The number families from ℕ to ℝ, factors and multiples, prime factorisation, HCF and LCM, and the properties of operations.
6 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.
Every number belongs to a family — and every whole number is built from primes. Learn the family tree and you can solve HCF and LCM problems in seconds.
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.
ℕ = {1, 2, 3, …}; 𝕎 = {0, 1, 2, …}; ℤ = {… −1, 0, 1 …}; ℚ = {p/q : p, q ∈ ℤ, q ≠ 0}; irrationals cannot be written as terminating or recurring decimals; ℝ = rationals ∪ irrationals. ℕ ⊂ 𝕎 ⊂ ℤ ⊂ ℚ ⊂ ℝ.
Factors divide exactly (list in pairs). Multiples are the times table. For integers, include negative factors.
Exactly two factors. 2 is the only even prime; 1 is neither prime nor composite. Test divisibility by primes up to √n.
Use a factor tree and write with indices, e.g. 72 = 2³ × 3².
Common primes to the LOWEST power. Use for “largest”, “greatest”, “equal groups”.
All primes to the HIGHEST power. Use for “least”, “smallest”, “next time together”.
Closure, commutative, associative (for + and × only), identities 0 and 1, inverses −a and 1/a, distributive a(b + c) = ab + ac.
HCF × LCM = product of the two numbers (for exactly two numbers).
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 (16 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [9 marks]
Let the numbers 36 and 84 be given.
(a) List ALL the factors of 36. [2]
(b) Express 84 as a product of its prime factors, using indices where appropriate. [2]
(c) Hence, or otherwise, determine (i) the HCF and (ii) the LCM of 36 and 84. [3]
(d) State whether each number is rational or irrational: 0.25, √7, π, 4/9. [2]
Question 2 [7 marks]
Mrs Lee has 48 pencils and 72 erasers. She wants to make identical gift bags using ALL of them, with nothing left over.
(a) What is the greatest number of gift bags she can make? [2]
(b) How many pencils and how many erasers will each bag contain? [2]
(c) Two buses leave the terminal together at 6:00 a.m. Route A buses leave every 15 minutes and Route B buses every 20 minutes. At what time will they next leave together? [2]
(d) How many times, in total, do the two routes leave together between 6:00 a.m. and 9:00 a.m. inclusive? [1]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.