How to tackle the 9-mark investigation question in Module 1 of Paper 02: tabulate, find the pattern, generalise with an algebraic rule, test it, and justify.
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.
Nine marks, no formula given, a pattern you have never seen. It looks scary — but the method is always the same five steps.
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.
9 marks in Module 1 of Paper 02, set on any Module 1 objectives; tests reasoning.
Simple numbers; sketch; table; guess and check; patterns; algebra; calculator.
Constant difference d → Tₙ = dn + c.
Differences change by a constant (second difference); rule has an n² term. Test with at least two known values.
Substitute n = 1, 2, 3 in your rule to reproduce the given terms.
Use the rule for large n and reverse problems (solve Tₙ = a value).
Explain WHY the rule works in terms of the situation (what each step adds).
Table → words → rule → test → use → reason.
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 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 (18 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [9 marks]
A circular cake is cut by n straight lines, so that the number of pieces is as large as possible. With 0 cuts there is 1 piece, with 1 cut there are 2 pieces, with 2 cuts there are 4 pieces and with 3 cuts there are 7 pieces.
(a) (a) Complete the table for n = 4, 5 and 6 cuts. [2]
(b) (b) Write down the differences between successive numbers of pieces. [1]
(c) (c) Use the pattern in the differences to predict the number of pieces for 7 cuts. [1]
(d) (d) Show that the rule p = (n² + n + 2)/2 gives the correct number of pieces for n = 3 and n = 6, and hence calculate the number of pieces for 12 cuts. [3]
(e) (e) Use the rule to show that exactly 100 pieces cannot be obtained with a whole number of cuts. [2]
Question 2 [9 marks]
A square swimming pool measures n metres by n metres. It is surrounded by a path made of square tiles, each 1 m by 1 m, one tile wide. With n = 1 the path needs 8 tiles, with n = 2 it needs 12 tiles and with n = 3 it needs 16 tiles.
(a) (a) Write down the number of tiles needed for n = 4 and n = 5. [2]
(b) (b) Write down a rule for the number of tiles T in terms of n. [2]
(c) (c) Calculate the number of tiles for a pool with n = 25. [1]
(d) (d) A pool needs exactly 200 tiles for its path. Find n. [2]
(e) (e) Explain why the rule is 4n + 4, by considering the shape of the path. [2]
Everything in this lesson is based on these parts of the CXC syllabus and papers.