How to choose, formulate, solve and write up a Project A investigation for the Additional Mathematics SBA, using the mark scheme criterion by criterion, with a worked exemplar on minimum surface area.
5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
A drink company wants cans that use the least metal. Is a cylinder really better than a box? Project A turns a question like this into 30 marks.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Copy these into your notebook in your own words — that is how they stick.
Theory-based; proof or direct application; data collection not usually required.
Title 2, Purpose 2, Formulation 6, Solution 11, Application 3, Discussion/Conclusion 4, Presentation 2 = 30.
Clear, concise, linked to a real-world problem.
States what you will find out; appropriate difficulty.
Define variables, state assumptions, build the model, use diagrams.
Use syllabus mathematics; show every step; check second derivatives.
Use the answer for a practical decision.
Title page, contents, diagrams, references.
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Additional Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (30 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [30 marks]
Use the exemplar on the minimum surface area of a closed container of volume 1 000 cm³. A calculator may be used.
(a) (a) Show that the surface area of a closed cylinder of volume 1 000 cm³ is S = 2πr² + 2000/r. [3]
(b) (b) Find the radius that makes S a minimum, to 3 significant figures. [4]
(c) (c) Show that this value gives a minimum, and calculate the minimum surface area. [4]
(d) (d) The cube of side 10 cm has surface area 600 cm². Calculate the percentage saving in metal by using the cylinder. [3]
(e) (e) Write a purpose and a conclusion for this project in one sentence each. [4]
(f) (f) State TWO practical reasons why a company might still use a box instead of the cylinder. [2]
(g) (g) List FOUR assumptions you would state in the report. [4]
(h) (h) State TWO features of good presentation for the written report. [2]
(i) (i) For 10 000 cylinders at $0.002 per cm², find the total metal cost. [4]
Everything in this lesson is based on these parts of the CXC syllabus and papers.