What word means a formal agreement between nations?

The word that means a formal agreement between nations, on the USCIS reading vocabulary list, is Treaty. A treaty is a written, legally binding agreement under international law between two or more sovereign states or international organizations.

In the United States the power to make treaties is shared between the President and the Senate. Article II, section 2, clause 2 of the Constitution provides that the President "shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur." This two-thirds Senate ratification requirement is one of the highest supermajority thresholds in the Constitution and reflects the Framers' view that international commitments should require broad national support.

Once ratified, a treaty has the force of federal law under the Supremacy Clause of Article VI, which lists treaties alongside the Constitution and federal statutes as the supreme law of the land. The United States has entered into thousands of treaties since the first one, the Treaty of Amity and Commerce with France in 1778. Notable treaties include the Treaty of Paris of 1783 (ending the Revolutionary War and recognizing American independence from Great Britain), the Louisiana Purchase Treaty of 1803, the Treaty of Guadalupe Hidalgo of 1848 (ending the Mexican-American War and ceding the Southwest to the United States), the Treaty of Versailles of 1919 (which the Senate refused to ratify), and the North Atlantic Treaty of 1949 (creating NATO).

Modern executive agreements with foreign powers may be entered without Senate ratification but do not carry the same legal weight as treaties. On the reading test Treaty may appear in a sentence about war, peace, or diplomacy.