169 lessons
9:15Two worked matrix problems: find the unknown in the relation A squared equals kA minus 2I for a 2 by 2 matrix, then prove a 3 by 3 matrix satisfies A cubed minus 23A minus 40I equals the zero matrix.
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15:20Worked solutions to the key questions of Exercise 3.3 on the transpose of a matrix, covering how to find a transpose, verifying the transpose identities, and splitting a matrix into symmetric and skew-symmetric parts.
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5:15A Class 12 worked question from Exercise 3.2: given the rotation matrix f(x), multiply f(x) by f(y) and use the angle-addition formulas to show the product equals f(x + y).
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18:35An introduction to multiplying matrices for Class 12: when two matrices can be multiplied, the row-into-column method, and the laws that matrix multiplication obeys, worked through several questions from Exercise 3.2.
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17:00Worked solutions to selected questions from Class 12 matrices Exercise 3.2, covering matrix addition with algebraic identities, trigonometric matrices, and solving for unknown matrices and variables.
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6:20Learn how to add and subtract matrices of the same order, multiply a matrix by a scalar, and apply the main properties of matrix addition.
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22:16A first lesson on matrices: what a matrix is, how to read its order, how to build a matrix from a formula for its entries, the common types of matrices, and how to use equality of matrices to find unknowns.
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9:05Two short Class 12 derivative questions: a logarithmic differentiation proof and the second derivative of a parametric function.
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8:09Two worked short questions on finding the area of a shaded region using definite integration, covering a region bounded by a parabola and a line, and a region under a sideways parabola.
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7:31Worked solutions to three short questions from a Class 12 pre-board model paper: an inverse trigonometry evaluation, a differentiation proof, and an integration using the e^x rule.
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5:22A worked 3D geometry problem: find the foot of the perpendicular from a point to a line, the image of the point in that line, and the perpendicular distance.
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18:18Eight high-yield three-mark questions worked end to end for Class 12 board prep, spanning vectors, conditional probability, definite integrals, and 3D coordinate geometry.
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7:31A worked proof showing that the curves 2x = y squared and 2xy = k intersect at right angles exactly when k squared equals 8, using derivatives to find the slopes of the tangents.
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4:32A class 10 trigonometry proof showing that a sum of three trigonometric terms simplifies to the constant 13, completely independent of the angle theta.
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8:20Two important Class 10 trigonometric identity proofs that use the Pythagorean identities to rewrite and simplify each expression step by step.
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7:33Two frequently asked Class 12 integration problems worked end to end, using clever substitutions to turn awkward roots into standard forms.
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5:51A step-by-step proof of the standard result that the integral of log sin x from 0 to pi/2 equals minus pi over 2 times log 2, using the properties of definite integrals.
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7:43A full walkthrough of Question 19 from the Chapter 7 (Integration) miscellaneous exercise: integrating the square root of (1 minus root x) over (1 plus root x) using a trigonometric substitution.
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4:19A worked Class 12 integration problem showing how to integrate log(log x) plus one over (log x) squared using integration by parts twice.
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15:54Step by step proofs of six trigonometric identities from Class 10 Exercise 8.3, working each side back to known results like sec, tan, and the Pythagorean identity.
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13:08Worked proofs from Exercise 8.3 of the Class 10 trigonometry chapter, showing how to prove identities by simplifying one side until it matches the other.
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7:00Two worked trigonometric identity proofs from Class 10 Exercise 8.3, using the conjugate trick and the Pythagorean identities.
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8:17Worked proofs of seven trigonometric identities from Exercise 8.3, showing how to convert everything to sine and cosine and simplify each side.
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6:17A worked distance, speed and time word problem that turns into a quadratic equation. We find the original duration of a 600 km flight that was slowed down by bad weather.
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9:53Learn the sign rules for multiplying and dividing positive and negative numbers, then apply them to worked examples including brackets and zero.
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6:06Learn the sign rules for multiplying and dividing positive and negative numbers, then apply them to worked examples including expressions with brackets.
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9:52Learn the simple rules for adding and subtracting positive and negative numbers, worked through with many step-by-step examples (Malayalam explanation).
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6:58Learn the sign rules for adding and subtracting positive and negative numbers, then apply them to longer expressions with brackets.
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7:16Five worked simplifications of inverse trigonometric expressions, using trig substitutions and the tangent compound-angle identities to reduce each one to a clean closed form.
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10:03Worked solutions to the key questions of Class 12 inverse trigonometry Exercise 2.2, using the substitution trick to prove identities and simplify expressions.
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3:44A quick reference run through the key inverse trigonometry identities for Class 12, covering negative arguments, complementary pairs, and the double-angle and sum results.
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12:52Learn how to find the principal value of inverse trigonometric functions, using their domains and ranges together with the quadrant signs to pick the correct angle.
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7:39A step-by-step guide to simplifying numerical expressions with the BODMAS rule, worked through several examples that mix brackets, powers, division, multiplication, addition, and subtraction.
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9:42How to simplify numerical expressions with the DMAS rule, doing division first, then multiplication, then addition, then subtraction, worked through ten examples.
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11:25Work through five proof-style derivative problems involving logarithmic and exponential functions, using the chain rule, the quotient rule, and the laws of logarithms.
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10:55A run through the standard algebraic identities, applying each one to expand expressions and to evaluate numbers like 102 squared or 105 times 95 quickly.
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8:02Solve three linear equations in one variable that mix fractions and decimals, clearing denominators and using cross multiplication to reach the answer.
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7:00Worked practice in simplifying algebraic expressions by expanding brackets, multiplying each term, and collecting like terms.
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11:59Multiply algebraic expressions, substitute given values to evaluate them, and then add or subtract the products using the column and row methods.
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6:46Learn how to multiply algebraic expressions, from simple monomials to multiplying two and three term polynomials, through ten fully worked examples.
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6:37Learn how to solve linear equations in one variable using transposition, collecting like terms, clearing fractions with the LCM, and cross multiplication.
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12:26Learn how to add and subtract algebraic expressions by collecting like terms, using both the column method and the row method, with several worked examples.
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6:45Learn how to divide algebraic terms by combining the sign rules, dividing the number coefficients, and subtracting the powers of each variable, with several worked examples.
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4:02Learn how to multiply algebraic terms by combining the sign rules, the numerical coefficients, and the laws of exponents, with several worked examples.
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14:07An introduction to algebraic expressions and how to add and subtract their terms. Covers terms, coefficients, like and unlike terms, and the sign rules for combining like terms.
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7:03Worked solutions to four integration problems from Class 12 Miscellaneous Exercise 7, covering rationalising a definite integral, partial fractions, a clever substitution, and a definite-integral property.
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12:00A worked walkthrough of high-yield 2-mark questions from previous CBSE Class 10 board papers, spanning trigonometric identities and evaluations, probability, circle tangents, quadratics, arithmetic progressions, and coordinate geometry.
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11:09Worked solutions to four integration problems from CBSE Class 12 Miscellaneous Exercise 7, using half-angle identities, substitution, and the integral of e to the x times a function plus its derivative.
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4:24A quick run through ten one mark questions from older Class X CBSE board papers, covering polynomials, sectors, LCM and HCF, probability, trigonometry, discriminants, and coordinate geometry.
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15:33A step-by-step walkthrough of ten high-yield 2-mark questions from previous CBSE Class 10 board papers, covering trigonometry, coordinate geometry, probability, arithmetic progressions, quadratic polynomials, and prime factorisation.
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11:42Worked solutions to three integration questions from Class 12 Miscellaneous Exercise 7, using substitution, integration by parts, and partial fractions.
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13:03Worked solutions to six integration problems from Miscellaneous Exercise 7 of class 12, showing how to simplify, substitute, and use partial fractions to evaluate each integral.
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14:48Worked solutions to the first five questions of the Class 12 integration miscellaneous exercise, using partial fractions, conjugates, and clever substitutions.
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10:05Learn how to find a square root correct to two decimal places using the long division method, working two places further and then rounding.
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7:56Find the square root of decimal numbers that are not perfect squares, using the long division method to a chosen number of decimal places.
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5:59Learn how to find the square root of decimal numbers using the long division method, worked through three examples: 6.25, 10.24, and 5.0625.
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11:08Learn the long division method for finding the square root of perfect squares, worked through three, four, five and six digit examples.
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6:07A quick shortcut for pairs of linear equations where the x and y coefficients are swapped between the two equations, solved by adding and subtracting instead of full elimination or substitution.
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10:28Three worked examples that solve pairs of linear equations in two variables using the elimination method, including equations with literal coefficients.
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9:34Three exam-favourite integration problems for Class 12, solved step by step using algebraic identities, substitution, and integration by parts.
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5:08Two exam-style quadratic equation problems for Class 10: proving a condition for equal roots using the discriminant, and finding a train's speed from a word problem.
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7:27Use a given matrix product that equals the identity to find an inverse, then solve a three-variable system of linear equations by the matrix method.
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11:00Evaluate the definite integral of x divided by a squared cosine squared x plus b squared sine squared x from 0 to pi, the last and most important question of the miscellaneous exercise.
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8:17Evaluate the definite integral of a sum of absolute value functions by splitting the range at the points where each modulus changes sign.
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7:49Worked solutions to ten multiple-choice questions from previous Class 12 board papers, covering inverse trigonometry, matrices and determinants, definite integrals, vectors, linear programming, and probability.
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14:14Worked solutions to twenty one-mark MCQ questions from Class 12 board papers, spanning inverse trigonometry, matrices, determinants, vectors, and differential equations.
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5:57Two worked problems on areas related to circles: the area a triangular field can be grazed by tethered horses, and the area left after cutting quadrants from a rectangle.
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6:26Three sure-shot Class XII board integration questions worked end to end, each using a different standard technique.
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6:26Three likely board exam integration problems worked in full, covering integrals with an exponential factor, a substitution, and integration by parts.
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10:30Two exam-style vector questions worked in full: finding the values of a parameter that make the angle between two vectors obtuse, and proving the magnitude of a sum of three mutually balanced vectors.
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7:40Work through two Class 12 three-dimensional geometry questions: proving two lines intersect and finding the meeting point, then finding the value that makes two lines perpendicular.
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4:57A Class 12 3D geometry problem: find the foot of the perpendicular from a point to a line, the image of the point in that line, and the distance from the point to the foot.
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9:14Three worked Class 12 questions on 3D lines: writing the equation of a line through a point in a given direction, and finding the shortest distance between skew lines and between parallel lines.
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6:32Three worked Class 12 probability questions: drawing balls with replacement, finding a posterior probability with Bayes' theorem, and testing whether events from three coin tosses are independent.
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5:19A reference guide to converting between units of length, area, volume, mass, capacity, money, time, and speed, listing the factor to multiply or divide by for each change.
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6:57Use the vector cross product to find the area of a triangle, a parallelogram, and a rectangle from the position vectors of their vertices.
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10:14Worked solutions to Class XII vector cross product problems from Exercise 10.4, covering magnitudes, perpendicular unit vectors, direction cosines, and the angle between two vectors.
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10:21Worked solutions to the dot product questions from Exercise 10.3, covering angles between vectors, projections, unit vectors, and applications to a triangle.
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6:40A formula reference for the scalar (dot) product and vector (cross) product of two vectors, including projections, angles, areas, and component formulae.
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6:12Three worked exam questions on areas of shaded regions, sectors, and the area swept by a clock's minute hand, from the Class 10 chapter Area Related to Circles.
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9:46Works through the remaining problems of Exercise 10.2 on vectors: the section formula for internal, external, and midpoint division, plus proving a right-angled triangle, testing collinearity, and finding direction cosines.
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8:30Worked solutions to the first questions of Class 12 Exercise 10.2, covering the magnitude of a vector, equal vectors, scalar and vector components, sums of vectors, and finding unit vectors.
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9:22Worked proofs of the remaining trigonometric identities from CBSE Class 10 Exercise 8.3, including a longer exam-favourite proof solved step by step.
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12:11Worked proofs from Class 10 Exercise 8.3, showing how to prove several trigonometric identities by switching to sine and cosine and using the Pythagorean relations.
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10:46A set of likely Class 10 board questions on trigonometric identities, from expressing every ratio in terms of cot A to multiple choice simplifications and full identity proofs.
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8:52Two important CBSE definite integral problems solved with the standard properties: the king rule for swapping limits, and the proof that the integral of log sine from 0 to half pi equals minus half pi times log 2.
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11:30Worked solutions from Exercise 8.2: finding triangle angles from a known ratio, solving angle systems with standard ratios, and evaluating and proving expressions built from special angles.
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7:56Worked solutions from Exercise 8.1: finding all trigonometric ratios from one given ratio and from right triangles built with the Pythagoras theorem.
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12:38More worked questions on the properties of definite integrals, including the complementary substitution that replaces x with a minus x, and the odd and even function rules.
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12:06Learn how to evaluate definite integrals that contain a modulus (absolute value) by splitting the interval where the inside of the modulus changes sign, using property P2 from Exercise 7.10.
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5:48Evaluate definite integrals over symmetric limits by first testing whether the function is odd or even, using property P7 from Exercise 7.10.
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10:21Work through Class XII definite integrals of trigonometric functions using the substitution method, including how to change the limits when you change the variable.
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9:22A worked walkthrough of selected definite integrals of trigonometric functions from Exercise 7.8, evaluating each integral using standard results and substituting the limits.
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11:46Work through sure-shot Class XII definite integral questions from Exercise 7.10, solving each by a suitable substitution and handling the limits two ways.
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9:38An introduction to right triangle trigonometry covering the six trig ratios, the reciprocal and square (Pythagorean) identities, and the standard values for the special angles.
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10:10A walkthrough of seven definite integral questions for Class 12, applying limits with the fundamental theorem and techniques like partial fractions, a standard formula, and substitution.
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12:11Solve classic motorboat upstream and downstream word problems by turning the time conditions into quadratic equations and finding the speed of the stream.
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13:25Solve Class 10 speed, time and distance word problems by setting them up as quadratic equations and finding the speed of a train two ways.
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8:43Three worked word problems on quadratic equations: consecutive odd integers, a marks problem, and the sides of a rectangular field, each set up and solved by factorisation.
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6:24Learn the special integral rule for exponential functions and use it to solve six worked questions, including ones where you first rearrange the integrand to fit the pattern.
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7:17Integrate products of an exponential and a trig function using integration by parts and the returning-integral trick, worked through two full examples.
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11:48Work through seven integration by parts problems involving trigonometric and inverse trigonometric functions, using the ILATE rule to choose the first and second functions.
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13:16Learn how to find the square root of a decimal or whole number using the long division method, then round the answer to a set number of decimal places.
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14:22Learn how to find the square root of a decimal number using the long division method, including how to group the digits around the decimal point and how to handle numbers that are not perfect squares.
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14:56Eight exam-favourite integration by parts problems for Class 12, worked step by step using the ILATE rule to choose the first and second functions.
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12:09A set of worked exam style coordinate geometry questions for Class X, all built on the section formula: finding ratios of division, points on the axes, midpoints, trisection points, and a triangle's centroid.
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14:00A set of exam-style coordinate geometry questions for Class 10, covering distance, collinearity, the section formula, and finding unknown coordinates.
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13:56Four Class 12 integration questions from Exercise 7.5, each solved by substituting to remove the trigonometry or the square term, then splitting into partial fractions.
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9:06Four worked integrals that combine a substitution with partial fractions, from the Class 12 integrals exercise. Each one is reduced to a simple rational function and then split into partial fractions to integrate.
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5:33A quick revision of the key results and formulae of coordinate geometry, the kind needed for one mark questions: quadrants and signs, the distance and section formulae, the midpoint, and the centroid.
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13:49More Class 12 integration problems from Exercise 7.5, solved with partial fractions, including cases where you must divide first and a neat shortcut for integrals like one over x times x to the n plus one.
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14:29Learn how to integrate rational functions by splitting them into partial fractions, worked through three Class 12 examples with distinct, repeated, and mixed linear factors.
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3:38An introduction to partial fractions before integration, setting out the six standard forms used to split a proper rational function into simpler pieces.
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10:32How to integrate a linear expression over a quadratic, and over the square root of a quadratic, by splitting the numerator into a multiple of the derivative of the quadratic plus a constant.
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11:28Class 12 integration: how to handle integrals with a quadratic in the denominator or under a square root by completing the square and reducing them to standard forms.
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14:33Class 12 integration using the standard special-form formulas, working through integrals that reduce to logarithm, inverse tangent, and inverse sine results.
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14:49More worked solutions from Exercise 7.3, integrating tricky trigonometric and exponential expressions by choosing the right substitution and simplifying first.
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11:29More worked integrals from Exercise 7.3 of Class 12 Integration, using trigonometric identities and substitution to simplify each integrand before integrating.
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9:30Worked solutions to the first set of integrals from Exercise 7.3, using trigonometric identities and substitution to integrate powers of sine and cosine.
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16:29Solve the Class 12 Exercise 7.2 integration problems involving trigonometric functions, each cracked by choosing the right substitution.
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8:02Four exam-style Class 12 integrals solved by substitution, including a special case where you adjust the numerator before substituting.
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11:37Eight worked Class 12 integrals solved by the substitution method, including how to spot a function and its derivative and how to handle exponential expressions.
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11:26A worked set of straightforward integration problems for Class 12, focused on trigonometric integrands and recovering a function from its derivative using a given condition.
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5:07A quick reference run-through of the standard integration formulas for Class 12: basic results, the rules for constants and sums, integrals of special forms, and the integration by parts formula.
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8:17Five worked indefinite integrals for Class XII, showing how to simplify each integrand before integrating term by term.
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8:39Learn how to differentiate parametric functions, where x and y are both given in terms of a parameter, using the chain-rule formula and three fully worked examples.
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10:44Two exam-style differentiation problems worked in full: finding dy/dx for the implicit equation x to the power y plus y to the power x equals 1, and evaluating the derivative of a four-factor product at x equals 1.
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12:27Three worked problems on logarithmic differentiation: proving the product rule for a product of three functions, and differentiating equations where the variable appears in the exponent.
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12:25Learn how to differentiate functions raised to powers, complicated products, and quotients by taking logarithms first. Three worked examples show the full method step by step.
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6:24Differentiate three inverse trigonometric functions by first simplifying each with a clever substitution. A worked Class 12 example set on finding dy/dx.
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8:05Derive the derivatives of all six inverse trigonometric functions using implicit differentiation and basic trigonometric identities.
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6:45Learn how to find dy/dx for equations where trigonometric functions tie x and y together implicitly, through four fully worked examples.
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7:21Two worked Class 12 problems on implicit differentiation: proving a derivative identity for a general conic and finding the derivative of a nested square-root function.
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10:43Learn how to differentiate implicit functions, where x and y are mixed together in one equation, and find dy/dx step by step.
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14:15Learn how to differentiate a function of a function using the chain rule, worked through many algebraic, exponential, logarithmic, and trigonometric examples.
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2:43A quick reference run-through of the standard derivative formulas: power, root, reciprocal, exponential, logarithmic, trigonometric, and inverse trigonometric functions, plus the basic rules of differentiation.
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12:41Learn the elimination method for solving a pair of linear equations in two variables, deciding when to add the equations and when to subtract them.
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6:42A quick method for solving a pair of linear equations where the coefficients of x and y are swapped between the two equations, avoiding large numbers.
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10:25Worked solutions to the sure questions on symmetric and skew-symmetric matrices: proving that a skew-symmetric matrix has zero diagonal entries, and expressing a square matrix as the sum of a symmetric and a skew-symmetric part.
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5:14Verify that a 2 by 2 matrix A satisfies the equation A squared minus 3A minus 7I equals zero, then use that relation to find the inverse of A without computing a determinant.
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8:58Learn what the transpose of a matrix is and how to use it to show that a matrix plus its transpose is symmetric, its difference is skew symmetric, and that the transpose of a product reverses the order.
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9:00A notes lesson on the transpose of a matrix: its definition, its main properties, symmetric and skew symmetric matrices, and proofs of the two key theorems about them.
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11:44Worked solutions to commonly asked Class 12 matrix questions, covering the commutative and associative laws of matrix addition, solving for unknowns in a matrix equation, and finding a constant from a matrix product.
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0:59Find the second derivative of a curve given parametrically by x = sin θ and y = cos θ, working through the chain rule step by step.
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10:17Find the square root of five and six digit perfect squares using the long division method, worked through three full examples.
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11:18Learn the long division method to find the square root of three and four digit perfect squares, step by step through several worked examples.
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5:21Three board-style proofs about symmetric and skew-symmetric matrices, using the transpose properties of matrix products.
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0:42A quick look at how to build a quadratic polynomial when its two zeros are known, using the sum and product of those zeros.
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5:39Two exam-style polynomial questions solved with cube identities: finding a difference of cubes from a linear relation and a product, and proving a three-term sum of cubes factorises neatly.
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5:02A quick reference run-through of the standard algebraic identities, covering the squares and cubes of binomials and the related factorisation formulae.
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0:23A short worked example finding the common difference of an arithmetic progression when the sum of the first n terms is given as n squared.
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14:02An easy method for multiplying and dividing fractions without taking the LCM, including handling signs, mixed numbers, and cancelling before you multiply.
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10:27Learn how to subtract fractions with different denominators by finding the LCM, rewriting each fraction over a common denominator, and subtracting. Worked through with several examples, including mixed numbers and a negative result.
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10:14Learn how to add fractions with different denominators by finding the LCM, rewriting each fraction over a common denominator, and adding the numerators. Worked through with several examples, including mixed numbers and sums of three fractions.
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11:15Learn the sign rules for multiplying and dividing positive and negative numbers, including how zero behaves and why dividing by zero is undefined.
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13:53A clear, step-by-step introduction to adding and subtracting positive and negative numbers, with the sign rules and plenty of worked examples.
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18:32A Class XII multiple-choice walkthrough of matrix basics, covering order and number of elements, the general form of a matrix, and the main special matrix types.
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31:03A second set of worked CBSE Class 10 Real Numbers questions, covering LCM and HCF by prime factorization, why certain numbers can never end in zero, spotting composite numbers, proofs that surds like the square root of two are irrational, and two word problems on HCF and LCM.
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24:38A quick-revision run through the most important one-word and short-answer questions on real numbers, covering number sets, the Fundamental Theorem of Arithmetic, and finding LCM and HCF.
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15:15Learn what makes a function injective, surjective or bijective, with two fully worked Class XII examples that prove a function is one to one but not onto, and that another is bijective.
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16:39Worked CBSE board questions on proving a relation is an equivalence relation and finding the domain and range of real functions.
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14:52A walkthrough of high-yield Class 12 three-dimensional geometry questions: finding the image of a point in a line, and converting line equations between Cartesian and vector form.
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19:38Three exam-style 3D geometry problems on lines in space: proving two lines intersect and finding the point, finding the value that makes two lines perpendicular, and finding the direction cosines of a parallel line.
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27:57A revision of the key quadratic equation facts and formulae, then worked solutions by factorisation and by the quadratic formula.
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21:23A formula walkthrough of three dimensional geometry: direction cosines and ratios, the equations of a line, the angle between two lines, and the distance between skew and parallel lines.
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36:01A worked set of Class X polynomial questions: finding degrees and zeros, building quadratic polynomials from their zeros, and factorising quadratics using sum and product rules.
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14:44A rapid revision of the key one-word questions on polynomials, covering degree, zeros, linear, quadratic, and cubic polynomials, and the relationships between zeros and coefficients.
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12:53A quick recap of the arithmetic progression formulae, then four exam-style questions on counting terms and finding a first negative or middle term.
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2:34Three worked exam questions on arithmetic progressions for Class 10, covering how to read the common difference from the nth term and how to use the sum formula.
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