Knewton Topics Covered:
Vectors
- Sketch a vector in two dimensions
- Express a vector in terms of unit vectors
- Solve applications using vectors
- Perform vector operations in three dimensions
- Solve applications using vectors in three dimensions
- Calculate the dot product
- Find angles using the dot product
- Solve applications of the dot product
- Use properties of the cross product
- Solve applications using the cross product
Vector Valued Functions
- Find the parametric and symmetric equations of a line
- Write equations of vector-valued functions
- Use linear properties of the derivative of vector-valued functions
- Compute tangent and unit tangent vectors for vector-valued functions
- Find integrals of vector-valued functions
- Find the arc length for a vector-valued function
- Find the curvature of a vector-valued function
- Find the normal and binormal vectors for a vector-valued function
- Find the velocity and acceleration vectors of particle in motion
- Find the tangential and normal components of acceleration
Instructions
- Time limit: 75 minutes.
- Grading Policy: Problems are equally weighted.
- Formatting: Show your work neatly and organize it logically. Box your final answers.
Resources
- Formula sheet: 4 pages of your own notes (handwritten, no worked examples)
- Calculators: Any calculator (including phone apps) may be used for arithmetic.
- Prohibited Features: You may not use calculator features for solving, graphing, limits, derivatives, integrals, or vector operations unless stated differently in individual problems.
- Communication: No outside communication or use of AI tools is permitted.