Dielectric constant

One number, three readings, all of them equivalent and all of them printed by the AP Physics C: E&M course.

is the definition, EK 10.4.A.2, and it is on the equation sheet. Then EK 10.4.A.4 gives the derived form $\kappa = E_0/E$, the factor by which the field inside an isolated parallel-plate capacitor drops when the slab goes in, and EK 10.4.A.5 gives $C = \kappa C_0$, the factor by which the capacitance rises. Permittivity ratio, field reduction, capacitance multiplier: same $\kappa$.

Properties worth stating on a free response. It is dimensionless, since it divides one permittivity by another. It is 1 for vacuum by construction, and greater than 1 for real insulating materials, because EK 10.4.A.3 puts the polarized material's own field opposite in direction to the external one rather than reinforcing it.

It is already in your capacitance formula. Both the AP Physics 2 and the C: E&M sheets print $C = \kappa \varepsilon_0 A / d$, and the AP Physics 2 sheet also prints $E_c = Q/(\kappa \varepsilon_0 A)$. Set $\kappa = 1$ and both collapse to the air-filled case, which the exam conventions box on both sheets makes the default: capacitors are air-filled with $\kappa = 1.0$ unless a question says otherwise.

So a capacitor problem that never mentions a slab has already told you the value of $\kappa$. The material itself, and what happens with the battery attached or removed, is dielectric.