12th Grade – Calculus

Philosophy
God created humans with a rational and inquiring mind. He blessed them with the ability to count, tell time and make change. In Mathematics we will explore and develop this God given gift systematically. As the Bible says “precept upon precept, line upon line …” (Isaiah 28:10), students will systematically build up their knowledge of Mathematics. As they learn the different disciplines of Mathematics students will recognize the logic and order God imbued in the world and by implication that God is a God of logic and order. They will develop a greater understanding and appreciation of God through their study of mathematics.

Course Objectives
In Calculus, students will explore deeper (ESLR: ET) into ideas of limits, differentiation and integration and their application in everyday situations. They will be able to understand and use correct mathematical notational in any situation. (ESLR: DC) This will enable to further appreciate God’s hand in ordering our universe. (ESLR: RUC) It will be an exploration of this fun and essential area of mathematics that will prepare students for college calculus. (ESLR: NLL) We will tie in some history of mathematics as we look at new concepts and when they were discovered. (ELSR: ECW) There is an expectation that students taking this course will be prepared for and take the Calculus AP exam.

Textbooks
Calculus with Trigonometry and Analytic Geometry, Saxon and Wang, Saxon Publishers Inc ©1997

Materials and Equipment
Textbook
Graphing Calculator

Time Allotment
50 minutes per day, 5 days a week

Course Content
I. Functions, Graphs and Limits

• Analysis of graphs
• Limits of functions (including one-sided limits)
• Asymptotic and unbounded behaviour
• Continuity as a property or functions

II. Derivatives

• Concept of a derivative
• Derivative at a point
• Derivative as a function
• Second derivatives
• Applications of derivatives
• Computation of Derivatives

III. Integrals

• Interpretation and properties of definite integrals
• Applications of integrals
• Fundamental Theorem of Calculus
• echniques of antidifferentiation
• Applications of antidifferentiation
• Numerical approximations to definite integrals

Evaluation