Factorising x² + bx + c and ax² + bx + c, difference of two squares revisited, and rearranging formulae with powers, roots and repeated letters.
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 quadratic is a puzzle: find two numbers that multiply to one thing and add to another. Solve it in seconds and you unlock quadratic equations and graphs.
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.
Find two numbers: product c, sum b. Factors (x + p)(x + q).
Find numbers with product ac and sum b; split the middle term; factorise by grouping.
Common factor → difference of two squares → quadratic → grouping. Check by expanding.
a² − b² = (a − b)(a + b), e.g. 9x² − 4 = (3x − 2)(3x + 2).
Undo operations in reverse; squares ↔ roots; fractions → multiply out.
Collect terms with the subject on one side, factorise, divide.
x² + 6x + 9 = (x + 3)²; x² − 10x + 25 = (x − 5)².
V = ⁴⁄₃πr³ → r = ∛(3V/4π); T = 2π√(l/g) → l = gT²/4π².
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 (19 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [10 marks]
Factorise each expression completely.
(a) x² − 7x + 10 [2]
(b) 3x² + 5x − 2 [3]
(c) 2x² − 8x − 10 [3]
(d) Hence, or otherwise, simplify (x² − 7x + 10)/(x² − 25). [2]
Question 2 [9 marks]
Answer all parts.
(a) Make r the subject of V = ⁴⁄₃πr³. [3]
(b) Make l the subject of T = 2π√(l/g). [3]
(c) Make x the subject of y = (x + 1)/(x − 2). [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.