Sets are the opening chapter of Class 11 Mathematics and the foundation for almost everything that follows. You will learn what a well-defined collection of objects is, how to write a set in roster and set-builder form, and the different types of sets: empty, finite, infinite and equal. The chapter explains subsets, intervals, the power set and the universal set, then uses Venn diagrams to picture the operations of union, intersection, difference and complement, along with De Morgan's laws. The number of subsets, De Morgan's law and the counting formula are all proved step by step. With twelve worked examples and four graded practice sets, students preparing for board exams and competitive tests can revise, practice and excel.
Relations and Functions build the language that the rest of higher mathematics depends on. You will learn how ordered pairs join two sets through the Cartesian product, what makes a relation a function, and how to read the domain, co-domain and range. The chapter covers the standard real functions, namely the identity, constant, polynomial, modulus, signum and greatest integer functions, along with the algebra of adding, subtracting, multiplying and dividing them. Clear figures and worked examples show how every input is matched to exactly one output. With step-by-step solutions and graded practice, students preparing for board exams and competitive tests can revise, practice and excel.
Trigonometric Functions extend the trigonometry of right triangles to angles of any size using the unit circle. You will work with radian measure, the signs of the ratios in each quadrant, and the graphs and periodic nature of sine, cosine and tangent. The chapter develops the fundamental identities, the sum and difference formulae, and the double angle results, and then applies them to simplify expressions and prove identities. Real figures and patient, line-by-line working make each step easy to follow. With twelve solved examples and four graded practice sets, students preparing for board exams and competitive foundations can revise, practice and excel.
Complex Numbers and Quadratic Equations introduces the number i, whose square is minus one, so that every quadratic equation has a solution. You will learn to add, subtract, multiply and divide complex numbers, to find the modulus and conjugate, and to picture a complex number on the Argand plane. The chapter solves quadratic equations with negative discriminants and explains why complex roots always appear in conjugate pairs. Clear diagrams and step-by-step working make the algebra straightforward. With twelve worked examples, careful proofs and graded practice, students preparing for board exams and competitive tests can revise, practise and excel.
Linear inequalities turn from equations to comparisons, where two quantities need not be equal. You will learn to read the signs of inequality, the rules for solving them, and the important rule that multiplying or dividing by a negative number reverses the sign. The chapter shows how to solve inequalities in one variable and picture the answer on a number line, how to solve them in two variables by shading the correct half-plane, and how to handle systems of inequalities and their common region. With clear figures, line-by-line working and graded practice, students preparing for board exams and competitive foundations can revise, practice and excel.
Permutations and Combinations is the mathematics of counting arrangements and selections without listing them one by one. You will learn the Fundamental Principle of Counting, factorials and why zero factorial equals one, permutations where order matters, how to arrange objects when some are alike, and combinations where order does not matter. The chapter explains the difference between an arrangement and a selection with clear figures, and proves the formulae for nPr, nCr and the symmetry rule. With twelve worked examples and four graded practice sets shown step by step, students preparing for board exams and competitive tests can revise, practice and excel.
The binomial theorem gives a fast way to expand a bracket raised to a whole-number power without multiplying it out by hand. You will read the coefficients from Pascal's triangle, use the binomial coefficients nCr, and apply the general term formula to find any single term, the middle term, or the term independent of x. The chapter proves the general term, the sum of the coefficients and Pascal's rule, with clear figures and patient working throughout. With twelve worked examples and four graded practice sets shown step by step, students preparing for board exams and competitive foundations can revise, practice and excel.
Sequences and Series studies ordered lists of numbers and the neat formulae for adding them. You will work with arithmetic progressions, where each term increases by a fixed amount, and geometric progressions, where each term is multiplied by a fixed ratio, including the sum of a finite GP and of an infinite GP. The chapter also covers the arithmetic mean, the geometric mean and the relationship that the arithmetic mean is never less than the geometric mean. With proofs shown line by line, twelve worked examples and graded practice, students preparing for board exams and competitive tests can revise, practice and excel.
Straight Lines shows how a single equation can describe a line in the coordinate plane. You will learn to measure the slope, to tell when two lines are parallel or perpendicular, and to write the equation of a line in point-slope, two-point, slope-intercept, intercept and general form. The chapter also finds the distance of a point from a line and the distance between two parallel lines, with clear figures and step-by-step working. The point-slope form, the perpendicular condition and the slope of the general form are all proved. With graded practice, students preparing for board exams and competitive foundations can revise, practice and excel.
Conic Sections studies the four curves formed when a plane cuts a cone: the circle, parabola, ellipse and hyperbola. You will find the centre and radius of a circle, the focus, directrix and latus rectum of a parabola, and the foci, eccentricity and latus rectum of an ellipse and a hyperbola. The chapter shows how a single number, the eccentricity, ties all four curves together and proves the equations of the circle and parabola step by step. With clear summary tables, twelve worked examples, and graded practice, students preparing for board exams and competitive tests can revise, practice and excel.
Introduction to Three Dimensional Geometry adds a third axis so that points can be described anywhere in space, not just on a flat page. You will learn the three coordinate planes and the eight octants, how to read the coordinates of a point and the sign pattern of each octant, and how to find the distance between two points and the distance from the origin. The distance formula is proved by applying Pythagoras twice, with patient, line-by-line working. With twelve worked examples and four graded practice sets, students preparing for board exams and competitive foundations can revise, practice and excel.
Limits and Derivatives is the first taste of calculus, the mathematics of change. You will build an intuitive feel for a limit, the value a function approaches as the input nears a number, learn the algebra of limits and two standard limits, and then define the derivative from first principles as the slope of a curve. The chapter gives the rules for differentiating powers, sums, products and quotients, and the derivatives of sine and cosine. With the power rule, the sum rule and the derivative of sine all proved step by step, plus twelve worked examples and graded practice, students can revise, practice and excel.
Statistics looks beyond the average to measure how spread out a set of numbers is. You will learn the range, the mean deviation about the mean and the median, the variance and the standard deviation, the quick shortcut formula for variance, and the coefficient of variation for comparing consistency. The chapter shows clearly how a computation table is built, and proves the shortcut formula and how adding or multiplying by a constant changes the spread. With twelve worked examples and four graded practice sets shown step by step, students preparing for board exams and competitive foundations can revise, practice and excel.
Probability measures how likely an event is, on a clear scale from impossible to certain. You will learn what a random experiment, an outcome and a sample space are, the different types of events and the operations of union, intersection and complement, and the meaning of mutually exclusive events. The chapter builds probability from a few simple axioms, uses the rule of favourable outcomes over total outcomes, and proves the complement rule and the addition theorem step by step. With twelve worked examples and four graded practice sets, students preparing for board exams and competitive tests can revise, practice and excel.
