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Welcome to Class 11 Mathematics

Class 10 taught you to solve equations and measure shapes. Class 11 builds the language and tools of higher mathematics: sets and functions, trigonometric functions, counting, sequences, conics, limits and probability.

1. Where Class 10 left you

In Class 10 you factorised quadratics and used the quadratic formula, found the $n$th term and the sum of an arithmetic progression, measured distances between points with the distance formula, met the trigonometric ratios of an acute angle, and computed simple probabilities with coins, dice and cards. Those are real skills, and every one of them is used again this year.

Class 11 changes the kind of mathematics you do. Instead of single answers you will work with whole sets of answers and with functions that turn one set into another. Angles stop being corners of triangles and become rotations of any size, measured in radians. Counting becomes a subject of its own. Curves such as the parabola and the ellipse get exact equations, and a new operation — the limit — opens the door to calculus. This is also the first year of preparation for JEE Main and JEE Advanced, and this course is built so that the Board syllabus and the JEE syllabus grow together.

📦 Class 10 ended with…

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ $$\sin^2A+\cos^2A=1$$

🚀 Class 11 begins with…

$$\{x : x\in\mathbb{R},\ x^2\lt4\}$$ $$\pi\ \text{rad}=180^\circ$$

2. A story that needs Class 11

You deposit ₹10,000 in a bank at $10\%$ interest per year. If interest is added once a year, after one year you have ₹11,000. But many banks add interest more often — half-yearly, quarterly, monthly, even daily — each time at the matching fraction of the yearly rate. With interest added $n$ times a year at the rate $\tfrac{10\%}{n}$, the money is multiplied by $1+\tfrac{0.1}{n}$ again and again, so after one year it is $$A_n=10000\left(1+\frac{0.1}{n}\right)^{n}.$$ More frequent compounding always earns more. But does it earn without limit if the bank compounds every hour, every second? Expanding $\left(1+\tfrac{0.1}{n}\right)^n$ is the binomial theorem (Chapter 7); the balances year after year form a geometric progression (Chapter 8); and asking what happens "as $n$ grows without bound" is the idea of a limit (Chapter 12). Run the lab and watch the answer appear.

Interactive 1 — Compounding More and More Often

Each bar shows the extra interest earned in one year on ₹10,000 compared with adding interest just once a year, for compounding $n$ times a year. The bars grow as $n$ grows — but by less and less, and they never pass the dashed ceiling. Change the rate and see the same levelling-off.

compounded $n$ times a year—
balance after 1 year (₹)—
extra over yearly compounding (₹)—
ceiling (₹)—
✏️ Example 1 — Quarterly compounding by the binomial theorem
Find the balance after one year when ₹10,000 earns $10\%$ per year compounded (a) half-yearly and (b) quarterly. Use the expansion of $(1+x)^n$ rather than a calculator.
(a) Half-yearly: $n=2$, rate $5\%$ per half-year. $(1.05)^2=1+2(0.05)+(0.05)^2=1.1025$, so the balance is ₹11,025.
(b) Expand Quarterly: $n=4$, rate $2.5\%$ per quarter. Using the coefficients $1,4,6,4,1$ of Pascal's triangle (Chapter 7): $$\begin{aligned}(1.025)^4&=1+4(0.025)+6(0.025)^2\\&\quad+4(0.025)^3+(0.025)^4\end{aligned}$$ After the leading $1$, the four terms are $0.1$, $0.00375$, $0.0000625$ and $0.000000390625$, so $$(1.025)^4=1.103812890625 .$$
Balance $10000\times1.103812890625\approx$ ₹11,038.13 — that is ₹38.13 more than yearly compounding.
Meaning The first two terms $1+4(0.025)=1.1$ are the simple-interest answer; the remaining terms are the "interest on interest". Each later term is much smaller than the one before — which is why the extra interest levels off in the lab.

3. The fourteen chapters at a glance

Language: sets, relations, functions (1–2)→Algebra: trigonometry, complex numbers, inequalities, counting, binomial, sequences (3–8)→Geometry: lines, conics, 3-D (9–11)→Calculus, statistics, probability (12–14)
Chapter 1

Sets

Roster and set-builder forms, subsets, intervals, Venn diagrams, union, intersection, complement.

$(A\cup B)'=A'\cap B'$
Open chapter → Chapter 2

Relations and Functions

Cartesian products, relations, functions and their graphs: modulus, signum, greatest integer.

$n(A\times B)=n(A)\,n(B)$
Open chapter → Chapter 3

Trigonometric Functions

Radians, the unit circle, graphs and periods, sum and multiple-angle formulae.

$\cos2x=1-2\sin^2x$
Open chapter → Chapter 4

Complex Numbers and Quadratic Equations

The number $i$, algebra of $a+ib$, conjugate, modulus and the Argand plane.

$|z|=\sqrt{a^2+b^2}$
Open chapter → Chapter 5

Linear Inequalities

Rules for inequalities and solving linear inequalities in one variable on the number line.

$3x-5\lt7\iff x\lt4$
Open chapter → Chapter 6

Permutations and Combinations

The counting principle, arrangements and selections.

${}^nC_r=\dfrac{n!}{r!\,(n-r)!}$
Open chapter → Chapter 7

Binomial Theorem

Pascal's triangle, expanding $(a+b)^n$, and quick estimates.

$(a+b)^n=\sum_{r=0}^{n}{}^nC_r\,a^{n-r}b^r$
Open chapter → Chapter 8

Sequences and Series

Geometric progressions, infinite GP sums, arithmetic and geometric means.

$S_\infty=\dfrac{a}{1-r}\ (|r|\lt1)$
Open chapter → Chapter 9

Straight Lines

Slope, angle between lines, forms of the equation, distance of a point from a line.

$y-y_1=m(x-x_1)$
Open chapter → Chapter 10

Conic Sections

Circle, parabola, ellipse and hyperbola: foci, eccentricity, latus rectum.

$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$
Open chapter → Chapter 11

Introduction to 3-D Geometry

Axes, coordinate planes, octants and the distance between two points in space.

$PQ=\sqrt{\Delta x^2+\Delta y^2+\Delta z^2}$
Open chapter → Chapter 12

Limits and Derivatives

Limits from both sides, standard limits, the derivative from first principles and its algebra.

$\displaystyle\lim_{x\to0}\frac{\sin x}{x}=1$
Open chapter → Chapter 13

Statistics

Range, mean deviation, variance and standard deviation.

$\sigma^2=\dfrac1n\sum(x_i-\bar x)^2$
Open chapter → Chapter 14

Probability

Events as sets, the axiomatic approach, and the addition rule.

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$
Open chapter →
🗺️ How the chapters connect
  1. Sets and functions (Ch. 1–2) are the language. Solution sets, intervals, domains and ranges, and events in probability are all sets; every later chapter studies some kind of function.
  2. Trigonometric functions (Ch. 3) extend the ratios of Class 10 to every real number using the unit circle; complex numbers (Ch. 4) give the equation $x^2+1=0$ its solutions.
  3. Counting (Ch. 6) powers two later chapters: the coefficients ${}^nC_r$ of the binomial theorem (Ch. 7) and the counting of outcomes in probability (Ch. 14).
  4. Sequences (Ch. 8) continue the arithmetic progressions of Class 10 with geometric progressions, and their infinite sums give the first taste of a limit.
  5. Coordinate geometry (Ch. 9–11) turns lines, conics and points in space into equations, building on the distance formula of Class 10.
  6. Limits and derivatives (Ch. 12) begin calculus, which fills most of Class 12 — and statistics (Ch. 13) and probability (Ch. 14) prepare you for data in every science.

Looking ahead: relations and functions return in Class 12 Mathematics (Chapter 1), together with inverse trigonometric functions, matrices, and the full calculus of derivatives and integrals.

🧭 How to use this course
  • Read with a pen. Try every worked example before opening its solution, then compare step by step. Every step is written out — nothing is left as "obvious".
  • Play with the labs. Each section has two interactives; change the settings until you can predict what will happen before you press ▶ Play.
  • Do the exercises in order. They run from routine to challenging, and every part has a full solution. Small check-labs let you test your answers.
  • 🎯 Exam corner. Every section ends its teaching with exam-style problems tagged Board · 1 mark … Board · 5 marks, JEE Main and JEE Advanced, each with a full solution and the trap to avoid. Board students: do every Board problem. JEE aspirants: do them all.
  • 📘 School assessment only. Some topics (for example mathematical induction, composition of functions and the chain rule) are in the CBSE syllabus but are assessed only in school, not in the year-end board exam. They are taught in boxes marked 📘 — study them for your school tests, and note which entrance exams also list them.
  • 🚀 Beyond the board syllabus. A few sections contain one boxed topic that is not in the CBSE syllabus; its first line names the entrance exams that list it. Board-only students may skip these boxes.
  • Use the quiz as a gate. Five questions end every section; if you score below 4, reread before moving on.
  • Words and formulas. Dotted words show their meaning when you point at them. The Glossary (with flashcards) and the Formula Sheet collect everything in one place.

4. Prerequisite diagnostic — are you ready?

Eight quick questions on the Class 10 skills this course uses most. Answer all of them; for each one you miss you will be told which Class 10 Mathematics section to review.

Q1. $\text{HCF}(96,404)=$
Q2. The roots of $2x^2-7x+3=0$ are
Q3. The equation $x^2+2x+5=0$ has
Q4. The $10$th term of the AP $3,7,11,\dots$ is
Q5. The distance between $(1,2)$ and $(4,6)$ is
Q6. If $\sin\theta=\tfrac35$ and $\theta$ is acute, then $\tan\theta=$
Q7. A fair die is thrown once. The probability of a prime number is
Q8. The solution of $x+y=5$, $x-y=1$ is

When you are ready, start with Chapter 1 — Sets.

← Class 11 Mathematics — ContentsChapter 1 — Sets →