Mastering Algebra and Trigonometry Fundamentals

📋 Course Outline

1. Algebra and quadratics
2. Functions and graphing
3. Trigonometry
4. Probability and combinatorics

📖 1. Algebra and quadratics

🔑 Key Concepts & Definitions

• Surds: Surds are radicals that cannot be simplified into rational powers, such as square roots that remain non-rational after simplification.
• Discriminant: The discriminant is a value computed from a quadratic that predicts how many real solutions the quadratic has.
• Completing the square: Completing the square is a method that rewrites a quadratic in a squared form to reveal key features like the vertex.

📝 Essential Points

• Simplifying surds involves extracting perfect-square factors so the radical part becomes as simple as possible.
• For a quadratic $ax^2+bx+c$, the discriminant is $b^2-4ac$ and its sign determines whether there are 2, 1, or 0 real roots.
• Completing the square converts $ax^2+bx+c$ into a form related to $(x-h)^2$ so the axis of symmetry and vertex can be read off.

💡 Memory Hook

Discriminant sign: negative means no real x-intercepts, zero means one repeated root, positive means two distinct roots.

📖 2. Functions and graphing

🔑 Key Concepts & Definitions