = 1 \) |

\( \tan ^2 A + 1 = \sec ^2 A \) |

\( \cot ^2 A + 1 = {\rm{cosec}}^2 A \) |

Relations between Trigonometric Identities |

\( \tan A = \frac{{\sin A}}{{\cos A}} \) |

\( \cot A = \frac{{\cos A}}{{\sin A}} \) |

\( {\rm{cosec}}\,A = \frac{1}{{\sin A}} \) |

\( \sec A = \frac{1}{{\cos A}} \) |

Trigonometric Ratios of Complementary Angles |

\( \sin \left( {90^\circ – A} \right) = \cos A \) |

\( \cos \left( {90^\circ – A} \right) = \sin A \) |

\( \tan \left( {90^\circ – A} \right) = \cot A \) |

\( \cot \left( {90^\circ – A} \right) = \tan A \) |

\( \sec \left( {90^\circ – A} \right) = {\rm{cosec}}\,A \) |

\( {\rm{cosec}}\left( {90^\circ – A} \right) = \sec A \) |

Values of Trigonometric Ratios of 0° and 90° |
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\(\angle A\) | \(0^\circ \) | \(30^\circ \) | \(45^\circ \) | \(60^\circ \) | \(90^\circ \) |

\(\sin A\) | \(0\) | \( \frac{1}{2} \) | \( \frac{1}{{\sqrt 2 }} \) | \( \frac{{\sqrt 3 }}{2} \) | \(1\) |

\(\cos A\) | \(1\) | \( \frac{{\sqrt 3 }}{2} \) | \( \frac{1}{{\sqrt 2 }} \) | \( \frac{1}{2} \) | \(0\) |

\(\tan A\) | \(0\) | \( \frac{1}{{\sqrt 3 }} \) | \(1\) | \( \sqrt 3 \) | Not Defined |

\(\sec A\) | \(1\) | \( \frac{2}{{\sqrt 3 }} \) | \( \sqrt 2 \) | \(2\) | Not Defined |

\(\text{cosec } A \) | Not Defined | \(2\) | \( \sqrt 2 \) | \( \frac{2}{{\sqrt 3 }} \) | 1 |

\(\cot A\) | Not Defined | \( \sqrt 3 \) | \(1\) | \( \frac{1}{{\sqrt 3 }} \) | 0 |

#### Class 10 Circles Formulas

\[\ Area\;of\;a\;circle =\pi r^{2}=\frac{{\pi}d^{2}}{4}=\frac{{C} \times {r}}{2}\] |

\[\ Perimeter\;of\;Circle = 2 \pi r \] |

\[\ Area\;of\;a\;half\;circle =\frac{{\pi}r^{2}}{2}\] |

\[\ Area\;of\;a\;Quarter\;circle =\frac{{\pi}r^{2}}{4}\] |

Where,r is the radius of the circle.d is the diameter of the circle.C is the circumference of the circle. |

#### Class 10 Areas Related to Circles Formulas

\[\ Area\;of\;Sector\;of\;a\;circle: A=\frac{θ}{360}\pi r^{2}\] |

\[\ Length\;of\;an\;arc\;of\;a\;sector: Arc=\frac{θ}{360}{2 \pi r}\] |

\[\ Sector\;angle\;of\;circle = \frac{180 \times l}{\pi r}\] |

\[\ Area\; of\;the \;sector = \frac{θ}{2} \times r^{2}\] |

\[\ Area \;of\; the \;circular \;ring = \pi \times (R^{2} – r^{2})\] |

Where,r is the radius of the circle.θ is the Angle between two radius R is the Radius of Outer Circle |

#### Class 10 Surface Areas and Volume Formulas

\[\ Surface\;area\;of\;Cube=6a^{2}\] |

\[\ Volume\;of\;a\;cube=a^{3}\] |

Where, a is the side length of the cube. |

\[\ Surface\;area\;of\;Cuboid = 2(lb + bh + hl)\] |

\[\ Volume\;of\;a\;Cuboid = h \times l \times w\] |

Where, l: Height, h: Legth, w: Depth |

\[\ Diameter\;of\;a\;sphere=2r\] |

\[\ Circumference\;of\;a\;sphere=2\pi r\] |

\[\ Surface\;area\;of\;a\;sphere=4\pi r^{2}\] |

\[\ Volume\;of\;a\;sphere=\frac{4}{3}\: \pi r^{3}\] |

\[\ Curved\;Surface\;area\;of\;a\;Hemisphere =4\pi r^{2}\] |

\[\ Total\;Surface\;area\;of\;a\;Hemisphere =3\pi r^{2}\] |

\[\ Volume\;of\;a\;Hemisphere =\frac{2}{3}\: \pi r^{3}\] |

Where, r: Radius |

\[\ Curved\;Surface\;area\;of\;a\;Cylinder =2\pi rh\] |

\[\ Total\;Surface\;area\;of\;a\;Cylinder =2\pi r(r+h)\] |

\[\ Volume\;of\;a\;Cylinder = \pi r^{2} h\] |

Where, r: Radius, h: Height |

\[\ Total\;Surface\;Area\;of\;cone=\pi r \left (s+r \right )\] |

Where, r: Radius |

\[\ Vomule\;of\;cone=\frac {1}{3}\pi r^{2}h\] |

\[\ Curved\;Surface\;Area\;of\;cone=\pi rs\] |

Where, r: radius of cone. h:height of cone. s: slant height of the cone. |

#### Class 10 Statistics Formulas

\[Direct\; Method: x̅ = \frac{\sum_{i=1}^{n}f_i x_i}{\sum_{i=1}^{n}f_i}\] |

where f_{i }x_{i } is the sum of observations from value i = 1 to n And f_{i }is the number of observations from value i = 1 to n |

\[Assumed\; mean\; method : x̅ = a+\frac{\sum_{i=1}^{n}f_i d_i}{\sum_{i=1}^{n}f_i}\] |

\[Step \;deviation \;method : x̅ = a+\frac{\sum_{i=1}^{n}f_i u_i}{\sum_{i=1}^{n}f_i}\times h\] |

\[Mode = l+\frac{f_1 – f_0}{2f_1 – f_0 – f_2} \times h\] |

\[Median = l+\frac{\frac{n}{2} – cf}{f} \times h\] |

#### Class 10 Probability Formulas

\[\ Probability = \frac{No. \;of\; Favorable \;outcome}{No.\; of\; all\; possible\; outcome} \] |

**Chapter-wise Marks in Exam **

Formulas are the basic building blocks that are vital to learning from the future perspective of a child. They are used to clear tough competitive exams too and can be downloaded in PDF format online. Here, in this section, we have given the chapter-wise marking scheme for different mathematics chapter.

Chapter |
Marking Scheme |

Algebra | 26 |

Geometry | 12 |

Trigonometry | 10 |

Circle Theory | 22 |

Probability | 12 |

Mensuration | 10 |

Co-ordinate Geometry | 8 |

**NCERT Solutions Class 10 Maths By Chapters**

Maths is a crucial subject and an integral part of the study during your early schools. For the class 10^{th} standard, there is a critical phase when students have to learn typical mathematics formulas. These formulas are the solid foundation of your study in class 10^{th} and they should be practiced wisely. Here, we have a complete list of chapters of maths for class 10^{th}.

- Chapter 1 Real Numbers
- Chapter 2 Polynomials
- Chapter 3 Linear Equations in Two Variables
- Chapter 4 Quadratic Equations
- Chapter 5 Arithmetic Progressions
- Chapter 6 Triangles
- Chapter 7 Coordinate Geometry
- Chapter 8 Introduction to Trigonometry
- Chapter 9 Some Applications of Trigonometry
- Chapter 10 Circles
- Chapter 11 Constructions
- Chapter 12 Areas Related to Circles
- Chapter 13 Surface Areas and Volume
- Chapter 14 Statistics
- Chapter 15 Probability

**Chapter-wise Maths Formulas for Class 10**

These days online coaching is at the top where you may get almost everything in an easy format. The same is true for mathematical formulas too. Online you may download a complete list of chapter-wise maths formulas for class 10^{th} CBSE for Algebra, Trigonometry, Geometry, Probability, and Mensuration etc.

- Chapter 2 Polynomials
- Chapter 4 Quadratic Equations
- Chapter 5 Arithmetic Progressions
- Chapter 6 Triangles
- Chapter 7 Coordinate Geometry
- Chapter 8 Introduction to Trigonometry
- Chapter 10 Circles
- Chapter 12 Areas Related to Circles
- Chapter 13 Surface Areas and Volume
- Chapter 14 Statistics
- Chapter 15 Probability

Getting good mathematics teachers who focus on studies completely is difficult to find. So, the best find idea is to make a list of formulas yourself or download them online start practicing right away. During practice, you will face problems too but never lose hope because every time there is some problem, there is one solution too.

Try to improve your weaknesses with the right practice and efforts. Design an effective study plan and give more time to the topics that seem difficult than others. You should utilize a set of problems for practice and try to solve them in a given timeframe only. The topics given in the syllabus of class 9^{th} and 10^{th} are the foundation of mathematics especially for the students who want to get into engineering and research studies.

If you are not sure of basic problems then how can you solve typical problems in the future. Math concepts are used everywhere around us. Construction, shapes, motion, and manufacturing, machines are the result of mathematical applications in real-time. So, a deep understanding is vital for effective learning in the future as well. Also, this is easy for you to get into higher studies and passing competitive exams in the first attempt only.