Lesson 5: Revision and Practice

📚 Introduction

Congratulations! 🎉 You’ve completed all the lessons in Module 1: Sets and Number Foundations.

Before we move forward, let’s review and practice everything you’ve learned about:

• Understanding and writing sets
• Operations on sets (union, intersection, difference, complement)
• Properties of natural numbers (commutative, associative, distributive, identity)
• Numeration systems (tally, Roman numerals, Egyptian, decimal system)

This practice will help you strengthen your memory and skills! 🧠💪

🧠 Quick Summary

Sets

• A set is a collection of distinct, well-defined objects.
• Use curly brackets {} to list elements.
• Symbols: ∈ (is an element of), ∉ (is not an element of).

Operations on Sets

• Union (∪): Combine all elements.
• Intersection (∩): Common elements.
• Difference (–): Elements in one set but not the other.
• Complement (A’): Elements outside the set.

Properties of Natural Numbers

• Commutative: Order does not matter (for + and ×).
• Associative: Grouping does not matter (for + and ×).
• Distributive: a × (b + c) = (a × b) + (a × c).
• Identity: Adding 0 or multiplying by 1 keeps number same.

Numeration Systems

• Tally: Counting with strokes (||||).
• Roman Numerals: I, V, X, L, C, D, M.
• Decimal System: Modern place value using digits 0–9.

📝 Mixed Practice Exercises

Part A: Sets and Operations

1. List all the elements of the set A = natural numbers less than 8.
2. If B = {2, 4, 6, 8}, and C = {4, 5, 6, 7}, find:
   • (i) B ∪ C
   • (ii) B ∩ C
   • (iii) B – C
3. If the universal set U = {1,2,3,4,5,6,7,8} and A = {2,4,6}, find A’.

Part B: Properties of Natural Numbers

4. Show that 7 + 5 = 5 + 7 using the commutative property.
5. Use the associative property to solve: (2 + 3) + 4 = 2 + (3 + 4).
6. Apply distributive property: 3 × (4 + 5) = ?

Part C: Numeration Systems

7. Write 492 in expanded form.
8. What is the Roman numeral for 74?
9. Using tally marks, represent the number 11.
10. Fill the place value table for the number 527:

📝 Extra Challenge Problems

Challenge 1:

Set A = {1,2,3,4,5} and B = {4,5,6,7,8}. Draw a Venn diagram to represent A ∩ B and shade it.

Challenge 2:

Convert the Roman numeral XCIV to a decimal number and explain your steps.

Challenge 3:

Explain why base-10 place value is better than using tally marks for writing very large numbers.

🔁 Recap

Well done! In this revision, you practiced listing sets, performing set operations, applying number properties, and working with different numeration systems.
Practising mixed questions like these will prepare you for any type of BECE exam question!

🪞 Reflection Prompt

Which part of Module 1 did you find easiest? Which part do you want to practice more?
Think about your answer and plan how you can improve before moving to the next module!