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f(x+h)−f(x) sin²θ + cos²θ = 1 z = a + bi ⁿCᵣ = n! / r!(n−r)!
IIT Hyderabad × Summer 2026

Class 11 and 12 Maths Foundation
Summer Program

Sets · Functions · Trigonometry · Complex Numbers · Sequences · Co-ordinate Geometry · Calculus Intro · 8 Weeks · Online · Small batches

8-week intensive program to build complete command over Class 11 Maths — so boards, JEE, and every exam that follows feels manageable.

📐 Trig Identities & Equations 🔢 Complex Numbers 📈 Sequences & Series 👥 Max 9 Students / Batch ✅ Free Demo Class
Total Seats Available 18 3 batches · 1 slot each · filling fast
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💬 Book Free Demo Class Try These Problems ↓

No payment · Free first class · Instant WhatsApp reply

These Are Real Class 11 Questions
Most Students Get Wrong

Try them honestly — no peeking

Straight from topics we cover in this program. If even two of these stump you, this Summer Program was built for you.

Q.01 🔗 Sets & Relations Week 1
Let A = {1, 2, 3, 4} and R be a relation on A defined by:

R = {(a, b) : b = a + 1}

Is R reflexive? Symmetric? Transitive?
Justify each answer with a counterexample.
💡 Hint: Check each property definition carefully. For transitive, try to find (a,b) ∈ R and (b,c) ∈ R — does (a,c) ∈ R follow?
Not reflexive · Not symmetric · Not transitive
(1,1) ∉ R (not reflexive) · (1,2)∈R but (2,1)∉R (not symmetric) · (1,2),(2,3)∈R but (1,3)∉R (not transitive)
Sets & Relations is the foundation of all Class 11 Maths. We spend Week 1 making this crystal clear.
Q.02 📊 Functions & Graphs Week 2
Find the domain of:

f(x) = 1√(x² − 5x + 6)

Then check if f is one-one and onto.
💡 Hint: For domain: the expression inside √ must be > 0 (strict, since it's in denominator). Factorise x² − 5x + 6.
Domain: (−∞, 2) ∪ (3, ∞)
x² − 5x + 6 = (x−2)(x−3) > 0 → x < 2 or x > 3. Not onto onto ℝ.
Advanced functions with domain, range, and graph sketching — all covered in Week 2.
Q.03 📐 Trigonometry Week 3
Prove that:

cos 3x = 4cos³x − 3cosx

Then find the exact value of:
cos 20° × cos 40° × cos 80° = ?
💡 Hint: Expand cos(2x + x) using addition formula. For the product — substitute x = 20° into the identity you just proved.
cos 20° × cos 40° × cos 80° = 1/8
Multiply both sides by sin 20° and use sin 3θ = 3sinθ − 4sin³θ
This product question appeared in JEE Mains 2023. We cover the full method in Week 3 — Trig Identities & Equations.
Q.04 🔢 Complex Numbers Week 4
If z = (1 + i)/(1 − i), find z⁴.

Also solve: x² + x + 1 = 0 and express roots in a + bi form.
💡 Hint: Multiply numerator and denominator by the conjugate (1 + i). Then z = i. What is i⁴?
z = i → z⁴ = 1  ·  Roots: −½ ± (√3/2)i
Quadratic formula with negative discriminant gives complex roots — Week 4 topic.
Complex numbers + quadratic equations covered together in Week 4 — they are deeply connected.
Q.05 📈 Sequences & Series Week 5
The sum of first n terms is:

Sn = 3n² + 5n

Find Tn. Is the series an AP? If yes, find first term and common difference.
💡 Hint: Tn = Sn − Sn−1 for n ≥ 2. Always check T1 = S1 separately.
Tn = 6n + 2  ·  Yes, AP with a = 8, d = 6
This Sn → Tn shortcut saves 2 mins in the exam. Taught in Week 5 along with Binomial.
Most students guess the formula and lose all 4 marks. We teach the guaranteed method in Week 5.
Q.06 🎲 Permutation & Probability Week 6
A fair coin is tossed 5 times.

Find the probability of getting at least 3 heads.

Now given the first toss was heads, what's the probability of getting at least 3 heads total?
💡 Hint: Part 1: list favourable outcomes using ⁵C₃ + ⁵C₄ + ⁵C₅. Part 2 uses conditional probability — sample space reduces.
At least 3 heads: 1/2  ·  Given first = H: 11/16
Part 2 catches almost everyone — sample space shrinks from 32 to 16 outcomes.
Permutation, combination and probability — taught together in Week 6 with 6 different question types.
Couldn't solve 2 or more? That's exactly why this program exists.

In 8 weeks, you will be the student who solves all 6 — and the harder ones too. IIT Hyderabad mentors. Small batches. Free demo to start. No risk.

💬 I Want to Learn This →

Where Class 11 Students Actually Get Stuck

📊
Based on teaching 500+ Class 11 students, these are the exact 6 places where most students silently lose marks — not because they're not smart, but because no one showed them the right way to think about it.
📐 Trigonometry 73%
Memorising identities without knowing when to use which
Students cram 20+ trig identities but freeze in exams because they never built a mental map of which identity unlocks which type of problem.
  • Trying random identities hoping one works
  • Forgetting the double angle formula under pressure
  • Not recognising cos 3x = 4cos³x − 3cos x form
We teach a 3-step recognition framework. Any trig question — you identify the pattern first, then apply.
📊 Functions 68%
Confusing domain, range, one-one and onto — all four at once
Functions have 4 properties students must check simultaneously. Most mix them up or only partially solve, losing partial marks even when they know the concept.
  • Writing domain without checking denominator AND under root
  • Claiming "onto" without actually proving codomain = range
  • Skipping the horizontal line test for one-one
We use a 4-box checklist for every function problem. No step gets missed, no mark gets lost.
🔢 Complex Numbers 61%
The powers of i — and the algebra of conjugates — trip everyone up
Complex numbers feel abstract until you see the geometry. Students who only do algebra get lost when the question mixes modulus, argument, and conjugate in one go.
  • Computing i⁵² by multiplying out (instead of mod 4 trick)
  • Forgetting to rationalise by multiplying with conjugate
  • Sign errors in (a+bi)(a−bi) = a² + b² (not a² − b²)
We connect every algebraic rule to its Argand plane picture. Once you see it geometrically, errors vanish.
📈 Sequences 79%
The Sₙ → Tₙ trap — most students lose all 4 marks here
When asked to find the nth term from a sum formula, students skip the n=1 check. This one oversight causes a completely wrong answer with zero marks.
  • Using Tₙ = Sₙ − Sₙ₋₁ without verifying n=1 separately
  • Not confirming the series is actually an AP after finding Tₙ
  • Confusing "first term" with T₁ vs the given a
We drill the 3-line method: find Tₙ, verify T₁ = S₁, then conclude AP/GP. Takes 90 seconds, guarantees full marks.
🎲 Permutations 82%
Overcounting (or undercounting) in arrangement problems
Permutation and Combination is the chapter where students most confidently write a wrong answer. The logic feels correct but the counting is off — usually by a factor of 2 or more.
  • Using nPr when the question needs nCr (or vice versa)
  • Not fixing identical objects — treating them as distinct
  • Forgetting the "complementary counting" shortcut for "at least/at most"
We use the ODAI framework (Order? Distinct? Arrangement? Identical?) before touching any P&C problem. Confidence goes up immediately.
⚠ The Hidden One 91%
Weak Class 10 base — and students don't even know it
91% of struggling Class 11 students have a gap in basic algebra, factorisation, or co-ordinate geometry from Class 10 — and it silently blocks every new topic they try to learn.
  • Struggling with trig? Often it's weak quadratic solving
  • Struggling with functions? Often it's unclear graph intuition
  • Struggling with sequences? Often it's weak algebraic manipulation
Week 1 of the program includes a targeted base-repair session. We find the gap and close it before moving forward.
8-Week Roadmap
Your Week-by-Week Journey

Every topic builds on the previous. No gaps. No skipping. Just a solid foundation from Week 1 to Week 8.

Month 1

Foundation Building

Week 1
Sets, Relations + Functions (Basics)
Types of sets, Venn diagrams, relations, domain & range, types of functions
Week 2
Advanced Functions + Graphs & Identities
Composite functions, inverse functions, graph transformations, key identities
Week 3
Trigonometry — Identities + Equations 73% struggle here
All major trig identities, multiple angle formulas, solving trig equations
Week 4
Complex Numbers + Quadratic Equations
Algebra of complex numbers, Argand plane, nature of roots, sum/product of roots
Month 2

Application + Advanced

Week 5
Sequences & Series + Binomial Theorem 79% lose marks
AP, GP, special series, Binomial expansion, general term, middle term
Week 6
Permutations, Combinations + Probability 82% get this wrong
Counting principles, nPr, nCr, conditional probability, basic probability theorems
Week 7
Co-ordinate Geometry — Lines + Conics (Basics)
Straight lines, circles, parabola, ellipse and hyperbola introduction
Week 8
Limits, Derivatives + Vectors & Intro to 3D
Basic limits, first principle of derivatives, vector basics, direction cosines intro
Your Mentors
Learn From IIT Minds

Not just teachers — IIT graduates who've been through the same exams your child will face.

ST
MSc Maths · IIT Hyderabad · 3+ Years Coaching
Sarthak Tiwari
MSc Mathematics, IIT Hyderabad. 500+ students mentored, 100+ IIT selections. Specialises in building strong foundations in Calculus, Algebra, and Trigonometry — the backbone of both boards and JEE. Rated 4.9★ on Google by 120+ students.
S
M.Sc. Maths Hons · JAM Qualified · 7 Yrs Exp.
Simran Ma'am
7 years of teaching experience across Class 11, 12 and JEE. Expert in Statistics, Probability, Linear Programming, and Binomial Theorem. Known for making abstract topics genuinely understandable with real-world analogies.
Our Approach
Why Students Actually Improve

Not just covering chapters — building real mathematical thinking that lasts beyond the exam.

🧠
Concept-First, Not Rote
We teach the "why" behind every formula. Students who understand the derivation never forget — or get confused under pressure.
Live Doubt Clearing
Small batches (max 9) mean no question goes unanswered. Every doubt resolved in class — no "ask offline" delays.
📝
Weekly Mock Tests
Board-pattern and JEE-pattern tests every week with detailed review. You know exactly where you stand at all times.
📦
Full Study Material
Curated notes, practice sheets, and question banks — all included from Day 1. No extra cost.
Student Results
Real Success Stories

From "I hate Maths" to board toppers and JEE qualifiers — in one summer.

"
★★★★★
Went from 45 to 85 in Class 11 Maths in just 2 months. The way each concept was built from scratch made everything click — something a whole year of school couldn't do.
R
Rahul S.
Class 11 Student
📈 45 → 85 in 2 months
"
★★★★★
Sarthak sir never lets you memorise formulas. He makes you understand the "why." I finally stopped being scared of Maths and started enjoying it.
P
Priya M.
Class 11 Student
🎯 90+ in Class 11 Finals
"
★★★★★
Cleared JEE Main 94 percentile. The foundation this summer program gave me was something my coaching institute never built. Especially Trig and Functions.
A
Amit K.
JEE Main 2025
🏆 JEE Main 94 Percentile
Batch Investment
Choose Your Batch Size

All batches cover identical 8-week curriculum. Smaller batch = more personal attention. Only 1 batch slot available per size.

3-Student Batch
Maximum attention — nearly private tutoring
25,000
per student · 8 weeks
1 batch slot only
  • Near-private mentoring from IIT faculty
  • Custom pacing to your exact level
  • All study material included
  • Weekly mock tests + personal review
Enquire on WhatsApp →
9-Student Batch
Group energy, structured learning
16,000
per student · 8 weeks
1 batch slot only
  • Competitive classroom atmosphere
  • Affordable without losing quality
  • All study material included
  • Weekly mock tests + group review
Enquire on WhatsApp →
Questions?
Frequently Asked
8 weeks covering: Sets & Relations, Advanced Functions & Graphs, Trigonometry (Identities & Equations), Complex Numbers & Quadratic Equations, Sequences & Series + Binomial Theorem, Permutations, Combinations & Probability, Co-ordinate Geometry (Lines & Conics), and Limits, Derivatives & Vectors introduction.
We have 3 batch sizes — 3 students, 6 students, or 9 students. There is only ONE batch slot available for each size. Once a batch is full, it's closed.
This is live, interactive, in small batches. Unlike YouTube, you get real-time doubt clearing, personalised feedback, weekly mock tests, and a mentor who knows exactly where you're struggling.
100% free, zero obligation. Attend the first class, see the teaching style, ask questions — and then decide. WhatsApp +91 7601047556 to book your slot.
Fully online via Zoom or Google Meet. Live and interactive — not pre-recorded videos. Available to students from any city in India.
Everything — live sessions, curated notes, practice sheets, PYQ question sets, weekly mock tests, and doubt clearing support. No hidden charges.

Claim Your Free Demo

18 total seats. 3 batches. 8-week Class 11 Maths Foundation. May batch starting soon — don't let your summer go to waste.

💬 WhatsApp for Free Demo

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