Mathematics- First Year Secondary- First term

Klassenstufen:

Bildungssystem: National English

1. Mastery of algebraic concepts including quadratic equations and complex numbers, and geometric concepts of similarity with applications in polygons and circles

Lernziele:

1. Analyze quadratic equations: sum/product of roots, coefficients, discriminant, and root types

2. Form quadratic equations from given conditions and analyze function signs

3. Perform operations with complex numbers (algebraic form, powers of i, equality)

4. Solve quadratic inequalities in one variable

5. Apply similarity theorems to polygons and triangles (corresponding sides/angles)

6. Calculate area ratios of similar polygons and triangles

7. Apply circle theorems involving chords, secants, and tangents

8. Relate similarity ratios to perimeters and areas of geometric figures

Module

1. Unit One: Algebra, Relations and Functions

1. 1. 1-1 Introduction in Complex Numbers

Lernergebnisse:

1. Understand the concept of the imaginary number.

2. Calculate integer powers of i.

3. Understand the concept of the complex number.

4. Determine the equality of two complex numbers.

5. Perform operations on complex numbers.

1. 2. 1-2 Determining the Types of the Two Roots of a Quadratic Equation

Lernergebnisse:

1. Determine the type of the two roots of a quadratic equation.

1. 3. 1-3 The Relation Between the Two Roots of the Second Degree Equation and the Coefficients of its Terms

Lernergebnisse:

1. Find the sum of the two roots of a given quadratic equation.

2. Find the product of the two roots of a quadratic equation.

3. Construct a quadratic equation in terms of another quadratic equation.

Mathematics- First Year Secondary- First term

Klassenstufen:

Bildungssystem: National English

1. Mastery of algebraic concepts including quadratic equations and complex numbers, and geometric concepts of similarity with applications in polygons and circles

Lernziele:

1. Analyze quadratic equations: sum/product of roots, coefficients, discriminant, and root types

2. Form quadratic equations from given conditions and analyze function signs

3. Perform operations with complex numbers (algebraic form, powers of i, equality)

4. Solve quadratic inequalities in one variable

5. Apply similarity theorems to polygons and triangles (corresponding sides/angles)

6. Calculate area ratios of similar polygons and triangles

7. Apply circle theorems involving chords, secants, and tangents

8. Relate similarity ratios to perimeters and areas of geometric figures

Module

1. Unit One: Algebra, Relations and Functions

1. 1. 1-1 Introduction in Complex Numbers

Lernergebnisse:

1. Understand the concept of the imaginary number.

2. Calculate integer powers of i.

3. Understand the concept of the complex number.

4. Determine the equality of two complex numbers.

5. Perform operations on complex numbers.

1. 2. 1-2 Determining the Types of the Two Roots of a Quadratic Equation

Lernergebnisse:

1. Determine the type of the two roots of a quadratic equation.

1. 3. 1-3 The Relation Between the Two Roots of the Second Degree Equation and the Coefficients of its Terms

Lernergebnisse:

1. Find the sum of the two roots of a given quadratic equation.

2. Find the product of the two roots of a quadratic equation.

3. Construct a quadratic equation in terms of another quadratic equation.

Mathematics- First Year Secondary- First term

Klassenstufen:

Bildungssystem: National English

1. Mastery of algebraic concepts including quadratic equations and complex numbers, and geometric concepts of similarity with applications in polygons and circles

Lernziele:

Module

1. Unit One: Algebra, Relations and Functions

1. 1. 1-1 Introduction in Complex Numbers

Lernergebnisse:

1. 2. 1-2 Determining the Types of the Two Roots of a Quadratic Equation

Lernergebnisse:

1. 3. 1-3 The Relation Between the Two Roots of the Second Degree Equation and the Coefficients of its Terms

Lernergebnisse:

Mathematics- First Year Secondary- First term

Klassenstufen:

Bildungssystem: National English

1. Mastery of algebraic concepts including quadratic equations and complex numbers, and geometric concepts of similarity with applications in polygons and circles

Lernziele:

Module

1. Unit One: Algebra, Relations and Functions

1. 1. 1-1 Introduction in Complex Numbers

Lernergebnisse:

1. 2. 1-2 Determining the Types of the Two Roots of a Quadratic Equation

Lernergebnisse:

1. 3. 1-3 The Relation Between the Two Roots of the Second Degree Equation and the Coefficients of its Terms

Lernergebnisse:

1. 4. 1-4 Sign of a Function

Lernergebnisse:

1. 5. 1-5 Quadratic Inequalities

Lernergebnisse:

2. Unit Two: Similarity

2. 1. 2-1 Similarity of Polygons

Lernergebnisse:

2. 2. 2-2 Similarity of Triangles

Lernergebnisse:

2. 3. 2-3 The Relation Between the Area of Two Similar Polygons

Lernergebnisse:

2. 4. 2-4 Applications of Similarity in the Circle

Lernergebnisse:

2. Mastering geometric theorems on parallelism and proportionality, angle bisectors, and circle properties, along with comprehensive trigonometric concepts including angle measurement, functions, and equations

Lernziele:

Module

1. Unit Three: The Triangle Proportionality Theorems

1. 1. 3-1 Parallel Lines and Proportional Parts

Lernergebnisse:

1. 2. 3-2 Angle of a Triangle Bisectors and Proportional Parts

Lernergebnisse:

2. Unit Four: Trigonometry

2. 1. 4-1 Directed Angle

Lernergebnisse:

2. 2. 4-2 Systems of Measuring Angle (degree – radian)

Lernergebnisse:

2. 3. 4-3 Trigonometric Functions

Lernergebnisse:

2. 4. 4-4 Related Angles

Lernergebnisse:

2. 5. 4-5 Graphing Trigonometric Functions

Lernergebnisse:

2. 6. 4-6 Finding the Measure of an Angle in Terms of the Value of One of Its Trigonometric Ratios

Lernergebnisse: