MATHEMATICS
Study Guide
A Creative Journey Through Core Concepts
01 Number Systems 02 Products
03 Factorisation 04 Exponents
05 Equations & Inequalities
Designed for clarity • Built for curiosity • Made to inspire
, 1 Number Systems
Numbers are the alphabet of mathematics. Understanding the different types of numbers and
how they relate to each other is the foundation of all mathematical thinking.
Types of Numbers
Mathematics classifies numbers into distinct sets, each nested inside the next like Russian dolls.
• Natural Numbers (N) — Counting numbers: 1, 2, 3, 4 …
• Whole Numbers (W) — Natural numbers plus zero: 0, 1, 2, 3 …
• Integers (Z) — Positive, negative, and zero: … −2, −1, 0, 1, 2 …
• Rational Numbers (Q) — Any number expressible as p/q where q ≠ 0.
• Irrational Numbers — Cannot be written as a fraction: π, √2, e …
• Real Numbers (R) — All rational and irrational numbers combined.
N ⊂ W ⊂ Z ⊂ Q ⊂ R
Quick Example
Is 0.75 rational? Yes! 0.75 = 3/4 (p=3, q=4)
Is sqrt(3) rational? No! It is irrational.
Number Line & Absolute Value
Every real number has a position on the number line. The absolute value |x| gives the distance
from zero, always non-negative.
|x| = x if x >= 0
|x| = -x if x < 0
|-7| = 7 |5| = 5
Try It
|-12| = ? Answer: 12
|3 - 8| = |-5| = ? Answer: 5
Mathematics Study Guide • Creative Learning Series
Study Guide
A Creative Journey Through Core Concepts
01 Number Systems 02 Products
03 Factorisation 04 Exponents
05 Equations & Inequalities
Designed for clarity • Built for curiosity • Made to inspire
, 1 Number Systems
Numbers are the alphabet of mathematics. Understanding the different types of numbers and
how they relate to each other is the foundation of all mathematical thinking.
Types of Numbers
Mathematics classifies numbers into distinct sets, each nested inside the next like Russian dolls.
• Natural Numbers (N) — Counting numbers: 1, 2, 3, 4 …
• Whole Numbers (W) — Natural numbers plus zero: 0, 1, 2, 3 …
• Integers (Z) — Positive, negative, and zero: … −2, −1, 0, 1, 2 …
• Rational Numbers (Q) — Any number expressible as p/q where q ≠ 0.
• Irrational Numbers — Cannot be written as a fraction: π, √2, e …
• Real Numbers (R) — All rational and irrational numbers combined.
N ⊂ W ⊂ Z ⊂ Q ⊂ R
Quick Example
Is 0.75 rational? Yes! 0.75 = 3/4 (p=3, q=4)
Is sqrt(3) rational? No! It is irrational.
Number Line & Absolute Value
Every real number has a position on the number line. The absolute value |x| gives the distance
from zero, always non-negative.
|x| = x if x >= 0
|x| = -x if x < 0
|-7| = 7 |5| = 5
Try It
|-12| = ? Answer: 12
|3 - 8| = |-5| = ? Answer: 5
Mathematics Study Guide • Creative Learning Series
