Alzar School Curriculum Guide Alzar School Curriculum Guide 2021-2022 | Page 16

MATHEMATICS :

Precalculus Honors ( continued ):
Fall : The Precalculus A semester ( fall only ) involves a deeper exploration of analytical algebra and techniques developed previously in Algebra II . Students study the common families of functions and their graphs and explore the differences between linear , quadratic , rational , inverse , radical , power , and exponential relationships . Learning is focused on how each type of function can be used to model various situations and how changes to the parent equation manifest themselves graphically and practically . Additionally , students analyze polynomial and rational functions by comparing their equations to their graphs . Next , students focus on the properties of exponents and logarithms to explore inverse relationships and different types of growth . The semester typically concludes with an introduction to sequences and series .
The Precalculus B semester ( fall only ) starts with a deeper exploration of analytical algebra and techniques developed previously in Algebra II . Students study the common families of functions and their graphs and explore the differences between linear , quadratic , rational , inverse , radical , power , and exponential relationships . This course then transitions to trigonometry , starting with radian and degree angle measure and the unit circle . Students focus on graphing the six trigonometric functions , modeling the natural world , solving equations , and verifying identities . The class also covers analytical trigonometry and trigonometric identities , including : Pythagorean , sum and difference formulas , half-angle , double angle , and co-function identities . Additionally , students explore oblique triangles using the law of sines , law of cosines , and find the areas of oblique triangles .
Spring : The Precalculus C semester ( spring only ) starts with radian and degree angle measures and uses this to understand trigonometric functions in terms of the unit circle . Students focus on graphing the six trigonometric functions , modeling the natural world , solving equations , and verifying identities . The course also covers analytical trigonometry and trigonometric identities , including : Pythagorean , sum and difference formulas , half-angle , double angle , and co-function identities . Students apply trigonometry to oblique triangles using the law of sines , law of cosines , and find the areas of oblique triangles . Time permitting , this course introduces students to analytic geometry .
This Precalculus D semester ( spring only ) starts with arithmetic and geometric sequences and series . Students then get a glimpse into some statistics with counting principles , probability , and binomial theorem . Next , students investigate geometric shapes through the polar coordinate system and polar equations . Then , students are introduced to parametric equations and application problems using parametrics as well as vectors . Lastly , students are introduced to Calculus , with a focus on limits and derivatives .
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