Apas · Learning content for schools and colleges

Teaching content that calculates, draws and moves

We make lessons, questions, notes and videos for your classes. Nothing below is a picture of our work: every calculation, diagram, graph and animation on this page is being made in your browser right now by our own engine.

Calculations

Exact mathematics, worked out and typeset

Answers are calculated, never typed in by hand. Fractions stay fractions, roots stay roots, and algebra and calculus are done in symbols, so a solution cannot carry an arithmetic slip into the classroom.

What the author writesWhat the engine gives
Questions

One question, as many versions as you need

A question is written once with its numbers left open. Each press below gives the same question with new numbers, and the answer and the full solution are worked out again to match. Useful for practice sheets, different sets for different sections, and retests.

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How this question is written
Diagrams

Diagrams drawn from a description, stroke by stroke

Circuits, geometry, force diagrams and more are described in a few lines and drawn to scale. They can appear part by part, the way a teacher builds a figure on the board.

A circuit, built branch by branch

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A 3, 4, 5 triangle, side by side

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Animated graphs

Graphs that draw themselves

Give the formula and the graph is plotted from it. Ordinary, polar and parametric curves can trace themselves so students watch the shape form.

Sine and cosine together

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How it is written

A polar curve: the cardioid

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A parametric curve: Lissajous

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Animations

Motion computed from the physics

An animation is a formula for where things are at each moment. The engine works out every frame, so the motion on screen is the motion the equations give.

A projectile: 20 m/s upward, 10 m/s forward

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How it is written

Circular motion and its shadow on the x axis

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How it is written
Video lessons

Narrated lessons, ready for the classroom screen or a phone

The same diagrams, graphs and calculations are put in order, narrated, and recorded as a short video. Each lesson explains one topic or solves one exam question in about two minutes, in English or in Hindi.

Printable notes

Teaching notes as PDFs, ready to print and hand out

Questions with complete solutions, figures and graphs, set as A4 pages. These three are from our physics course; open any of them to read it in full.

What this gives a school or college

One source, every form you teach in