Simplifying surds, adding, subtracting and multiplying them, rationalising denominators, and solving equations that contain square roots.
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.
√2 never ends and never repeats — so we keep it exact. Surds let you give answers like 2 + √3 that are perfectly precise, and CSEC loves them.
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.
√(ab) = √a√b; pull out the largest perfect square factor.
Only like surds: 3√2 + 5√2 = 8√2.
√a√a = a; expand brackets; (a + √b)(a − √b) = a² − b.
Multiply top and bottom by √b.
Multiply by the conjugate (b − √c).
a + √b ↔ a − √b; product a² − b.
Isolate the root, square both sides, solve, check every answer.
Leave answers as surds unless a decimal is asked for.
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 Additional 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 (28 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [15 marks]
Answer all parts, giving exact answers.
(a) Express √75 + √12 − √27 in the form a√3. [3]
(b) Express (2 + √3)/(2 − √3) in the form a + b√3. [4]
(c) Given that (1 + √5)(a + b√5) = 7 + 3√5, find the integers a and b. [4]
(d) Solve √(x + 5) = x − 1. [4]
Question 2 [13 marks]
A right-angled triangle has legs (3 + √2) cm and (3 − √2) cm.
(a) Show that the area of the triangle is 7/2 cm². [3]
(b) Show that the hypotenuse is √22 cm. [4]
(c) Express 1/(3 + √2) in the form (a − √2)/b, where a and b are integers. [3]
(d) Hence, or otherwise, evaluate 1/(3 + √2) + 1/(3 − √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.