Solving quadratic equations by factorisation, by the quadratic formula and by completing the square, the discriminant and worded problems.
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 ball is thrown, a field is fenced, a profit is maximised — all quadratics. CSEC gives you three methods; learn when to use each.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Change a, b and c and see the roots.
Copy these into your notebook in your own words — that is how they stick.
Rearrange to = 0; factorise; set each bracket to 0.
x = (−b ± √(b² − 4ac)) ÷ 2a. It is printed on the formula sheet; substitute carefully with signs.
x² + bx + c = (x + b/2)² + (c − (b/2)²). For ax² + bx + c take a out first.
a(x + h)² + k has its vertex at (−h, k); the axis of symmetry is x = −h.
b² − 4ac: > 0 two roots, = 0 one root, < 0 no real roots.
Define the letter, form the equation, rearrange to = 0, solve, reject impossible values.
Quadratic formula answers: give to the accuracy asked (usually 2 d.p. or 3 s.f.).
Substitute each root in the original equation.
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]
Answer all parts.
(a) Solve 2x² + 3x − 2 = 0 by factorising. [3]
(b) Solve x² + 4x − 3 = 0 using the quadratic formula, giving answers correct to 2 decimal places. [4]
(c) Express x² + 6x + 5 in the form (x + h)² + k, and hence state the coordinates of the minimum point of y = x² + 6x + 5. [3]
Question 2 [9 marks]
The length of a rectangular garden is 3 m more than its width, w metres. The area of the garden is 40 m².
(a) Show that w² + 3w − 40 = 0. [2]
(b) Solve the equation to find the width and length of the garden. [4]
(c) Fencing costs $12 per metre. Calculate the cost of fencing the garden. [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.