Magnetic flux

The AP Physics 2 sheet prints it twice, as a dot product and as its expansion:

The unit is the weber, one tesla square metre. AP Physics C: Electricity and Magnetism generalises the same idea to a non-uniform field with $\Phi_B = \int \vec{B} \cdot d\vec{A}$, its topic 13.1.

The angle is the trap. $\theta$ sits between the field and the area vector, which points perpendicular to the surface, not along it. A loop lying face-on to the field has $\theta = 0$ and maximum flux; turn it edge-on and $\theta = 90$ degrees puts the flux at zero even though the field never changed. Students who measure from the plane of the loop get every answer backwards.

Flux is a signed scalar, and the dot product supplies the sign: positive when the field runs along the area vector, negative when it runs against it. That sign is what makes "the flux is decreasing" a meaningful sentence rather than a comparison of magnitudes.

Nothing about a steady flux induces anything. Only $\Delta \Phi_B / \Delta t$ appears in Faraday's law, and there are exactly three ways to change it: change $B$, change the area $A$, or rotate the loop to change $\theta$. Topic 12.4 works all three.