This is a preliminary course for the calculus courses. Starting with functions and graphs, you will learn how to play with
basic functions such as trigonometric functions, exponentials, and logarithms. You will also learn how to solve quadratic
equations, how to draw the graph of quadratic functions as well as how to use polar coordinates to express complex numbers
and solve basic equations with De Moivre's Theorem.
Students with enough background and understanding of the mathematics at the IB higher level do not need to take this course.
Students with enough background and understanding of the mathematics at the IB higher level do not need to take this course.
Through this course, students will be able to obtain basic knowledge & understanding of mathematics required to take the course
"Calculus I".
| Goals and objectives | Course Outcomes | |
|---|---|---|
| 1. | Students will be able to compute the values of basic functions such as linear functions, quadratic functions, and polynomial functions and their combinations & inverses. Students will also be able to draw the graphs of those functions. |
A-1
|
| 2. | Students will be able to solve quadratic equations. Students will also be able to use division of polynomials to solve basic polynomial equations. |
A-1
|
| 3. | Students will be able to compute the values of exponential functions and logarithms as well as solve basic equations with those functions. Students will also be able to draw the graphs of exponential and logarithmic functions. |
A-1
|
| 4. | Students will be able to compute the values of trigonometric functions and their inverses using laws of sines and cosines and trigonometric identities. Students will also be able to draw the graphs of those functions. |
A-1
|
| 5. | Students will be able to express complex numbers using polar coordinates and solve basic equations using De Moivre's Theorem. |
A-1
|
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | Guidance Real numbers Exponents and radicals Algebraic expressions Rational expressions |
Review the content of the lecture (1.1-1.4 in the textbook) | 100分 |
| Work on homework problems | 90分 | ||
| 2. | Equations Modeling with equations Inequalities Coordinate geometry |
Review the content of the lecture (1.5, 1.7-1.9 in the textbook) | 100分 |
| Work on homework problems | 90分 | ||
| 3. | Functions Graphs Average rate of change Linear functions |
Review the content of the lecture (2.1-2.5 in the textbook) | 100分 |
| Work on homework problems | 90分 | ||
| 4. | Transformations of functions Combining functions |
Review the content of the lecture (2.6-2.7 in the textbook) | 60分 |
| Work on homework problems | 130分 | ||
| 5. | One-to-one functions and inverses Quadratic functions Polynomial functions |
Review the content of the lecture (2.8, 3.1-3.2 in the textbook) | 80分 |
| Work on homework problems | 110分 | ||
| 6. | Dividing polynomials Real roots of polynomials Complex numbers and fundamental theorem of algebra Rational functions |
Review the content of the lecture (1.6, 3.3-3.6 in the textbook) | 100分 |
| Work on homework problems | 90分 | ||
| 7. | Mid-term presentation and discussions on the solutions afterwards | Preparation for mid-term presentation | 190分 |
| 8. | Exponential functions and logarithms Properties of logarithms Equations with exponents and logarithms |
Review the content of the lecture (4.4-4.6 in the textbook) | 100分 |
| Work on homework problems | 90分 | ||
| 9. | Trigonometric functions via the unit circle Graphs of trigonometric functions |
Review the content of the lecture (5.1-5.4 in the textbook) | 80分 |
| Work on homework problems | 110分 | ||
| 10. | Inverse trigonometric functions and their graphs Trigonometric functions via right angles |
Review the content of the lecture (5.5-5.6, 6.1-6.3 in the textbook) | 100分 |
| Work on homework problems | 90分 | ||
| 11. | Inverse trigonometric functions and right triangles Laws of sines and cosines Trigonometric identities |
Review the content of the lecture (6.4-6.6, 7.1-7.2 in the textbook) | 80分 |
| Work on homework problems | 110分 | ||
| 12. | More identities on trigonometric functions Working with equations involving trigonometric functions |
Review the content of the lecture (7.3-7.5 in the textbook) | 60分 |
| Work on homework problems | 130分 | ||
| 13. | Polar coordinates | Review the content of the lecture (8.1-8.3 in the textbook) | 60分 |
| Work on homework problems | 130分 | ||
| 14. | Final presentation and discussions on the solutions afterwards | Preparation for final presentation | 190分 |
| Total. | - | - | 2660分 |
| Homework | Presentations | Total. | |
|---|---|---|---|
| 1. | 10% | 5% | 15% |
| 2. | 15% | 6% | 21% |
| 3. | 15% | 6% | 21% |
| 4. | 20% | 8% | 28% |
| 5. | 10% | 5% | 15% |
| Total. | 70% | 30% | - |
Homework reports will contribute to 70% of the grade.
Presentations will contribute to 30% of the grade.
Those who get at least 60% of the full score will pass this course.
Presentations will contribute to 30% of the grade.
Those who get at least 60% of the full score will pass this course.
| ways of feedback | specific contents about "Other" |
|---|---|
| The Others | The lecturer will provide feedback on the classroom exercises and the student presentations in the classroom. Feedback on the assignments and the reports of presentations will be provided through ScombZ. |
Precalculus: Mathematics for Calculus (7th edition) by James Stewart, Lothar Redlin, Saleem Watson
ISBN: 978-1305071759
ISBN: 978-1305071759
- By appointment. Contact e-mail address: ahmet@shibaura-it.ac.jp
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic problem-solving skills
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | N/A |
Last modified : Sat Sep 09 06:40:06 JST 2023