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H2 Math 2025 Prelim P2 · Demo Student · read-only sample
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Student
For Q3(b) I got x = 2a when I factorised 4a²x³ − 6x⁵ = 0, but the marking says that is wrong. Where did I go?
Cherlock
Factor carefully: 4a²x³ − 6x⁵ = 2x³(2a² − 3x²) = 0. So either x = 0 (reject for a positive length) or 2a² − 3x² = 0 → x² = (2/3)a². You dropped the square when solving for x.
Student
So the max volume in terms of a should be a³/3?
Cherlock
Yes — once you substitute the correct x into V, you get max V = a³/3. That also unlocks Q3(c)’s surface area at that volume (exact form with √3).
Student
And for Q11(b) — why was my sample variance wrong for the hypothesis test?
Cherlock
You need the unbiased estimate: (n/(n−1)) × sample variance. With n = 35 and s² = 250 that is (35/34)×250 ≈ 257.35. Using the biased figure changes your test statistic and can flip the conclusion.
Student
Got it. Q2 and Q8 felt solid — thanks.
Cherlock
They were — full marks on functions and binomial modelling. Biggest free marks next time: finish incomplete parts (Q3(c), Q6(b), Q7(d), Q11(d)) and keep algebra factorisation careful on optimisation.
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