Mastering Vectors
Mathematics
GCSE Higher
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A worksheet covering Vectors for GCSE Higher students.
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Mastering Vectors
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Introduction
Study the key concepts of vectors, including vector addition, subtraction, scalar multiplication, and their geometric interpretations. Recall the formula for the magnitude of a vector: |→v| = √(x² + y²).
B
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Given vectors →A = (3, 4) and →B = (1, -2), calculate →A + →B.
[2 marks]2.
Find the magnitude of vector →C = (6, 8).
[2 marks]3.
Subtract vector →B = (1, -2) from →A = (3, 4).
[2 marks]4.
Multiply vector →A = (3, 4) by scalar 2.
[2 marks]5.
Determine whether vectors →A = (2, 3) and →B = (4, 6) are parallel.
[1 mark]6.
Find the vector that is twice →B = (1, -1) and points in the same direction.
[2 marks]7.
A triangle has vertices at A(1, 2), B(4, 6), and C(1, 6). Find the vectors →AB and →AC.
[3 marks]8.
Using the vectors from the previous question, determine if triangle ABC is right-angled at A.
[3 marks]9.
Given →D = (5, 12), verify that its magnitude matches the Pythagorean theorem.
[2 marks]10.
A ship moves with a velocity vector →V = (8, 15) km/h. Find the speed of the ship.
[2 marks]11.
A person walks 3 km east and then 4 km north. Represent this journey as a vector and find its magnitude.
[3 marks]12.
Challenge: Two forces, represented by vectors →F1 = (7, 24) and →F2 = (24, 7), act on an object. Find the resultant vector and its magnitude.
[4 marks]Quick Actions
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- Created
- 12/30/2025
- Updated
- 12/30/2025
- Type
- worksheet