Zenith Academy

Your Complete Mathematics Education Resource

Algebra Fundamentals

Understanding algebraic expressions is crucial for mathematical success. Let's explore the key concepts:

(a + b)² = a² + 2ab + b²

Example Problem:

Question: Solve for x: 2x + 5 = 15

Solution:

Step 1: Subtract 5 from both sides: 2x = 10

Step 2: Divide both sides by 2: x = 5

Answer: x = 5

Geometry Basics

Geometry helps us understand shapes, sizes, and the properties of space.

Area of Circle = πr²
Circumference = 2πr

Practice Exercise:

Question: Find the area of a circle with radius 5 cm.

Solution:

Using the formula A = πr²

A = π × 5² = π × 25 ≈ 78.54 cm²

Answer: 78.54 cm²

The Pythagorean Theorem

One of the most important theorems in mathematics:

a² + b² = c²

Where c is the hypotenuse and a, b are the other two sides of a right triangle.