A large share of examination errors come from information that was never actually given. This EMS workshop builds an assumption audit across English, Mathematics and Science: given, derived, inferred and assumed.
It follows Vol 0072 and extends the source discipline in Vol 0069 and the evidence discipline in Vol 0065. Use the G3 SEC learner hub for the wider route.
For 2027 school candidates, use the official K300 English, K310 Mathematics and K326/K327/K328 combined Science syllabuses, plus the SEAB G3 directory, for assessment requirements. Every case below is original teaching material.
The fastest way to derail a good answer is to smuggle in an assumption
An assumption is something the learner treats as true without the question or evidence establishing it. Some assumptions are reasonable modelling choices; others are silent mistakes. The examination skill is to know which is which and to keep them separate from given information.
Use four labels: given, derived, inferred, assumed
Given information is stated or shown. Derived information comes from valid calculation or reasoning. Inferred information is supported but not directly stated. Assumed information is introduced by the learner. These categories create a clean audit trail across EMS.
Given information should remain visible
A condition such as equal mass, fixed temperature, two-hour duration or voluntary respondents may completely change the answer. Highlight or note critical givens before adding your own reasoning. Many wrong answers begin by ignoring one small condition.
Derived information must be traceable
A derived value should have a visible route from the givens. If you cannot explain where the number, conclusion or relationship came from, it may have been guessed or carried from memory rather than derived from this task.
Inference needs evidence
An inference is not arbitrary imagination. It should be the smallest justified step beyond explicit information. In English, this might concern motive or attitude. In Science, it may concern a mechanism supported by observations. In Mathematics, it may concern what a solved value means in context.
Assumptions can be legitimate when stated and relevant
A modelling problem may require an assumption such as constant speed or negligible change over a short interval. If the question invites modelling, state the assumption and use it consistently. Hidden assumptions are riskier because neither the learner nor the marker can see what the solution depends on.
English: separate writer statement from learner assumption
If a passage says the committee is considering a change, do not assume the change has already been approved. The source gives consideration; approval is an added assumption unless another sentence confirms it.
English: separate character action from motive
A character leaves early. The action is given. “The character was angry” may be an inference if language supports it, but it should not be treated as fact merely because anger is one possible explanation.
English: separate respondents from population
A survey result about respondents does not automatically describe all students. The respondent group is given. Extending the percentage to the entire school is an assumption unless sampling information supports that inference.
English: separate chronology from cause
If attendance rose after a timetable change, sequence is given. “The timetable caused the rise” is a causal inference requiring stronger support. Another change during the same period may provide an alternative explanation.
English: distinguish writer view from quoted view
A passage may quote a critic. The quotation is evidence of what that critic said, not necessarily the writer’s own position. Track attribution before summarising or evaluating.
English: situational writing assumptions
In Situational Writing, use the information provided by the visual text and task. Do not invent dates, facilities, prices or policy details unless the task invites reasonable elaboration. An invented detail can accidentally contradict the source.
English: argumentative examples should be labelled honestly
A personal example can illustrate a point without becoming a fake statistic. Write “In my experience…” rather than inventing “research shows 80%…” when no real source is known.
English: Oral answers can state conditions
If an examiner asks about a hypothetical policy, you may explain the condition under which your view changes. This is different from assuming hidden facts about the policy. Make the conditional nature of your reasoning visible.
Mathematics: define the variable before using it
A symbol should represent a stated quantity. If x means number of tickets, it should not later become total cost. Variable definitions prevent silent assumption shifts inside algebra.
Mathematics: units expose hidden assumptions
Treating 4 minutes as 4 seconds is not merely arithmetic error; it assumes compatible units when they are not compatible. Writing units beside quantities makes the hidden assumption visible.
Mathematics: diagrams are not automatically to scale
A triangle that looks right-angled is not evidence of a right angle unless marked, stated or derived. Assuming appearance is a common geometry error. Use given properties, not visual impression.
Mathematics: linearity is an assumption unless given or derived
A word problem may tempt the learner to assume each extra unit adds the same amount. If the task gives a constant rate, the linear model is supported. If not, a straight-line model may be an unsupported assumption.
Mathematics: proportionality is stronger than increase
If y increases when x increases, that does not prove y is proportional to x. Proportionality requires a specific relationship. A graph passing through the origin with constant gradient can support it under suitable conditions; a general upward trend cannot.
Mathematics: averages hide assumptions about what is representative
Using the mean as a representative value may be sensible in some contexts but misleading in skewed data or with outliers. If the question asks for interpretation, explain why the chosen summary fits the situation.
Mathematics: whole-number constraints are implied by some contexts
Number of buses, people and boxes generally require integers. The question may not explicitly write n ∈ integers, but the real-world meaning imposes it. This is an implied constraint, not an arbitrary assumption.
Mathematics: a model can be valid only on a stated domain
If a formula is given for 0 ≤ t ≤ 20, using it at t = 30 assumes validity outside its domain. The algebra may still produce a number, but the model no longer supports the interpretation.
Mathematics: extrapolation is an assumption
A trend observed between x = 0 and x = 10 does not automatically continue to x = 100. Extrapolation assumes the relationship persists. In modelling tasks, state that assumption or avoid overclaiming.
Science: observation is not explanation
“The temperature decreased” is an observation or data description. “Heat was transferred to the surroundings” is an explanation. The mechanism may be justified, but it should not be confused with the measured fact.
Science: one factor changing with another creates ambiguity
If temperature and stirring both differ between two trials, attributing the rate change to temperature alone assumes stirring had no effect. Vol 0068 treats this as a confounding problem. The assumption audit makes that hidden step explicit.
Science: a control condition does not guarantee perfect isolation
A control may rule out one alternative explanation while others remain. Do not assume that the presence of a control makes every causal conclusion automatically valid. Inspect the whole design.
Science: repeats do not prove accuracy
Consistent repeats support repeatability. Assuming they are accurate ignores possible systematic bias. Measurement quality requires separate reasoning about calibration, method and uncertainty.
Science: an anomaly is not automatically an error
A result that differs from the pattern may be a mistake, natural variation or real behaviour. Deleting it assumes the cause before investigation. Check evidence first.
Science: familiar mechanism can become an assumption
A learner may recognise a classic topic and write the textbook mechanism before reading the conditions. If the apparatus or variable differs, the familiar explanation may no longer fit. Source conditions come before memory.
Science: a graph trend is not automatically causal
A rising graph can show association between variables under the measured conditions. Explaining why requires relevant scientific knowledge and a design that supports causal interpretation.
Science: no visible change does not mean nothing happened
An instrument may lack the resolution to detect a small effect, or competing processes may cancel. “No observed change” is given; “no process occurred” can be an unsupported assumption.
Worked EMS case 1: transport survey
A fictional survey finds that 45 of 60 respondents prefer a shuttle. Given: 45 responses for the shuttle. Derived: 75% of respondents. Inferred with caution: the shuttle is popular among respondents. Assumed without evidence: 75% of all students prefer it.
Worked EMS case 2: Mathematics rate
A machine produces 240 parts in 6 hours under a stated constant rate. Given: total and time. Derived: 40 parts per hour. If asked for output after another 3 hours at the same rate, the constant-rate condition supports adding 120. Without that condition, the extension would be an assumption.
Worked EMS case 3: cooling data
Two cups are measured after ten minutes. Given: starting and final temperatures. Derived: temperature changes. Inferred: one cup retained more thermal energy under the tested conditions if the setup is comparable. Assumed: material alone caused the difference if geometry or starting conditions also changed.
Worked EMS case 4: narrative inference
A character checks the door repeatedly and lowers their voice when another person approaches. Given: actions. Inferred: the character may be anxious about being overheard. Assumed: the character committed a crime, unless the passage gives stronger evidence.
Worked EMS case 5: graph interpretation
A straight line is observed over a measured range. Given: plotted points. Derived: gradient over that range. Inferred: a linear model fits the observed interval. Assumed: the same linear relationship continues indefinitely beyond the measured domain.
Assumption audit step 1: underline givens
Mark quantities, conditions, qualifiers, roles and time limits. These form the boundary of the problem. Missing one can make every later step look reasonable while being based on the wrong situation.
Assumption audit step 2: label derived facts
Beside each calculated or reasoned result, know the route that produced it. This is especially important in long Mathematics chains and Science calculations where one value feeds several later parts.
Assumption audit step 3: test inferences
Ask what evidence makes the inference more likely than alternatives. If the evidence merely fits the inference without uniquely supporting it, reduce the claim or state the competing possibility.
Assumption audit step 4: expose assumptions
Write the assumption in plain language: speed stays constant; respondents represent the population; the diagram is to scale; the control removes all other causes. Once visible, the assumption can be tested against the source.
Assumption audit step 5: decide whether the assumption is allowed
Some assumptions are provided by the question, some are standard consequences of definitions, and some are unsupported. Keep the first two; reject or qualify the third. Do not treat every unstated idea as equally problematic.
Assumption audit step 6: check sensitivity
If the answer depends heavily on an assumption, ask what happens if the assumption changes. This connects to Vol 0067. A conclusion that survives reasonable variation is more robust than one that flips immediately.
Given versus implied
Not all valid information is explicitly written. If a probability is required, it must lie between 0 and 1. If x counts students, x must be a non-negative integer. These are implications of the variable’s meaning, not arbitrary inventions.
Derived versus memorised
A remembered formula is not yet a derived answer. The learner must show that the formula applies to the given quantities and conditions. Familiarity is not a substitute for model fit.
Inferred versus guessed
An inference is anchored in evidence. A guess is merely possible. If several explanations fit equally well, the learner should not present one as established without additional support.
Assumed versus stipulated
A stipulated condition is explicitly set by the problem: assume constant speed. That is allowed. An assumed condition is introduced by the learner without instruction. The distinction matters in modelling and evaluation.
Hidden assumption: same denominator
Two percentages may look comparable but use different denominators. Assuming the same base can create a false comparison. Restore the denominator before interpreting the difference.
Hidden assumption: same time window
A daily rate and monthly total cannot be compared directly without aligning the time basis. Treating them as equivalent assumes a shared window that may not exist.
Hidden assumption: same population
A survey of volunteers and a school-wide administrative count refer to different groups. Combining them as though they describe the same population can distort the conclusion.
Hidden assumption: same measurement method
Two Science readings collected with different instruments or procedures may not be directly comparable. The method difference can itself explain part of the discrepancy.
Hidden assumption: same criterion
One source may rank options by cost and another by preference. Calling the rankings contradictory assumes they use the same decision criterion. They may both be correct under different criteria.
Hidden assumption: same direction of causation
If two variables move together, the learner may assume A causes B. B could cause A, both could respond to C, or the association could be coincidental. Causal direction requires evidence.
Independent task A
A passage says “several respondents reported shorter waiting times.” Write one given fact, one justified inference and one assumption that would go too far.
Independent task B
A graph is linear between x = 0 and x = 8. Write what is given, what can be derived, and what assumption is required to predict the value at x = 20.
Independent task C
A geometry diagram looks isosceles but no equal sides are marked. Explain why using equal base angles would be an assumption and what evidence would make the step valid.
Independent task D
Two Science groups differ in temperature and stirring rate. State the intended comparison, the confounder and the assumption made by attributing the outcome only to temperature.
Independent task E
A survey gives 80% support among 50 volunteers. Write a calibrated statement about the volunteers and an overgeneralised statement about the whole school.
Worked feedback A
Given: several respondents reported shorter waits. Inference: some respondents perceived an improvement. Overreach: the change definitely reduced actual waiting times for everyone, because perception and population scope have both been enlarged.
Worked feedback B
Given: the measured relationship is linear on the observed interval. Derived: its gradient and equation over that interval. Predicting x = 20 assumes the linear relationship continues beyond the measured domain.
Worked feedback C
Visual appearance is not a stated property. Equal base angles become valid if equal sides are given or derived, allowing the relevant isosceles-triangle property to be used.
Worked feedback D
If temperature is intended to be tested but stirring also changes, attributing the result only to temperature assumes stirring has no effect. The design does not justify that assumption without further evidence.
Worked feedback E
Calibrated: 40 of the 50 volunteers supported the proposal. Overgeneralised: 80% of all students support it. The second statement changes the population without sampling evidence.
Repair route
Start with short problems and label every statement G, D, I or A: given, derived, inferred or assumed. Explain one label at a time until the distinctions become automatic.
Stabilisation route
Use mixed EMS tasks where some unstated information is legitimately implied by definitions while other unstated ideas are unsupported. The learner should not reject everything merely because it was not written verbatim.
Extension route
Use problems where an explicit assumption is required for modelling. Ask the learner to state the assumption, solve, then change it and discuss how the answer or conclusion changes.
What progress should look like
Progress is visible when learners preserve source boundaries, trace calculations, state modelling assumptions explicitly, reject diagram-based guesses, distinguish inference from fact and recognise when two sources use different populations, times or criteria.
Frequently asked: are assumptions always bad?
No. Models often require assumptions. The problem is an assumption that is hidden, irrelevant or contradicted by the source. Good modelling states important assumptions and understands what depends on them.
Frequently asked: should I write every assumption in an examination?
Only when the task requires or the assumption matters to the reasoning. Do not clutter a direct calculation with unnecessary commentary. But if the model or conclusion depends on a non-obvious condition, make it visible.
Frequently asked: is an inference an assumption?
No. An inference is supported by evidence even though it is not directly stated. An assumption is introduced without that support, or stipulated by the modelling task. The difference is evidential.
Frequently asked: can a derived value be wrong even if the arithmetic is right?
Yes. The calculation can be based on the wrong denominator, unit, formula or model. Trace derivation back to the givens and conditions, not just to the calculator result.
Final operating rule
Before trusting an answer, ask: what was given, what did I derive, what did I infer, and what did I assume? If an important step belongs in the last category, either justify it, state it as a modelling condition or remove it.
EMS assumption-audit checklist
- underline critical givens
- label derived values and conclusions
- trace each inference to evidence
- state modelling assumptions when they matter
- reject assumptions based only on appearance or familiarity
- restore population, time and denominator boundaries
- test whether the conclusion changes if an assumption changes
- return the final answer to the original conditions
Advanced EMS assumption laboratory
Advanced audit: premise tracking
A long answer can contain several premises. Write or identify the chain: source fact, intermediate result, conclusion. If one premise changes, only the dependent parts should change. This prevents the learner from treating a local correction as proof that the entire answer has failed.
Advanced audit: first unsupported step
When a conclusion is wrong, find the earliest step that lacks support. Fixing the final sentence without repairing the first unsupported assumption leaves the reasoning unstable. This is especially useful in long Mathematics chains and Science explanations.
Advanced audit: counterexample test
A universal claim can often be tested by looking for one plausible counterexample. If the claim says all students prefer digital notes, one student who does not is enough to disprove the universal. The test reveals when the quantifier is stronger than the evidence.
Advanced audit: boundary-case test
In Mathematics, test values at or near the boundary of a constraint. If a rule says x < 10, check what happens at x = 10. Boundary cases expose hidden assumptions about inclusion, rounding and feasibility.
Advanced audit: impossible-case test
Ask whether the assumption permits impossible results. A probability above 1, negative number of people or area larger than its enclosing region can show that the model or interpretation contains an invalid premise.
Advanced audit: reverse-question test
If you claim A causes B, ask whether B could occur without A or whether another factor could produce B. This does not automatically disprove causation, but it reveals what evidence the causal claim still needs.
Advanced audit: attribution test
If a passage quotes a speaker, ask who owns the claim. If a report says residents believe the policy is effective, the belief is attributed to residents. Converting it into the writer’s factual conclusion changes the source status.
Advanced audit: denominator test
Every percentage should answer percentage of what. A result of 70% may describe respondents, completed trials, original cost or another base. Hidden denominator assumptions are among the fastest ways to create plausible but wrong answers.
Advanced audit: time-window test
Ask whether two statements cover the same period. Daily rate and monthly total, before and after, short-term and long-term are different scopes. Treating them as equivalent inserts an unstated time assumption.
Advanced audit: unit test
Ask whether both sides of an equation or comparison represent the same kind of quantity. Dollars cannot equal dollars per item without a multiplier; metres cannot be compared directly with square metres. Unit mismatch often exposes an assumption before arithmetic begins.
Advanced audit: variable-identity test
A symbol can silently change meaning in messy working. Write the variable definition beside long solutions when necessary. If x begins as number of items, do not later use x as cost without explicitly defining a new quantity.
Advanced audit: diagram-evidence test
Cover the visual impression mentally and list only marked or stated properties. If the solution collapses without the shape looking square, parallel or symmetrical, an appearance-based assumption may have entered the reasoning.
Advanced audit: model-domain test
Ask where the formula or trend is actually supported. A linear relationship observed over a small interval may not remain linear beyond it. Extrapolation is a modelling assumption that should be visible when it matters.
Advanced audit: mechanism test
In Science, ask whether the explanation is required by the data or merely compatible with them. Several mechanisms can fit the same observation. A stronger causal statement needs evidence that distinguishes among alternatives.
Advanced audit: control test
If a control condition is present, identify exactly which alternative explanation it addresses. Assuming that one control rules out every other factor gives the control more evidential power than it actually has.
Advanced audit: repeatability test
If repeats agree, ask what they establish. They support consistency under the method. They do not automatically establish accuracy, validity or absence of bias. The assumption audit prevents one quality of evidence from being mistaken for another.
Advanced audit: no-change test
If no difference is observed, ask whether the method could have detected a small difference. “No measured change” and “no change occurred” are not always equivalent, especially near instrument-resolution limits.
Advanced audit: average-as-representative test
Before calling a mean typical, inspect spread or context where available. The average may be mathematically correct while the interpretation assumes a distribution the data do not show.
Advanced audit: most-likely-story trap
Human reasoning prefers a coherent story. In narrative comprehension and Science interpretation, the first plausible explanation can feel correct. Ask what evidence uniquely supports it over alternatives before committing.
Advanced audit: familiar-template trap
A question can resemble a known worksheet while changing one condition. If the learner immediately applies the old template, that condition may be ignored. Read the givens before retrieving the method.
Advanced audit: answer-space trap
A large answer box does not prove that a long explanation is required. A small box does not prove the task is simple. Command, marks and reasoning requirements define the response, not the visual size of the space.
Advanced audit: authority trap
A quotation from an expert can be relevant evidence, but the learner should still identify what the expert is actually claiming and in what context. Authority does not automatically extend the claim beyond the quoted scope.
Advanced audit: majority trap
The most selected option is not necessarily a majority. If A gets 40%, B 35% and C 25%, A has the largest share but less than half. Calling it the majority choice assumes a threshold that has not been met.
Advanced audit: causation-from-order trap
If event A happens before B, chronology is given; causation is not. Ask whether the source supplies mechanism, comparison or control evidence that supports the stronger relationship.
Advanced audit: certainty-from-confidence trap
A confident speaker may still be uncertain, and a cautious speaker may have strong evidence. Separate delivery style from evidential certainty. This matters especially in Listening and Oral analysis.
Advanced audit: assumption sensitivity
Change the assumption and observe whether the conclusion changes. If a recommendation survives several reasonable assumptions, it is more robust. If it reverses immediately, the assumption should be made explicit in the final answer.
Advanced audit: necessary versus sufficient conditions
A condition can be required without being enough. A ticket may be necessary for entry but not sufficient if age verification is also required. In Mathematics and logic-heavy prose, confusing necessary and sufficient conditions creates overclaims.
Advanced audit: correlation direction
If high study time and high scores occur together, the learner should not assume the direction runs only from study to score. Prior attainment, motivation or course difficulty may also matter. Association is given; directional cause requires more.
Advanced audit: classification before rejection
Not every unstated step is a bad assumption. Some are definitions, mathematical implications or stipulated modelling conditions. Classify first: implied by meaning, derived, explicitly assumed, or unsupported. Only the last category demands rejection.
Advanced audit: minimal-assumption principle
When several interpretations fit the source, prefer the one that requires the fewest unsupported additions while still answering the task. This does not mean choose the simplest story blindly; it means do not invent facts that are unnecessary for the conclusion.
Workshop drill: G-D-I-A labelling
Take a worked answer and label each sentence G, D, I or A. If a sentence contains two categories, split it. This reveals where the reasoning changes status and where the learner may be presenting an inference as though it were given.
Workshop drill: remove one assumption
Delete one assumption from a model and ask whether the conclusion still follows. If not, the assumption is load-bearing. Decide whether the task justifies it or whether the conclusion must be qualified.
Workshop drill: add a counterexample
For a universal statement, construct one case that would make it false. If such a case is compatible with the evidence, narrow the claim. This is particularly useful for Writing and data interpretation.
Workshop drill: trace a wrong answer backward
Start from the final wrong response and move backward until the first step that no longer follows from the previous one. That first divergence is the real repair target; everything after it may simply be downstream damage.
Workshop drill: explicit modelling assumptions
For an invented real-world Mathematics problem, state one assumption such as constant rate, then solve. Change the assumption and recalculate. Explain which part of the conclusion depends on it.
Workshop drill: evidence hierarchy
List direct observation, calculated result, supported inference and personal assumption separately. Rank them by how directly they answer the question. This reduces the temptation to let a memorable story outweigh stronger source evidence.
Workshop drill: source boundary
Take two sources about the same topic and write the strongest sentence each supports separately. Then write one sentence both support. This prevents evidence from one source being silently imported into another.
Workshop drill: condition extraction
Underline every if, only if, unless, at least, no more than, when and provided that. Translate each into a condition. Many hidden assumptions begin when these words are skipped.
Workshop drill: denominator restoration
For every rate, percentage or average, write the denominator. If the denominator changes, rewrite the claim. This makes hidden scope shifts visible.
Workshop drill: assumption ledger
During practice, keep a small ledger with three columns: assumption, reason allowed, consequence if false. The aim is not to create more paperwork but to make modelling dependencies explicit.
Assumption audit in final checking
During the last review, target answers with high assumption risk: long inferences, geometry from diagrams, extrapolated trends, causal explanations, population claims and contextual rounding. Secure direct calculations need less assumption auditing.
Assumption audit and time control
Do not audit every trivial step during the live paper. Use the skill to catch high-risk transitions. Preparation should make the distinction automatic so the examination check remains quick.
Assumption audit and confidence
The purpose is not to become suspicious of everything. Strong learners know which steps are given, which are logically derived and which genuinely need caution. Precision should increase confidence because the reasoning is easier to defend.
Assumption audit and communication
When an assumption matters, state it clearly enough that another reader can understand the model. Hidden reasoning is harder to evaluate and easier to contradict accidentally.
Assumption audit and revision
After marking, do not record only the wrong answer. Record the unsupported assumption that produced it. Similar assumptions often reappear across different topics, making the repair transferable.
Final EMS assumption standard
The skill is secure when the learner can keep givens, derivations, inferences and assumptions separate, explain which unstated conditions are legitimate, and recognise the first point where an answer depends on something the task never established.
