Calculus 12

Course Info
Course Title: 
Calculus 12 Paper
Grade Level: 
Course Format: 
J Templeton
Course Description

Students require a graphing calculator for this course.  A programmable scientific calculator is also helpful.  The final exam requires students to bring a graphing calculator that does not have a QWERTY keyboard, or any external devices like memory cards or a printer.


This course will teach the essentials of a branch of Mathematics called Calculus.  Students will learn what derivatives are, how to calculate some of them, and some of their applications.  Similarly, students will learn about the flip-side of calculus—what integrals are and how to use them. Throughout, the emphasis will be on the application of these concepts.

It is recommended that students complete: Principles of Mathematics 12 with at least a C+ standing
No. Exams: 
Proctored Exams: 

No textbook is required for this course.

No. Modules: 
Course Modules: 

Module 1: Functions and Derivatives

Section 1: Relations and functions; Graphing techniques; Absolute value; Point-slope form of a line

Section 2: Tangent and sectant lines; Position and velocity; Rates of change; Definition of a derivative

Section 3: Limit of a function; One-sided limits; Continuity; Limit properties; Indeterminate forms

Section 4: Rules for differentiation: polynomials, product, quotient, and power rules; Composition of functions


Module 1 Test covers the work of Module 1.


Module 2: Properties and Derivatives

Section 1: Implicit differentiation; Velocity and acceleration

Section 2: Tangent line approximation; Newton’s method

Section 3: Related rates; Maximum and minimum values; Optimization problems

Section 4: Relative extreme; Vertical asymptotes; Horizontal asymptotes

Section 5: Graphing overview; Concavity; Miscellaneous graphing techniques; Other graphing problems


Module 2 Test covers the work of Modules 1 and 2.


Module 3: Trigonometric Derivatives

Section 1: Trigonometry review; Trigonometric limits; Derivatives of sine and cosine

Section 2: Derivatives of other trig functions; Applications; Inverse functions, arcsine and arctangent; Derivatives of arcsine and arctangent

Section 3: Exponential and logarithmic functions review; The fundamental exponential limit, and the natural logarithmic and exponential functions; Derivatives of logarithmic functions

Section 4: Derivatives of exponential functions; Applications; Logarithmic differentiation

Section 5: Another look at limits; L’Hôpital’s Rule; Mean Value theorem


Module 3 Test covers the work of Modules 1, 2 and 3.


Module 4: Integral Calculus

Section 1: Calculating antiderivatives; Position, velocity, and acceleration—a new look; Differential equations

Section 2: Approximating area; Riemann sums; The fundamental theorem of calculus; The definite integral

Section 3: Properties of the definite integral; Area between curves; Mean value of a function

Section 4: Integration by substitution; Integration by parts; Volumes of revolution-disk/washer method and shell method of volumes with known cross sections


Module 4 Test covers the WHOLE COURSE.

Textbook Deposit: 

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