Learning pack · IGCSE handout

Vectors

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). Vectors describe movement with both size and direction. This Vectors summary pairs the IGCSE Vectors worksheet with its answers PDF: practise from the sheet (diagrams included), then check every method in the solutions.

Resources at the top · full summary · videos with short notes below.

🎒 Resources in this pack

Jump straight to the printable files, or scroll to the summary and videos.

Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 🎬 More topic videos (6)📖 Full summary

Files: 39_vectors_handout.pdf · 39_vectors_handout_answers.pdf

Full topic summary

Vectors describe movement with both size and direction. This Vectors summary pairs the IGCSE Vectors worksheet with its answers PDF: practise from the sheet (diagrams included), then check every method in the solutions.

Key learning points

A column vector $\begin{pmatrix}x\\y\end{pmatrix}$ means $x$ right (negative = left) and $y$ up (negative = down).
Arrow notation $\overrightarrow{AB}$ is the displacement from A to B; $\overrightarrow{BA}=-\overrightarrow{AB}$ .
Bold/underlined letters name the same displacement in column form.
Add/subtract component-wise; multiply by a scalar to stretch or reverse.
Magnitude $|\mathbf{a}|=\sqrt{x^2+y^2}$ ; geometry links use midpoints and parallelograms.

Worked example 1 — Addition

$\mathbf{a}=\begin{pmatrix}2\\1\end{pmatrix}$ , $\mathbf{b}=\begin{pmatrix}3\\-4\end{pmatrix}$ . $\mathbf{a}+\mathbf{b}$ ?

Working

\begin{pmatrix}5\\-3\end{pmatrix}

Add components.

Worked example 2 — Midpoint vector

M is midpoint of $AB$ . Express $\overrightarrow{OM}$ if $\overrightarrow{OA}=\mathbf{a}$ , $\overrightarrow{OB}=\mathbf{b}$ .

Working

\overrightarrow{OM}=\tfrac{1}{2}(\mathbf{a}+\mathbf{b})

Position vector of a midpoint.

Worked example 3 — Scalar multiple

$3\begin{pmatrix}2\\-1\end{pmatrix}$ .

Working

\begin{pmatrix}6\\-3\end{pmatrix}

Multiply each component.

Worked example 4 — Magnitude

Find $\left|\begin{pmatrix}3\\4\end{pmatrix}\right|$ .

Working

5

$\sqrt{3^2+4^2}$ .

Worked example 5 — Reverse

If $\overrightarrow{AB}=\mathbf{v}$ , then $\overrightarrow{BA}$ ?

Working

-\mathbf{v}

Opposite direction.

Worked example 6 — Successive translations

A point is translated by $\begin{pmatrix}4\\1\end{pmatrix}$ then $\begin{pmatrix}-1\\3\end{pmatrix}$ . Find one equivalent translation.

Working

\begin{pmatrix}4\\1\end{pmatrix}+\begin{pmatrix}-1\\3\end{pmatrix}=\begin{pmatrix}3\\4\end{pmatrix}

Order does not matter for free-vector addition — both slides land on the same image.

🎬 Topic videos

Two Ships Collision Problem | Position & Velocity Vectors with Animation
IMProjectLessons · 4 min
Position & velocity vectors; bearings; relative motion / collision time; distance after a velocity change. Classic noon ships problem — 0606 Additional Maths + 9709 vectors/mechanics; useful for IGCSE-style boards (incl. Pearson 4MA1) as well.
Vectors — Proving Points Are Collinear | CIE IGCSE Additional Maths (0606)
IMProjectLessons · 4 min
Prove points are collinear with position vectors: routes through O, ratios as fractions of a whole, matching coefficients when vectors share a start point. Matches slides ed95652d (Vectors — Proving points are collinear). Primary CIE 0606; also 0607 vectors, 9709, and IB AA/AI vector geometry.
Vectors in a Triangle — Find Intersection P | CIE IGCSE Additional Maths (0606)
IMProjectLessons · 4 min
Vectors in a triangle: X on AB, Y on OA, P = OX ∩ BY; express OP two ways; solve λ, μ by equating coefficients (section/ratio style). Matches slides 3f4a3ae9 (Vectors in a Triangle — Find Intersection P). Primary CIE 0606; also 0607 vectors, 9709, and IB AA/AI vector geometry.
A quick trick for computing eigenvalues | Chapter 15, Essence of linear algebra
3Blue1Brown · 13 min
Classroom-ready explain of vectors. Use when teaching this topic in Lower Secondary / IGCSE.
Change of basis | Chapter 13, Essence of linear algebra
3Blue1Brown · 13 min
Classroom-ready explain of vectors. Use when teaching this topic in Lower Secondary / IGCSE.
Cramer's rule, explained geometrically | Chapter 12, Essence of linear algebra
3Blue1Brown · 12 min
Classroom-ready explain of vectors. Use when teaching this topic in Lower Secondary / IGCSE.

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