A public program that is jointly funded jointly administered and jointly determined by both state and national government is an example of cooperative federalism.
A government that divides power between the states and the national government
reserved powers
Federalism
Passports and Visas.
reserved powers
National government deals with the entire nation; for example, what is the legal voting or drinking age. State government does the same thing, but on the state level; for example, at what age can a teenager receive a driver's permit. State laws cannot contradict national laws; for example, the state could not say that the legal drinking age was 15, because the national law has set it at 21.
The power of the national government to declare war is an example of an expressed power. Another example is the power to levy taxes.
In a unitary system, power is concentrated in the hands of the national government, which holds authority over subnational entities such as regions or provinces. Subnational governments derive their power from the national government and can be created, altered, or abolished by it.
Loans made by the National Government to the States.
A government program that provides funding to states for education initiatives would be an example of a grant-in-aid.
The Wechsler Scale is an example of an intelligence test that would be administered on an individual basis.
The Department of Defense, which is charged with national defense (and some would say the Department of Homeland Security as well) is part of the Executive branch, answering directly to the President of the USA.