Study notes
The notebook, shared.
Clean, exam-ready notes and formula sheets for grades 6–12 — maths, physics, and middle-school science. Use them to revise, or to see exactly how I lay an idea out.
- 2 Jun 20262 min readphysics
Simple harmonic motion: the maths of anything that oscillates
Pendulums, springs, vibrating strings — they all obey one condition and one equation. Here's what defines SHM, where the energy goes, and the graphs that catch everyone out.
Grade 11-12#shm#oscillations#mechanics→ - 28 May 20262 min readphysics
Momentum: conservation, impulse, and collisions
One conservation law solves every collision and explosion you'll be set. Here's momentum, the impulse that changes it, and the difference between elastic and inelastic that decides what's conserved.
Grade 11-12#momentum#mechanics#collisions→ - 10 May 20262 min readmaths
Differentiation: the five rules you actually need
Power, sum, product, quotient, chain — the whole toolkit on one page, with the one question to ask before you pick a rule.
Grade 11-12#calculus#differentiation#algebra→ - 10 May 20262 min readphysics
Kinematics: the equations of motion
The four equations for constant acceleration — what each one is for, when to reach for it, and the one decision that picks the right equation every time.
Grade 11-12#mechanics#kinematics#formula sheet→ - 12 Apr 20262 min readmaths
Trigonometric identities worth memorising
The short list of identities that actually earn their keep in exams — plus how each one is really just the Pythagorean theorem in disguise.
Grade 11-12#trigonometry#algebra#formula sheet→ - 15 Mar 20262 min readphysics
Newton's three laws, in plain language
What each of Newton's laws actually says, the everyday picture behind it, and the mistake students make with each one.
Grade 11-12#mechanics#forces#newton→ - 12 Dec 20252 min readphysics
Work, energy and power: the equations and the traps
Three closely related ideas that students blur together. Here's precisely what each means, the equations linking them, and the angle that quietly turns up in every 'work done' question.
Grade 11-12#energy#mechanics#work→ - 20 Nov 20252 min readmaths
Arithmetic and geometric series on one page
Two kinds of sequence cover most of what exams ask: ones that grow by adding, and ones that grow by multiplying. Here are the formulas, the one that surprises everyone, and how to tell them apart.
Grade 11-12#sequences#series#algebra→ - 25 Oct 20252 min readmaths
Logarithms: the laws, and what a log really asks
A logarithm is just the question 'what power?' Once you see that, the laws stop being arbitrary and become a way of turning multiplication into addition — and solving equations with x in the exponent.
Grade 11-12#logarithms#exponentials#algebra→ - 8 Oct 20252 min readscience
Acids, alkalis and the pH scale
What makes something an acid or an alkali, how the pH scale measures it, and what happens when the two meet. The reliable middle-school chemistry that turns up every year.
Grade 9-10#chemistry#acids#ph→ - 18 Sept 20252 min readmaths
Integration: the standard integrals and how to choose a method
Differentiation has rules; integration has a toolkit and a decision. Here are the standard results, the three techniques, and the question that tells you which technique a problem wants.
Grade 11-12#calculus#integration#algebra→ - 2 Sept 20252 min readmaths
Standard form: writing very big and very small numbers
Scientists don't write out the mass of an electron with thirty zeros. Standard form is the shorthand — one rule for the format, and a quick way to multiply and divide enormous numbers in your head.
Grade 9-10#standard-form#indices#arithmetic→ - 30 Aug 20252 min readscience
Speed, velocity and acceleration: reading motion graphs
Three words students use interchangeably and shouldn't. Here's what each one means, the equations, and how to read a distance–time and velocity–time graph at a glance.
Grade 9-10#motion#kinematics#graphs→ - 22 Jul 20252 min readscience
Reflection and refraction: how light bends
Light bounces off surfaces and bends through them by two simple rules. Get the normal line right and you'll never muddle the angles again — including why a straw looks broken in water.
Grade 9-10#light#optics#refraction→ - 28 Jun 20252 min readmaths
Pythagoras and trigonometry: finding sides and angles
Two tools for right-angled triangles: Pythagoras for sides when you know two sides, trigonometry for everything involving an angle. Here's how to tell instantly which one a question needs.
Grade 9-10#trigonometry#geometry#pythagoras→ - 10 Jun 20252 min readscience
Waves: the properties, and the one equation
Every wave — sound, light, water — shares the same handful of properties and a single equation linking them. Plus the difference between transverse and longitudinal that examiners love.
Grade 9-10#waves#physics#frequency→ - 15 May 20252 min readmaths
Straight-line graphs: everything from y = mx + c
One equation describes every straight line. Learn to read the gradient and intercept off it — and to find the equation of a line from two points — and the whole topic opens up.
Grade 9-10#graphs#algebra#gradients→ - 22 Apr 20252 min readmaths
Averages: mean, median, mode and range
Three different 'averages' that answer three different questions, plus the range. Which one to use, how to find each, and the outlier that quietly breaks one of them.
Grade 6-8#statistics#averages#data→ - 9 Apr 20252 min readmaths
Simultaneous equations: substitution vs elimination
Two unknowns need two equations. Here are the two methods that solve them, a clear rule for which to use, and the check that catches almost every mistake.
Grade 9-10#algebra#equations#simultaneous→ - 20 Mar 20252 min readscience
Energy: its forms, and how it moves around
Energy is never made or destroyed — it only changes form or moves from one place to another. Once you can track it, you can explain almost any machine or process.
Grade 6-8#energy#transfers#foundations→ - 5 Mar 20252 min readscience
Electric circuits: current, voltage, resistance
Three quantities, one equation, and two rules for series and parallel. Here's the whole of basic circuits — plus the water analogy that makes every part of it intuitive.
Grade 9-10#electricity#circuits#ohms-law→ - 25 Feb 20252 min readmaths
The laws of indices on one page
Six rules cover every power you'll meet, and they all come from one idea: an index just counts how many times you multiply. Includes the negative and fractional ones everyone forgets.
Grade 9-10#indices#exponents#algebra→ - 8 Feb 20252 min readscience
Light: how we see, shadows, and reflection
Light travels in straight lines — and almost everything about shadows, mirrors, and how your eye works follows from that one fact.
Grade 6-8#light#optics#reflection→ - 28 Jan 20252 min readmaths
Quadratic equations: three methods, and when to use each
Factorising, the quadratic formula, completing the square — they all solve the same equation. The skill is reading the question and knowing which one is fastest here.
Grade 9-10#algebra#quadratics#equations→ - 14 Jan 20252 min readmaths
Area and perimeter of every shape they'll ask
The formulas on one page, the difference students keep mixing up, and the two-step trick for any awkward compound shape.
Grade 6-8#geometry#mensuration#area→ - 9 Jan 20252 min readscience
Atoms, elements and compounds
The three words students use as if they mean the same thing — and don't. Sorting out atom, element, and compound is the foundation the whole of chemistry is built on.
Grade 6-8#chemistry#atoms#matter→ - 5 Dec 20242 min readscience
Forces: what a push or a pull actually does
A force is just a push or a pull. What matters is whether the forces on an object are balanced — that single idea decides whether anything speeds up, slows down, or stays still.
Grade 6-8#forces#motion#foundations→ - 26 Nov 20242 min readmaths
Algebra basics: collecting like terms and substituting
The first real step into algebra. What a letter actually stands for, which terms you're allowed to add together, and how to put numbers back in — the foundation everything later sits on.
Grade 6-8#algebra#expressions#foundations→ - 12 Nov 20242 min readmaths
Ratio, proportion and percentage are the same idea three ways
These three topics power half of every word problem, and they're secretly one idea. Learn to switch between them and 'find 15% of 240' stops being scary.
Grade 6-8#ratio#percentages#proportion→ - 15 Oct 20242 min readmaths
The rules of signs, and why two negatives make a positive
Negative numbers trip up more middle-schoolers than anything else. Here are the four rules, the number-line picture behind them, and a reason 'minus times minus' isn't just something to memorise.
Grade 6-8#integers#arithmetic#foundations→ - 2 Oct 20242 min readscience
States of matter, and the particle model that explains them
Solid, liquid, gas — what's really different is how the particles are arranged and how much they move. One picture explains melting, boiling, and why a gas fills its container.
Grade 6-8#matter#states#particle-model→ - 20 Sept 20242 min readmaths
Fractions: every operation on one page
Add, subtract, multiply, divide — the four things you can do to a fraction, the one rule each needs, and the trap that catches everyone with division.
Grade 6-8#fractions#arithmetic#foundations→ - 28 Aug 20242 min readmaths
BODMAS: the order operations actually happen in
Why 2 + 3 × 4 is 14 and not 20. The order maths is done in isn't a suggestion — it's a fixed rule, and one line of the rule trips up almost everyone.
Grade 6-8#arithmetic#order-of-operations#foundations→