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May 2026 Mathematics I — Quiz 2 pattern atlas
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May 2026 Mathematics I — Quiz 2 pattern atlas
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2026-08-16
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Now · The five-move loop
Mathematics I pattern atlas
Scope: Weeks 1–4 match the May 2026 workspace and graded assignments on disk. Weeks 5–8 are syllabus extensions (derivative rules, optimisation, integration, matrices) for deeper review — label them as extension, not live Quiz 2 promises.
Interactive version with filters and visuals: Quiz 2 pattern atlas.
The five-move loop
- Name the object (set, function, equation, rate).
- State permissions (domain, quantifier, reversible step).
- Execute one transformation with reason.
- Check boundaries (endpoints, holes, extraneous roots).
- Report with units (especially rates and derivatives).
Pattern families
| Family | Weeks | Shapes | Core move |
|---|---|---|---|
| Sets & Venn | 1 | MCQ, MSQ, NAT | Translate symbols, then count with inclusion–exclusion |
| Logic & quantifiers | 1 | MCQ, MSQ | One counterexample disproves “for all” |
| Functions & domains | 2, 5 | MCQ, MSQ, NAT | Domain before simplify |
| Algebraic transformation | 3 | NAT, MCQ | Each line needs a reversible permission |
| Limits, rates, derivatives | 4–8 | NAT, MCQ, MSQ | Limit ≠ function value; keep units |
Week 1 — easy: membership
Shape: MCQ — which statement is true?
Method: Test
∈ on single elements first. For ⊆, verify every element of the left set lies in the right set — overlap is not enough.Trap: Declaring
A ⊆ B because they share some elements.Week 1 — medium: Venn counting
Shape: NAT — how many in at least one set?
Steps:
- Draw overlap region.
- Compute region-only counts:
|A only| = |A| − |A ∩ B|. - Apply
|A ∪ B| = |A| + |B| − |A ∩ B|.
Week 3 — hard: extraneous roots
Shape: MCQ after solving √(expression) = linear side.
Steps:
- State radical domain and sign of RHS.
- Square and solve.
- Substitute each candidate into the original — discard any that violate domain or sign.
Week 4 — medium: limits
Shape: MCQ on
(x² − a)/(x − b) as x → b.Factor, cancel only where defined, then approach the hole value. Do not claim
f(b) unless separately defined.Extension week 5 — power rule
d/dx[xⁿ] = n·xⁿ⁻¹. Differentiate term by term; constants vanish. Evaluate at a point only after finding f′(x).Visual companions
- Sets and relations
- Limit and continuity
- Derivative chooser (extension)
Practice loop
- Open week notes.
- Pick one pattern at your difficulty on the interactive atlas.
- Attempt an original drill without looking at the approach.
- Archived mock only for pattern diagnosis — exam portal.
Linked References
Ref [1]
Mathematics I · Week 2 — Coordinate system & straight lines
Ref [2]
Mathematics I · Week 3 — Quadratic functions
Ref [3]
Mathematics I · Week 4 — Algebra of polynomials
Ref [4]
Mathematics I · Week 5 — Functions & composition
Ref [5]
Mathematics I · Week 6 — Logarithmic functions
Ref [6]
Mathematics I · Week 7 — Sequences, limits & continuity
Ref [7]