Scalars and vectors, column and i, j notation, equal vectors, addition, subtraction and scalar multiples, unit vectors, position and displacement vectors, magnitude and direction.
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 plane flies at 300 km/h — but in which direction? Quantities with direction are vectors, and i, j notation lets you calculate with them like algebra.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Change the components and see a + b.
Copy these into your notebook in your own words — that is how they stick.
Scalar: size only. Vector: size and direction.
a = xi + yj = (x over y); i = (1, 0), j = (0, 1).
Add/subtract/scale component by component.
Equal: same components. Parallel: a = λb.
|a| = √(x² + y²).
â = a/|a|.
AB = OB − OA.
tan θ = y/x (adjust for quadrant); bearing from North.
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 (26 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [14 marks]
a = 3i − 2j and b = −i + 5j.
(a) Find a + b, 2a − b and |a|. [5]
(b) Write down the unit vector in the direction of b. [3]
(c) Find the value of λ for which a + λb is parallel to the vector i. [3]
(d) Find the angle that b makes with the positive x-axis, to 1 decimal place. [3]
Question 2 [12 marks]
O is the origin, A is (4, 1) and B is (1, 5).
(a) Write down OA and OB, and find AB and |AB|. [5]
(b) M is the midpoint of AB. Find OM. [2]
(c) OACB is a parallelogram. Find OC. [2]
(d) A boat moves with velocity (6i + 8j) km/h in a current of (−2i + j) km/h. Find the resultant velocity and the actual speed. [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.