The 15-mark A* decider
One optimisation question, worth a whole grade boundary. The calculus is not hard — but capable students throw marks away all the way through it. Here's exactly where.
A solid triangular prism has an equilateral triangular cross-section of side 2x cm and length l cm. Its total surface area is S cm² and its volume is V cm³.
(a) Show that S = 2x²√3 + 6xl (3)
(b) Given S = 960, show that V = 160x√3 − x³ (5)
(c) Use calculus to find the maximum value of V (nearest integer) (5)
(d) Justify that your value of V is a maximum (2)
Guffick Tuition · Premium online A-Level & GCSE mathematics · Examiner-informed. Questions are original, written in the style of recurring exam types.
THIS IS EXACTLY HOW I TEACH
What You Just Saw Is Exactly How I Teach
- I never just hand over the answer. I ask what you'd do, give you a moment to think, then reveal the next step — because the pause is where understanding forms.
- Every step comes with the reason it's necessary. Not "here's the rule," but "here's why this has to come next." That reasoning is what transfers to the next question.
- I show you exactly where marks are won and lost — method, accuracy and reasoning marks — because I mark these papers and I know what the scheme actually rewards.
- Then you prove it on a fresh question, unaided. That's the moment a student stops following along and genuinely owns the topic.
If your child found this helpful, that's because they just had a single lesson in the way I teach. The small-group programme is this — across every question type that decides the top grades.
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