High Precalculus

Segment 1 

• Determine key features of functions and their graphs
• Solve and graph polynomial functions, rational functions, radical functions, logarithmic functions, and piecewise functions
• Apply functions to real-world settings and determine their constraints
• Compare key features of functions
• Solve systems of equations
• Combine functions
• Compose functions
• Determine inverse functions
• Find and apply the difference quotient
• Analyze real-world applications of function combinations
• Learn the process by which conic sections are formed
• Determine equations for and key features of circles, parabolas, ellipses, and hyperbolas
• Analyze real-world applications of conic sections
• Determine and differentiate between arithmetic and geometric sequences
• Investigate and fully understand series
• Analyze real-world applications of sequences and series

 

Segment 2

• Define trigonometric functions
• Convert angle measures from degrees to radians and radians to degrees
• Determine and differentiate between reference angles and coterminal angles
• Apply the Law of Sines and Law of Cosines
• Determine the area of a triangle, given two sides and the included angle
• Determine the values present on the unit circle and investigate their applications
• Apply the unit circle for all six trigonometric functions
• Apply technology with trigonometric functions
• Graph trigonometric functions and determine their key features
• Analyze real-world applications of trigonometric functions
• Prove and apply Pythagorean identities
• Simplify expressions using trigonometric identities
• Prove and apply the Angle Sum formula for sine, cosine, and tangent
• Prove and apply the Angle Difference formula for sine, cosine, and tangent
• Prove and apply the Double-Angle formula for sine, cosine, and tangent
• Prove and apply the Half-Angle formula for sine, cosine, and tangent
• Solve trigonometric equations
• Analyze real-world applications of trigonometric equations
• Define vectors using magnitude and direction
• Represent vectors in component, linear, and trigonometric form
• Add, subtract, and multiply vectors algebraically and graphically
• Apply the dot product and vector projections to solve mathematical problems involving vectors
• Analyze real-world applications including vectors in two dimensions
• Compute the magnitude and direction of a vector scalar multiple and the sum of two or more vectors
• Analyze real-world applications of vectors representing velocity and other quantities
• Define and plot polar coordinates, both by hand and using technology
• Convert coordinates from polar to rectangular and from rectangular to polar
• Represent equations given in polar coordinates in rectangular coordinates
• Represent equations given in rectangular coordinates in polar coordinates
• Graph polar equations including circles, cardioids, limacons, rose curves, and lemniscates
• Represent complex numbers using polar and rectangular coordinates
• Calculate midpoint and distance on the complex coordinate plane
• Represent and multiply complex numbers in trigonometric form
• Add, subtract, and multiply, and determine the conjugate of complex numbers geometrically on the complex coordinate plane
• Analyze real-world applications of complex numbers applied geometrically and algebraically
• Graph parametric equations
• Convert parametric equations to rectangular equations and rectangular equations to parametric equations
• Analyze real-world applications of parametric equations involving motion in the plane

 

Besides engaging students in challenging curriculum, the course guides students to reflect on their learning and evaluate their progress through a variety of assessments. Assessments can be in the form of practice lessons, multiple choice questions, writing assignments, projects, research papers, oral assessments, and discussions. This course will use the state-approved grading scale. Each course contains a mandatory final exam or culminating project that will be weighted at 20% of the student’s overall grade.***

***Proctored exams can be requested by FLVS at any time and for any reason in an effort to ensure academic integrity. When taking the exam to assess a student’s integrity, the exam must be passed with at least a 59.5% in order to earn credit for the course.  

To achieve success, students are expected to submit work in each course weekly. Students can learn at their own pace; however, “any pace” still means that students must make progress in the course every week. To measure learning, students complete self-checks, practice lessons, multiple choice questions, projects, discussion-based assessments, and discussions. Students are expected to maintain regular contact with teachers; the minimum requirement is monthly. When teachers, students, and parents work together, students are successful.