Calculus 12 Course Details

Teacher

Kathleen Pugh

Prerequisite

Principles of Mathematics 12 with at least a B standing.

Description

This course teachs 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, they 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.

The course consists of four modules. You must have a graphing calculator; a programmable scientific calculator is also helpful. The final exam requires you to bring a graphing calculator that does not have a QWERTY keyboard, or any external devices like memory cards or a printer.

Unit 1: Functions and Derivatives
Unit 2: Properties and Derivatives
Unit 3: Trigonometric Derivatives
Unit 4: Integral Calculus

Type

Credit

Delivery

Student-paced
Students can correspond in writing with the course marker through the submission sheets with each assignment.
Students will communicate with the teacher/advisor to get any needed support.

Summary

4 print modules (18 send-in assignments)
4 module tests, 2.5 hours each, with test 4 covering the entire course

Evaluation

40% Coursework
60% Tests

Support

Limited tutorial support by appointment at SIDES

More Info

Unit 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

Unit 1 Test covers the work of Unit 1

Unit 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

Unit 2 Test covers the work of Units 1 and 2

Unit 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

Unit 3 Test covers the work of Units 1, 2 and 3

Unit 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

Unit 4 Test covers the ENTIRE COURSE

Outcome

Calculus 12 Prescribed Learning Outcomes