Purpose of study: To review mathematics learned through junior high school, further develop them, and acquire the basic mathematics knowledged needed for specialized subjects to be learned in the future.
Attainment target:
1. To aibe to solve problems including factorization, addition / subtraction / multiplication / division of fractional formulas, square roots / complex numbers.
2. To aibe to solve problems related to equations, inequalities, quadratic functions, etc.
3. To aibe to solve problems related to fractions, exponentials, logarithmic functions, etc.
4. To understand and calculate elementary functions such as trigonometric functions.
Outline:
General or Specialized :: General
Learning field: Natural science basics
Required, Elective: Elective must complete subjects
Foundational academic disciplines: Mathematical science / mathematics / foundations of mathematics
Relationship with Educational Objectives: This subject is equivalent to "② Acquire basic science and thecnical knowledge".
Relationship with JABEE programs: The main goal of learning / education in this subject is "(A) .
Course outline: This subject is the basis for studying specialized subjects based on mathematics learned in the second grade and beyond. Factorization, equations and inequality, permutations and combinations, sequences, exponential / logarithmic functions, trigonometric functions, etc. Practice elementary functions.
Style:
Course method: In the first semester, lectures will be given on the contents of Chapters 1 and 7, and exercises will be conducted leading to an exercise report. In the second semester, we will explain the basics of Chapters 4 and 5, perform exercises, and assign an exercise report.
Grade evaluation method: Exercise reports (50%) and 4 regular exams (50%).
Notice:
Precautions on enrollment: It is necessary to take this course in order to complete the course for the academic year.
Course advice: Students should solve not only the problems from class but also problems from textbooks used in basic mathematics.
Foundational subjects: Mathematics learned through junior high school
Related subjects: Fundamental Mathematics (1 year)
Attendance advice: If you are late after, you may be treated as absent after a warning.
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Theme |
Goals |
| 1st Semester |
| 1st Quarter |
| 1st |
・ Guidance, calculation of numbers and formulas (including review of junior high school. Lectures and exercises) |
p1-p4 Addition / subtraction of rectification, product and quotient of monomial
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| 2nd |
・ Calculation of numbers and formulas (including addition / subtraction / product of formulas, review of junior high school. Lectures and exercises) |
p5-p10 Formal product, basic expansion formula, evolutionary expansion formula
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| 3rd |
・ Calculation of numbers and formulas (expansion of formulas, factorization. Lectures and exercises) |
p11-p16 Factorization (common factorization), quadratic factorization, factorization (tasukigake)
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| 4th |
・ Calculation of numbers and formulas (factorization. Lectures and exercises.) |
p17-p22 Factorization (3rd order), division of formulas, greatest common divisor / least common multiple
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| 5th |
・ Calculation of numbers and formulas (greatest common divisor, addition / subtraction / multiplication / division of fractional formulas. Lectures and exercises) |
p23-p28 Subdivision / multiplication / division of fractional formulas, addition / division of fractional formulas, fractional formulas
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| 6th |
・ Calculation of numbers and formulas (calculation including square root, rationalization of denominator. Lectures and exercises)
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p29-p34 Calculation including square root, rationalization of denominator, absolute value
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| 7th |
・ Calculation of numbers and formulas (complex numbers, realization of denominators. Lectures and exercises) |
p35-p38 Complex numbers, realization of denominator
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| 8th |
(First term midterm exam) |
60% or more of basic content up to p34
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| 2nd Quarter |
| 9th |
・ Return of the first half of the exam, explanation of answers, number of cases |
Correct the wrong answer. Textbook p194-p196 Number of cases
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| 10th |
・ Permutation, combination |
Textbook p196-p199 Permutation
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| 11th |
・ Various permutations and binomial theorems |
Textbook p200-p202 combination
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| 12th |
・ Sequence, arithmetic progression, geometric progression |
Textbooks p202-p206 Various permutations, two-law theorems
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| 13th |
・ Sum of various sequences |
Textbook p211-p214 Sum of arithmetic progression and sum of geometric progression
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| 14th |
・ Recurrence formula and mathematical induction |
Textbook p215-p216 Sum of various sequences
Textbook p218 Recurrence formula
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| 15th |
(Last term exam) |
Understanding the number of cases
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| 16th |
・ Return of the final exam, explanation of answers, mathematical induction |
p218-p220 Mathematical induction
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| 2nd Semester |
| 3rd Quarter |
| 1st |
・ Review of exponential function 1 (exercise) |
p119-p122 Power root, exponential law
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| 2nd |
・ Review of exponential function 2 (exercise) |
p123-p126 Exponential function and its graph, exponential equations and inequalities
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| 3rd |
・ Review of logarithmic function 1 (exercise) |
p127-p130 Logarithmic nature, base conversion formula
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| 4th |
・ Review of logarithmic functions 2 (exercise) |
p131-p134 Logarithmic function graphs, logarithmic equations and inequalities
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| 5th |
・ Review of logarithmic functions 3 (exercise) |
p135-p138 Common logarithm, acute angle triangle ratio
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| 6th |
・ Review of triangle ratio 1 (exercise) |
p139-p142 Calculation of trigonometric ratio, cosine theorem
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| 7th |
・ Review of triangle ratio 2 (exercise) |
p143-p146 Law of sines, area of triangle
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| 8th |
(Late midterm exam) |
Exponential. Understanding the trigonometric ratio
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| 4th Quarter |
| 9th |
・ Review of triangle ratio 3 (exercise) |
p147-p150 General angle and radian method, fan-shaped arc length and area
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| 10th |
・ Review of triangle ratio 4 (exercise) |
p151-p154 General angle trigonometric function, interrelationship of trigonometric functions
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| 11th |
・ Review of trigonometric functions 1 (exercise) |
p155-p158 Trigonometric function properties, sine function graph
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| 12th |
・ Review of trigonometric functions 2 (exercise) |
p159-p162 Cosine function graph, tangent function graph
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| 13th |
・ Review of trigonometric functions 3 (exercise) |
p163-p166 Trigonometric graph properties, trigonometric addition theorem
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| 14th |
・ Review of trigonometric functions 4 (exercise) |
p167- p172 Double-byte / half-width formula, trigonometric function composition (Note. Excluding p169-p170)
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| 15th |
(Late term exam) |
Understanding trigonometric functions
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| 16th |
・ Return of the final exam, explanation of answers, review of trigonometric functions 5 (practice) |
p173-p174 Triangular equations and inequalities
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