MRS. Rania Elfar - IGCSE Math Teacher

Sunday, 7 September 2025

IGCSE Mathematics - General Exam Prep

IGCSE Mathematics | Lessons, Past Papers, Revision Notes & Exam Tips

IGCSE Mathematics - General Exam Prep

10 Proven Tips to Score High in IGCSE Mathematics
How to Revise Effectively for IGCSE Maths Exams
The Ultimate IGCSE Mathematics Study Plan (Step by Step)
Common Mistakes in IGCSE Maths Exams and How to Avoid Them
Best Resources to Prepare for IGCSE Mathematics Online

Topic-Specific Lessons

IGCSE Algebra Made Easy: Step-by-Step Guide with Examples
Understanding Geometry in IGCSE Maths: Key Formulas and Tricks
How to Solve Trigonometry Problems in IGCSE Mathematics
Probability and Statistics in IGCSE Maths: Complete Revision Guide
Mastering Graphs and Functions for IGCSE Mathematics

Practice & Past Papers

Where to Find Free IGCSE Mathematics Past Papers with Solutions
How to Use Past Papers to Improve Your IGCSE Maths Grade
IGCSE Maths Exam-Style Questions with Step-by-Step Solutions
Top 20 IGCSE Mathematics Questions Every Student Must Practice
Grade 9 in IGCSE Maths: Solved Past Paper Secrets

Advanced / Special Content

IGCSE Mathematics Formula Sheet – Learn What You Need for the Exam
Time Management Strategies for IGCSE Maths Exam Success
How Online Tutoring Can Boost Your IGCSE Mathematics Grades
IGCSE Core vs Extended Mathematics – Which One Should You Choose?
Top Apps and Tools Every IGCSE Maths Student Should Use

IGCSE Mathematics - General Exam Prep

10 Proven Tips to Score High in IGCSE Mathematics
How to Revise Effectively for IGCSE Maths Exams
The Ultimate IGCSE Mathematics Study Plan (Step by Step)
Common Mistakes in IGCSE Maths Exams and How to Avoid Them
Best Resources to Prepare for IGCSE Mathematics Online

Topic-Specific Lessons

IGCSE Algebra Made Easy: Step-by-Step Guide with Examples
Understanding Geometry in IGCSE Maths: Key Formulas and Tricks
How to Solve Trigonometry Problems in IGCSE Mathematics
Probability and Statistics in IGCSE Maths: Complete Revision Guide
Mastering Graphs and Functions for IGCSE Mathematics

Practice & Past Papers

Where to Find Free IGCSE Mathematics Past Papers with Solutions
How to Use Past Papers to Improve Your IGCSE Maths Grade
IGCSE Maths Exam-Style Questions with Step-by-Step Solutions
Top 20 IGCSE Mathematics Questions Every Student Must Practice
Grade 9 in IGCSE Maths: Solved Past Paper Secrets

Lesson 1: Understanding Numbers in IGCSE Mathematics – The Foundation of Success

Mathematics begins with numbers. In IGCSE Mathematics, mastering the basics of numbers is the first step toward building confidence and scoring well in exams. This lesson will guide you through the essential number concepts you must know.

🔹 1. Place Value and Standard Form

Place Value:
Every digit in a number has a value depending on its position. For example:

In 4,582,
- 4 → Thousands
- 5 → Hundreds
- 8 → Tens
- 2 → Units

Standard Form (Scientific Notation):
A way to write very large or very small numbers.

👉 Formula:

a \times 10^n \quad \text{where } 1 \leq a < 10

Examples:

45,000 = $4.5 \times 10^4$
0.0062 = $6.2 \times 10^{-3}$

🔹 2. Prime Numbers, Factors, and Multiples

Prime Number → A number with exactly two factors (1 and itself).
Examples: 2, 3, 5, 7, 11, 13 …
Factors → Numbers that divide exactly into another number.
Example: Factors of 12 → 1, 2, 3, 4, 6, 12
Multiples → Products of a number.
Example: Multiples of 4 → 4, 8, 12, 16 …

Exam Tip: Learn prime numbers up to 50 – they often appear in factorization questions.

🔹 3. Highest Common Factor (HCF) & Lowest Common Multiple (LCM)

HCF: The biggest number that divides exactly into two numbers.
LCM: The smallest number that is a multiple of both numbers.

Example:
Find the HCF and LCM of 18 and 24.

18 = 2 × 3²
24 = 2³ × 3

👉 HCF = 2 × 3 = 6
👉 LCM = 2³ × 3² = 72

🔹 4. Types of Numbers in IGCSE Mathematics

Integers → Whole numbers (… -3, -2, -1, 0, 1, 2 …)
Rational Numbers → Fractions & decimals that can be written as $\frac{p}{q}$ .
Irrational Numbers → Numbers that cannot be written as fractions (e.g. √2, π).
Real Numbers → All of the above combined.

🔹 5. Practice Questions

Try these questions (answers below 👇):

Write 0.00054 in standard form.
List all prime numbers between 20 and 30.
Find the HCF and LCM of 30 and 45.
Classify each number as integer, rational, or irrational:
- 7, 0.25, √3, -12

✅ Answers

$5.4 \times 10^{-4}$
23, 29
- 30 = 2 × 3 × 5
- 45 = 3² × 5
- HCF = 15
- LCM = 90
- 7 → Integer, Rational
- 0.25 → Rational
- √3 → Irrational
- -12 → Integer, Rational