ISC Class XI Mathematics Syllabus 2026 – 27

1. Sets and Functions

(i) Sets

Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of a set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and Intersection of sets. Difference of sets. Complement of a set. Properties of Complement of Sets.

(ii) Relations & Functions

Ordered pairs, Cartesian product of sets. Number of elements in the cartesian product of two finite sets. Cartesian product of the set of reals with itself (upto R × R × R). Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special type of relation. Function as a type of mapping, domain, co-domain and range of a function. Real valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions. Sum, difference, product and quotient of functions.

Sets: Self-explanatory.

Basic concepts of Relations and Functions

• Ordered pairs, sets of ordered pairs.
• Cartesian Product (Cross) of two sets, cardinal number of a cross product.

Relations as:

• an association between two sets.
• a subset of a Cross Product.
• Domain, Range and Co-domain of a Relation.

Functions:

• As special relations, concept of writing “y is a function of x” as y = f(x).
• Domain and range of a function
• Reading, sketching and understanding the graphs of all standard real valued functions.

(iii) Trigonometry

Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin² x + cos² x = 1, for all x. Signs of trigonometric functions. Domain and range of trignometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple applications. Deducing the identities like the following:

\tan(\text{x} \pm \text{y}) = \frac{\tan \text{x} \pm \tan \text{y}}{1 \mp \tan \text{x}\tan \text{y}}

\cot(\text{x} \pm \text{y}) = \frac{\cot \text{x}\cot \text{y} \mp 1}{\cot \text{y} \pm \cot \text{x}}

\sin \text{α} \pm \sin \text{β} = 2\sin\frac{1}{2}(\text{α} \pm \text{β})\cos\frac{1}{2}(\text{α} \mp \text{β})

\cos \text{α} + \cos \text{β} = 2\cos\frac{1}{2}(\text{α}+\text{β})\cos\frac{1}{2}(\text{α}-\text{β})

\cos \text{α} - \cos \text{β} = -2\sin\frac{1}{2}(\text{α}+\text{β})\sin\frac{1}{2}(\text{α}-\text{β})

Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x.

Angles and Arc lengths

• Angles: Convention of sign of angles.
• Magnitude of an angle: Measures of Angles; Circular measure.
• The relation S = rθ where θ is in radians. Relation between radians and degree.
• Definition of trigonometric functions with the help of unit circle.
• Truth of the identity sin² x + cos² x = 1

NOTE: Questions on the area of a sector of a circle are required to be covered.

Trigonometric Functions

• Relationship between trigonometric functions.
• Proving simple identities.
• Signs of trigonometric functions.
• Domain and range of the trigonometric functions.
• Trigonometric functions of all angles.
• Periods of trigonometric functions.
• Graphs of simple trigonometric functions (only sketches).

NOTE: Graphs of sin x, cos x, tan x, sec x, cosec x and cot x are to be included.

Compound and multiple angles

• Addition and subtraction formula: sin(A±B); cos(A±B); tan(A±B); tan(A+B+C) etc., Double angle, triple angle, half angle and one third angle formula as special cases.
• Sum and differences as products \sin \text{C} + \sin \text{D} = 2\sin\left(\frac{\text{C}+\text{D}}{2}\right)\cos\left(\frac{\text{C}-\text{D}}{2}\right), etc.
• Product to sum or difference i.e. 2 sin A cos B = sin(A + B) + sin(A − B) etc.

2. Algebra

(i) Complex Numbers

Introduction of complex numbers and their representation, Algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Square root of a complex number. Cube root of unity.

• Conjugate, modulus and argument of complex numbers and their properties.
• Sum, difference, product and quotient of two complex numbers additive and multiplicative inverse of a complex number.
• Square root of a complex number.
• Cube roots of unity and their properties.

(ii) Quadratic Equations

Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with real coefficients).

• Use of the formula: \text{x} = \frac{-\text{b} \pm \sqrt{\text{b}^2-4\text{ac}}}{2\text{a}} in solving quadratic equations.
• Equations reducible to quadratic form.
• Nature of roots
  • Product and sum of roots.
  • Roots are rational, irrational, equal, reciprocal, one square of the other.
  • Complex roots.
  • Framing quadratic equations with given roots.

NOTE: Questions on equations having common roots are to be covered.

Quadratic Functions.

Given α, β as roots then find the equation whose roots are of the form α³, β³, etc.

Case I: a > 0 — Real roots, Complex roots, Equal roots

Case II: a < 0 — Real roots, Complex roots, Equal roots

Where ‘a’ is the coefficient of x² in the equations of the form ax² + bx + c = 0.

Sign of quadratic

Sign when the roots are real and when they are complex.

Graph of quadratic function.

Maximum/minimum value of quadratic function and value of x for which maximum/minimum occurs.

Inequalities

Linear Inequalities

Algebraic solutions of linear inequalities in one variable and their representation on the number line. Self-explanatory.

Quadratic Inequalities

Using method of intervals for solving problems of the type: x² + x − 6 ≥ 0. A perfect square e.g. x² − 6x + 9 ≥ 0.

Inequalities involving rational expression of type f(x)/g(x) ≤ a, etc. to be covered.

(iii) Permutations and Combinations

Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of formulae for ⁿPᵣ and ⁿCᵣ and their connections, application.

• Factorial notation n!, n! = n(n − 1)!
• Fundamental principle of counting.
• Permutations
  • ⁿPᵣ.
  • Restricted permutation.
  • Certain things always occur together.
  • Certain things never occur.
  • Formation of numbers with digits.
  • Word building - repeated letters - No letters repeated.
  • Permutation of alike things.
  • Permutation of Repeated things.
  • Circular permutation – clockwise counterclockwise – Distinguishable / not distinguishable.
• Combinations
  • ⁿCᵣ, ⁿCₙ=1, ⁿC₀=1, ⁿCᵣ=ⁿCₙ₋ᵣ, ⁿCₓ=ⁿCᵧ, then x+y=n or x=y, ⁿ⁺¹Cᵣ=ⁿCᵣ₋₁+ⁿCᵣ.
  • When all things are different.
  • When all things are not different.
  • Mixed problems on permutation and combinations.

(iv) Binomial Theorem

History, statement and proof of the binomial theorem for positive integral indices. Pascal's triangle, General and middle term(s) in binomial expansion, applications.

• Significance of Pascal’s triangle.
• Binomial theorem for positive integral powers, i.e. (x+y)ⁿ = ⁿC₀xⁿ + ⁿC₁xⁿ⁻¹y + ...... + ⁿCₙyⁿ.
• Binomial coefficients.

Questions based on the above.

(v) Sequence and Series

Sequence and Series. Arithmetic Progression (A.P.). Arithmetic Mean (A.M.) Geometric Progression (G.P.), general term of a G.P., sum of first n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), relation between A.M. and G.M. Formulae for the following special sums ∑n, ∑n², ∑n³.

Arithmetic Progression (A.P.)

• T_n = a + (n − 1)d
• \text{S}_{\text{n}} = \frac{\text{n}}{2}\{2\text{a}+(\text{n}-1)\text{d}\}
• Arithmetic mean: 2b = a + c
• Inserting two or more arithmetic means between any two numbers.
• Three terms in A.P.: a−d, a, a+d
• Four terms in A.P.: a−3d, a−d, a+d, a+3d

Geometric Progression (G.P.)

• T_n = arⁿ⁻¹
• \text{S}_{\text{n}} = \frac{\text{a}(\text{r}^{\text{n}}-1)}{\text{r}-1}, \quad |\text{r}|>1
• \text{S}_{\text{n}} = \frac{\text{a}(1-\text{r}^{\text{n}})}{1-\text{r}}, \quad |\text{r}|<1
• S∞ = a/(1−r); r<1
• Geometric Mean, b = √ac
• Inserting two or more Geometric Means between any two numbers.
• Three terms are in G.P. ar, a, ar⁻¹
• Four terms are in GP ar³, ar, ar⁻¹, ar⁻³

Special sums ∑n, ∑n², ∑n³

Using these summations to sum up other related expression. Finding nth. term of a sequence using Method of difference.

3. Coordinate Geometry

(i) Straight Lines

Brief recall of two-dimensional geometry from earlier classes. Shifting of origin. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, point-slope form, slope-intercept form, two-point form, intercept form and normal form. General equation of a line. Equation of family of lines passing through the point of intersection of two lines. Distance of a point from a line.

Brief recall of basic concepts of Points and their coordinates.

• Section formula (internally/externally)
• Coordinates of incentre, Area of triangle when vertices are given
• Condition for collinearity of three points

The straight line

• Slope or gradient of a line.
• Angle between two lines.
• Condition of perpendicularity and parallelism.
• Various forms of equation of lines.
• Slope intercept form.
• Two-point slope form.
• Intercept form.
• Perpendicular /normal form.
• General equation of a line.
• Distance of a point from a line.
• Distance between parallel lines.
• Equation of lines bisecting the angle between two lines.
• Equation of family of lines
• Definition of a locus.
• Equation of a locus.

(ii) Circles

Equations of a circle in:

• Standard form.
• Diameter form.
• General form.
• Parametric form.

• Given the equation of a circle, to find the centre and the radius.
• Finding the equation of a circle.
  • Given three non collinear points.
  • Given other sufficient data for example centre is (h, k) and it lies on a line and two points on the circle are given, etc.
  • When circles touching each other externally/internally.
• Intercepts made by the circle on the axes.
• Relative position of two circles.

(iii) Conic Section

Sections of a cone, ellipse, parabola, hyperbola, a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola.

Conics as a section of a cone.

• Definition of Foci, Directrix, Latus Rectum.
• PS = ePL where P is a point on the conics, S is the focus, PL is the perpendicular distance of the point from the directrix.

(i) Parabola

• e = 1, y² = ±4ax, x² = 4ay, y² = −4ax, x² = −4ay.
• Rough sketch of the above.
• The latus rectum; quadrants they lie in; coordinates of focus and vertex; and equations of directrix and the axis.
• Finding equation of Parabola when Foci and directrix are given, etc.
• Application questions based on the above.

(ii) Ellipse

• \frac{\text{x}^2}{\text{a}^2} + \frac{\text{y}^2}{\text{b}^2} = 1, \quad \text{e}<1, \quad \text{b}^2=\text{a}^2(1-\text{e}^2)
• Cases when a>b and a<b.
• Rough sketch of the above.
• Major axis, minor axis; latus rectum; coordinates of vertices, focus and centre; and equations of directrices and the axes.
• Finding equation of ellipse when focus and directrix are given.
• Simple and direct questions based on the above.
• Focal property i.e. SP + SP′ = 2a.

(iii) Hyperbola

• \frac{\text{x}^2}{\text{a}^2} - \frac{\text{y}^2}{\text{b}^2} = 1, \quad \text{e}>1, \quad \text{b}^2=\text{a}^2(\text{e}^2-1)
• Cases when coefficient y² is negative and coefficient of x² is negative.
• Rough sketch of the above.
• Focal property i.e. SP − S′P = 2a.
• Transverse and Conjugate axes; Latus rectum; coordinates of vertices, foci and centre; and equations of the directrices and the axes.

(iv) Introduction to three-dimensional Geometry

Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.

• As an extension of 2-D
• Distance formula.
• Section and midpoint form

4. Calculus

(i) Limits and Derivatives

Derivative introduced as rate of change both as that of distance function and geometrically.

Intuitive idea of limit. Limits of polynomials and rational functions trigonometric, exponential and logarithmic functions.

Definition of derivative relate it to scope of tangent of the curve, Derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

Limits

• Notion and meaning of limits.
• Fundamental theorems on limits (statement only).
• Existence of \lim_{\text{x} \to \text{a}} \text{f(x)}
• Left hand limit, Right hand limit
• Limits of algebraic, trigonometric exponential and logarithmic functions.

NOTE: Indeterminate forms are to be introduced while calculating limits.

Differentiation

• Meaning and geometrical interpretation of derivative.
• Derivatives of simple algebraic and trigonometric functions and their formulae.
• Differentiation using first principles.
• Derivatives of sum/difference.
• Derivatives of product of functions.
• Derivatives of quotients of functions.

5. Statistics and Probability

(i) Statistics

Measures of dispersion: range, mean deviation, variance and standard deviation of ungrouped/grouped data.

• Mean deviation about mean.
• Standard deviation - by direct method, short cut method and step deviation method.
• Combined mean and standard deviation

(ii) Probability

Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events, 'not', 'and' and 'or' events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability, connections with other theories studied in earlier classes. Probability of an event, probability of 'not', 'and' and 'or' events.

• Random experiments and their outcomes.
• Events: sure events, impossible events, mutually exclusive and exhaustive events.
• Definition of probability of an event
• Laws of probability addition theorem.