CBSE syllabus for 10th grade (2024-25)

Introduction

10th grade mathematics gives equal importance to all branches of mathematics dealt till 9th grade and introduces a new branch, Trigonometry, over two chapters.

It is easier to score high grades in 10th-grade mathematics than in 9th grade due to many factors. The one relevant in this blog is the rigor in the concepts and problems discussed in the 9th grade, before which it was relatively straightforward till the 8th grade. The four chapters in Geometry introduced in the 9th grade would have trained the student to apply logic and reasoning over long periods for problem-solving. This is probably the reason why even professionals like lawyers for centuries studied Euclid's Elements. The Elements, based on Geometry, is supposed to be the most-read book after the Bible, put forward by Euclid in 300 BC as a consolidation of what was known in Alexandria at that time. Alexandria was a center of learning at that time.

Now, the chapters are spread across seven branches of Mathematics

ARITHMETIC

The first chapter of the book consolidates your understanding of Real numbers, the set of all numbers that can be represented on one line, known as the real number line. The only other number system that is outside this will be taught in 11th-grade mathematics, Complex numbers. Complex numbers can be represented and used only with two real number lines perpendicular to each other in a plane, known as the Argand plane.

The second chapter under this branch is on Arithmetic progression. Here, you are taught just two major formulas. The first one is to calculate the Nth term, and the second is for the sum to the Nth term of an Arithmetic progression. Though this is a favorite topic for the CBSE board to test 95 percentile students in the final exam.

ALGEBRA

The study of Algebra is spread across four chapters. The understanding of the factor theorem introduced in the 9th grade is very important to appreciate this section of the syllabus.

The first chapter is on the factorisation of linear and quadratic polynomials, the second on how a system of two linear equations in two variables will behave, and finally, the third one introduces the discriminant formula to solve a quadratic equation in one variable. Polynomials in one variable of higher degree than two do not have a formula to arrive at their factors.

The fourth chapter discusses the purpose of Coordinate Geometry for the first time to convince you how it helps to stitch Geometry and Algebra by discussing the measurement of a line segment and the section formula. This helps you understand how 2D geometry can be studied on a plane.

TRIGNOMETRY

Though sometimes mathematicians consider Trigonometry as a part of Algebra, we at Mathpinnacle feel that it should be considered as a separate branch. This is because Trigonometry was well in use in India and other early civilizations for Astronomy, and it was only in 800 AD, Algebra was formalized by Islamic scholars in Baghdad. This happened immediately after the Prophet, when Baghdad became a center of learning. Though most of the knowledge came from the East.

Two chapters of Trigonometry cover the introduction to the three basic ratios of sides wrt an angle and the values it can have for standard angles. The second chapter uses this understanding to apply to problems on Heights and Distances, which was the original purpose of trigonometry in Astronomy and Navigation on the seas.

GEOMETRY

The volume of Geometry dealt with in 10th grade is only 25% of that which was introduced in 9th grade. Though only a student who has a mastery of theorems and basic problem solving in 9th grade on Lines & Angles, Congruency of Triangles, and Basic theorems on different types of Parallelograms can score 100% marks from the two chapters dealt with.

The first chapter on Similarity of triangles will be easier only if you have mastered the art of considering how two triangles can be Congruent, dealt with in 9th grade.

The chapter on Circles has one fresh theorem introduced, on the tangent to a circle. Though all the theorems discussed in 9th grade circles would help you to master this part of the syllabus.

MENSURATION

Here again, you have two chapters.

Areas of Circles discusses the perimeter and area of a sector and segment of a circle. However, only someone with mastery over the perimeter and area of different types of triangles, quadrilaterals, and a circle will be able to solve every problem from this chapter.

Next, the chapter on Surface area and Volumes of all standard 3D figures. Here, unlike straightforward problems on various standard figures discussed till the 9th grade, the problems will be based on a combination of solids.

STATISTICS

Statistics, similar to Mensuration it is also treated at a higher level than considered till 9th grade. A new representation of data, a grouped frequency distribution, is considered. Here, three different methods are discussed to calculate the mean. And the chapters become tricky when two formulas with more than five variables each are introduced to find the Median and Mode of a grouped frequency distribution.

PROBABILITY

This chapter marks the end of the syllabus. There is nothing new discussed in this chapter compared to 9th grade, except probably giving more importance to conditional probability. Though the CBSE Board may ask tough questions from this chapter, like in Arithmetic progression. Since both chapters are based purely on the application of your intelligence through simple formulas.