What term directly applies to the total amount of kinetic energy of a sample of matter and is dependent on the amount of matter present in the sample?

The kinetic energy of a body is given by the following expression:

Kinetic energy = 1/2 mv^2

where m is the mass of the body and v is its velocity.

As we can see from the expression, kinetic energy of a body is a function of its mass and velocity.

Mass of a body is the amount of matter contained in the body. This is a quantity that remains fixed wherever we go, as long as the amount of matter stays the same. Note that mass is different from weight of a body. The weight is the force with which Earth attracts the body and is given as the product of mass and acceleration due to gravity.

Velocity of a body is the rate of change of position or, dx/dt. 

Thus, the term you are looking for is the mass.

Hope this helps.