Choose your next learning step
Check an EMS answer against the original passage, equation or physical model; distinguish a candidate solution from a result that satisfies every condition.
1. Start here · 2. Equation · 3. Domain · 4. Passage · 5. Model · 6. Select the check · 7. Practise · 8. Continue
An original integrated English, Mathematics and Science learning workshop. The candidate-answer audit is a study routine, not a SEAB marking rubric. Examples and data are fictional; subject-specific requirements still apply.
Chapter index
Chapters 1–3
Chapters 4–6
A candidate answer is something your working suggests might be right. It becomes a justified answer only after it survives the relevant conditions. In Mathematics, a transformed equation may admit an extra value. In English, a plausible inference may exceed the passage. In Science, a set of numbers may violate the circuit’s connections.
For G3 SEC revision, make one distinction visible: producing an answer and validating that answer are different jobs. Generating the result asks “What could follow?” Validating asks “Does this result satisfy the original task, including the conditions I may have set aside while working?”
This workshop develops that distinction through three subject cases. The aim is not to add a long ritual to every short question. It is to choose a check capable of exposing the particular error the method might introduce. A repeated calculation using the same mistaken model can reproduce the same wrong answer perfectly.
Solve √(x + 6) = x. The square root is the non-negative square root, so any solution must have x ≥ 0. Squaring gives x + 6 = x², hence x² − x − 6 = 0 and (x − 3)(x + 2) = 0. The transformed equation produces x = 3 and x = −2.
Put each candidate into the original equation. For x = 3, √9 = 3, so it works. For x = −2, √4 = 2, which is not −2. The answer is x = 3 only. The negative candidate satisfies the squared equation but fails the original one.
Why did the extra value appear? Squaring loses the distinction between positive and negative signs: 2² and (−2)² both equal 4. The transformed condition is necessary here, but satisfying it is not sufficient. State the sign restriction early, and use original substitution to check the candidates at the end. Do not label the rejected value an arithmetic mistake when the algebra that generated it was valid.
Consider (x² − 9)/(x − 3) = 6. The original expression is undefined at x = 3, so record x ≠ 3 before simplifying. Factoring gives (x − 3)(x + 3)/(x − 3) = 6, which reduces to x + 3 = 6 only for allowed values. This gives the candidate x = 3, which is excluded. The original equation has no solution.
Cancelling the factor does not fill the missing point in the original domain. If you substitute x = 3 into the simplified expression, you obtain a number, but substituting into the original denominator produces zero. Check the expression that the question actually supplied.
Context can impose further restrictions even when the algebra is defined. A negative number of visitors, a non-integer count of whole items or a length beyond the stated range may fail the task. Write the specific reason for rejection. “Reject because impossible” hides whether the problem is a denominator, a square-root sign, a count or a physical condition.
Read this fictional source: “Several students who joined the lunchtime reading club said they enjoyed the quiet room. The organiser planned to collect attendance figures at the end of the term.” A student answers: “The club improved the examination results of every participant.”
That answer contains several claims the source does not establish. Enjoying a quiet room is not the same as improving examination results. “Several” is not “every”. A planned collection of attendance figures is not a completed measure of academic improvement. The answer may sound like a sensible benefit of reading, but it does not satisfy a source-based evidence task.
A supported statement is: “Some participating students reported enjoying the quiet room.” If asked whether examination results improved, say that the supplied passage does not establish that outcome. Match the scope of the answer to the scope of the evidence. In an inference question, explain the textual details that support the inference rather than importing a general belief about the activity.
An ideal 12 V source powers 6 Ω and 3 Ω resistors in parallel. A candidate solution says each branch carries 3 A, so the total current is 6 A. The total happens to be correct, but both branch currents are wrong. A correct final total does not validate the intermediate model.
Check the shared potential difference. Each branch spans the same 12 V source. Ohm’s law gives 2 A through 6 Ω and 4 A through 3 Ω. If both currents were 3 A, the implied branch voltages would be 18 V and 9 V, contradicting the shared-node condition.
Now consider a different candidate: branch currents 2 A and 4 A, total current 5 A. The individual branch calculations work, but the junction check fails because 2 + 4 is 6. Use both local component relationships and the whole-circuit relationship. A check should challenge the answer at the point where a hidden inconsistency could survive.
CHAPTER 6 OF 8 · Select the check
6. Choose a check with a different route to failure
A useful check targets what your method might have lost. After squaring, check the original signs. After cancelling, check the original denominator. After interpreting a passage, check who, how many, what outcome and which time the sentence actually establishes. After reducing a circuit, check shared nodes as well as arithmetic.
Re-entering the same expression can catch a typing error. It cannot establish that the expression represents the question. Estimating a sensible size can catch a wildly wrong magnitude. It cannot prove that a plausible answer is unique. Each check has a job and a limit.
Nor does one successful example prove an algebraic identity for all inputs. To establish an identity, use valid symbolic reasoning over its domain. Conversely, a single valid counterexample can disprove an “always” claim. Match the logical strength of the check to the claim you are making. Verification is not merely finding something reassuring about the answer.
A: Solve √(x + 2) = x. B: Solve (x² − 4)/(x − 2) = 4. C: A fictional report says, “Of the 30 respondents, 18 preferred the earlier session.” Is “most students in the school prefer the earlier session” established? D: An ideal 8 V source powers 4 Ω and 8 Ω resistors in parallel. Check the candidate branch currents 2 A and 1 A and total current 3 A.
Answers: A gives candidates 2 and −1 after squaring; only 2 satisfies the original equation. B requires x ≠ 2. Simplification produces x = 2, so there is no solution. C establishes a majority among those 30 respondents, not necessarily across the school. The schoolwide claim needs information about the survey and the wider population.
D satisfies both component checks, since 2 × 4 = 8 and 1 × 8 = 8, and the junction check, since 2 + 1 = 3. This verifies the supplied ideal-circuit calculation. It does not establish that a real experiment used ideal meters or had no source resistance; those are separate model assumptions.
Keep an error record with three short entries: candidate answer, failed condition and next repair. For the square-root task, write “negative candidate; original right side must be non-negative; check before and after squaring”. For the reading task, write “schoolwide claim; source only describes respondents; preserve population scope”.
Retest using a new example that fails for the same underlying reason but has a different surface story. Then mix it with an example that genuinely satisfies the conditions. The learner must decide whether to accept or reject, rather than learning to reject every answer in a checking exercise.
Return to the subject chapter for any missing concept. The audit cannot replace knowledge of roots, evidence or circuits. It helps those ideas remain connected to the original task. A strong finish says what works, why it works and where its validity ends, without claiming more than the working and evidence can support.
Continue learning and official sources
Official G3 Mathematics syllabus · Official G3 English Language syllabus · Official combined G3 Science syllabus · Complete G3 EMS Learner’s Guide · Compound-interest worked examples · Parallel-circuit worked examples · Build a precise paragraph transition
