Mathematics 3 – Course Content

 

On this page, you can find the general overview of all the topics we will cover in the Mathematics 3 course. Detailed explanations, fundamental concepts, formulas, and sample problem solutions for each topic will be presented on separate pages. These topics are of great importance, especially for the development of advanced mathematical thinking skills.

 

1. Trigonometry

 

Trigonometry is a branch of mathematics that studies the relationship between the angles and sides of triangles. It is also used to model and analyze periodic motions.

The topic of trigonometry includes the following subheadings:
– Trigonometric ratios (sin, cos, tan, cot)
– Trigonometric functions and their graphs
– Unit circle
– Angle measurement units (degrees, radians)
– Trigonometric transformations and identities
– Trigonometric equations…

2. Complex Numbers

 

Complex numbers are number sets developed for equations that cannot be solved with real numbers. They provide an important abstraction in mathematics.

Topics to be covered:
– Definition and representation of complex numbers
– The concept of \(i\) (imaginary unit)
– Addition, subtraction, multiplication, and division operations
– The complex plane and geometric interpretation
– Polar representation and exponentiation operations

3. Logarithm

 

Logarithm is the inverse of exponential functions and is used in many fields such as growth, decay, and scaling.

Under this heading:
– Definition and properties of logarithms
– Operations with logarithmic expressions
– Exponential and logarithmic equations
– Logarithm rules (change of base, product-quotient-power rules)

4. Permutation

 

Permutation refers to the ordered arrangements of objects. It is used to calculate different arrangements.

Content:
– Basic permutation rules
– Permutations with identical and distinct elements
– Special cases and practical methods

5. Combination

 

Combination refers to the unordered selections of objects. It is a fundamental topic in selection-related problems.

– Definition and formula of combination
– Relationship with permutation
– Sample applications

6. Binomial Theorem

 

The binomial theorem provides the expansion of the powers of binomial expressions and is frequently used in questions regarding coefficients.

– Binomial formula: \((a + b)^n\)
– Pascal’s triangle
– Binomial coefficients and finding terms
– Sample question solutions

7. Probability

 

Probability is the process of making decisions and evaluating outcomes under uncertainty. It has a wide range of applications in daily life and statistics.

– Basic definition of probability
– Classical probability, union and intersection of events
– Conditional probability, dependent and independent events
– Probability calculation methods

 

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