As an introductory course to calculus, the first semester of calculus usually emphasizes the main point and origins of calculus. However, since calculus is a math course, teachers of mathematics tend to merely mention the historical aspects of calculus instead of delving deep into the subject. You can make up for this lack of knowledge by creating a project that analyzes the history behind calculus. Ideas for such a project are the initial applications of calculus, Newton's development of calculus and the debate between Newton and Leibniz.
The notion of a tangent plays an important role in introductory calculus. In the first semester of calculus, students study the tangent and how to find it. Projects can look at the tangent from other perspectives. Some ideas are finding a tangent through algebra and this method's parallels to the calculus approach; the geographical interpretations of a tangent; and different applications of tangents.
Newton gradually developed calculus through his study of physics. Because of this, calculus and physics are strongly interconnected. A project from the angle of physics can explain many of the things you learn in introductory calculus from the standpoint of their applications to science. Examples for this type of project are the relationships between distance, velocity and acceleration as derivatives; optimization problems in the physics of motion; and describing the path of a trajectory.
Most of the derivatives presented in the first semester of calculus are simple functions. Teachers focus on these functions because their derivatives are easy to remember. However, the definition of a derivative is all you need to compute the derivative of even the most intricate functions. For an impressive calculus project, you can apply the definition of the derivative to complex functions, and present the derivatives of these functions to the class and professor, displaying the robustness of a single calculus definition.