ZeyrnLab

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Some ideas take time. Choose a stage, review the foundations and open a lesson to understand the reasoning, step by step.

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This is a suggested study organisation. The 9th-stage topics include a review of the foundations of the first cycle; the sequence by school year should be adjusted with your teacher. The 13th stage offers general advanced study and preparation for higher education.

Year 9 — Give ideas a foundation

Review the basics and build confidence.

Mathematics

  1. Real numbers and scientific notation

    Compare quantities and write very large or small numbers without losing their meaning.

    First, it helps to review: Operations with rational numbers.

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  2. Expressions, equations and systems

    Simplify expressions, factorise and discover values satisfying one or two conditions.

    First, it helps to review: Operations and properties of powers.

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  3. Graphs and quadratic functions

    Connect an expression to its graph and recognise roots, the vertex and concavity.

    First, it helps to review: Coordinates in the plane · Quadratic equations.

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  4. Similarity, Pythagoras and trigonometry

    Use relationships between sides and angles to solve problems involving triangles.

    First, it helps to review: Fractions and proportionality.

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Physics

  1. Quantities, units and measurements

    Choose units, convert measurements and distinguish a measurement from an estimate.

    First, it helps to review: Operations with decimals.

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  2. Motion and reading graphs

    Relate position, time and velocity in simple everyday situations.

    First, it helps to review: Coordinates and proportionality.

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  3. Forces, work and energy

    Distinguish mass from weight and understand how forces can transfer energy.

    First, it helps to review: Units and motion.

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  4. Heat, pressure, sound, light and electricity

    Recognise the basic models explaining thermal phenomena, waves and simple circuits.

    First, it helps to review: Physical quantities and energy.

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Year 10 — See the connections

Bring together expressions, graphs and real situations.

Mathematics

  1. Functions, domain and representations

    Interpret domain, range, tables and graphs without confusing the input with the result.

    First, it helps to review: Algebra and coordinates.

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  2. Linear and quadratic functions

    Investigate the effect of coefficients and compare a line with a parabola.

    First, it helps to review: Equations and graphs.

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  3. Analytic geometry in the plane

    Calculate distances and interpret lines, circles and sets of points.

    First, it helps to review: Pythagoras and coordinates.

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  4. From the triangle to the trigonometric circle

    Give meaning to sine, cosine and radians through geometric relationships.

    First, it helps to review: Trigonometric ratios.

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Physics

  1. Vectors and motion in one dimension

    Interpret direction, orientation and signs, and connect position, velocity and acceleration graphs.

    First, it helps to review: Units and graphs.

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  2. Newton’s laws

    Represent forces and relate the resultant force to changes in motion.

    First, it helps to review: Vectors and acceleration.

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  3. Work and conservation of energy

    Track transfers between kinetic and potential energy and identify losses in the model.

    First, it helps to review: Forces and displacement.

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  4. Temperature, gases and electric current

    Relate quantities in thermal and circuit models to their respective conditions of validity.

    First, it helps to review: Energy and proportionality.

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Year 11 — Test and connect

Explore patterns and build models.

Mathematics

  1. Sequences and progressions

    Recognise formation rules and compare additive growth with multiplicative growth.

    First, it helps to review: Algebra and functions.

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  2. Exponentials and logarithms

    Connect exponential growth to its inverse operation and respect domains.

    First, it helps to review: Powers and functions.

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  3. Trigonometric functions and equations

    Interpret periodicity, amplitude and solutions through the circle and graph.

    First, it helps to review: Trigonometric circle.

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  4. Data and probability — supplement

    Read distributions and distinguish an observed frequency from a probability in a model.

    First, it helps to review: Fractions and percentages.

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Physics

  1. Motion in a plane and projectile motion

    Separate horizontal and vertical motion and study range, height and flight time.

    First, it helps to review: Vectors · Trigonometry · Accelerated motion.

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  2. Circular motion and gravitation

    Understand acceleration directed towards the centre and relate velocity, radius and period.

    First, it helps to review: Forces and acceleration · Circle.

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  3. Oscillations and waves

    Relate period, frequency, wavelength and energy propagation.

    First, it helps to review: Motion and periodic functions.

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  4. Gases and thermal processes

    Interpret pressure, volume, absolute temperature and energy exchanges in a gas model.

    First, it helps to review: Energy · Temperature and pressure.

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Year 12 — Go deeper and solve

Consolidate ideas and explain your reasoning.

Mathematics

  1. Limits and continuity

    Distinguish the value of a function from the behaviour of its values near a point.

    First, it helps to review: Functions and domain.

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  2. Derivatives and rates of change

    Interpret the derivative as instantaneous change and tangent slope.

    First, it helps to review: Limits and slope.

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  3. Function analysis and optimisation

    Use signs and variation to justify extrema and solve problems with constraints.

    First, it helps to review: Derivatives and inequalities.

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  4. Geometry, trigonometry and functions

    Choose suitable representations and connect techniques from algebra, geometry and analysis.

    First, it helps to review: Analytic geometry and trigonometry.

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Physics

  1. Circuits and electrical energy

    Relate current, potential difference, resistance, power and energy in circuits.

    First, it helps to review: Electric current and energy.

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  2. Fields and electromagnetic induction

    Distinguish fields from forces and understand induction in modelled situations.

    First, it helps to review: Vectors and electricity.

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  3. Waves and optics

    Explain reflection, refraction and wave phenomena by identifying the model’s assumptions.

    First, it helps to review: Waves and geometry.

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  4. Forces and motion in synthesis

    Review relationships between trajectory, forces and energy in motion problems.

    First, it helps to review: Newton’s laws · Motion in a plane.

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Year 13 — Take the next step

General further study and preparation for higher education; this does not correspond to a single official Year 13 syllabus.

Mathematics

  1. Change and approximation

    Use rates of change to interpret approximations and understand their limits.

    First, it helps to review: Derivatives.

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  2. Integral as area and accumulation

    Build the idea of accumulation from sums and geometric interpretation.

    First, it helps to review: Limits and areas.

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  3. Modelling and critical reading of data

    Choose a model, check units and identify when a conclusion goes beyond the data.

    First, it helps to review: Functions and statistics.

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  4. Problems connecting several ideas

    Organise solutions linking algebra, geometry and calculus, justifying each step.

    First, it helps to review: Foundations of algebra, geometry and analysis.

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Physics

  1. Forces, energy and momentum

    Choose between force and conservation approaches and discuss each one’s assumptions.

    First, it helps to review: Mechanics and vectors.

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  2. Resonance and applications of waves

    Understand the response of an oscillating system and connect models to applications.

    First, it helps to review: Oscillations and waves.

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  3. Electricity and energy in context

    Read data and diagrams of real systems, distinguishing power, energy and efficiency.

    First, it helps to review: Circuits and energy conservation.

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  4. An introduction to modern physics

    Recognise the limits of classical models and place new ideas in context without confusing them with earlier models.

    First, it helps to review: Waves and energy.

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How we are organising these paths

The initial reference is INADE’s assessment domains. The distribution above is a ZeyrnLab proposal to be adjusted with teachers; the documents consulted do not define a complete, current sequence for each school year.

Each lesson develops the foundations and principles with worked examples, exercises and explained solutions. All 40 lessons already include these elements. Independent pedagogical review by teachers remains a stage of the project; the six labs offer an additional way to explore some topics.