1) To understand numbers and equations, and be able to calculate them.
2) To understand Equation and inequality, and be able to solve them.
3) To understand and functions and graphs, and be able to use them.
4) To understand exponential and logarithmic functions, and be able to use them.
5) To understand the principles of the number of possible outcomes and probability, and be able to calculate them.
Outline:
The objective is to develop basic mathematical formulas and logical thinking skills and acquire the fundamentals of mathematics necessary in college.
Style:
Preparation study for the lectures is a prerequisite, and the teacher will check it on each lesson. In the manner that the student can concentrate on the lecture, he/she should ask about everything he/she could not understand in the preparatory study for the lectures or during the lectures. Please do not leave anything you did not understand for later. Be sure to review regularly and try to solve the problem collection in the textbooks. The teacher will conduct small tests without prior notice. Therefore the student should study hard every day.
Notice:
Examination 50%, assignments 20 %, and presentation 30% of the final grade. The students should acquire more than 60 points to receive the credits. However, this ratio is for the final grade, the cumulative evaluation up to the latter middle term exams is a tentative ratio and may result in a different grade than the final one.
If assignments, presentations, are done well and handle in time, they may have a positive impact in the final grade.
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Theme |
Goals |
1st Semester |
1st Quarter |
1st |
Numbers and equations |
To calculate additive, subtractive, and multiplicative equations. Also, you can factor decompose simple equations.
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2nd |
Numbers and equations |
To calculate the division of the formula. Also, to understand the remainder theorem and factor theorem, and factorize higher-order polynomial equations.
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3rd |
Numbers and equations |
To calculate addition, subtraction, multiplication, division, of fractional expressions. To understand the meaning of real numbers and absolute values, and to do simple calculation with absolute values.
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4th |
Numbers and equations |
To calculate basic square root equations (including rationalization of denominator). To understand the equivalence of complex numbers, and do the four arithmetical operations: addition, subtraction, multiplication, and division.
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5th |
Equation |
To solve the quadratic equation using the official formula. To understand the relationship between the solutions and the coefficients, and factorize quadratic expressions.
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6th |
Equation |
To solve various equations (simultaneous equations, irrational equations, fractional equations, etc.). To understand the identity operator, and do partial fraction decomposition.
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7th |
Summary |
To review what was studied so far.
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8th |
Mid term exam |
To check was learned so far.
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2nd Quarter |
9th |
Equation |
To prove various equations.
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10th |
Inequality |
To understand the nature of inequality and solve linear inequality.
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11th |
Inequality |
To solve various inequalities (simultaneous inequality, quadratic inequality, higher order inequality).
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12th |
Inequality |
To prove various inequalities, including the additive geometric mean.
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13th |
Inequality |
To understand set, and to judge the truth of the proposition.
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14th |
Quadratic function |
To understand the relationship between functions and graphs, and use the domain, range, and quadrant.
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15th |
Summary |
To review what was studied so far.
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16th |
End term exam |
To check was learned so far.
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2nd Semester |
3rd Quarter |
1st |
Quadratic function |
To be able to draw a quadratic function graph and calculate maximum and minimum values.
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2nd |
Quadratic function |
Can solve quadratic equations and quadratic inequalities using quadratic function graphs.
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3rd |
Various functions |
Can understand even function, odd function, and the parallel movement of a graph, and draw a power function or fraction function graph.
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4th |
Various functions |
Can draw irrational functions and calculate inverse functions.
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5th |
Exponential functions |
Can understand the exponentiation roots and the use of the exponential extension.
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6th |
Exponential functions |
Can draw a graph of an exponential function, and solve equations and inequalities with simple exponents.
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7th |
Summary |
To review what was studied so far.
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8th |
Mid term exam |
To check was learned so far.
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4th Quarter |
9th |
Log function |
Can understand logarithms, and use base conversion formulas, and the properties of logarithms.
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10th |
Log function |
Can draw a graph of a logarithmic function, and solve a simple logarithm equation or inequality. Can use common logarithms.
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11th |
Number of possible outcomes |
Can understand the law of product and law of sum, and solve simple cases of the number of possible outcomes.
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12th |
Number of possible outcomes |
Can calculate the value of the permutation.
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13th |
Basics of probability |
Can understand and calculate the probability of independent trial, the probability of a surplus event, the probability of exclusion event.
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14th |
Basics of probability |
Can understand and calculate the conditional probability, and the establishment of independent events.
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15th |
Summary |
To review what was studied so far.
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16th |
End term exam |
To check was learned so far.
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