The Fundamental Theorem of Calculus connects two important math concepts: differentiation and integration.

It helps us understand how they work together. Here’s what it says:

If $F$ is the antiderivative of a function $f$, then:

$\int_a^b f(x) \, dx = F(b) - F(a)$

So, what does this mean for Year 9 students?

1. Connecting Ideas: This theorem shows how finding areas under curves is linked to finding the slopes of curves.

2. Real-Life Use: It helps us understand motion. For example, you can find distance by looking at the speed using integration.

Let’s think about a car that drives at different speeds. If we can calculate the area under the speed-time graph, we can figure out the total distance the car has traveled.

This idea is really useful in real life!