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Saturday, 10 October

85 simulations · 27 chapters

Maths simulations

Lumi has 85 free interactive Maths simulations for JEE, on the NCERT syllabus: 59 in Class 11 (14 chapters) and 26 in Class 12 (13 chapters). Each one lets you move a slider, drag a point or change a value and watch the idea respond, and each sits inside a lesson with the notes.

Also: Physics (187), Chemistry (115), Biology (180) · Maths lessons

Sets · Class 11

4
Element or subset?In: SubsetsBuild an intervalIn: Intervals as subsets of RShade the regions of a Venn diagramIn: Complement and De Morgan's lawsThe complement depends on UIn: Complement and De Morgan's laws

Relations and Functions · Class 11

5
A × B is not B × AIn: Working with Cartesian productsRelation or function?In: FunctionsFour standard graphsIn: Signum and greatest integer functionsDomain and range as shadowsIn: Domain and range of real functionsAdding and dividing functions point by pointIn: Algebra of real functions

Trigonometric Functions · Class 11

8
What one radian looks likeIn: Radian measure and arc lengthSine and cosine on the unit circleIn: Sine and cosine on the unit circleAll six values from oneIn: Signs in the four quadrantsThe six graphs and their periodsIn: Domain, range and graphsWhy sin (A + B) is not sin A + sin BIn: Sine and cosine of sums and differencesAllied angles are mirror imagesIn: Allied anglestan (A + B) as the slope of a turned lineIn: Tangent and cotangent of sumsDoubling the angle is not doubling the valueIn: Double and triple angle formulas

Complex Numbers and Quadratic Equations · Class 11

5
Powers of i go round in foursIn: Powers of iWhen √a × √b is not √(ab)In: Square roots of negative numbersMultiplying by the conjugate makes a real numberIn: Modulus and conjugatePoints of the Argand planeIn: The Argand planeWhere the roots go when D turns negativeIn: Quadratics with a negative discriminant

Linear Inequalities · Class 11

3
Multiplying by x when you do not know its signIn: Rules for solving an inequalitySolve and draw a linear inequalityIn: Showing solutions on the number lineWhere two conditions overlapIn: Systems of inequalities in one variable

Permutations and Combinations · Class 11

6
Fill the places, then countIn: Permutations of distinct objectsGlue them together, or keep them apartIn: Arrangements with conditionsTag the twins, then take the tags offIn: Permutations with repeated objectsSelections, and the orders inside themIn: CombinationsPatterns in the table of nCrIn: Properties of combinationsWhere a word sits in the dictionaryIn: Selecting then arranging, and dictionary order

Binomial Theorem · Class 11

4
Pick a or b from every bracketIn: Coefficients as nCrFind any term of (a + b)ⁿIn: The general termTrack the power of x in every termIn: The general termEstimate (1 + x)¹⁰ term by termIn: Numbers, estimates and remainders

Sequences and Series · Class 11

3
What the common ratio doesIn: Geometric progressionsSteady jar against doubling jarIn: Summing n terms of a GPThe A.M. is never below the G.M.In: AM and GM

Straight Lines · Class 11

4
Slope and intercepts of y = mx + cIn: Slope from two pointsTurn the slope triangle through 90°In: Parallel and perpendicular linesThe angle between two linesIn: Angle between two linesHow far is the point from the line?In: Point-to-line distance

Conic Sections · Class 11

7
Slice a double coneIn: Sections of a coneComplete the square, find the circleIn: The circleFocus, directrix and the parabolaIn: Parabola and its standard formsA string, two pins and an ellipseIn: Ellipse: foci and axesRead a and b off the equationIn: Standard equations of an ellipseA hyperbola keeps a constant differenceIn: Hyperbola: foci and axesWhy reflectors are parabolicIn: Conics in applied problems

Introduction to Three Dimensional Geometry · Class 11

2
Which octant is P in?In: The eight octantsPythagoras twice: the distance across a boxIn: Distance between two points

Limits and Derivatives · Class 11

2
How fast at exactly 2 s?In: From average speed to instant speedDo both sides agree?In: Left and right hand limits

Statistics · Class 11

4
Where is the total distance least?In: Mean deviation for ungrouped dataFind the median class, then the medianIn: Mean deviation for class intervalsSquares on the deviationsIn: Variance and standard deviationShift the scores, stretch the scoresIn: Shifting, scaling and correcting data

Probability · Class 11

2
Load the six and watch every faceIn: Probability of an eventCount the overlap onceIn: Probability of A or B

Relations and Functions · Class 12

2
Build a relation on {1, 2, 3}In: Equivalence relationsOne-one, onto, or both?In: Onto and bijective functions

Inverse Trigonometric Functions · Class 12

2
Pick a branch of sin⁻¹In: sin⁻¹ and its principal branchDoes sin⁻¹ undo sin?In: Undoing an inverse

Matrices · Class 12

2
Row by columnIn: Multiplying row by columnTwo moves, two ordersIn: Order matters in a product

Determinants · Class 12

2
Determinant as an areaIn: Second-order determinantsTwo lines, one determinantIn: Consistent and inconsistent systems

Continuity and Differentiability · Class 12

2
Left and right limitsIn: Continuity at a pointSecant to tangentIn: Differentiability

Application of Derivatives · Class 12

2
How fast a ripple's area growsIn: Rate of changeWhere f rises, falls and turnsIn: Increasing and decreasing functions

Integrals · Class 12

2
One derivative, a whole familyIn: Antiderivatives and the constant CThe area functionIn: The definite integral and the fundamental theorem

Application of Integrals · Class 12

2
Adding up thin stripsIn: Area from thin stripsWhen the integral and the area disagreeIn: Regions below the x-axis

Differential Equations · Class 12

2
A family of solution curvesIn: General and particular solutionsHow long to double?In: Growth, decay and cooling

Vector Algebra · Class 12

2
Tip to tailIn: Adding vectorsShadow and areaIn: Vector (cross) product

Three Dimensional Geometry · Class 12

2
Walk the lineIn: Equation of a lineSkew gapIn: Skew lines and the shortest distance

Linear Programming · Class 12

2
Hunt for the most profitable planIn: The corner point methodSlide the profit lineIn: Multiple optimal solutions

Probability · Class 12

2
Shrink the sample spaceIn: Conditional probabilityFlip the conditionIn: Bayes' theorem