1. Calculus is a branch of mathematics that studies how things change. It focuses on two main concepts: differentiation and integration. 2. Differentiation is about finding the rate at which a quantity changes. For example, if you have a function $f(x)$, its derivative $f'(x)$ tells you how fast $f(x)$ changes as $x$ changes. 3. The derivative of a function $f(x)$ is defined as $$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$ which means the slope of the tangent line to the curve at point $x$. 4. Integration is the reverse process of differentiation. It is used to find the total accumulation of a quantity, such as area under a curve. 5. The definite integral of a function $f(x)$ from $a$ to $b$ is written as $$\int_a^b f(x) \, dx$$ and represents the area under the curve between $x=a$ and $x=b$. 6. Fundamental Theorem of Calculus connects differentiation and integration, stating that integration can be reversed by differentiation and vice versa. 7. In Grade 12 calculus, you learn to apply these concepts to solve problems involving rates of change, optimization, and areas under curves. 8. Example: If $f(x) = x^2$, then the derivative is $f'(x) = 2x$, and the integral from 0 to 2 is $$\int_0^2 x^2 \, dx = \left[ \frac{x^3}{3} \right]_0^2 = \frac{8}{3}$$. 9. Practice with these concepts helps build a strong foundation for advanced mathematics and science subjects.