Biblical Saving Faith is not the mental nodding or mental assent to a proposition. It begins with this but it is not entirely this. If what you call faith stops here then it is not true faith. For Biblical Saving faith is more than this.
Saving faith is trust, confidence, and reliance on an effectual work that could truly affect your spiritual position and condition before God. Mental Assent --- You see an elevator and you nod your head that yes it could carry you up. Saving Faith --- You don't just mentally agree that the elevator could carry you up, you take it to the next level --- you step into it. You put yourself in it, trusting and relying on it to actually lift you up. Don't just mentally agree that the Lord Jesus is the Savior, rather, take it to the next level, trust and rely on Him and what He did on the cross that what He did there was sufficient and enough to save you completely.