Mathematics

Scale a square and compare the original with the enlarged copy. The side length changes by k, while the area changes by k². The grid reveals the extra rows as well as the extra columns.

02Trigonometry

Trigonometric ratios

Sine, cosine and tangent compare the sides of a right triangle. Reshape the triangle with the angle slider, then resize it: the ratios depend on the angle, not the size.

Suggested-level exploration

03Algebra

Quadratic graphs

A quadratic graph is a parabola. Change a to turn it upwards or downwards and adjust its width. Change c to move its vertex along the vertical axis.

04Geometry

Coordinate geometry

Move point B while A stays at the origin. Horizontal and vertical distances form a right triangle whose hypotenuse is the distance AB.

05Sequences

Arithmetic progressions

An arithmetic progression adds the same common difference each time. Change the first term and common difference to build an increasing, decreasing or constant sequence.

06Mensuration

Area of a circle

A circle’s area grows with the square of its radius. Compare it with a sector cut out by a central angle. The graph shows sector area as radius changes, with angle held fixed.

Suggested-level exploration

07Sequences

Geometric progressions

A geometric progression multiplies by a common ratio. Explore the nth term for different positive ratios and first terms.

08Geometry

Similar shapes

Scale every length of a rectangle by the same factor. The original rectangle is 4 cm long; choose its width. The new area changes with the square of the scale factor.