GCSE Vectors Higher Worksheet 2 + Mark Scheme

Worksheet 2 of the Vectors series — 15 questions on position vectors and geometry for GCSE Higher (Edexcel 1MA1, AQA 8300, OCR J560). 47 marks, 50 minutes.

Builds directly on Vectors 1 (Column Vectors and Arithmetic) and prepares students for vector geometry and proof in Worksheet 3. Perfect for Year 10 progression or Year 11 revision.

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): finding vectors between points, midpoints, and magnitudes from position vectors
• Section B — Exam-Style (Q8–Q11, 14 marks): point dividing a line in a given fraction, distance problems with surd answers, algebraic position vectors, collinearity
• Section C — Problem-Solving (Q12–Q15, 18 marks): ratio AP:PB along a line segment, two-unknown algebraic midpoints, parallelogram fourth-vertex problems, magnitude with surds

TOPICS COVERED
Position vectors, finding the vector AB as b − a, midpoints, magnitude (Pythagoras), distance between points, ratio division of a line segment, parallelograms in vector form, collinearity proofs, algebraic position vectors with unknowns, surd simplification.

PERFECT FOR

• Year 10 Higher students moving beyond column vector arithmetic
• Year 11 Higher revision and intervention
• Setting as homework, in-class practice, or end-of-topic assessment
• Stretching top-set students with Section C ratio and parallelogram problems

The Word .docx files are fully editable so you can adjust questions, swap names, or rebrand for your school.

Pairs with Vectors 1: Column Vectors and Arithmetic. Worksheet 3 (vector geometry and proof) will follow shortly.