CBSE Class 12 Maths — Chapters, Formulas & PYQs

CBSE Class 12 Maths covers six big units: Relations and Functions, Algebra, Calculus, Vectors and Three-Dimensional Geometry, Linear Programming, and Probability. If you searched for chapters, formulas, and PYQs, that is the practical map: know the unit list, learn the formulas with their conditions, and use previous-year questions to test method, not just memory.

For most students, Calculus takes the most time because it has the largest concentration of methods. Algebra, Vectors/3D, and Probability usually reward steady practice. Exact coverage can change by session, so treat the current CBSE outline as the final source for deleted portions or updated scope.

What Chapters Are In CBSE Class 12 Maths?

• Relations and Functions: relations, one-one and onto functions, inverse trigonometric functions.
• Algebra: matrices and determinants.
• Calculus: continuity and differentiability, applications of derivatives, integrals, applications of integrals, and differential equations.
• Vectors and Three-Dimensional Geometry: vector algebra, lines in 3D, angle between two lines, and shortest distance between two lines.
• Linear Programming: graphical optimization in two variables.
• Probability: conditional probability, independence, total probability, and Bayes' theorem.

The point of this list is not to memorize chapter names in isolation. It is to see the natural clusters. For example, Calculus is easier to revise when derivatives, integrals, and differential equations are treated as one connected block instead of five unrelated chapters.

Key Class 12 Maths Formulas To Learn First

Do not try to memorize every formula on day one. Start with the formulas that keep reappearing and attach each one to the condition that makes it valid.

Matrices

For a $2 \times 2$ matrix,

$$A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$$ $$\det(A) = ad - bc$$

and

$$A^{-1} = \frac{1}{ad-bc}\begin{pmatrix} d & -b \\ -c & a \end{pmatrix}$$

but only when $ad-bc \ne 0$. If the determinant is zero, the inverse does not exist.

Calculus

$$\frac{d}{dx}\left(\sin^{-1}x\right) = \frac{1}{\sqrt{1-x^2}}$$

for $|x| < 1$.

$$\int \frac{1}{x}\,dx = \ln|x| + C$$

for $x \ne 0$.

If $F'(x)=f(x)$, then

$$\int_a^b f(x)\,dx = F(b)-F(a)$$

This definite-integral result applies when $F$ is an antiderivative of $f$ on the interval you are using.

Vectors

$$\vec{a}\cdot\vec{b} = |\vec{a}|\,|\vec{b}|\cos \theta$$

Here, $\theta$ is the angle between the two vectors. That detail matters because students often mix it up with an angle a line makes with an axis.

Probability

$$P(A \mid B) = \frac{P(A \cap B)}{P(B)}$$

for $P(B) > 0$.

$$P(A_i \mid B) = \frac{P(A_i)P(B \mid A_i)}{\sum P(A_j)P(B \mid A_j)}$$

This Bayes' theorem form applies when $\{A_j\}$ is a partition of the sample space and $P(B) > 0$.

Worked Example: Area Between Two Curves

This is a board-style pattern, not a quoted previous-year question.

Find the area enclosed by $y=x$ and $y=x^2$.

Step 1: Find where the curves meet

Set the two expressions equal:

$$x = x^2$$ $$x(x-1) = 0$$

So the intersection points are at $x=0$ and $x=1$.

Step 2: Decide which curve is on top

On the interval $0 \le x \le 1$, we have $x \ge x^2$. So the upper curve is $y=x$ and the lower curve is $y=x^2$.

That condition matters. If the curves changed order inside the interval, you would need to split the integral.

Step 3: Set up and evaluate the area

$$\text{Area} = \int_0^1 (x-x^2)\,dx$$ $$= \left[\frac{x^2}{2} - \frac{x^3}{3}\right]_0^1$$ $$= \frac{1}{2} - \frac{1}{3} = \frac{1}{6}$$

So the enclosed area is

$$\frac{1}{6}$$

This is a strong Class 12 example because it checks three skills at once: finding intersection points, deciding which curve is above, and setting up the correct integral.

Common Mistakes In CBSE Class 12 Maths Prep

Treating a unit as one fixed exam pattern

A big unit deserves more revision time, but that does not mean each chapter inside it will appear in one fixed way. Study the method behind the chapter, not just a guessed question pattern.

Memorizing a formula without its condition

Students often remember $A^{-1}$ but forget to check whether $\det(A) \ne 0$, or they use conditional probability without checking whether $P(B) > 0$.

Jumping straight to mixed PYQs

PYQs work best after the chapter method is already clear. If your setup is shaky, mixed papers only hide the real weakness.

Ignoring NCERT-style basics

Board questions often look harder than they are because they combine standard chapter moves. If the NCERT examples and basic exercises are weak, PYQs usually feel harder than they should.

How To Use PYQs Without Wasting Time

PYQs, or previous-year questions, are most useful after you already know the chapter method. Use them to spot repeat patterns: a matrix inverse with a determinant check, an area-between-curves setup, or a Bayes' theorem question with the partition already defined.

If you miss a PYQ, classify the miss. Was it a concept gap, an algebra slip, or the wrong formula trigger? That is more useful than simply re-reading the solution.

Try A Similar Class 12 Maths Problem

Pick one chapter from Calculus and one from a shorter unit such as Probability or Matrices. Make a one-page formula sheet with conditions, solve three PYQ-style questions without notes, and then rewrite only the formulas or triggers you missed. That loop is usually more effective than reading the whole syllabus again.