Stage 4 · about 15–18
Systems and Argument
Many-factor systems; rigorous argument, writing and modelling.
Worked-problem videos, projects, bridges to exams and competitions.
All subjects at this stage
C
E
English
How do I say it accurately and appropriately?
P
Physics
Why must things be conserved?
- A ball dropped on a moving train Sideways and downward motion are independent: the passenger sees the ball fall straight down, someone on the platform sees a parabola. Try it
- What sets a pendulum's beat? For small swings the period depends only on the length (T = 2π√(L/g)); height energy and speed energy keep trading places. Try it
- Who pushes harder in a crash? Both carts push each other equally hard for the same time, so the total momentum is the same before and after, even when energy turns into heat. Try it
- Drawing a force you cannot see Field lines leave positive charges and end on negative ones; where they crowd together the force on a test charge is strongest. Try it
- Does the water travel with the wave? A wave moves a pattern and its energy along while each bit of the medium only moves back and forth or round a small loop in place; its speed is frequency times wavelength, v = fλ. Try it
- Which way does the ball fly when the string breaks? Going round a circle needs a force pointing to the centre; take it away and the ball flies off in a straight line along the tangent, not outward and not in a curve. Try it
C
Chemistry
Why do reactions happen, and how fast?
- Where reaction heat comes from Breaking bonds costs energy and making bonds releases it; a reaction is exothermic when the new bonds are stronger. Try it
- Hotter means harder hits Warming speeds a reaction mainly because many more collisions carry enough energy to react, not just because there are more collisions. Try it
- Equilibrium is busy, not stopped At equilibrium the forward and backward reactions run at the same rate, so amounts stay constant while particles keep changing. Try it
- Why the table has rows and columns Elements in a column behave alike because they have the same number of outer electrons. Try it
- Why salt water carries a current and sugar water doesn't Salt is built of charged ions that come apart and move freely when it dissolves or melts; sugar dissolves as whole neutral molecules, so nothing carries the charge. Try it
- Adding base: the pH jump at the end H⁺ and OH⁻ pair into water one for one, so the pH barely moves until the counts are almost equal, then a single drop pushes it up several units. Try it
B
Biology
How does life continue and change?
- Who leaves more offspring? No individual changes; the mix of a population shifts because some variants leave more offspring than others. Try it
- From DNA letters to a protein Almost every cell in your body holds the same DNA; cells differ by which genes they read, three letters (a codon) per amino acid. Try it
- Hares and lynx: why do the numbers cycle? Predators and prey can rise and fall in repeating cycles with the predator peak arriving after the prey peak, because predators multiply only after food is plentiful and starve only after it is gone. Try it
- The body's thermostat Body temperature and blood sugar stay near a set point because any change switches on a response that pushes it back: negative feedback. Try it
G
Geography
How does this system work?
H
History
Why did it happen this way, and how else could it have gone?
- Why did printing spread so fast? Big changes rarely have one cause: long-term conditions, a trigger and people's choices work together, and taking one away changes the outcome. Try it
- What changed, and what stayed the same? Different parts of life change at different speeds: how fast people could travel or how they lit their homes changed within a few generations, while staple foods, languages and family customs often lasted for centuries. Try it
C
Computing
Is this algorithm fast enough?
- Halve it: how search gets fast Halving a sorted list each time finds one item among a million in about 20 looks. Try it
- One artificial neuron learns to sort A neuron multiplies each input by a weight, adds them up and says 'yes' if the total passes a threshold, so it splits the plane with a straight line; learning is nudging the weights after every mistake. Try it