# In-Depth Mathematics

### 11th

ScienceGenic introduces the Senior Philosophy Classroom Program, a premier educational offering for students in grade 11. This program is designed to prepare students for the challenges of higher education and beyond, offering comprehensive support and advanced learning experiences. Here’s what sets our program apart:

Specialized Subject Teachers: Our program features highly qualified and specialized teachers for each core subject—Physics, Chemistry, Biology, and Mathematics. These expert educators bring a deep understanding of their subjects and a passion for teaching, offering personalized instruction to every student.

Supervised and Supported Teaching: The Senior Philosophy Classroom Program ensures quality teaching through careful supervision and support for educators. Teachers receive guidance from the syllabus manager and psychologist to create an engaging and holistic learning environment.

Integrated Communication Channels: Seamless communication between the syllabus manager, psychologist, and teachers enables a collaborative approach to education. This teamwork fosters a comprehensive understanding of each student’s academic and emotional needs.

Deep Understanding of Subject Knowledge: Our curriculum focuses on in-depth exploration of advanced concepts in each subject. Students are encouraged to think critically, analyze complex topics, and apply their knowledge in real-world contexts.

Personalized Guidance and Support: We recognize that every student is unique, and we tailor our approach to meet their individual needs. Our collaborative team works closely with students to provide personalized guidance and support throughout their educational journey.

Regular Assessments and Feedback: Continuous evaluation helps us track student progress and adapt teaching strategies accordingly. Regular assessments and feedback keep students engaged and motivated, allowing them to achieve their full potential.

Parental Engagement: Open communication with parents and guardians is key to student success. We provide regular updates and opportunities for dialogue, ensuring you are involved and informed about your child’s educational progress.

Prepare your 11th grader for academic excellence and personal growth with the Senior Philosophy Classroom Program at ScienceGenic. Enroll your child today and equip them with the knowledge and skills needed to excel in their studies and beyond!

Syllabus 11th CBSE Mathematics

Unit-I: Sets and Functions

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). Universal set. Venn diagrams. Union and Intersection of sets. Difference of sets. Complement of a set. Properties of Complement.

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 x R x R).Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special type of relation. Pictorial representation of a function, 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, with their graphs. Sum, difference, product and quotients of functions.

Trigonometric Functions

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 sin2x + cos2x = 1, for all x. Signs of trigonometric functions. Domain and range of trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple applications.

Unit-II: Algebra

Complex Numbers and Quadratic Equations

Need for complex numbers, especially√−1, to be motivated by inability to solve some of the quadratic equations. Algebraic properties of complex numbers. Argand plane

Linear Inequalities

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

Permutations and Combinations

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

Binomial Theorem

Historical perspective, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, simple applications.

Sequence and Series

Sequence and Series. Arithmetic Mean (A.M.) Geometric Progression (G.P.), general term of a G.P., sum of n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), relation betweenA.M. and G.M.

Unit-III: Coordinate Geometry

Straight Lines

Brief recall of two dimensional geometry from earlier classes. 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, Distance of a point from a line.

Conic Sections

Sections of a cone: circles, 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. Standard equation of a circle.

Introduction to Three-dimensional Geometry

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

Unit-IV: Calculus

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.

Unit-V Statistics and Probability

Statistics

Measures of Dispersion: Range, Mean deviation, variance and standard deviation of ungrouped/grouped data.

Probability

Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability, connections with other theories of earlier classes. Probability of an event, probability of ‘not’, ‘and’ and ‘or’ events.