40 lessons to explore
Each lesson starts with a step-by-step visual demonstration and lets you explore the explanation in greater depth and practise afterwards. The stages help organise your studies; the 13th is a general further-study path. The six interactive laboratories are still in the experiment library.
9th · Mathematics
Real numbers and scientific notation
How can the same fraction represent very different lengths?
See the idea step by step9th · Mathematics
Expressions, equations and systems
Why can we remove the same number from both sides?
See the idea step by step9th · Mathematics
Graphs and quadratic functions
How do squares reveal symmetry, the vertex and zeros?
See the idea step by step9th · Mathematics
Similarity, Pythagoras and trigonometry
How do the legs determine the hypotenuse and the angle ratios?
See the idea step by step9th · Physics
Quantities, units and measurements
How can the same measurement be written in centimetres and metres without inventing precision?
See the idea step by step9th · Physics
Motion and reading graphs
After walking out and back, does distance equal displacement?
See the idea step by step9th · Physics
Forces, work and energy
How does a horizontal force increase a frictionless box's speed?
See the idea step by step9th · Physics
Heat, pressure, sound, light and electricity
Does the same energy warm a cup and a pan of water equally?
See the idea step by step10th · Mathematics
Functions, domain and representations
Why does √(x − a) not accept every real input?
See the idea step by step10th · Mathematics
Linear and quadratic functions
How can differences distinguish a line from a parabola?
See the idea step by step10th · Mathematics
Analytic geometry in the plane
Which points are all the same distance from the center?
See the idea step by step10th · Mathematics
From the triangle to the trigonometric circle
How can trigonometric ratios extend beyond 90°?
See the idea step by step10th · Physics
Vectors and motion in one dimension
Can positive acceleration make an object slow down?
See the idea step by step10th · Physics
Newton’s laws
Is friction always at its maximum value when you pull a box?
See the idea step by step10th · Physics
Work and conservation of energy
During a descent, how is the initial energy divided between motion and heating?
See the idea step by step10th · Physics
Temperature, gases and electric current
In a rigid, sealed container, does doubling the temperature in degrees Celsius double the pressure?
See the idea step by step11th · Mathematics
Sequences and progressions
Why do growth patterns with the same start diverge?
See the idea step by step11th · Mathematics
Exponentials and logarithms
What does log_b(y) ask when we already know bˣ?
See the idea step by step11th · Mathematics
Trigonometric functions and equations
How do amplitude and period change the curve of circular motion?
See the idea step by step11th · Mathematics
Data and probability — supplement
Why is P(A and B) different from P(B given A)?
See the idea step by step11th · Physics
Motion in a plane and projectile motion
Why does the projectile keep moving at the highest point?
See the idea step by step11th · Physics
Circular motion and gravitation
Can acceleration occur at constant speed?
See the idea step by step11th · Physics
Oscillations and waves
How far does a wave's shape travel in one period?
See the idea step by step11th · Physics
Gases and thermal processes
How is incoming heat divided in a gas expanding at constant pressure?
See the idea step by step12th · Mathematics
Limits and continuity
Does the limit change if I move only the point at x = 1?
See the idea step by step12th · Mathematics
Derivatives and rates of change
What slope appears as the second point approaches the first?
See the idea step by step12th · Mathematics
Function analysis and optimisation
With 20 m of fencing, which rectangle has the largest area?
See the idea step by step12th · Mathematics
Geometry, trigonometry and functions
How can an angle become a point and an identity?
See the idea step by step12th · Physics
Circuits and electrical energy
Do two series resistors carry the same current or have the same voltage?
See the idea step by step12th · Physics
Fields and electromagnetic induction
What determines the direction of induced current in a loop?
See the idea step by step12th · Physics
Waves and optics
When does a propagating refracted ray cease to exist?
See the idea step by step12th · Physics
Forces and motion in synthesis
How can there be acceleration when speed is constant?
See the idea step by step13th · advanced study · Mathematics
Change and approximation
What is the error when replacing a curve by its tangent?
See the idea step by step13th · advanced study · Mathematics
Integral as area and accumulation
Does a negative velocity count as negative distance?
See the idea step by step13th · advanced study · Mathematics
Modelling and critical reading of data
Does a good fit to the data guarantee the prediction beyond them?
See the idea step by step13th · advanced study · Mathematics
Problems connecting several ideas
How does a root on the graph relate to braking distance?
See the idea step by step13th · advanced study · Physics
Forces, energy and momentum
Is momentum conserved even when kinetic energy decreases?
See the idea step by step13th · advanced study · Physics
Resonance and applications of waves
Why does the displacement peak depend on damping?
See the idea step by step13th · advanced study · Physics
Electricity and energy in context
Why does increasing voltage reduce cable heating?
See the idea step by step13th · advanced study · Physics
An introduction to modern physics
Can more light compensate for insufficient energy per photon?
See the idea step by stepShall we try another idea?
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