1. The problem is to understand and apply various fundamental concepts in general mathematics including differentiation, integration, set theory, and algebraic operations. 2. We start with differentiation rules: sum rule $\frac{d}{dx}(f+g) = f' + g'$, product rule $\frac{d}{dx}(fg) = f'g + fg'$, quotient rule $\frac{d}{dx}\left(\frac{f}{g}\right) = \frac{f'g - fg'}{g^2}$, and the chain rule $\frac{d}{dx}f(g(x)) = f'(g(x))g'(x)$. 3. For definite integrals, the Fundamental Theorem of Calculus states $\int_a^b f(x) dx = F(b) - F(a)$ where $F'(x) = f(x)$. 4. Set theory basics include union $A \cup B$, intersection $A \cap B$, subset $A \subseteq B$, complement $A^c$, empty set $\emptyset$, and universal set $U$. 5. The Remainder Theorem states that the remainder of dividing a polynomial $f(x)$ by $(x - a)$ is $f(a)$. 6. Inequalities can be solved using algebraic manipulation and properties of inequalities. 7. Partial fractions decompose rational functions into simpler fractions for easier integration. 8. Surds and indices follow rules like $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$ and $a^m \times a^n = a^{m+n}$. 9. Logarithm properties include $\log(ab) = \log a + \log b$ and $\log(a^n) = n \log a$. This summary covers the key formulae and concepts for MTH 101 General Mathematics I.