Short interactive lessons that ask a question before they explain. One session takes about ten minutes and ends with questions to check what you have understood.
One number fixes a point on a line; a point in a plane needs two, measured along perpendicular axes.
Class 9 · Maths Coordinates FreeThe axes, the origin and the ordered pair (x, y). The x-coordinate is the distance from the y-axis.
Class 9 · Maths Coordinates FreeFour quadrants, four sign patterns. (3, 5) and (5, 3) are different points, and reflection changes one sign.
Class 9 · Maths Coordinates FreeThe coordinate differences are the legs of a right triangle, and the Baudhayana-Pythagoras theorem gives the distance.
Class 9 · Maths Coordinates FreeThe midpoint is the average of the coordinates. The same idea finds a missing endpoint and the trisection points.
Class 9 · Maths Coordinates FreeWidths, overlaps of circles and collinearity, all calculated from coordinates on floor plans, grids and screens.
Class 10 · Maths Real Numbers FreeEvery composite number is a product of primes in exactly one way, apart from order.
Class 10 · Maths Real Numbers FreeThe HCF is the shared primes at their smaller powers; the LCM is all the primes at their larger powers.
Class 10 · Maths Real Numbers FreeFor two numbers, HCF × LCM equals their product. Prime factorisations decide divisibility questions for every case at once.
Class 10 · Maths Real Numbers FreeA fraction in lowest terms terminates exactly when its denominator has no prime factors other than 2 and 5.
Class 10 · Maths Real Numbers FreeAssume √2 is a fraction in lowest terms and show both parts are even: proof by contradiction.
Class 11 · Maths Sets FreeA set is a well-defined collection, written in roster form or in set-builder form.
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