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Class 11–12 Maths: Calculus & Algebra Foundation (CBSE, JEE)

Functions, complex numbers, series, matrices, limits, derivatives, integrals and differential equations, step by step

Ghosla Academy · School Academics Team

This course covers the algebra and calculus backbone of NCERT Class 11 and Class 12 Mathematics: sets and functions, complex numbers and quadratics, sequences and the binomial theorem, permutations and combinations, matrices and determinants, limits and continuity, differentiation and its applications, integration, area under curves and differential equations. Every concept comes with fully worked examples that have been checked, plus the common errors that cost marks. The explanations follow the board-exam style of writing steps, with a few extra techniques that are useful for JEE Main. Two hands-on projects use free tools such as Google Sheets, GeoGebra or Python to check your own answers. CBSE and NTA decide syllabus and exam patterns and these can change, so always check cbseacademic.nic.in and jeemain.nta.nic.in. No course can promise a rank; regular practice is what improves scores.

What you will be able to do

  • Work with sets, relations, functions, complex numbers and quadratic equations confidently
  • Use AP, GP and the binomial theorem to find terms, sums and coefficients
  • Count arrangements and selections and solve linear systems with matrices and determinants
  • Evaluate limits, check continuity and differentiate using chain, implicit and logarithmic rules
  • Apply derivatives to rates of change, monotonicity and maxima–minima problems
  • Integrate by substitution, parts and partial fractions and solve first-order differential equations

What you build

  • Matrix and linear-system checker in Google Sheets or Python
  • Calculus in real life: optimise a box and find areas with GeoGebra

What you need to start

  • Current NCERT Mathematics textbooks for Class 11 and Class 12 (rationalised edition)
  • Comfort with Class 10 algebra and trigonometry
  • Notebook, graph paper and a phone or laptop with a free graphing tool

Curriculum · 5 sections, 20 lectures

Functions, Complex Numbers and Series4 lectures
  1. Sets, Relations and FunctionsFree preview14 min
  2. Complex Numbers and Quadratic EquationsFree preview14 min
  3. Sequences, Series and the Binomial Theorem12 min
  4. Quiz: Functions, Complex Numbers and Series7 min
Counting, Matrices and Determinants4 lectures
  1. Permutations and Combinations13 min
  2. Matrices and Determinants: Inverse and Linear Systems16 min
  3. Project: Matrix and Linear-System Checker in Sheets or Python20 min
  4. Quiz: Counting, Matrices and Determinants7 min
Limits, Continuity and Differentiation4 lectures
  1. Limits and Continuity14 min
  2. Differentiation: Chain, Implicit, Logarithmic and Parametric16 min
  3. Inverse Trigonometric Functions11 min
  4. Quiz: Limits, Continuity and Differentiation7 min
Applications of Derivatives3 lectures
  1. Rates of Change and Increasing–Decreasing Functions14 min
  2. Maxima and Minima with Real-Life Optimisation12 min
  3. Quiz: Applications of Derivatives7 min
Integration and Differential Equations5 lectures
  1. Indefinite Integrals: Substitution, Parts and Partial Fractions16 min
  2. Definite Integrals, Properties and Area Under Curves15 min
  3. Differential Equations: Order, Degree and First-Order Methods12 min
  4. Project: Calculus in Real Life with GeoGebra20 min
  5. Quiz: Integration and Differential Equations7 min

Who this is for

  • CBSE Class 11 and 12 students who find algebra and calculus difficult
  • Students building a JEE Main foundation alongside board preparation
  • Students heading into B.Sc., B.Tech, BBA or economics courses that use calculus