22 February 2026

Understanding Cash Flow (and why profitable businesses still go bust)

A and GCSE Business Studies

Cash flow is the movement of cash into and out of a firm’s bank account.
Profit is when revenue is greater than total costs.

Those two sentences look similar… right up until your “profitable” business can’t pay the rent on Friday.

Think of it like this:

Profit is your score (based on what you’ve earned and what you’ve incurred).
Cash flow is your oxygen (based on what has actually arrived in the bank, and what’s actually left it).

A business can “win on points” (profit) while still running out of oxygen (cash).

Why cash flow and profit don’t match

1) Timing: “Sold” doesn’t mean “paid”

You might invoice a customer today… but they might pay in 30, 60, or 90 days.

So your accounts may show a profitable sale, but your bank account is still doing its best impression of a tumbleweed.

Example:
You sell £10,000 worth of work in January on 60-day terms.
That’s great for profit in January… but the cash might not show up until March.

2) Cash leaves before you’ve “made” the sale

Businesses often pay for stock, wages, and rent before customers pay them.

That gap is where cash flow dramas live.

3) Non-cash costs affect profit (but not cash)

Some costs reduce profit without an immediate cash payment.

Depreciation is the classic: the value of equipment “wearing out” on paper.
The cash left the bank when you bought the kit, not each month afterwards.

So you can have:

Lower profit due to depreciation,
while cash flow that month looks fine.

4) Investment spending hurts cash flow (but not necessarily profit)

Buying a new van, refurbishing the shop, purchasing a 3D printer that you absolutely “need” (honestly)…
That’s a cash outflow now, even though the benefit is spread over years.

5) Loan repayments are cash outflows, but not all are “costs”

Repaying a loan:

Interest counts as a cost (affects profit),
Repaying the capital does not count as a cost, but it does reduce cash.

This catches students out all the time.

A simple cash flow example (the “how are we broke?” moment)

Imagine a small business in January:

Cash in:

Customers pay: £2,000

Cash out:

Rent: £1,200
Wages: £1,500
Stock purchase: £800

Net cash flow = £2,000 − (£1,200 + £1,500 + £800)
Net cash flow = £2,000 − £3,500 = –£1,500

So cash is falling.

But profit for January might look like this:

Sales made (invoiced): £6,000
Costs incurred: £4,000
Profit = £2,000

Profit: +£2,000
Cash flow: –£1,500

That’s how you can be profitable and panicking in the same month.

Why cash flow matters so much in Business Studies (and real life)

Cash flow problems can cause:

Late payments to suppliers (and damaged relationships)
Missed wages (and an instant morale collapse)
Emergency overdrafts (and extra costs)
In extreme cases: business failure, even when the business is “profitable”

In exams, you’ll often link this to:

Working capital (current assets − current liabilities)
Cash flow forecasting
Reasons for using finance (overdrafts, short-term loans)
Managing trade credit (both given and received)

Quick ways businesses improve cash flow

Increase cash inflows

Encourage faster customer payments (shorter credit terms)
Offer small discounts for early payment
Chase late invoices (politely at first… then less politely)
Take deposits or upfront payments

Reduce or delay cash outflows

Negotiate longer payment terms with suppliers
Reduce unnecessary spending
Manage stock levels (too much stock = cash sitting on shelves)
Lease rather than buy expensive assets (sometimes)

Mini “exam-ready” summary

Profit = revenue − total costs (measured over a period, includes non-cash items).
Cash flow = actual cash in − actual cash out (bank balance reality).
A business can be profitable but still fail if it can’t meet short-term payments.

21 February 2026

“Ask an AI to do extended thinking…” — and it tells you what it’s doing?! (Sort of.)

A Level Computing | Philip M Russell Ltd style | UK spelling

You’ve seen it happen:

You ask an AI a tricky question.
You click the button that says something like “extended thinking”.
And then—instead of just blurting out an answer like an overconfident Year 10—you get a response that sounds like the AI is narrating its brain:

“First I’ll break the problem down… then I’ll check edge cases… then I’ll verify…”

It feels like watching a student show their working. Which is oddly comforting.

But here’s the important bit for A Level Computing:

The AI isn’t “showing its thoughts” in the way you think

Most modern AI systems do not reveal their full internal reasoning (often called chain-of-thought). What you’re seeing is usually a summary of the approach: a tidy, human-readable explanation of the steps it took or would take.

That’s not a bad thing. In fact, for learning, it can be brilliant — but you need to understand what you’re getting.

What “extended thinking” usually means (in plain English)

When you request extended thinking, you’re generally asking the model to:

Spend more compute/time on reasoning
Break the task into sub-problems
Self-check for contradictions and missing cases
Explain the method more explicitly than usual

In A Level terms, it’s similar to switching from:

“Give me the answer”
to
“Show me your algorithm, and then run it carefully.”

Why it looks like the AI is narrating its process

Because narration is useful.

A well-structured explanation often includes:

Identifying inputs/outputs (specification thinking)
Planning a method (algorithm design)
Checking constraints (edge cases, assumptions)
Verifying results (testing / validation)

That’s basically the Computational Thinking toolkit:
Decomposition, abstraction, algorithmic thinking, evaluation.

So the AI is doing what your teacher has been nagging you to do all along. (Annoying, isn’t it?)

The catch: “explanations” are not the same as “proof”

Even if the AI gives you a lovely step-by-step explanation, it can still:

use a wrong assumption,
miss a constraint,
produce an answer that sounds correct but isn’t.

So treat it like a very fast study partner who sometimes confidently walks into lampposts.

A Level-friendly rule:

Use the AI’s explanation as a draft algorithm — then test it like you would test your own code.

How to prompt it properly (so it actually helps you learn)

Try these prompt styles:

1) Ask for a plan first (before the final answer)

Prompt:
“Give me a brief plan (like pseudocode / method) before the final answer.”

Why it helps: you can spot dodgy logic early.

2) Force it to state assumptions

Prompt:
“List your assumptions explicitly before solving.”

Why it helps: you can challenge the weak bits.

3) Ask it to check edge cases

Prompt:
“After answering, test your solution against 3 edge cases.”

Why it helps: that’s literally exam evaluation.

4) Ask for a marking-grid style response

Prompt:
“Answer like an A Level student: define terms, show method, give final result, then evaluate limitations.”

Why it helps: it mirrors how marks are awarded.

A quick example: “Explain how you’d search for the fastest route”

Instead of:
“Find the fastest route.”

Try:
“Explain how you’d approach this: identify the graph model, choose an algorithm, and justify it.”

Now you’re doing proper A Level:

Graph representation (nodes/edges/weights)
Algorithm choice (Dijkstra vs A* vs BFS)
Justification (constraints, complexity, correctness)

So… should you trust the “thinking”?

Trust it the way you trust a calculator:

Great for speed
Great for structure
Still your job to check it’s answering the right question

And if it gives you a neat method: brilliant. That’s basically revision.

Just don’t confuse “a convincing explanation” with “guaranteed correct”.

20 February 2026

A-Level Chemistry — Iodine and its Properties (the glamorous purple one)

If chlorine is the loud, attention-seeking halogen and bromine is the moody one, iodine is the dramatic artist: it sits there looking like a dull grey solid… then quietly produces a purple vapour that makes everyone in the lab suddenly pay attention.

This post is a tidy A-Level tour of iodine’s key physical and chemical properties, plus the bits exam questions love to poke.

1) Where iodine sits and what that tells you

Iodine is a Group 17 (halogen) element. Like the others, it exists as diatomic molecules: I₂.

Trends down Group 17 (F₂ → Cl₂ → Br₂ → I₂):

Melting/boiling points increase (bigger molecules → stronger intermolecular forces)
Colour gets darker
Reactivity decreases (harder to gain an electron as atoms get larger and shielding increases)

So iodine is less reactive than chlorine and bromine, but it still does plenty of chemistry.

2) Physical properties you can actually see

Appearance and state

Grey/black crystalline solid at room temperature
Produces a purple vapour when warmed

Sublimation (a favourite classroom moment)

Iodine can sublime: solid → gas without becoming a liquid first (under normal lab conditions).
That purple vapour is iodine gas (still I₂ molecules).

Why does iodine sublime easily?
Inside each I₂ molecule, the I–I covalent bond is strong. But between molecules the attractions are only London dispersion forces—and warming supplies enough energy to overcome those.

3) Solubility: iodine is fussy

Iodine is non-polar overall, so:

Low solubility in water
Much more soluble in non-polar solvents (e.g. cyclohexane / hexane)

Colour clue (classic practical / exam):

In water: brown/yellow-brown (a mixture of I₂ and some I₃⁻ if iodide is present)
In cyclohexane: vivid purple (I₂ really showing off)

If you add iodide ions (from KI), iodine forms triiodide:

$\mathrm{I_2(aq) + I^-(aq) \rightleftharpoons I_3^-(aq)}$

This helps “pull” iodine into aqueous solution.

4) Simple redox behaviour (the exam engine)

Iodine is an oxidising agent (it accepts electrons), but weaker than chlorine or bromine.

Reduction half-equation:

$\mathrm{I_2 + 2e^- \rightarrow 2I^-}$

That’s the backbone of loads of questions: titrations, displacement, and redox calculations.

5) Displacement reactions: who can bully whom?

A more reactive halogen displaces a less reactive one from its halide.

So:

Chlorine displaces iodide:

$\mathrm{Cl_2 + 2I^- \rightarrow 2Cl^- + I_2}$

Bromine displaces iodide:

$\mathrm{Br_2 + 2I^- \rightarrow 2Br^- + I_2}$

But iodine does not displace bromide or chloride.

Observation: formation of iodine gives brown solution (or purple in organic layer).

6) Iodine as a test reagent (two big ones)

(A) Starch test (iconic)

Iodine forms a deep blue-black complex with starch (specifically amylose helices).
This is used to detect iodine, and also in clock reactions where iodine appears/disappears.

(B) Iodometry / iodimetry (A-Level titration territory)

Iodine can be titrated with thiosulfate:

$\mathrm{I_2 + 2S_2O_3^{2-} \rightarrow 2I^- + S_4O_6^{2-}}$

Starch indicator is added near the end point (when solution is pale) for a sharp finish.

7) A quick word on safety and good lab habits

Iodine vapour is irritant — use a fume cupboard for heating/sublimation demos.
Avoid skin contact (stains and irritates).
Use small quantities: iodine is “spectacular per gram”.

Mini “exam-style” check questions (with answers)

Why are iodine’s melting and boiling points higher than chlorine’s?
Because iodine molecules are larger with more electrons, so London dispersion forces are stronger.
Write the ionic equation for chlorine reacting with potassium iodide solution.

$\mathrm{Cl_2 + 2I^- \rightarrow 2Cl^- + I_2}$

Why does iodine appear purple in cyclohexane but brown in water?
Cyclohexane dissolves molecular I₂ well (purple). In water iodine is poorly soluble and can form I₃⁻ in the presence of I⁻, giving brown shades.
State the half-equation for iodine being reduced.

$\mathrm{I_2 + 2e^- \rightarrow 2I^-}$

19 February 2026

Experiments with a PASCO Light Sensor (and why light is never ‘just light’)

If you’ve ever said, “It’s brighter over there,” congratulations — you’ve made a scientific observation. If you’ve ever argued with someone about it, you’ve made a scientific dispute. The PASCO Light Sensor is the peace treaty: it turns “bright” into numbers you can graph, analyse, and (most importantly) use to win the argument politely.

In this post I’ll share a set of simple, reliable experiments you can run with a PASCO Light Sensor (in class or at home), plus what to measure, what to plot, and the usual “why do my results look odd?” troubleshooting.

What you’ll need

PASCO Light Sensor (any PASCO light/illuminance sensor)
PASCO interface / SPARKvue or Capstone (or whatever you’re using)
A lamp (desk lamp is fine) and/or torch
Metre rule or tape measure
A sheet of white paper or card (as a reflector)
Optional: coloured filters/cellophane, sunglasses, polarising sheets, diffraction grating, blinds/curtains

Tip: Try to keep room lighting constant. Daylight through a window is lovely… and also a chaos agent.

Experiment 1: The inverse square law (the “physics that actually works” one)

Question: How does light intensity change with distance from a point source?

Method

Set the lamp at one end of a bench. Keep it still throughout.
Place the sensor facing the lamp.
Measure distance $d$ from the lamp to the sensor (start at, say, 10 cm, then 15, 20, 30, 40, 50 cm).
Record light intensity at each distance (lux).
Repeat each reading 2–3 times and average.

What to plot

Plot Intensity (lux) vs distance (m) → curve
Plot Intensity (lux) vs 1/d² → should be a straight line (ish!)

What you should find
If the lamp behaves like a point source, intensity $\propto 1/d^2$ .

Common problems

At small distances the lamp isn’t a point source.
If the sensor saturates, move further away or reduce brightness.
Reflections from walls and benches can lift the readings.

Experiment 2: Absorption and transmission (a.k.a. “how good are your sunglasses?”)

Question: How much light gets through different materials?

Method

Fix the lamp and sensor positions (don’t change distance).
Record baseline intensity $I_0$ .
Place a material between lamp and sensor (paper, tracing paper, plastic, sunglasses, tinted film, acetate).
Record transmitted intensity $I$ .
Calculate percentage transmission:

\%T = (I/I_0)\times 100

Extensions

Stack layers of the same material and see if transmission drops steadily.
Compare clear vs frosted plastic.
Compare different “SPF” sunglasses (if available).

Experiment 3: Reflection — colour, surface, and angle (the “why is it brighter off the white card?” one)

Question: What affects reflected light intensity?

Method

Put a white card on the bench.
Shine a lamp or torch at it at a fixed angle.
Point the sensor towards the card to measure reflected light.
Compare different surfaces: white paper, coloured paper, foil, matte card, glossy magazine.

Ideas to test

Colour: Which reflects more: white, yellow, red, black?
Texture: Glossy vs matte
Angle: Rotate the card and see how reflections change

Bonus physics
Specular reflection (mirror-like) vs diffuse reflection (scattered). Foil behaves very differently from paper.

Experiment 4: Light intensity and shadow patterns (because shadows have structure)

Question: How does intensity change across a shadow?

Method

Place a small object (ruler, pencil, hand) between lamp and sensor.
Move the sensor slowly sideways across the shadow edge.
Record intensity at each position.

What to plot

Intensity vs position → you’ll see a drop, then a rise.
With a small light source you get a sharp edge; with a bigger source you get a fuzzy “penumbra”.

Link to GCSE Physics
This is a brilliant way to measure umbra and penumbra rather than just draw them.

Experiment 5: Flicker and mains lighting (why 230 V lighting isn’t steady)

Question: Do lights actually stay constant?

Many LED lights and some fluorescents flicker at 100 Hz (UK mains is 50 Hz; brightness often varies twice per cycle).

Method

Put the sensor under a mains-powered lamp (not daylight).
Record intensity vs time at a high sample rate (if possible).
Look for periodic variation.

What you’ll see
Some lights are smooth; others are “invisible strobe lights”. Great discussion for cameras, headaches, and why slow-motion video looks odd under certain lights.

Experiment 6: Polarisation (if you have polarising filters)

Question: How does light intensity change through crossed polarisers?

Method

Place one polariser in front of the light source (or in front of sensor).
Place a second polariser in front of it.
Rotate one polariser and record intensity at angles 0° → 90°.

What to plot

Intensity vs angle (°)

Expected pattern
It follows Malus’ Law:

I = I_0 \cos^2(\theta)

(And yes, it’s one of those rare laws that behaves beautifully in a school lab.)

Data handling (make it look like proper science)

Take repeats and average.
Control one variable at a time (distance OR filter OR angle — not all at once).
Use units carefully (lux, metres, degrees).
Try at least one linearised graph (e.g., intensity vs $1/d^2$ ).

Troubleshooting: the “why are my readings weird?” section

Sunlight changed → close curtains or work at night (science is glamorous).
Reflections → move away from white walls, use a dark cloth behind.
Sensor orientation → keep it facing the same way each reading.
Auto-ranging → if the sensor/interface changes range, it can look jumpy. Lock range if possible.

If you’re teaching this (or revising)

These experiments are brilliant for:

GCSE Physics: inverse square, reflection/absorption, shadows
A-Level Physics: Malus’ law, measurement uncertainty, data linearisation, practical write-ups

And they’re perfect for filmed demonstrations too — you can see the graph change live, which is exactly the kind of “Ohhh, I get it” moment students remember.

18 February 2026

Maths: Applying Maths to Spreadsheets (GCSE & A-Level)

In exams, students often treat maths and computing as separate subjects.

In real life? They work together all the time.

If you’re studying GCSE or A-Level Maths, Business, or Computing, learning how maths applies inside a spreadsheet like Microsoft Excel or Google Sheets is a genuine superpower.

Because spreadsheets don’t just store numbers — they apply mathematics at scale.

1️⃣ Percentages – Profit, Growth & Error

Common GCSE Applications:

Percentage increase/decrease
Profit margins
Reverse percentages
VAT calculations

Example: Percentage Increase


=(NewValue-OldValue)/OldValue*100

This directly links to GCSE percentage change questions.

In Business Studies, this becomes:

Revenue growth
Inflation rates
Cost increases

And suddenly maths has context.

2️⃣ Algebra – Turning Equations into Formulas

Spreadsheets are algebra machines.

If you understand:

y = mx + c

You can model it directly:


= m*A2 + c
Applications:
Modelling taxi fares
Predicting future sales
Calculating depreciation
Physics motion equations
At A-Level, this becomes:
Iterative modelling
Recursive formulas
Financial modelling
You are effectively programming with maths.

3️⃣ Statistics – Mean, Standard Deviation & Correlation
Spreadsheets make statistics immediate.
Functions:
=AVERAGE()
=STDEV.S()
=CORREL()

GCSE:
Mean, median, range
Charts and data presentation
A-Level:
Standard deviation
Regression lines
Correlation coefficients
For my own sailing race analysis at Upper Thames Sailing Club, spreadsheets allow:
Personal handicap tracking
Improvement calculations
Race performance comparisons
That’s maths with purpose.

4️⃣ Financial Maths – Compound Growth
Compound interest appears constantly in exams.
In a spreadsheet:
=Initial*(1+rate)^years

Or use:
=FV()

This connects GCSE maths to:
Mortgages
Savings
Investment growth
Battery ROI calculations (something I’ve analysed in my own solar system modelling)
Real mathematics. Real consequences.

5️⃣ Logical Maths – IF Statements
This is where Maths meets Computing.
=IF(A2>50,"Pass","Resit")

You’re applying inequalities and logical reasoning.
In A-Level Computing this links directly to:
Boolean logic
Algorithms
Decision structures
Spreadsheets are the bridge between maths and code.

🎯 Why This Matters
Students often ask:
“When will I ever use this?”
If you can:
Build a working financial model
Analyse data properly
Model change
Test scenarios
You’re already thinking like:
An analyst
An engineer
A business owner
A scientist
Maths in spreadsheets turns abstract numbers into decisions.
And that’s powerful.

17 February 2026

A-Level Physics: AC Theory, RMS Voltages – and Why 230 V Isn’t 230 V at All

When students first meet alternating current in A-Level Physics, there’s a moment of quiet confusion:

“If the UK mains supply is 230 V… why does the graph go above 230 V?”

Excellent question.

Because 230 V isn’t the peak voltage. It isn’t even the average voltage. It’s something called the RMS voltage — and that changes everything.

1️⃣ What Is AC?

In the UK, our mains electricity is:

Alternating Current (AC)
Frequency = 50 Hz
Stated voltage = 230 V

Unlike DC (direct current), AC voltage:

Continuously changes direction
Follows a sine wave
Alternates between positive and negative values

Mathematically:

V = V_0 \sin(\omega t)

Where:

$V_0$ = peak voltage
$\omega$ = angular frequency
$t$ = time

2️⃣ Peak Voltage vs RMS Voltage

Here’s the key idea students must master:

V_{RMS} = \frac{V_0}{\sqrt{2}}

So if the RMS voltage is 230 V:

V_0 = 230 \times \sqrt{2}

V_0 \approx 325 \text{ V}

🚨 That means the UK mains actually reaches +325 V and –325 V every cycle.

Not 230 V.

3️⃣ So What Does RMS Actually Mean?

RMS stands for:

Root Mean Square

It is the DC voltage that would produce the same heating effect in a resistor.

This is crucial.

Because power in a resistor is:

P = \frac{V^2}{R}

If we simply averaged the AC voltage over a full cycle, we'd get zero (positive and negative cancel).

But heating depends on V², which is always positive.

So we:

Square the voltage
Find the mean
Take the square root

Hence: Root Mean Square.

4️⃣ Why Engineers Use RMS

Imagine a 230 V electric heater.

If we replaced AC with DC, the DC voltage that would produce the same heating effect is:

230\text{ V DC}

That’s why appliances are rated using RMS values.

It allows fair comparison between AC and DC power delivery.

5️⃣ Common Exam Mistakes

From years of teaching A-Level Physics, these errors appear again and again:

❌ Confusing peak and RMS
❌ Forgetting the √2 factor
❌ Using 230 V as peak in power calculations
❌ Forgetting RMS current obeys the same rule:

I_{RMS} = \frac{I_0}{\sqrt{2}}

6️⃣ Why This Matters Beyond the Exam

Understanding RMS is vital for:

Designing power supplies
Understanding transformers
Working with oscilloscopes
Safety calculations
Interpreting energy transfer

It also explains why touching a “230 V” supply is far more dangerous than students imagine — because the peaks are significantly higher.

7️⃣ A Quick Exam-Style Question

The UK mains supply is 230 V RMS.

a) Calculate the peak voltage.
b) Calculate the peak current if a 2 kW heater is connected.

(Hint: Start with $P = VI$ using RMS values.)

Final Thought

AC theory is one of those topics that feels abstract — until you realise your entire house is powered by a sine wave swinging between +325 V and –325 V fifty times every second.

Suddenly it feels rather more real.