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Animations and Simulations

A textbook picture stands still; these move. Every animation is a small lab: drag a slider, move a point, and watch nature and mathematics follow their rules. Pick a subject below.

Subjects

Physics

Light, electricity, motion, oscillation and waves: change a value and watch the formula work.

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All animations: Physics

Grade 8–12

Refraction of light

Change the angle and watch light bend. Snell's law, refractive index, critical angle and total internal reflection, explained simply with worked examples.

Grade 9–12

Ohm's law

Adjust voltage and resistance and watch the current change. Ohm's law formula, V-I graph, series and parallel resistors, with solved problems.

Grade 11

Projectile motion

Set the launch angle and speed and trace the path. Time of flight, maximum height and range formulas, why 45° goes farthest, with solved numbers.

Grade 9–11

Simple pendulum

Change length and gravity and time the swing. Simple pendulum period T = 2π√(L/g), SHM, energy conservation and finding g, with solved numbers.

Grade 10–12

Electric field

Drop positive and negative charges and watch the field lines form. Coulomb's law, E = kq/r², units and field-line rules, with solved examples.

Grade 11–12

Wave interference

Move two wave sources and watch bright and dark fringes appear. Superposition, constructive vs destructive conditions, fringe width, solved examples.

Grade 9–11

Free Fall

What is free fall? Drop a coin and a feather with and without air. Learn the free fall formulas for time, velocity and height (g = 9.8 m/s²) with worked examples.

Grade 10–12

Lens ray diagrams

Interactive convex and concave lens ray diagrams: drag the object through all six cases, see the three principal rays, and read u, v, f, magnification and power live.

Grade 9–11

Newton's Laws of Motion

Newton's laws of motion explained with an interactive cart: inertia, F = ma, momentum, impulse and action–reaction pairs, with examples and worked problems.

Grade 10–12

Spherical mirror ray diagrams

Drag an object in front of a concave, convex or plane mirror and watch the rays find the image. Mirror formula, magnification, all six cases, solved problems.

Grade 10–12

Electromagnetic Induction

What is electromagnetic induction? Drag a bar magnet through a coil and watch a centre-zero galvanometer. Learn Faraday's law e = −N dΦ/dt and Lenz's law with worked examples.

Grade 9–11

Conservation of Momentum and Collisions

What is the conservation of momentum? Collide two carts and drag the restitution slider from a sticking e = 0 to a bouncy e = 1. See momentum and kinetic-energy bars update live, with worked examples.

Grade 9–11

Work, Energy and Power

What is work, and what are the formulas for kinetic and potential energy and power? Release a cart on a curved track, watch energy turn to heat, with worked examples.

Grade 9–11

Inclined Plane

How does a block’s weight split on a slope, what is the angle of repose, and when does friction hold a block still or let it slide? Change the angle yourself and watch the force-arrow diagram.

Grade 9–11

Uniform circular motion

Whirl a ball on a string and read ω, T, a = v²/r and F = mv²/r live. Cut the string to see it fly off tangentially, then try banked curves with solved numbers.

Grade 8–10

Transverse and Longitudinal Waves

See a rope wave and a slinky or sound wave driven by one source. Learn crest, trough, compression, rarefaction, wavelength, v = fλ and why particles never travel with the wave, with solved problems.

Grade 9–11

Levers and moments

Slide weights on a seesaw and watch the moment M = F × d on each side. Learn the principle of moments, three classes of lever and mechanical advantage, with solved problems.

Grade 9–11

Centre of mass

Drag masses along a rod or plate and watch the centre of mass x = Σmx/Σm move. Find the balance point, see when a bus topples, and learn stable, unstable and neutral equilibrium with solved problems.

Grade 9–11

Spring-mass SHM

Run a mass on a spring in simple harmonic motion. Explore Hooke’s law, T = 2π√(m/k), energy swapping, springs in series and parallel, with worked problems and exam practice.

Grade 9–11

Vector addition: triangle and parallelogram laws

Add two vectors by the triangle and parallelogram laws, split them into components, then test a river-crossing boat and a walker with an umbrella. With solved problems.

Grade 9–11

Relative velocity: trains and river crossing

Play with two trains and a swimmer crossing a river. Learn relative speed, train crossing time, heading angle, drift, shortest time vs shortest path, with solved problems.

Grade 11–12

Kepler's laws and elliptical orbits

Drag the eccentricity and see an orbit stretch. Equal-time sectors with equal areas, the period law T² ∝ a³ and escape speed, with solved problems.

Grade 11–12

Newton’s law of gravitation, g and satellites

Play with two masses, the inverse-square graph, g above and below the Earth and a satellite orbit. Learn the law of gravitation, orbital speed, period and escape speed with solved problems.

Grade 11–12

Standing waves in strings and pipes

Pluck a string and blow across open and closed pipes in a simulation. See nodes, antinodes, harmonics, and learn how length, tension and temperature set the pitch, with solved problems.

Grade 11–12

Resonance tube and the speed of sound

Slide the water level in a resonance tube and find the loud spots yourself. See L1 = λ/4 − e and L2 = 3λ/4 − e, compute the speed of sound with v = 2f(L2 − L1), and practise solved problems.

Grade 11–12

Beats: when two close notes pulse

Add two waves of nearly equal frequency and watch the loudness pulse. See the envelope, read the beat frequency |f1 − f2|, hear the effect, and learn how guitarists tune by beats, with solved problems.

Grade 11–12

Doppler effect: moving sources, listeners and sonic booms

Drag a sound source faster and slower and watch the wavefronts bunch up ahead and stretch out behind. Learn the Doppler formula, moving listener, ambulance and train problems, and the sonic boom.

Grade 10–12

Prism, dispersion of light and the rainbow

Send white light through a prism, change the prism angle and incidence, and watch the spectrum form. Learn deviation, minimum deviation, dispersive power and how a raindrop makes a rainbow, with solved problems.

Grade 11–12

Kirchhoff’s laws: junction rule and loop rule

Build a two-loop circuit with two batteries and three resistors. Watch the currents split at a junction, see the voltage sums land on zero and learn how to solve Kirchhoff’s laws problems step by step.

Grade 12

Wheatstone bridge and metre bridge

Unbalance a Wheatstone bridge and watch the galvanometer needle swing. Find balance at P/Q = R/S, then slide the jockey on a metre bridge to measure an unknown resistance with solved examples.

Grade 11–12

Single-slit diffraction

Change the slit width and wavelength and watch light spread behind a single slit. See the intensity graph I = I₀(sin β/β)², the minima at a sin θ = mλ and the central maximum width 2λD/a, with solved problems.

Grade 10–12

Defects of the human eye and their correction

Switch between a normal, short-sighted, long-sighted and ageing eye. See why the image lands in front of or behind the retina, then fit the right lens and work out its power in dioptres.

Grade 12

Polarisation of light: Malus’s law and Brewster’s law

Rotate an analyser behind a polariser and watch I = I₀cos²θ on a graph, then bounce light off glass to find the Brewster angle. Includes polaroid sunglasses, three-filter puzzles and solved problems.

Grade 12

Charging and discharging a capacitor: the RC time constant

Charge and discharge a capacitor through a resistor. Change E, R and C, watch V = E(1 − e^(−t/RC)) and the current curve draw live, find the 63% time constant and the energy stored.

Grade 10–12

Magnetic field lines: bar magnet, current-carrying wire and solenoid

See magnetic field lines of a bar magnet, a straight current-carrying wire and a solenoid. Drag a compass, flip the current, and learn B = μ₀I/2πr, B = μ₀nI and the right-hand grip rule.

Grade 12

AC generator

Spin a coil between magnet poles and watch the sine wave of an AC generator build live. Change N, A, B and rpm, read E0 = NBAω and the rms value, and see why mains is 50 Hz.

Grade 10–12

Transformer

Change the primary and secondary turns of a transformer and watch the voltage step up or down. See Vs = Vp·Ns/Np, power conservation, real efficiency and why power lines use high voltage.

Grade 9–12

Heat transfer: conduction, convection and radiation

Heat a copper, aluminium, glass or wooden rod and watch Q/t = kAΔT/L, see convection currents circulate in a beaker, and see how radiated power grows as T⁴. With tables and solved problems.

Grade 12

Photoelectric effect: Einstein’s equation and the stopping potential

Shine light of any wavelength on sodium, zinc or copper in a vacuum tube. See why electrons leave only above the threshold frequency, how K = hf − φ sets the stopping potential, and why brightness changes only the current.

Grade 10–12

Motor effect: force on a current-carrying wire and the DC motor

Put a current-carrying wire in a magnetic field and watch it get pushed. Change B, I, L and the angle, test Fleming’s left-hand rule, then spin a DC motor with a split-ring commutator and see its torque graph.

Grade 11–12

Gas molecules and kinetic theory: pressure, temperature and speed

Watch gas molecules bounce around a box. Raise the temperature, change the gas, squeeze the volume, and see wall hits turn into pressure that matches PV = NkT. Compare speeds with the Maxwell–Boltzmann curve and calculate rms speed.

Grade 12

The semiconductor diode: p–n junction, I–V curve and rectifier

Bias a p–n junction and watch the depletion layer shrink or grow, carriers cross, and the Shockley I–V curve trace live. Compare silicon and germanium, see breakdown, then build a half-wave rectifier.

Grade 10–12

Radioactive decay: half-life, the decay law and penetration

Watch 240 nuclei decay at random, see the count follow N = N₀e^(−λt), measure the half-life from the graph, then test how alpha, beta and gamma radiation pass through paper, aluminium and lead.

Grade 11–12

The Bohr atom: orbits, energy levels and the hydrogen spectrum

Make a hydrogen electron jump between orbits n = 1 to 6, watch the photon colour come from 1/λ = R(1/n₁² − 1/n₂²), and see the Lyman, Balmer and Paschen series on an energy diagram and spectrum strip.

All animations: Chemistry

Grade 8–11

Structure of the atom

Structure of the atom explained with an interactive simulation: protons, neutrons, electrons, atomic and mass number, isotopes and electron configuration, with solved examples.

Grade 8–11

Acids, Bases and the pH Scale

What is pH and what does the pH scale show? Drip a base into an acid, watch the indicator change colour and trace a live titration curve, with worked pH problems.

Grade 9–11

Electron configuration

How to write electron configurations: Aufbau order, Pauli and Hund rules, the Cr and Cu exceptions, ions and noble-gas shorthand. Watch electrons fill, Z 1–36.

Grade 9–11

Gas laws: Boyle, Charles, Gay-Lussac, Avogadro and PV = nRT

Push a piston and heat a gas: Boyle's, Charles's, Gay-Lussac's and Avogadro's laws, the ideal gas law PV = nRT, graphs, R values and solved problems.

Grade 8–11

How an Ionic Bond Forms

What is ionic bonding, and how does a metal atom transfer electrons to a non-metal to form ions? Drop NaCl, MgO or CaCl2 into the simulation and watch charge balance derive the formula, with worked examples.

Grade 9–12

Electrolysis and Faraday’s Laws

What is electrolysis, what forms at the cathode and anode, and how does Faraday's law compute the mass deposited? Choose molten NaCl, CuSO2 or acidified water and watch, with worked examples.

Grade 9–12

Covalent Bond

What is a covalent bond? Build H₂O, NH₃, CH₄ and CO₂ atom by atom in a dot-and-cross simulation: single, double and triple bonds, lone pairs, the octet rule and bond polarity, with worked examples.

Grade 9–11

Periodic Trends

What are periodic trends? See how atomic radius, ionization energy, electronegativity and metallic character change across a period and down a group, on a heat map of the first 36 elements, with the real exceptions.

Grade 9–12

Reaction rate and collision theory

What decides how fast a reaction goes? Run a collision-theory simulation: change temperature, concentration and a catalyst, and watch the activation-energy graph and the product curve respond.

Grade 8–10

States of matter: solid, liquid, gas and the heating curve

Watch particles vibrate in a solid, slide in a liquid and fly free in a gas. A live heating curve for water, melting, boiling, latent heat, sublimation, and Q = mcΔT and Q = mL worked out.

Grade 11–12

Atomic orbitals: the shapes of s, p and d, quantum numbers and nodes

Rotate the 1s, 2s, 2p and 3d orbitals in 3D. Orbit versus orbital, the four quantum numbers, counting radial and angular nodes, subshell capacities and worked examples.

Grade 11–12

Molecular shapes and VSEPR theory: bond pairs, lone pairs and angles

Build molecules in 3D and rotate them. See how bond pairs and lone pairs set the shape, bond angle and hybridisation of CH4, NH3, H2O, PCl5, SF6 and more, with solved problems.

Grade 9–11

The mole concept: molar mass, Avogadro’s number and molar volume

What is a mole, what is Avogadro’s number, and how do you convert grams to moles to molecules? Weigh substances on a virtual balance, see 22.4 L at STP, and learn percentage composition with solved problems.

Grade 11–12

Diffusion and effusion: Graham’s law of gases

Watch ammonia and hydrogen chloride build a white ring in a tube, then race gases through a pinhole. Graham’s law of diffusion and effusion derived and solved with live numbers.

Grade 9–10

Balancing chemical equations: method, examples and practice

How do you balance a chemical equation? Change coefficients and watch the atom counts on both sides match. Five worked reactions (water, methane, rust, acid, propane) with the method and exam tips.

Grade 11–12

Chemical equilibrium: the equilibrium constant Kc and Le Chatelier’s principle

What is chemical equilibrium, how do you find Kc, and which way does a reaction shift when you change concentration, temperature or pressure? Watch the Haber process rate curves and see Le Chatelier at work.

Grade 9–12

Titration: finding an unknown concentration with a burette and an indicator

What is a titration? See how a burette and an indicator work, why the end point and equivalence point differ, and how to use V₁M₁ = V₂M₂ with the mole ratio. Run it yourself with a live pH curve.

Grade 11–12

Galvanic cell: the Daniell cell, EMF and the Nernst equation

How does a galvanic cell make electricity? See which way electrons and salt-bridge ions move in the Daniell cell, how the rod masses change, and what the standard and Nernst EMF are. Change the concentrations and watch.

Grade 9–11

Redox reactions: oxidation numbers, electron transfer and half-equations

What are oxidation and reduction, how do you find oxidation numbers, and which species is the oxidising agent? Watch electrons move in five redox reactions, with half-equations and worked examples.

Grade 10–12

Hydrocarbons: alkanes, alkenes, alkynes and structural isomers in 3D

See alkanes, alkenes and alkynes as spinning ball-and-stick models. Slide the carbon count, read the general formula and IUPAC name, and view every structural isomer of butane, pentane and hexane.

Grade 10–12

Functional groups: alcohols, aldehydes, ketones, acids, esters and amines

What is a functional group, and how do you tell an alcohol, aldehyde, ketone, acid, ester or amine apart? Explore eight organic families with IUPAC names, lab tests and worked problems.

Grade 11–12

Polymerisation: addition and condensation polymers, polythene and nylon

What is a polymer, and how do addition and condensation polymerisation differ? Watch ethene become polythene and nylon-6,6 form, with chain molar masses and water released worked out.

Grade 9–11

Separation techniques: filtration, distillation, chromatography, crystallisation

Watch filtration, simple and fractional distillation, paper chromatography and crystallisation run. Compute Rf, read the boiling-point plateaus and work out crystal yield.

Grade 11–12

Crystal lattice: SC, BCC and FCC unit cells, packing efficiency and density

Rotate the simple, body-centred and face-centred cubic unit cells. Count atoms per cell, coordination number, packing efficiency (52.4%, 68%, 74%) and density.

Grade 11–12

Radioactivity: Alpha, Beta, Gamma Decay and Half-Life

Watch alpha, beta and gamma decay change A and Z, build balanced nuclear equations and see 100 atoms decay at random along the half-life curve, with a carbon-14 dating example. Free simulation.

All animations: Biology

Grade 9–11

Mitosis cell division

Watch mitosis happen: interphase, prophase, metaphase, anaphase, telophase and cytokinesis in an interactive animation, with chromosome counting rules and solved problems.

Grade 8–11

Diffusion and Osmosis

Diffusion vs osmosis explained with a live particle simulation: definitions, the difference table, tonicity, plasmolysis, turgor and imbibition, with solved examples.

Grade 7–11

Photosynthesis

Photosynthesis explained: the equation, light-dependent stage, Calvin cycle and limiting factors. Change light, CO₂ and temperature in a live leaf simulation.

Grade 9–11

The human heart: structure and function

See the four chambers, valves, lub-dub sounds and a live ECG in one animated heart. Learn double circulation, the cardiac cycle and cardiac output.

Grade 10–12

Mendelian Genetics

Learn Mendel's laws with a real Punnett-square builder: monohybrid and dihybrid crosses, test crosses, incomplete dominance, blood-type codominance, and sex determination — every ratio computed live.

Grade 11–12

DNA Replication

DNA replication explained: semi-conservative copying, key enzymes, leading vs lagging strand, Okazaki fragments and the Meselson-Stahl proof — in a live simulation.

Grade 9–11

Cellular Respiration

Cellular respiration explained: aerobic vs anaerobic respiration, glycolysis, the Krebs cycle, the electron transport chain and ATP yield. Run the mitochondrion simulation and see the numbers add up.

Grade 9–11

Enzyme Action

What an enzyme is, the active site, lock-and-key vs induced-fit models, how temperature, pH and inhibitors change its rate, and the Michaelis-Menten equation — explore it live in a simulation.

Grade 10–11

The Nerve Impulse and the Action Potential

See a stimulus above threshold (-55 mV) fire an action potential that races down the axon — continuous or saltatory — and release neurotransmitter at the synapse, with the real formulas.

Grade 9–11

The Nephron and Urine Formation

See how a kidney filters about 180 litres of fluid a day yet passes only around 1.50 litres of urine — filtration, reabsorption and the glucose threshold, with the real formulas.

Grade 9–11

Meiosis Cell Division

What is meiosis, what is crossing over, and how is it different from mitosis? Run a 2n = 4 cell through prophase I to telophase II yourself, with worked examples.

Grade 9–10

Digestive System

What is digestion, which enzyme acts where, and how do villi absorb nutrients? Run food's journey from mouth to large intestine yourself, with worked examples.

Grade 8–10

Breathing Mechanism: Inhalation and Exhalation

Watch the diaphragm, ribs and intercostal muscles move air in and out of the lungs. Pressure gauge, spirometer trace, bell jar model and alveolus gas exchange, with solved problems.

Grade 10–12

Protein synthesis

Watch RNA polymerase copy a gene into mRNA, then a ribosome read codons and build a protein. Edit the gene, mutate a base and use the codon table.

Grade 9–12

Blood circulation: double circulation and cardiac output

Watch blood travel from the heart to the lungs, round the body and back, in a live diagram. Pulmonary and systemic circulation, artery vs vein vs capillary, and cardiac output worked examples.

Grade 8–11

Cell structure and organelles: plant cell vs animal cell

See a plant cell and an animal cell side by side. Click the nucleus, mitochondria, chloroplast, Golgi body, ribosomes and more to learn each job. Includes a comparison table, magnification maths and exam questions.

Grade 9–11

Reflex action and the reflex arc

Touch something hot and watch the impulse run receptor, sensory neuron, spinal cord, motor neuron, muscle. Compute reflex time (24.33 ms) and see why pain is felt after you move.

Grade 9–11

The human eye: parts, image formation and accommodation

See how the cornea, iris, lens, ciliary muscles, retina, fovea and blind spot work in a live cross-section. Explore accommodation, myopia and hypermetropia, with solved lens-power problems.

Grade 11–12

Muscle contraction and the sliding-filament model

Watch actin and myosin slide inside a sarcomere. The A band stays 1.6 µm while the I band and H zone shrink; follow the cross-bridge cycle, calcium and ATP step by step.

Grade 9–11

Transport in plants: xylem, phloem and transpiration

See water rise through the xylem and sugar sink through the phloem. Change light, humidity and wind and compute the transpiration rate (54.8 g/m²/h on the default day).

Grade 9–12

Food chain and food web: energy flow and the 10 % rule

Build a food web, remove a species and watch the knock-on effects, then run the 10% rule on an energy pyramid (10,000 kJ of producer energy leaves just 1 kJ at the top).

Grade 11–12

Population growth: exponential and logistic curves

Drag r and the carrying capacity K and watch exponential and logistic curves diverge. With r = 0.40 per hour and K = 1,000, a culture doubles every 1.73 h and levels off near K.

Grade 11–12

Natural selection: peppered moths and the sooty tree

Slide the soot level and watch birds pick off the more visible moths. With 80 % soot and 40 % selection, dark moths climb from 10 % to 90 % of the moths in 15 generations.

Grade 10–12

Immune response: primary and secondary antibody response

Compare a vaccinated and an unvaccinated person on one antibody graph. In this model memory cuts the wait for protection from 8.1 to 2.5 days and raises the peak 5.1 times.

Grade 10–12

Pollination and fertilisation

Follow pollen from anther to stigma, down the pollen tube and into the ovule. Watch double fertilisation make the 14-chromosome zygote and 21-chromosome endosperm, then seed and fruit.

All animations: Mathematics

Grade 8–10

Pythagorean Theorem

The Pythagorean theorem explained: formula a² + b² = c², two proofs you can watch, the converse, Pythagorean triples and 10 worked examples. Drag the triangle yourself.

Grade 10–11

Trigonometric Ratios and the Unit Circle

Drag a point round the unit circle and watch sin, cos and tan change. Standard angle table, ASTC signs, identities, radians and graphs, with solved examples.

Grade 9–11

Quadratic functions and their graphs

Drag the vertex and change a, b, c to see how a quadratic function graph moves. Learn factoring, completing the square, the quadratic formula and discriminant.

Grade 9–10

Circle theorems

All the circle theorems with drag-and-check diagrams: angle at the centre, same segment, semicircle, cyclic quadrilateral, chords, tangents and alternate segment.

Grade 9–10

Heights and distances: elevation and depression angles

What angle of elevation and angle of depression mean, how the height-and-distance formula works, and how two observations solve a tower's height without ever measuring it — with an interactive simulation and solved problems.

Grade 9–11

Probability: experimental vs theoretical probability

What probability means, how the sample-space formula P(E) = n(E)/n(S) works, and why experimental frequency edges closer to theoretical probability the more you flip, roll or draw — with a coin, dice and coloured-ball simulator.

Grade 10–11

Arithmetic and Geometric Sequences

Learn the arithmetic and geometric sequence formulas for the nth term and sum, Gauss's pairing trick, and the sum-to-infinity formula a/(1−r), with a drag-and-slide bar-chart simulation and worked examples.

Grade 9–10

Mean, Median and Mode

Learn the mean, median and mode formulas, why the median resists an outlier while the mean does not, and the grouped-data median/mode formulas, by dragging points on a number line, with worked examples.

Grade 7–11

Sets and Venn Diagrams

Shade union, intersection, difference and complement on a live Venn diagram, drop numbers into regions, check n(A ∪ B) and test De Morgan’s laws, with solved problems.

Grade 8–10

Linear equations: graphs, slope and simultaneous pairs

See slope, intercepts and angle on a straight line, then graph two linear equations to find where they meet. Learn the ratio test for one, none or infinite solutions.

Grade 10–12

Graphs of sin, cos and tan

Plot y = A sin(Bx + C) + D with sliders: see amplitude, period, phase shift, range and the asymptotes of tan live. Trigonometric graphs with solved examples.

Grade 9–10

Completing the Square and the Quadratic Formula

Watch algebra tiles complete the square, then solve quadratic equations, find the vertex and see why the formula works. Free interactive simulation with solved examples.

Grade 7–10

Area of a Circle: Proof, Formula and Solved Problems

Cut a circle into slices, slide them into a rectangle and watch the area become πr². Free interactive simulation with circumference, pi, sectors, arcs and solved problems.

Grade 8–10

Volume and Surface Area of Solids: Cube, Cuboid, Cylinder, Cone, Sphere

Rotate six solids in 3D, unfold their nets and pour a cone into a cylinder to see why it takes exactly three. Free simulation with volume, CSA and TSA formulas and solved problems.

Grade 8–10

Similar Triangles: Scale Factor, AA, SSS, SAS and Shadow Heights

Scale a triangle with a slider and watch angles stay equal, side ratios stay k and area grow by k². Free interactive similar triangles simulation with AA, SSS, SAS tests and shadow problems.

Grade 9–11

Coordinate Geometry: Distance, Midpoint, Slope, Section Formula and Locus

Drag points on a grid and watch the distance formula, midpoint, slope and section formula update live. Free coordinate geometry simulation with the perpendicular-bisector locus and solved problems.

Grade 11–12

Conic Sections: Circle, Ellipse, Parabola and Hyperbola

Tilt a plane through a double cone and watch a circle, ellipse, parabola or hyperbola appear, with its standard equation, foci and eccentricity. Free conic sections simulation with solved problems.

Grade 9–11

Function Transformations: Shifts, Stretches and Reflections

Pick x², |x|, √x, sin x or 2^x and drag sliders for a, b, h and k. Watch shifts, stretches, squeezes and reflections move the graph, with the parent faded behind. Free simulation with solved problems.

Grade 11–12

Derivative as the Slope of a Tangent: Secant to Tangent

Drag a point P on x², x³, sin x, eˣ or 1/x and shrink the gap h to zero. Watch the secant become the tangent and its slope become the derivative, with the derivative graph below. Free simulation.

Grade 11–12

Riemann Sums and Integration: Area Under a Curve

Cut the area under x², x³, sin x, eˣ or √x into up to 100 strips and compare left, right, midpoint and trapezoid sums with the exact integral. Watch the error melt away. Free simulation.

Grade 11–12

Limits and the ε–δ Definition: A Visual Guide

See the epsilon-delta definition of a limit. Pick a function, shrink ε and watch the δ band follow it, with left and right limits, a hole, sin x / x and a jump where no δ works. Free simulation.

Grade 11–12

3D Vectors: Sum, Dot Product and Cross Product

Drag to rotate two 3D vectors. See the sum as a parallelogram, the dot product as a shadow and an angle, and the cross product as a perpendicular arrow whose length is the area. Free simulation.

Grade 11–12

Matrix Transformations: Rotation, Reflection, Shear and the Determinant

Change a 2×2 matrix and watch the grid, a unit square and an F-shape move. See where i-hat and j-hat land, the determinant as signed area, and the inverse. Free simulation.

Grade 11–12

Complex Numbers: Sum, Product, Powers and Roots on the Argand Plane

Drag two complex numbers on the Argand plane. See the sum as a parallelogram, the product as a rotation and stretch, conjugates, powers as a spiral and roots of unity. Free simulation.

Grade 9–12

Binary Number System: Place Value, Conversion and Addition

Flip bits and see decimal, binary, octal and hex change together. Watch conversion by repeated division by 2, regrouping into octal and hex, and binary addition with carries. Free, with worked examples.

Keep studying this topic

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