Class 11 Mathematics

Chapters

1. 1SetsLesson: Sets · 15 sections · chapter quiz

   A music app groups songs into playlists; a school groups students into clubs. Sets give a precise language for collections, and nearly every later topic — functions, probability, calculus — is written in this language.

   • • I can represent sets in roster and set-builder form and classify them as empty, finite, infinite or equal.
   • • I can work with subsets, power sets, intervals and the universal set.
   • • I can perform union, intersection, difference and complement, use Venn diagrams and prove simple set laws.
2. 2Relations and FunctionsLesson: Relations and Functions · 15 sections · chapter quiz

   Every student has exactly one roll number; a mobile number may be linked to several apps. Relations describe links between sets; functions are the special links where every input has exactly one output.

   • • I can form Cartesian products and count n(A × B).
   • • I can identify relations and functions with their domain, co-domain and range.
   • • I can sketch and use standard real functions and combine functions algebraically.
3. 3Trigonometric FunctionsLesson: Trigonometric Functions · 15 sections · chapter quiz

   Sound waves, tides, alternating current and the motion of a Ferris wheel repeat in cycles. Trigonometric functions of any angle describe these periodic patterns.

   • • I can measure angles in degrees and radians and convert between them.
   • • I can define trigonometric functions of any real number using the unit circle and state their signs, domains, ranges and graphs.
   • • I can prove and apply the sum, difference, multiple-angle and sum-to-product identities.
4. 4Complex Numbers and Quadratic EquationsLesson: Complex Numbers and Quadratic Equations · 15 sections · chapter quiz

   x² + 1 = 0 has no real solution, yet engineers analysing circuits and signals need such equations solved. Introducing i, with i² = −1, completes the number system.

   • • I can explain why √−1 is needed and write complex numbers as a + ib.
   • • I can add, subtract, multiply and divide complex numbers and find modulus and conjugate.
   • • I can represent complex numbers on the Argand plane, in polar form, and solve quadratics with negative discriminant.
5. 5Linear InequalitiesLesson: Linear Inequalities · 15 sections · chapter quiz

   A student needs at least 60 marks overall; a lift carries at most 680 kg. 'At least' and 'at most' create inequalities, whose solutions are ranges rather than single numbers.

   • • I can distinguish strict and slack inequalities and state the rules for manipulating them.
   • • I can solve linear inequalities in one variable algebraically and show solutions on the number line.
   • • I can model real situations with inequalities and solve them graphically in two variables.
6. 6Permutations and CombinationsLesson: Permutations and Combinations · 15 sections · chapter quiz

   How many 4-digit OTPs exist? How many ways can a captain and vice-captain be chosen, or a committee of 3 from 10? Counting without listing is the power of permutations and combinations.

   • • I can apply the fundamental principle of counting.
   • • I can derive and use ⁿPᵣ = n!/(n − r)! and permutations with repeated objects.
   • • I can derive ⁿCᵣ = n!/(r!(n − r)!), connect it to ⁿPᵣ and solve selection problems.
7. 7Binomial TheoremLesson: Binomial Theorem · 15 sections · chapter quiz

   Computing (1.02)¹⁰ for compound interest or 99⁵ by hand is tedious. The binomial theorem expands any (a + b)ⁿ in one step.

   • • I can describe the historical development and Pascal's triangle.
   • • I can state and prove the binomial theorem for positive integer index.
   • • I can expand binomials, find specific terms and use the theorem in simple applications.
8. 8Sequences and SeriesLesson: Sequences and Series · 15 sections · chapter quiz

   A bouncing ball rises to 80% of its previous height each time; a bank doubles an investment every few years. Geometric progressions describe repeated multiplication — and sometimes add up to a finite total even with infinitely many terms.

   • • I can describe sequences, series and the arithmetic mean.
   • • I can find the general term, sum of n terms and infinite sum of a geometric progression and the geometric mean.
   • • I can prove A.M. ≥ G.M. and, as supplementary content, use mathematical induction and the special sums Σk, Σk², Σk³.
9. 9Straight LinesLesson: Straight Lines · 15 sections · chapter quiz

   Road gradients, ramp designs and trend lines on graphs are described by slope. The equation of a line lets a computer draw it, a surveyor locate it and an economist forecast with it.

   • • I can find the slope of a line and the angle between two lines and test parallel and perpendicular lines.
   • • I can write the equation of a line in point-slope, slope-intercept, two-point, intercept and axis-parallel forms.
   • • I can find the distance of a point from a line and between parallel lines.
10. 10Conic SectionsLesson: Conic Sections · 15 sections · chapter quiz

    Satellite dishes are parabolic, planetary orbits are elliptical and some comet paths are hyperbolic. All these curves come from slicing a cone with a plane.

    • • I can describe circles, ellipses, parabolas, hyperbolas and degenerate conics as sections of a double cone.
    • • I can derive and use the standard equation of a circle.
    • • I can use the standard equations and simple properties (focus, directrix, axes, eccentricity, latus rectum) of parabolas, ellipses and hyperbolas.
11. 11Introduction to Three-dimensional GeometryLesson: Introduction to Three-dimensional Geometry · 15 sections · chapter quiz

    A drone's position needs height as well as map position; an air-traffic controller tracks aircraft in 3-D. A third axis extends coordinates into space.

    • • I can describe the coordinate axes, coordinate planes and octants in space.
    • • I can locate points with coordinates (x, y, z).
    • • I can derive and use the distance formula in three dimensions and, as supplementary content, the section formula.
12. 12Limits and DerivativesLesson: Limits and Derivatives · 15 sections · chapter quiz

    A speedometer shows speed at an instant, not over a whole trip. Calculus makes 'instantaneous rate of change' precise through limits.

    • • I can explain the derivative as an instantaneous rate of change and as the slope of a tangent.
    • • I can evaluate limits of polynomial, rational, trigonometric, exponential and logarithmic functions using limit laws and standard limits.
    • • I can find derivatives from first principles and use the sum, difference, product and quotient rules for polynomial and trigonometric functions.
13. 13Statistics: Measures of DispersionLesson: Statistics: Measures of Dispersion · 15 sections · chapter quiz

    Two batters may both average 50 runs, but one scores consistently while the other swings between 0 and 100. The average alone hides this; dispersion measures spread.

    • • I can explain why measures of dispersion are needed and find the range.
    • • I can find the mean deviation about the mean and median for ungrouped and grouped data.
    • • I can find the variance and standard deviation of ungrouped and grouped data, including by step-deviation.
14. 14ProbabilityLesson: Probability · 15 sections · chapter quiz

    Insurance companies, weather services and game designers need a probability theory that works consistently for any experiment. The axiomatic approach builds probability on set language.

    • • I can describe random experiments, outcomes and sample spaces using sets.
    • • I can identify 'not', 'and', 'or', exhaustive and mutually exclusive events.
    • • I can use the axiomatic definition of probability and the addition theorem.