GCSE Combined Science Equations You Must Know (AQA and Edexcel)
GCSE Combined Science Equations You Must Know (AQA and Edexcel)
Equations are not optional extras in GCSE Combined Science. They are the difference between picking up marks and leaving them on the table. Across your six exam papers, a significant proportion of the total marks -- often 30% or more in physics papers and a meaningful chunk in chemistry -- require you to recall, select, or apply a mathematical relationship. If you cannot produce the right equation when you need it, you cannot even begin the calculation, and you lose every mark on that question.
The challenge for Combined Science students is that you are covering three subjects, each with its own set of equations and formulae. That is a lot to keep track of. This guide organises every equation you need by subject, tells you clearly which ones you must memorise and which ones are provided on the formula sheet, and explains how the two main exam boards -- AQA and Edexcel -- handle equations differently.
How AQA and Edexcel Handle Equations Differently
Before diving into the equations themselves, it is worth understanding a key structural difference between the two boards.
AQA splits physics equations into two categories: those you must recall from memory and those printed on a formula sheet in the exam. The specification is explicit about which equations fall into each category. In chemistry and biology, all required formulae must be recalled -- there is no formula sheet for those subjects.
Edexcel also provides a physics formula sheet, but the split between recall and given equations is different from AQA. Some equations that AQA expects you to memorise are on the Edexcel formula sheet, and vice versa. The chemistry and biology calculation formulae must be recalled for both boards.
The tables below indicate the status for each board. If you are unsure which board you are sitting, check with your teacher -- using the wrong list could leave you underprepared for equations your board expects you to know from memory.
Physics Equations You Must Memorise
These equations are NOT on the formula sheet for either AQA or Edexcel (unless noted). You must commit them to memory.
| Equation | What It Calculates | Units | AQA Status | Edexcel Status |
|---|---|---|---|---|
| v = s / t | Speed or velocity | m/s | Recall | Recall |
| a = (v - u) / t | Acceleration | m/s^2 | Recall | Recall |
| W = F s | Work done | J (joules) | Recall | Recall |
| KE = 1/2 m v^2 | Kinetic energy | J | Recall | Recall |
| GPE = m g h | Gravitational potential energy | J | Recall | Recall |
| P = E / t | Power | W (watts) | Recall | Recall |
| Efficiency = useful output / total input | Efficiency | No unit (decimal or %) | Recall | Recall |
| v = f lambda | Wave speed | m/s | Recall | Recall |
| Q = I t | Charge | C (coulombs) | Recall | Recall |
| V = I R | Potential difference | V (volts) | Recall | Recall |
| P = I V | Electrical power | W | Recall | Recall |
| P = I^2 R | Electrical power (alternative) | W | Recall | Given |
| E = P t | Energy transferred | J | Recall | Recall |
| E = Q V | Energy transferred (charge) | J | Recall | Given |
| rho = m / V | Density | kg/m^3 | Recall | Recall |
| W = m g | Weight | N (newtons) | Recall | Recall |
| P = F / A | Pressure | Pa (pascals) | Recall | Recall |
| T = 1 / f | Period | s (seconds) | Recall | Recall |
These 18 equations form the core of your physics calculation toolkit. Every one of them could appear in a question where no formula is provided, so you must be able to write them from memory without hesitation.
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Physics Equations Given on the Formula Sheet
These equations are provided in the exam. You do not need to memorise them, but you must know what each one means, when to use it, and how to rearrange and substitute values into it.
| Equation | What It Calculates | Units | AQA Status | Edexcel Status |
|---|---|---|---|---|
| F = m a | Force (Newton's second law) | N | Recall | Given |
| p = m v | Momentum | kg m/s | Given | Given |
| E = 1/2 k x^2 | Elastic potential energy | J | Given | Given |
| delta E = m c delta theta | Change in thermal energy | J | Given | Given |
| E = m L | Energy for change of state | J | Given | Given |
| P = rho g h | Pressure in a column of liquid | Pa | Given | Given |
| v^2 = u^2 + 2 a s | Final velocity (suvat) | m/s | Given | Given |
| F = (delta p) / t | Force and momentum (Higher) | N | Given | Given |
| V_p / V_s = N_p / N_s | Transformer turns ratio | No unit (ratio) | Given | Given |
| V_p I_p = V_s I_s | Transformer power (Higher) | W | Given | Given |
| F = B I l | Force on a conductor (Higher) | N | Given | Given |
Important note on F = ma: This is a crucial difference between the two boards. AQA expects you to recall F = ma from memory. Edexcel provides it on the formula sheet. If you are an AQA student, add F = ma to your memorisation list. If you are an Edexcel student, you will find it on the sheet, but you should still be fluent with it because it appears in so many questions.
Chemistry Equations and Formulae
Chemistry does not have a formula sheet on either AQA or Edexcel. Every formula used in calculations must be recalled from memory. The good news is that the list is shorter than physics, and the formulae are more straightforward.
| Formula | What It Calculates | Units |
|---|---|---|
| Moles = mass / Mr | Number of moles from mass | mol |
| Concentration = moles / volume | Concentration of a solution | mol/dm^3 |
| Concentration = mass / volume | Concentration of a solution | g/dm^3 |
| Atom economy = (Mr of desired product / sum of Mr of all products) x 100 | Atom economy of a reaction | % |
| Percentage yield = (actual yield / theoretical yield) x 100 | Percentage yield | % |
| Rf = distance moved by substance / distance moved by solvent | Rf value in chromatography | No unit |
| Relative formula mass (Mr) = sum of relative atomic masses | Mr of a compound | No unit |
How These Formulae Are Tested
Chemistry calculation questions typically carry 3 to 4 marks and follow a multi-step structure. A common format is: given the mass of a reactant and the balanced equation, calculate the mass of product formed. This requires you to convert mass to moles, use the mole ratio from the equation, and then convert back to mass. Each step earns a mark, so even if your arithmetic goes wrong at the end, you can still pick up 2 or 3 marks for correct method.
Concentration questions often involve titration results. You might be given the volume and concentration of one solution and asked to calculate the concentration of the other. Always check whether the question wants mol/dm^3 or g/dm^3 -- using the wrong unit is a common error.
Atom economy and percentage yield are tested less frequently in calculations, but they appear regularly as short-answer or explain questions. Know the difference: atom economy is a theoretical measure of how much of the reactant mass ends up as useful product (based on the equation alone), while percentage yield compares what you actually made with what you could theoretically have made.
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Biology Calculations
Biology has fewer formal equations, but the calculations that do appear are tested regularly and catch students off guard because they do not expect maths in a biology exam.
| Formula | What It Calculates | Units |
|---|---|---|
| Magnification = image size / actual size | Magnification of a microscope image | No unit (x) |
| Percentage change = (change / original) x 100 | Percentage change in mass, length, etc. | % |
| Surface area to volume ratio = surface area / volume | SA:V ratio | No unit (ratio) |
Magnification
This is one of the most frequently tested calculations in GCSE biology. You may be given a microscope image with a scale bar and asked to calculate the actual size of a cell or organelle, or you may be given the actual size and magnification and asked to calculate the image size.
The formula rearranges to:
- Actual size = image size / magnification
- Image size = actual size x magnification
The most common mistake is unit conversion. Microscope images are often measured in millimetres, but actual cell sizes are given in micrometres (1 mm = 1000 micrometres). Always convert to the same unit before dividing.
Percentage Change
This appears in osmosis practicals, enzyme experiments, and population data questions. Students sometimes calculate the change but forget to divide by the original value, or they divide by the final value instead. The original value is always the denominator.
Surface Area to Volume Ratio
This calculation supports understanding of diffusion and exchange surfaces. As organisms get larger, their SA:V ratio decreases, which is why large organisms need specialised exchange surfaces (lungs, villi, root hair cells). You may be asked to calculate the SA:V ratio of cubes of different sizes and explain the biological significance.
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Tips for Memorising Equations
With over 20 equations to recall across three subjects, rote memorisation alone will not work. Here are strategies that actually stick.
Write Them Out by Hand, Repeatedly
There is strong evidence that handwriting engages memory more effectively than typing or reading. At the start of every revision session, take a blank sheet of paper and write out every recall equation from memory. Check against a correct list. Any you missed or got wrong, write out three more times. Do this daily in the weeks before the exam.
Use Flashcards with Active Recall
Put the name of the quantity on one side (for example, "kinetic energy") and the equation on the other. Test yourself by looking at the name and trying to write the equation before flipping the card. Shuffle the cards each time so you are not relying on the order to prompt your memory.
Group Equations by Topic
Rather than trying to learn all equations in one block, group them by the topic they belong to. When you revise energy, learn the energy equations. When you revise electricity, learn the circuit equations. This creates contextual links that make recall easier in the exam, because the question context will naturally trigger the right group of equations.
Practise with Past Paper Questions
The best way to make equations stick is to use them. Every time you complete a calculation question from a past paper, you reinforce the equation in your memory and build fluency with substitution and rearrangement. Passive reading of equation lists does not achieve this.
Use the Formula Triangle Method
For equations with three variables (like V = IR or rho = m/V), the formula triangle is a reliable way to rearrange. Place the quantity that is alone on one side of the equation at the top, and the two multiplied quantities at the bottom. Cover what you want to find: if the remaining two are side by side, multiply; if one is above the other, divide.
For equations like KE = 1/2 mv^2, the triangle method does not apply neatly. You need algebraic rearrangement: v = square root of (2KE / m). Practise these rearrangements until they are second nature.
How Equations Are Tested in the Exam
Both AQA and Edexcel test equations through similar question types, but the emphasis and style differ in ways that are worth knowing.
Straightforward Substitution (Both Boards)
The simplest format: you are given values and asked to calculate using a named equation. For example, "A car has a mass of 1200 kg and is travelling at 15 m/s. Calculate the kinetic energy." These typically carry 2-3 marks: one for the equation, one for correct substitution, one for the answer with unit.
Rearrangement Questions (Both Boards)
You are given the equation (or must recall it) and need to rearrange before substituting. For example, "The kinetic energy of a ball is 50 J and its mass is 0.4 kg. Calculate the speed of the ball." This requires rearranging KE = 1/2 mv^2 to v = square root of (2KE / m). These questions carry 3-4 marks and are where many students lose marks unnecessarily.
Multi-Step Calculations (Both Boards)
These combine two or more equations. For example, calculating the kinetic energy of a falling object by first using GPE = mgh and then equating this to KE = 1/2 mv^2 to find speed. These are typically worth 4-5 marks and appear more frequently on Higher tier papers.
AQA-Specific Points
AQA is explicit in its specification about which equations must be recalled and which are given. The AQA physics formula sheet is printed on the exam paper itself. AQA calculation questions often include the instruction "Use the equation..." followed by a word description (for recall equations) or the equation itself (for given equations). This instruction tells you which equation to use, but you must still recall it if it is a recall equation.
AQA also frequently tests unit conversions alongside equations. You might be given speed in km/h and asked for kinetic energy in joules, which requires converting to m/s first.
Edexcel-Specific Points
Edexcel provides a separate formula sheet at the front of the physics exam paper. The sheet includes more equations than AQA's, which means fewer to memorise, but it also means you need to be comfortable navigating the sheet quickly to find what you need.
Edexcel calculation questions tend to be slightly more context-heavy. Rather than simply asking "Calculate the speed," they might embed the calculation within a practical scenario: "A student measures the time for a trolley to travel 1.5 m down a ramp. The time recorded is 2.4 seconds. Calculate the average speed of the trolley." The physics is identical, but you need to extract the relevant values from the context.
Edexcel also places more emphasis on showing working for method marks. The mark scheme awards marks for writing the equation, substituting values, and arriving at the answer. Even if your final answer is wrong, correct working can earn you 2 out of 3 marks on a typical calculation.
Common Mistakes That Cost Marks
These errors appear in examiner reports year after year. Avoid them and you will outperform a large number of students.
Not squaring the velocity in KE = 1/2 mv^2. Students write KE = 1/2 x m x v instead of KE = 1/2 x m x v^2. This is the single most common equation error in GCSE physics.
Confusing mass and weight. Mass is in kilograms and does not change with location. Weight is a force in newtons and depends on gravitational field strength. If a question gives mass but an equation needs weight, you must use W = mg first.
Forgetting unit conversions. Questions frequently give values in non-standard units: grams instead of kilograms, centimetres instead of metres, minutes instead of seconds, kW instead of W. Always convert before substituting. If your answer is absurdly large or small, a missing unit conversion is the most likely cause.
In chemistry, confusing mol/dm^3 and g/dm^3. These are both valid units for concentration, but they are not interchangeable. Read the question to see which unit is required, and if you need to convert between them, use the relationship: concentration in g/dm^3 = concentration in mol/dm^3 x Mr.
In biology, using the wrong denominator for percentage change. Always divide by the original value, not the final value.
Rounding too early. Keep intermediate values to at least 3 significant figures. Only round your final answer. Early rounding can push your answer outside the acceptable range on the mark scheme.
Bringing It All Together
The students who perform best on equation questions are not the ones with the best natural maths ability. They are the ones who have practised recall until the equations are automatic, who show their working clearly for every step, and who check their units before and after every calculation.
Start by identifying which board you are sitting -- AQA or Edexcel -- and use the tables in this guide to build your personal list of recall equations. Write them out daily. Test yourself with flashcards. Apply them in past paper questions under timed conditions. By the time you sit your exams, producing the right equation should feel as natural as writing your name.
For a broader overview of Combined Science revision, see our Edexcel GCSE Combined Science Revision Guide. For subject-specific equation guides with full worked examples, see Edexcel GCSE Physics Equations and Edexcel GCSE Chemistry Equations.
To understand how examiners award marks for calculation questions, read How Edexcel Mark Schemes Work and How AQA Mark Schemes Work.
Explore all GCSE Combined Science courses on LearningBro and start practising with exam-style questions today.