Lesson 3: Revision and Practice

📘 Introduction

Well done getting this far! In this final lesson, we’ll bring everything together — both vectors and number patterns.
You’ll review the key points, solve mixed problems, and test yourself with word problems and reasoning exercises.
Let’s see how much you remember!

🧠 Quick Revision Notes

🔺 Vectors Recap

• Vectors have direction and magnitude.
• Written in component form:
  
• Add or subtract vectors by operating on each component:

  

🔢 Number Patterns Recap

• Look for rules in sequences (addition, multiplication, position).
• Arithmetic sequence rule:

  
  where a is the first term and d is the common difference.

• Geometric sequences multiply by the same number each time.
• Position-based patterns include:
  • Squares:
    
  • Triangles:
    

🧮 Mixed Example Problems

Example 1: Vector Addition and Subtraction

Add and then subtract these vectors:

Addition:

Subtraction:

Example 2: Sequence Rule and Formula

Find the rule and the 7th term of this sequence: 2, 5, 8, 11, …

Solution:
Rule: Add 3 (arithmetic sequence)
Formula:

7th term:

Example 3: Word Problem (Vectors)

Ama walks 3 meters east and then 4 meters north. Kwame walks 6 meters east and 2 meters north.
Who is further from the starting point?

Solution:
Ama’s vector:

→ Distance:

Kwame’s vector:

→ Distance:

Kwame is further from the start.

📝 Final Practice Exercises

Part A: Vectors

1. Add
   and
   
2. Subtract
   from
   
3. Find the displacement vector for someone walking 2 km west and 6 km south.

Part B: Number Patterns

4. What is the 10th term of the sequence 1, 4, 7, 10, …?
5. Write the nth term formula for 2, 4, 8, 16, …
6. The first five triangle numbers are: 1, 3, 6, 10, 15. What is the 6th triangle number?

✔ Answers and Explanations

• #1:
  
• #2:
  
• #3:
  
• #4: 10th term:
  
• #5: Multiply by 2 each time:
  
• #6:
  

🔁 Recap

• We revised vector operations: addition, subtraction, displacement.
• We reviewed arithmetic and geometric patterns and how to form formulas.
• You solved problems that combined both topics — great job!

🪞 Reflection Prompt

Which of the two topics — vectors or number patterns — do you find easier? Why?
Write down one real-life situation where you’ve used each of these without even knowing!