# Class 10 Maths

The broader objective of class 10 maths is to help the students consolidate the knowledge of mathematical skills and concepts gained at the upper primary stage. It emphasizes visualizing basic concepts, principles, theorems and symbols to master basic algebraic skills. The key topics included in class 10 maths are coordinate geometry, angles, polynomials, linear equations and more.

## Class 10 Maths Syllabus

Class 10 maths syllabus is thoroughly prepared to help young learners acquire basic mathematical concepts with ease. It comprises topics related to linear equations, algebra, coordinate geometry and more. Here is the complete syllabus of **class 10 maths** along with the hierarchy of subtopics.

**Number Systems**

**Real Numbers**- Fundamental Theorem of Arithmetic which states "every composite number can be expressed as the product of primes in a unique way"
- Writing rational numbers as terminating/non-terminating recurring decimals

**Algebra**

**Polynomials**- Degree of linear, quadratic, and cubic polynomials
- Zeroes of a polynomial
- Relationship between zeroes and coefficients of quadratic and cubic polynomials
- Division algorithm which states "for two polynomials p(x) and g(x) where g(x) ≠ 0, there exist two polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x), where degree of r(x) is less than that of g(x)"

**Pair of Linear Equations in Two Variables**- Pair of linear equations in two variables, finding their solution by graphical method, consistency/inconsistency
- Formula for number of solutions (one solution, no solution, infinitely many solutions)
- Solution of a pair of linear equations in two variables by substitution and by elimination methods
- Word problems on pair of linear equations in two variables

**Quadratic Equations**- The standard form of a quadratic equation ax
^{2}+ bx + c = 0, (a ≠ 0). - Solutions (real roots only) of quadratic equations by factorization, and by using the quadratic formula.
- Using discriminant to find the nature of roots.
- Applications of quadratic equations

- The standard form of a quadratic equation ax
**Arithmetic Progressions**- Definition and examples of arithmetic progressions(AP)
- nth term and sum of arithmetic progressions
- Applications of AP

**Coordinate Geometry**

**Straight Lines on Coordinate Plane**- Graphs of lines
- Distance formula
- Section formula (only internal division)

**Geometry**

**Triangles****Circles**- Tangent to a circle
- The tangent of a circle is perpendicular to the radius through the point of contact (along with proof)
- The lengths of tangents drawn from an external point to a circle are equal (along with proof)

**Constructions**- The internal division of a line segment in a given ratio
- Tangents to a circle from a point outside it

**Trigonometry**

**Introduction to Trigonometry**- Trigonometric ratios of an acute angle of a right-angled triangle.
- Values of the trigonometric ratios of 30°, 45° and 60°.
- Relationships between the ratios.

**Trigonometric Identities**- Basic identity sin
^{2}x + cos^{2}x = 1 along with its proof and applications - Other simple identities

- Basic identity sin
**Heights and Distances (Applications of Trigonometry)**- The angle of elevation, angle of depression
- Simple problems on heights and distances involving the angles 30°, 45°, 60° that involve maximum two right triangles

**Mensuration**

**Areas Related to Circles****Surface Areas and Volumes**- SA and volumes of combinations of the following shapes: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.
- Applications of these shapes

**Statistics and Probability**

**Probability**- Definition of probability
- Probability of an event

**Statistics**- Mean, median and mode of grouped data
- Finding mean by direct method and assumed mean method

## Develop Class 10 Maths Skills

Class 10 maths is outlined to impart the knowledge of analytical and practical skills in students. It develops a basic understanding of applying maths, for instance, using trigonometric functions to calculate the height or applying algebraic formulas to solve real-life problems. Students can acquire an understanding of these 10th maths concepts through various interactive activities and visualization. Here are some key class 10 maths skills that students need to develop.

**Trigonometric Functions:** Trigonometry functions and their applications are important topics covered under class 10 maths that students should understand and apply in solving various problems.

**Algebra:** Algebra is an important part of class 10 maths that enables students to write, read and apply expressions, rational numbers and polynomials. It also helps students to utilize these skills and knowledge to solve practical problems.

**Geometry:** It is important for students to understand the geometric transformation covered in mathematics class 10 which involves angles, circles, perpendicular lines, parallel lines, and line segments.

## 10th Maths Tips and Tricks

Class 10 maths is very important for the students for their future grades and courses. With small tips and tricks the students can make 10th maths easy and they can score very good grades in mathematics class 10.

**Practice Daily:**10th maths is crucial for developing higher-level maths skills thus students must practice daily and track their progress sincerely to improvise their skills.**Practice Past Years Question Papers:**Practicing question papers from past years will help students to get an idea of the complexity level of the exam. It will also benefit students by enhancing their speed and accuracy**Cover Full Syllabus:**Covering full syllabus of class 10 maths is a must for students to clarify all their doubts before exams.**Refer to Reliable Study material:**Refer to reliable study material like textbooks for the preparation of mathematics class 10. These are the best preparation resources as the class 10 maths exam is set according to them.

## Class 10 Maths Formulas

Memorizing all formulas of maths class 10 is really very important for the students to score better during board exams. Though the student is able to solve the problem but doesn't remember the formula, all the hard work will go in vain. Especially, students need to pay more attention in remembering trigonometry formulas for class 10 as they are new to trigonometry. Here are some important class 10 maths formulas.

- (a + b)
^{3}= a^{3}+ b^{3}+ 3ab(a + b) - (a – b)
^{3}= a^{3}- b^{3}- 3ab(a – b) - n
^{th}term of AP, a_{n}= a + (n - 1) d - Sum of AP, S
_{n}= n/2 [2a + (n - 1)d] - Volume of sphere = 4/3 ×π r
^{3} - Total surface area of a sphere = 4πr
^{2} - Volume of right circular cylinder = πr
^{2}h - Total surface area of right circular cylinder = 2πr (r + h)
- Volume of prism = Base area × height
- Lateral surface area of prism (LSA) = perimeter of the base × height

Here are some important trigonometry formulas for class 10.

- sin
^{2}θ + cos^{2}θ = 1 - cosec
^{2}θ - cot^{2}θ = 1 - sec
^{2}θ - tan^{2}θ = 1 - sin θ cosec θ = 1
- cos θ sec θ = 1
- tan θ cot θ = 1
- sin(90° - θ) = cos θ; cos(90° - θ) = sin θ
- tan(90° - θ) = cot θ; cot(90° - θ) = tan θ
- sec(90° - θ) = cosec θ; cosec(90° - θ) = sec θ

For the complete list of formulas of class 10 maths, click here.

## Class 10 Maths Worksheets

10th maths worksheets are curated by our experts such that they cover all concepts end to end. Further, they cover all types of questions including all difficulty levels. With these worksheets, students can access extra problems to practice mathematics class 10. Moreover, they can identify the areas of their weakness by working on these worksheets and comparing their answers with the answers given in them. This would help them to go back and correct themselves which is very helpful to achieve better grades in maths class 10. Just click here to get the links to the worksheets.

## Solved Examples on Class 10 Maths

**Example 1:** Find the sum and product of the roots of the polynomial 3x^{2} - 2x + 1.

**Solution:**

Comparing the given quadratic polynomial with ax^{2} + bx + c, we get a = 3, b = -2, and c = 1. Then

- the sum of the roots = -b/a = -(-2)/3 = 2/3
- the product of the roots = c/a = 1/3

**Answer:** The sum = 2/3 and the product = 1/3.

**Example 2:** Determine whether the sequence 2, 4, 6, 8, ... represent an arithmetic progression (AP).

**Solution:**

We will find the difference between every two consecutive terms:

- Second term - First term = 4 - 2 = 2
- Third term - Second term = 6 - 4 = 2
- Fourth term - Third term = 8 - 6 = 2, and so on

Thus, all the differences are the same. Hence, the sequence is an arithmetic progression.

**Answer:** Yes, the given sequence is an AP.

## FAQs on Class 10 Maths

### What are the Chapters in Class 10 Maths?

The following is the list of chapters that **class 10 maths** would cover. For the complete list, scroll up to this page.

- Real Numbers
- Polynomials
- Pair of Linear Equations in Two Variables
- Quadratic Equations
- Arithmetic Progressions
- Straight Lines
- Triangles
- Circles
- Constructions
- Introduction to Trigonometry
- Trigonometric Identities
- Heights and Distances
- Areas Related to Circles
- Surface Areas and Volumes
- Probability
- Statistics

### Is 10th Maths Easy?

Yes, 10th maths is very easy as long as students don't try to solve the problems until they understand the concepts. Concentrate well during the lessons and focus on learning the concept. Then it will be very easy to solve the problems in class 10 maths.

### How can I get 100 in Class 10 Maths?

It is not a good idea to study just before the main exams. Instead, keep practising maths on a daily basis by setting a timetable. Be up to date in finishing the class 10 maths syllabus along with the teacher. Use weekends for completing any pending portions. Revise the concepts very often so that there is no need to rework on the concepts completely. Make charts of class 10 maths formulas and hang them in the study room. Practice more questions to get more confidence and to attain 100 in 10th maths.

### What is a Very Important Chapter in Mathematics Class 10?

Triangles and quadratic equations have the highest weightage and hence these are some of the most important chapters of class 10 mathematics. Among these two, quadratic equations is easier than triangles.

### How are Class 10 Maths Solutions Useful?

Keeping 10th maths solutions handy is very helpful for the students of class 10. These would help them whenever they are unable to solve a problem as they provide step-by-step guidance.

### Is Understanding Mathematics Class 10 Difficult Compared to 9th Maths?

No, in fact, understanding mathematics class 10 is easier compared to 9th maths. It has many easy chapters like quadratic equations, statistics, real numbers, polynomials, etc which would help the students to score better in 10th maths exams.

### How can I Study Class 10 Maths?

Here are some important tips that a student of class 10 maths should follow:

- Make proper notes of everything that is being taught in the school right from the beginning.
- Learn the theory first before going to solve the questions.
- Try to understand how a formula or a theorem is derived before applying it.
- Stick an empty chart in the study room and keep adding formulas to it as when a chapter is completed. This would be helpful for the last-minute revision.
- Make a list of mistakes in all the slip tests/pre-finals and rework them.
- Practice as many sample papers and previous year papers as possible by setting a time limit.

visual curriculum