Pre-Calculus

Course Goals

• Write a function that describes a relationship between two quantities.
• Define and solve inverse functions, exponential functions, logarithmic functions, and trigonometric functions.
• Investigate exponential models and logarithmic models.
• Use the unit circle to manipulate, solve, and explain symmetry and periodicity of trigonometric functions.
• Find unknown measurements in right triangles.
• Examine and apply trigonometric identities.
• Measure the magnitude of vectors and use vectors to represent velocity in models.
• Apply vector operations of addition and multiplication to negative vectors.
• Examine polar coordinates in graphs.
• Perform advanced operations with complex numbers, including De Moivre's Theorem.
• Represent basic operations of complex numbers geometrically on the complex plane. Understand the conic section while exploring parabolas, ellipses, hyperbolas, and circles and their graphs.
• Use Cavalieri's principle to derive formulas for spheres, cylinders, and other solid figures.
• Solve systems of linear equations with two or three variables using Gauss-Jordan elimination.
• Identify and perform addition, subtraction, and multiplication on matrices.
• Compute the determinant of a matrix.
• Solve systems of linear equations using an inverse matrix.
• Use matrices to transform vectors in a plane.
• Calculate the expected value of a random variable and interpret it as the mean of the probability distribution.
• Develop a probability distribution for a random variable defined for a sample space in which you can calculate probabilities empirically or theoretically and find the expected value.
• Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
• Explore limits and techniques used to find the limit of a function.
• Explore tangent lines and area under curves.