Common factors, grouping, difference of two squares, simplifying algebraic fractions with the four operations, and the laws of indices.
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.
Factorising is expanding in reverse — and it is the key that opens quadratic equations, algebraic fractions and half of Module 2.
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.
1) common factor; 2) difference of two squares (2 terms); 3) grouping (4 terms); 4) quadratics (Module 2).
a² − b² = (a − b)(a + b). There is NO factorisation of a² + b² over the real numbers at this level.
Expand your factors; you must return to the original expression.
Factorise first; cancel FACTORS (things multiplied), never terms.
Common denominator, then combine the numerators.
Cancel across, multiply; divide by flipping.
Multiply → add; divide → subtract; power of power → multiply; x⁰ = 1; x⁻ⁿ = 1/xⁿ.
(2x³)² = 4x⁶: square the number too.
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 (17 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [9 marks]
Factorise each expression completely.
(a) 12ab − 18b² [2]
(b) 25x² − 4 [2]
(c) pq + 3p − 2q − 6 [3]
(d) Hence, or otherwise, simplify (25x² − 4)/(10x − 4). [2]
Question 2 [8 marks]
Answer all parts.
(a) Simplify (3a²b)³ ÷ 9ab². [3]
(b) Evaluate 2⁻³ × 16^(1/2). [2]
(c) Express 2/(x + 1) + 3/(x − 2) as a single fraction. [3]
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.