GCSE Vectors Higher Worksheet 3 + Mark Scheme

Worksheet 3 of the Vectors series — 15 questions on vector geometry and proof for GCSE Higher (Edexcel 1MA1, AQA 8300, OCR J560). 47 marks, 50 minutes.

Builds on Vectors 1 and Vectors 2, applying vector skills to triangles and parallelograms with full proof and collinearity questions. Perfect for top-set Year 11 revision and grade 8/9 stretch.

WHAT’S INCLUDED

• Worksheet (Word .docx and PDF) — 15 questions, 47 marks, ~50 minutes
• Mark scheme (Word .docx and PDF) — full method credit, examiner notes, common-error commentary

WORKSHEET STRUCTURE

• Section A — Fluency (Q1–Q7, 15 marks): expressing vectors in terms of given vectors a and b on triangles and parallelograms, midpoints, and points dividing line segments in given fractions
• Section B — Exam-Style (Q8–Q11, 14 marks): mid-segment theorem of triangles, parallelogram diagonals bisecting each other, parallel-line proofs
• Section C — Problem-Solving (Q12–Q15, 18 marks): combined ratio and midpoint problems, “show MN = pa + qb” stretch questions, and a full collinearity proof

TOPICS COVERED
Vector addition along chained paths, expressing vectors via two given vectors, midpoints of triangle sides, ratio division of a line segment, parallelogram diagonal properties, mid-segment theorem, parallel lines (vectors as scalar multiples), collinearity proofs (parallel + shared point).

PERFECT FOR

• Year 11 Higher revision targeting grade 8/9
• Top-set Year 10 stretch and challenge
• Setting as a timed assessment for high-attaining students
• Teacher-led model answer practice for vector proof technique

The Word .docx files are fully editable so you can adjust questions, swap names, or rebra