Write both intervals
State the upper and lower bound of every quantity to the stated accuracy.
AQA 8300 · N15/N16 · Directed bounds
Bounds in a subtraction: which endpoints to pair
The endpoint-selection mark. The maximum of a − b uses the UPPER bound of a with the LOWER bound of b, and the mark is for that choice rather than for the subtraction.
Reviewed family · Studara-authored items · No grade-uplift claim
The lost mark
One answer. Several places the method can fail.
Studara does not reduce the response to right or wrong. The reviewed contract checks these states independently.
Select the endpoints
Choose the endpoint of each quantity that pushes the expression toward the required extreme.
Evaluate
Substitute the chosen endpoints and give the bound to a suitable accuracy.
Why it goes wrong
The diagnosis stays uncertainty-safe.
A wrong response can support a specific measured diagnosis. A blind multiple-choice diagnostic records only a possible cause until later working provides stronger evidence.
01
The error
Pairing upper with upper and lower with lower inside a subtraction, as if the rule for a sum carried over unchanged.
02
Why it survives revision
For addition and for multiplication, same-side pairing IS correct. The rule is learned on those operations, confirmed by them, and then applied to subtraction and division where it silently inverts.
The worked repair
Repair the smallest broken step.
Teaching is not evidence. This one move is the repair; the proof checks begin after it disappears.
Before choosing bounds, decide which direction each variable pushes the result. The one being subtracted pushes the other way.
What happens after the repair
Correction is the start, not the result.
Immediate
Asked again straight away, on a different question
The repair leaves the screen and a new authored item checks the method unassisted. Being taught something is never evidence that it was learned, so this is the first stage that counts at all.
Delayed
Asked again after at least 1 day
A parallel form of the same method, unassisted, with the repair no longer on screen. A retest in the same session does not count.
Transfer
Asked again when the surface changes
The transfer form uses division, where the reversal applies to the denominator instead — the same reasoning, a different surface.
Exam
Asked again under exam conditions
Timed, carrying the mark tariff, in an exam-like response format and aligned to the specification. Any one of those missing and the evidence is refused.
REVIEWED BOUNDARY
This page covers one reviewed family: N15/N16 · Directed bounds. Build exact intervals, then choose endpoints through a subtractive expression. Other families within the same GCSE Maths topic are outside this reviewed journey, and Studara does not apply the proof label to material that has not been reviewed. No grade-uplift claim is made anywhere on this site.
Straight answers
Before you use this guide.
Which bounds do I use for a subtraction?
For the maximum of a − b, use the UPPER bound of a with the LOWER bound of b. Pairing upper with upper is correct for a sum, and wrong for a difference.
What about division?
The same reversal applies to the denominator. The maximum of a ÷ b uses the upper bound of a with the lower bound of b.
Does Studara guarantee a higher grade?
No. Studara has not run a controlled outcome study and publishes no grade-uplift claim. What has been measured, what is withheld, and the metric that failed its bar are all on the public evidence page.
Turn this method into evidence