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UAT-UK SPEC: MM6MODULE: MATHEMATICS 2TOPIC ID: ARCH-MM-09

Stationary Point Classification, Monotonic Cubics & Constrained 2D/3D Optimisation

Master Stationary Point Classification, Monotonic Cubics & Constrained 2D/3D Optimisation on the ESAT Mathematics 2 paper. Traditional classroom derivations waste valuable seconds. Using the 2-step Sub-90 invariant elimination method compresses solve time to 50s, saving +125s per question.

Standard Classroom Time
175s
Textbook multi-line derivations bleed exam clock
Sub-90 Target Pace
50s
Comfortably below the 88.8s per-question limit
Time Saved for Review
+125s
Banks clock buffer across 27 questions

2-Step Sub-90 Shortcut Formula

How to eliminate intermediate algebra and solve under 45 seconds.

Launch Interactive Lesson
STEP 1 • SETUP INVARIANT (LINE 1)10–15s
Line 1 (Factorised Derivative Identity): y′(x)=3x2+2px+q≡3(x−1)(x−3)=3x2−12x+9y'(x) = 3x^2 + 2px + q \equiv 3(x - 1)(x - 3) = 3x^2 - 12x + 9.

Establish the structural invariant and eliminate impossible options immediately.

STEP 2 • FAST SOLVE (LINE 2)15–25s
Line 2 (Read Off p,qp, q): 2p=−12  ⟹  p=−6,  q=9  ⟹  p+q=32p = -12 \implies p = -6,\; q = 9 \implies p + q = 3 (25s).

Evaluate the simplified expression using integer factoring or unit elimination.

Distractor Trap Forensics

The predictable cognitive traps engineered by examiners into the wrong options.

TRAP #1multi_statement_linchpin_foil

Assuming f'(a) = 0 guarantees a local maximum or minimum (ignoring stationary point of inflection)

Forgetting that f'(a)=0 and f''(a)=0 with no sign change in f'(x) is a point of inflection.

Sub-90 Fix: Test invariants before expanding equations.
TRAP #2fence_post_or_domain_trap

Using b² - 3ac < 0 instead of b² - 3ac <= 0 for a cubic ax³ + bx² + cx + d to be strictly increasing

Omitting the boundary case where a repeated root of f'(x) = 0 gives a single point of zero gradient.

Sub-90 Fix: Test invariants before expanding equations.
TRAP #3intermediate_stop_trap

Outputting the optimal radius/length x(opt) instead of the maximum volume/area V(x(opt))

Stopping after solving dV/dx = 0 for x without substituting back into V(x).

Sub-90 Fix: Test invariants before expanding equations.

Try 1 Timed Question: Stationary Point Classification, Monotonic Cubics & Constrained 2D/3D Optimisation

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Full Lesson All 15 Questions (ARCH-MM-09)
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ARCH-MM-09: Stationary Point Classification, Monotonic Cubics & Constrained 2D/3D Optimisation (Sample)Mathematics 2
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SUB-90 ZONE (<50S)
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Question 1 of 1ARCH-MM-09 (6-Card Lesson)Format: Standard 5-Option
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Question 1 of 1 • 90s Target

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