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DuckMath Blog

Math technique, learning science, and UEC exam prep.

SC06 topic weighting (%)
Calculus
28%
Trigonometry
22%
Functions
18%
Sequences
14%
Vectors
10%
Probability
8%
Exam Strategy· 8 min read

UEC Math Topic Weighting: Do You Actually Know Which Chapters Matter Most?

Spreading effort evenly across chapters loses marks on the topics that matter. A breakdown of SC04–SC07 topic frequency and weighting.

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Retention vs time (days)
0%50%100%0d1d2d4d7d14d21d30d
spaced reviewno review
Learning Science· 6 min read

Why You Forget After 100 Questions — and How Spaced Repetition Fixes It

The forgetting curve is blunt: doing questions is not the same as remembering them. Spaced repetition is the one research-backed fix, and here is how to use it.

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AI vs human grading (500-question test)
Speed (relative)
Human
DuckMath AI≈100×
Accuracy
Human97%
DuckMath AI97%
AI & Education· 5 min read

Is AI Grading Actually Accurate? We Tested It on 500 Questions

We had 500 SC06 structured questions graded blind by 3 teachers and by DuckMath AI, comparing accuracy, speed and step-level analysis. The result surprised us.

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Common slips · step marking
d/dx (3x²+1)⁵ = 5(3x²+1)⁴missing inner ×6x
= 30x(3x²+1)⁴chain rule completed
∫ 2x dx = x²missing + C
[x²] from 1 to 3 = 9 − 1upper − lower, right order
Exam Strategy· 7 min read

SC06 Calculus: The Six Places Students Lose Marks

Chain rule, quotient-rule signs, + C, integral limits, area sign, stationary-point classification — most calculus marks are lost in these six spots, and it is checking, not knowledge, that fails. With a pre-exam checklist.

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Core identities · know cold
sin²x + cos²x = 1
1 + tan²x = sec²x
sin 2x = 2 sin x cos x
cos 2x = 2cos²x − 1
Exam Strategy· 6 min read

Trig Identity Proofs: Four Ways In When You Are Stuck

Work one side only, convert everything to sin and cos, know the core identities cold, or squeeze both sides to a common form — four reliable ways into an identity proof when you are stuck, with a must-memorise list.

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Budgeting 120 minutes
Scan · 3mMCQ · 40mStructured · 65mCheck · 12m
Exam Strategy· 5 min read

UEC Math Exam: How to Budget Your Two Hours

Scan the whole paper first, a minute per MCQ, method marks on every structured question, ten minutes to check — a time plan that keeps one hard question from sinking your paper.

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The SC04 → SC06 step up
SC04
SC05 · bridge
SC06
Exam Strategy· 6 min read

Jumping from SC04 to SC06? Mind the Gap First

SC04 tests "can you do this method"; SC06 tests "which method, and how do they connect." The real gap, what SC05 bridges, and a four-week catch-up plan.

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Four error types
Concept
re-read the topic
Calculation
drill checking
Reading
circle keywords
Time
drill speed
Learning Science· 6 min read

You Copied a Whole Error Log — So Why Are You Still Stuck?

Copying is not analysing. Sort mistakes into concept / calculation / reading / time, ask three questions per mistake, and revisit on a forgetting-curve schedule — an error log that actually works.

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── COMING SOON
More articles in the works — updated weekly.
Practise first →