1. Let's start with **Sets**. A set is a collection of distinct objects, called elements. 2. Important rules: - Union ($A \cup B$) combines elements from both sets. - Intersection ($A \cap B$) includes only elements common to both. - Difference ($A - B$) includes elements in $A$ but not in $B$. 3. Example: If $A = \{1,2,3\}$ and $B = \{2,3,4\}$, then $$A \cup B = \{1,2,3,4\}$$ $$A \cap B = \{2,3\}$$ $$A - B = \{1\}$$ 4. Next, **Geometry** basics: It studies shapes, sizes, and properties of space. - Key formulas: - Area of rectangle: $A = l \times w$ - Area of triangle: $A = \frac{1}{2}bh$ - Pythagoras theorem: $c^2 = a^2 + b^2$ 5. Example: For a right triangle with legs 3 and 4, $$c^2 = 3^2 + 4^2 = 9 + 16 = 25$$ $$c = \sqrt{25} = 5$$ 6. Finally, **Statistics**: It deals with data collection, analysis, and interpretation. - Mean (average): $\bar{x} = \frac{\sum x_i}{n}$ - Median: middle value when data is ordered - Mode: most frequent value 7. Example: Data set $\{2,3,3,5,7\}$ - Mean: $\frac{2+3+3+5+7}{5} = \frac{20}{5} = 4$ - Median: 3 (middle value) - Mode: 3 (appears twice) Practice these concepts step-by-step to improve your understanding!