1. be able to perform four arithmetic operations on integer expressions
2. understand the concept of complex numbers and be able to calculate them.
3. be able to solve quadratic and higher-order equations
4. use differentiation to obtain tangent equations and tables of increase and decrease. Also, be able to plot graphs and find extrema from tables of increase and decrease.
5. be able to calculate indefinite and definite integrals. Also, use definite integrals to find the area of a figure.
Outline:
Mathematics is a fundamental subject in technical colleges. In this course, students learn how to handle various functions, how to solve equations, and how to calculate and apply derivatives and integrals, which are the most important subjects in technical college mathematics.
Style:
1. establish an efficient way of concentrating on the class. Preparation and review are essential.
2. do your best to study for competency tests, quizzes and homework as well as for regular examinations.
3. homework and other assignments must be submitted on time.
[120 hours of class time].
Notice:
1. establish an efficient way of concentrating on the class. Preparation and review are essential.
2. do your best to study for competency tests, quizzes and homework as well as for regular examinations.
3. homework and other assignments must be submitted on time.
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Theme |
Goals |
| 1st Semester |
| 1st Quarter |
| 1st |
Expansion and factorisation of cubic expressions |
The goal is to be able to expand expressions using cubic expansion formulae and to factorise them using cubic factorisation formulae.
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| 2nd |
Binomial theorem and Pascal's triangle |
The goal is to be able to use the binomial theorem to expand the equation, and also to be able to write Pascal's triangle and find the coefficients of the corresponding polynomial.
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| 3rd |
Integral division and fractional quadrature |
The goal is to be able to divide integer expressions and to perform four arithmetic operations on fractional expressions.
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| 4th |
Identity equation |
The goal is to be able to understand the identity equation and to be able to compare both sides of the identity to find the coefficients.
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| 5th |
Complex numbers and their basic properties and their four arithmetic operations. |
The goal is to be able to understand complex numbers and to perform their quadrature operations.
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| 6th |
Formulae and discriminant formulae for solutions of quadratic equations |
The goal is to be able to use the 'solution formula' for quadratic equations to find imaginary solutions.
The goal is also to be able to calculate the discriminant formula and determine the type of solution to a quadratic equation.
|
| 7th |
Surplus and factorisation theorems |
The goal is to be able to use the remainder theorem to find the remainder when dividing an integer by an integer and to factorise it using the factor theorem.
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| 8th |
Factoring of higher-order equations |
The goal is to be able to use the factor theorem to factorise higher-order equations and find solutions to the equations.
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| 2nd Quarter |
| 9th |
midterm examination |
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| 10th |
Limits and differential coefficients of functions |
The goal is to be able to find the limit of a function and to find the derivative coefficient as the limit of the mean rate of change.
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| 11th |
Differentiation of simple functions |
The goal is to be able to differentiate linear, quadratic and general polynomial functions and to find tangents on their graphs.
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| 12th |
Derivative of product, derivative of quotient |
The goal is to be able to differentiate the product fg of the function f and the function g and the quotient f/g.
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| 13th |
Differentiation of composite functions |
The goal is to be able to differentiate the function fg, which is the composite of the functions f and g.
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| 14th |
Differentiation of trigonometric functions |
The goal is to be able to differentiate trigonometric functions and also to differentiate slightly more complex trigonometric functions using differential formulae for products, quotients and composite functions.
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| 15th |
Differentiation of logarithmic and exponential functions |
The goal is to be able to perform basic calculations on logarithmic and exponential functions, and to be able to differentiate slightly more complex logarithmic and exponential functions using differential formulae for products, quotients and composite functions.
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| 16th |
Return of final examinations |
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| 2nd Semester |
| 3rd Quarter |
| 1st |
Differentiation of inverse trigonometric functions |
The goal is to be able to differentiate inverse trigonometric functions and, furthermore, to differentiate rather complex inverse trigonometric functions using differential formulae for products, quotients and composite functions.
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| 2nd |
Limits of fractional functions |
The goal is to be able to understand the concepts of convergence, divergence and infinity and to be able to find the limit of a fractional expression.
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| 3rd |
Limits of trigonometric, logarithmic and exponential functions |
The goal is to be able to calculate limits involving trigonometric, logarithmic and exponential functions.
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| 4th |
indefinite integral |
The goal is to be able to perform indefinite integrals of linear and quadratic functions, and of polynomial functions in general.
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| 5th |
definite integral |
The goal is to be able to perform definite integrals of linear and quadratic functions, and of polynomial functions in general.
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| 6th |
Definite integrals and areas of figures |
The goal is to be able to use definite integrals to find the area of a shape or the area between two curves.
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| 7th |
Indefinite integrals of trigonometric functions |
The goal is to be able to perform indefinite integrals of trigonometric functions.
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| 8th |
Midterm examination |
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| 4th Quarter |
| 9th |
Indefinite integrals of exponential functions |
The goal is to be able to perform indefinite integrals of exponential functions.
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| 10th |
subtractive integration method |
The goal is to be able to perform indefinite integrals using substitution integrals.
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| 11th |
integration by parts |
The goal is to be able to perform indefinite integrals using the method of integration by parts.
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| 12th |
Indefinite integrals of various functions |
The goal is to be able to perform indefinite integrals using formulae for fractional and trigonometric functions.
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| 13th |
definite integral |
The goal is to be able to perform definite integrals of polynomial, trigonometric and exponential functions.
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| 14th |
Substituted integral method of definite integrals |
The goal is to be able to perform definite integrals using substitution integrals.
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| 15th |
Integration by parts for definite integrals |
The goal is to be able to perform definite integrals using integration by parts.
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| 16th |
Return of final examinations |
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