CBSE Class 10 Maths — All Chapters, Formulas & Solutions

CBSE Class 10 Maths covers $14$ NCERT chapters across algebra, geometry, trigonometry, mensuration, statistics, and probability. If you want a fast overview, this page gives you the chapter list, the formulas worth memorizing, one worked example, and the mistakes that cost marks most often.

For most students, the main challenge is not the size of the syllabus. It is knowing which chapter a question belongs to, which formula applies, and how much working to show.

For CBSE, Mathematics Standard and Mathematics Basic are built on the same Class 10 NCERT textbook. The difference is the level of the question paper, not a separate book. If your school gives a different sequence or an updated exam notice, use that local guidance first.

CBSE Class 10 Maths Chapters

Here is the usual NCERT chapter sequence for CBSE Class 10 Maths:

1. Real Numbers
   Euclid's division lemma, Fundamental Theorem of Arithmetic, irrational numbers.

2. Polynomials
   Zeroes of polynomials and the relation between zeroes and coefficients for quadratics.

3. Pair of Linear Equations in Two Variables
   Graphical and algebraic methods, consistency and number of solutions.

4. Quadratic Equations
   Factorization, quadratic formula, and the discriminant.

5. Arithmetic Progressions
   The $n$th term and the sum of the first $n$ terms.

6. Triangles
   Similarity, Basic Proportionality Theorem, and ratio-based proofs.

7. Coordinate Geometry
   Distance formula and section formula.

8. Introduction to Trigonometry
   Trigonometric ratios, standard angles, and identities.

9. Some Applications of Trigonometry
   Heights and distances.

10. Circles
    Tangents and their properties.

11. Areas Related to Circles
    Sectors, segments, and mixed-area problems.

12. Surface Areas and Volumes
    Cylinders, cones, spheres, hemispheres, and combinations of solids.

13. Statistics
    Mean, median, and mode for grouped data.

14. Probability
    Classical probability for simple events.

What To Focus On First

The syllabus feels much smaller when you group it into four blocks.

Block 1: Algebra
Real numbers, polynomials, linear equations, quadratic equations, and arithmetic progressions build most of your symbolic skill. If you are losing marks early, start here.

Block 2: Geometry
Triangles, circles, and coordinate geometry test reasoning more than recall. Many mistakes come from using a theorem without stating why it applies.

Block 3: Trigonometry and Mensuration
These chapters connect formulas to diagrams. If the figure or angle choice is wrong, the whole solution usually goes wrong.

Block 4: Data Handling
Statistics and probability are more procedural. If you set up the table or formula carefully, the question usually becomes straightforward.

Must-Know Class 10 Maths Formulas

You do not need every formula at once. These are the ones that usually matter most in revision.

Algebra

For a quadratic equation

$$ax^2 + bx + c = 0,\quad a \ne 0$$

the quadratic formula is

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

and the discriminant is

$$D = b^2 - 4ac$$

For an arithmetic progression with first term $a$ and common difference $d$:

$$a_n = a + (n-1)d$$ $$S_n = \frac{n}{2}[2a + (n-1)d]$$

Coordinate Geometry

Distance between $(x_1, y_1)$ and $(x_2, y_2)$:

$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

If a point divides the line segment joining $(x_1, y_1)$ and $(x_2, y_2)$ internally in the ratio $m:n$, the coordinates are

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

Trigonometry

For an acute angle $\theta$ in a right triangle:

$$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}},\quad \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}},\quad \tan \theta = \frac{\text{opposite}}{\text{adjacent}}$$

The identity used most often is

$$\sin^2 \theta + \cos^2 \theta = 1$$

Useful standard values:

$$\sin 30^\circ = \frac{1}{2},\quad \cos 60^\circ = \frac{1}{2},\quad \tan 45^\circ = 1$$

Circles And Mensuration

Area and circumference of a circle:

$$A = \pi r^2,\quad C = 2\pi r$$

Area of a sector of angle $\theta$:

$$\text{sector area} = \frac{\theta}{360^\circ}\pi r^2$$

Arc length:

$$\text{arc length} = \frac{\theta}{360^\circ} \cdot 2\pi r$$

Volume formulas that appear often are:

$$\text{cylinder} = \pi r^2 h,\quad \text{cone} = \frac{1}{3}\pi r^2 h,\quad \text{sphere} = \frac{4}{3}\pi r^3$$

Probability

For equally likely outcomes,

$$P(E) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}$$

Worked Example: Solving A Quadratic Equation

Solve:

$$2x^2 - 5x - 3 = 0$$

Try factorization first:

$$2x^2 - 5x - 3 = 2x^2 - 6x + x - 3$$

Now group the terms:

$$= 2x(x - 3) + 1(x - 3)$$ $$= (2x + 1)(x - 3)$$

So

$$(2x + 1)(x - 3) = 0$$

That gives

$$2x + 1 = 0 \quad \text{or} \quad x - 3 = 0$$

Hence,

$$x = -\frac{1}{2} \quad \text{or} \quad x = 3$$

This is a common Class 10 pattern: rewrite the middle term, factor by grouping, then solve the two linear factors.

How To Write Solutions That Earn Marks

A good Class 10 Maths solution is usually not long. It is just clear.

Start by writing the formula, theorem, or method you are using. In algebra, that may be the quadratic formula or the $n$th-term formula. In geometry, that may be similarity or a tangent property. This makes the logic visible to the examiner.

Show substitutions in one line at a time. If you skip from the question straight to the final answer, you make it harder to earn method marks.

Keep units and labels where the question needs them. In heights and distances, area, and volume questions, missing units can cost clarity even when the arithmetic is correct.

Common Mistakes In CBSE Class 10 Maths

One common mistake is learning a formula without learning its condition. For example, the section formula above is for internal division in the stated ratio. If the condition changes, the setup changes too.

Another mistake is treating all trigonometry questions as formula recall. In Class 10, the diagram matters. You need the correct angle, the correct opposite side, and the correct adjacent side before using any ratio.

In mensuration, students often mix surface area and volume. If the question is about paint, sheet metal, or covering, it usually needs surface area. If it is about capacity or filling, it usually needs volume.

In geometry proofs, many students know the idea but do not state the reason. That weakens the solution even when the final conclusion is right.

Mathematics Basic Vs Standard

CBSE offers Mathematics Basic and Mathematics Standard in Class 10, but both use the same NCERT Class 10 book. The chapter list is the same. Mathematics Standard usually expects stronger multi-step application and algebraic handling in the exam paper.

That means your revision plan should not start by splitting the syllabus into two different books. Start with the same chapter set, then practice at the paper level you will take.

Where Class 10 Maths Is Used

Coordinate geometry shows up any time you work with location on a grid, map, or screen.

Trigonometry is the basic language of height, slope, and distance.

Statistics and probability appear in surveys, sports data, risk, and everyday comparisons.

Mensuration is the math behind paint coverage, water tanks, packaging, and construction measurements.

A Smart Revision Order

If you want a practical order instead of the textbook order, this is a strong sequence:

1. Quadratic Equations
2. Pair of Linear Equations in Two Variables
3. Arithmetic Progressions
4. Triangles
5. Introduction to Trigonometry
6. Surface Areas and Volumes
7. Statistics and Probability

This order works well because it brings high-use methods earlier and builds confidence quickly.

Try A Similar Problem

Pick one chapter you find weak, write the three formulas you use most in that chapter, and solve one textbook question without looking at the solution. Then compare your steps, not just the final answer. That is usually the fastest way to improve.