DONATSciences and Maths
Mathematics · Simulations and virtual labs Free New

Mathematics simulations

Change the variables, read the results at once and see what happens. Every simulation comes with a virtual lab: steps, a results table, a graph and questions with answers. They work on any phone, tablet or computer. All simulations are free: no payment and no account.

Quadratic functions

Move a, b and c and watch the parabola change. Discover how the discriminant tells you the number of roots.

  • Levels: S3 (also S4)
  • You measure: Roots, vertex, y-intercept and the discriminant Δ for each curve.
  • Time: about 25–35 min · Free
▶ Open simulation🧪 Open virtual lab

Trigonometry: unit circle and graphs

Turn the angle on the unit circle and watch the sine and cosine graphs being drawn. Then use trigonometry outside: measure the height of a tree.

  • Levels: S4 · S5 (also S3)
  • You measure: sin, cos and tan of angles; angle of elevation and the height of a tree (m); amplitude and period.
  • Time: about 30–40 min · Free
▶ Open simulation🧪 Open virtual lab

Statistics explorer

Show the same data as a dot plot, histogram, box plot or cumulative frequency curve, add your own values and outliers, and watch the mean, median, quartiles and spread change.

  • Levels: S1 · S2 · S4 (also S3 · S5)
  • You measure: Mean, median, mode, quartiles, range, IQR and σ for each data set; r for two variables.
  • Time: about 30–40 min · Free
▶ Open simulation🧪 Open virtual lab

Sequences and series

Add terms one at a time to savings, a bouncing ball and growing bacteria, and watch the sums grow or settle to a limit.

  • Levels: S5 · S6 (also S3)
  • You measure: uₙ and Sₙ for each n; the sum to infinity when it exists.
  • Time: about 25–35 min · Free
▶ Open simulation🧪 Open virtual lab

Transformations on a grid

Move a triangle with translations, reflections, rotations and enlargements, combine two of them, and solve find-the-transformation challenges.

  • Levels: S2 · S3 (also S4)
  • You measure: Coordinates of A′, B′ and C′; the matrix; the area ratio for each transformation.
  • Time: about 30–40 min · Free
▶ Open simulation🧪 Open virtual lab

Vectors in 2D

Tap the grid to set two vectors, then add, subtract, scale them and find the angle between them.

  • Levels: S2 · S3 (also S4 · S5)
  • You measure: Components and magnitudes of a, b and the result; a · b and θ.
  • Time: about 25–35 min · Free
▶ Open simulation🧪 Open virtual lab

Limits of functions

Move x closer and closer to a point and watch what number f(x) approaches, from the left and from the right.

  • Levels: S4
  • You measure: Values of f(x) as x approaches a from the left and the right (or as x grows).
  • Time: about 25–35 min · Free
▶ Open simulation🧪 Open virtual lab
Want a simulation for another unit? Tell us on WhatsApp: 0788 804 242. New simulations are added regularly.
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Each simulation opens with its virtual lab on the same page: the steps, a results table, a graph and questions with answers. Teachers: every simulation has a “For teachers” section with expected results.