Скачать или смотреть The Vector Method (Q23 IGCSE Paper 2HR 2018)

In this video, Lee Guffick tackles a high-tier IGCSE vectors question that tests some of the most powerful ideas in coordinate geometry — midpoints, ratios, vector paths, and parallel vectors.

Students must prove that points C, D and E lie on the same straight line using a vector method. Lee breaks this down into simple, logical steps: constructing vector diagrams, expressing paths using A and B, handling ratios such as 3:1 on AB, and forming vector expressions for CD and DE.

This is classic Grade 9 reasoning and an essential foundation for A-Level Mechanics and Pure Maths.

⏱️ TIMESTAMPS:
00:00 – Introduction to the Grade 9 vector problem
00:12 – Understanding the setup: OA = a, OB = b
00:45 – Identifying midpoint C on OA
01:05 – Using the ratio 3:1 to locate point D on AB
01:40 – Interpreting “OB is two lots of BE” to locate E
02:10 – Strategy: prove collinearity using parallel vectors
02:25 – Constructing vector path CD
03:05 – Simplifying CD into ¼(3b − a)
03:28 – Constructing vector path DE
04:05 – Simplifying DE into the same expression
04:30 – Concluding parallel vectors → straight line
04:45 – Final explanation of collinearity

✏️ TOPICS COVERED:

Vector diagrams

Midpoints and fractional vectors

Ratio vectors: dividing a line in a given ratio

Expressing paths such as A→B as b − a

Proving collinearity using parallel vectors

Scalar multiples and vector simplification

💯 EXAM TIPS:

When proving points lie on a straight line, aim to show two vectors are scalar multiples of each other.

Always convert ratio statements into fractions of the full vector (e.g. 3:1 → three-quarters and one-quarter).

Midpoints simply use half the vector — a great mark-grabber.

Build vector paths by breaking them into smaller steps you already know.

Clearly factorise at the end — it makes the parallel relationship obvious.

📚 ABOUT GUFFICK TUITION:
Lee Guffick is a former Head of Mathematics and A-Level Examiner helping students achieve A*/A grades and secure places at top universities including Oxford, Cambridge and the Ivy League. His vector explanations are known for clarity, structure and real exam precision.

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