Lab

See the idea. Put it to the test.

956 practicals from Kindergarten to Year 12, in 9 subjects. A practical gives the idea, what you need, the steps, what you should see and a safety card. A teacher-led practical gives the idea and its hazards; its method is for tutors on the learning platform.

Review

Reviewed before publication (owner’s confirmation, 24 September 2026). That covers every practical here, and a practical’s page lists the sources its author read.

A safety card on every page

The risk, who supervises and the hazards. The 38 teacher-led practicals show their idea and hazards here; their materials, steps and sources, and any result, control or note that states a number or an amount, are for tutors and administrators on the learning platform.

School laboratory, not for home

207 practicals are medium or high risk. Each says so on its page: In a school laboratory, with a teacher supervising, under the school's risk assessment. Not for home.

Curriculum references

Each practical lists the NSW syllabus outcomes and Australian Curriculum v9 codes it supports. They are references, not a verified or complete curriculum alignment.

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A practical is carried out at the bench, in the classroom or outdoors. A practical with its model not built stands on its own; the page says where a step mentions the model. A calculation and data practical works from published figures by hand, with a calculator or in a spreadsheet. No Lab page includes an interactive model; the Concept Studio holds the demonstrations.

202 practicals

Mathematics · page 5 of 5

  1. Mathematics 11–12 · Year 12

    Mass on a spring and a conical pendulum: period against mass, radius and angle

    A restoring force proportional to displacement gives simple harmonic motion whose period depends on the mass and the stiffness and not on the amplitude, and resolving the tension in a whirled line gives a conical pendulum whose period depends on the line length and the cone angle and not on the mass.

    Practical, model not builtLow risk
  2. Mathematics 11–12 · Year 12

    Means of dice: the sampling distribution of the mean and the central limit theorem

    A single die is flat, but the mean of ten dice is bunched around 3.5 with a spread that shrinks with the square root of the sample size, and its distribution looks normal although the population does not.

    Practical, model not builtLow risk
  3. Mathematics 11–12 · Year 12

    Setting up the hall: critical path analysis from timed activities

    When activities depend on one another, the longest chain of dependent activities fixes the shortest possible completion time, and activities off that chain have float.

    Practical, model not builtLow risk
  4. Mathematics 11–12 · Year 12

    Simple and compound interest at a real savings rate from the Reserve Bank

    Compound interest adds interest to the balance each period, so the balance grows geometrically, and compounding more often at the same annual rate adds slightly more each time.

    Calculation and dataLow risk
  5. Mathematics 11–12 · Year 12

    Superannuation as an annuity: 12 per cent super guarantee over a working life

    Equal contributions that each earn compound interest add to a geometric series, so the future value of an annuity has a closed form and grows much faster than the sum of the contributions.

    Calculation and dataLow risk
  6. Mathematics 11–12 · Year 12

    Tower of Hanoi: 2^n - 1 moves, from pattern to proof by induction

    Counting the fewest moves for one, two, three and four discs suggests 2^n - 1; counting how often each disc moves turns the total into the sum 1 + 2 + ... + 2^(n-1), and mathematical induction proves that this sum equals 2^n - 1 for every n.

    Practical, model not builtLow risk
  7. Mathematics 11–12 · Year 12

    Two measured tones added as phasors: the Argand plane on a phone oscilloscope

    Two tones of the same frequency add like two complex numbers: the modulus of the sum is the amplitude a microphone reads and its argument is the phase of the combined wave, so head-to-tail addition on the Argand plane predicts a measurement.

    Practical, model not builtLow risk
  8. Mathematics 11–12 · Year 12

    Volume of a flask, a horizontal pipe and a bottle neck, checked with water

    The measured profile of a vessel decides the form of the integral that gives its volume: a straight taper needs a linear substitution, a circular cross-section needs a trigonometric substitution and the double-angle identity, and a hyperbolic taper needs a rational integrand, and water in a measuring cylinder settles whether the integration was right.

    Practical, model not builtLow risk
  9. Mathematics 11–12 · Year 12

    Volume of a rotated solid checked with water: a cone and a curved glass

    Rotating a line or curve about an axis sweeps out a solid whose volume is the integral of pi y^2, and pouring water into the real object measures the same number.

    Practical, model not builtLow risk
  10. Mathematics 11–12 · Year 12

    Where does the spinner stop: a continuous uniform random variable

    The angle at which a fair spinner stops can take any value from 0 to 360 degrees, so probabilities come from areas under a flat density function rather than from counting outcomes.

    Practical, model not builtLow risk

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