# Mathematics Foundations Checklist
## MTH Student Academy

This checklist covers the essential foundations required for university-level calculus and engineering mathematics.

### 1. Algebra Fundamentals
- [ ] Simplifying complex fractions and rational expressions.
- [ ] Factoring polynomials (difference of squares, trinomials).
- [ ] Solving linear and quadratic equations.
- [ ] Working with exponents and radical rules.
- [ ] Understanding absolute value and inequalities.

### 2. Functions and Graphs
- [ ] Identifying domain and range of a function.
- [ ] Understanding function composition (f ∘ g).
- [ ] Finding inverse functions.
- [ ] Recognizing parent functions (linear, quadratic, cubic, reciprocal).
- [ ] Transformations (shifts, reflections, scaling).

### 3. Trigonometry
- [ ] Unit circle values (sine, cosine, tangent).
- [ ] Radians vs. Degrees conversion.
- [ ] Trigonometric identities (Pythagorean, Double-angle).
- [ ] Solving trigonometric equations.
- [ ] Graphing sine and cosine waves.

### 4. Logarithms and Exponentials
- [ ] Properties of logarithms (Product, Quotient, Power rules).
- [ ] Natural logarithm (ln) and base 'e'.
- [ ] Solving exponential equations.

### 5. Mathematical Notation
- [ ] Set notation (union, intersection, element of).
- [ ] Summation notation (Sigma Σ).
- [ ] Interval notation ([a, b), (-∞, ∞)).