MathsFreePrintable

Introduction to Vectors

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Introduction to Vectors worksheet preview

Introduction to Vectors

Vector arrows illustration

📚 Part 1: Vector Basics

1. Which of the following are examples of vector quantities?

Displacement of 5 metres north

Speed of 30 mph

Force of 10 N downwards

Temperature of 20°C

2. A vector has both ________ and ________.
3. Which notation correctly represents a vector?

v = 5

v⃗ = (3, 2)

v = 3 metres

v = fast

4. The vector (4, -2) means move _____ units right and _____ units down.

✏️ Part 2: Vector Operations

5. Calculate the following vector additions:

a) (3, 1) + (2, 4) = ( ____ , ____ )

b) (-1, 5) + (3, -2) = ( ____ , ____ )

6. Calculate the following vector subtractions:

a) (5, 3) - (2, 1) = ( ____ , ____ )

b) (1, -2) - (-3, 4) = ( ____ , ____ )

7. A triangle has vertices at A(1, 2), B(3, 1), and C(2, 4). If the triangle is translated by vector (2, -3), what are the new coordinates?

A' = ( ____ , ____ )

B' = ( ____ , ____ )

C' = ( ____ , ____ )

🎯 Part 3: Problem Solving

8. A robot moves 3 units east, then 4 units north, then 2 units west. What single vector describes its overall displacement?

Overall displacement vector = ( ____ , ____ )

9. Draw vectors on the grid below to show:

a) Vector (2, 3) starting from the origin

b) Vector (-1, 2) starting from point (1, 1)

10. Explain in your own words how to add two vectors graphically (tip-to-tail method):

About This Worksheet

Free in Kuraplan

Sign up free, grab the PDF, and customize it for your class.

Print-Ready

Formatted for standard paper. Clean layout, easy to read.

AI-Generated

Created with Kuraplan's AI, designed for real classroom use.

For Teachers & Parents

Use in classrooms, for homework, tutoring, or homeschool.

Need a custom version of this worksheet?

Kuraplan's AI generates custom worksheets in seconds — differentiated for every learner, aligned to your curriculum.

Generate Custom Worksheets — Free
No credit card Curriculum-aligned Under 60 seconds