9th grade
Students develop deeper skills in algebra and geometry, including being introduced to functions, equations and inequalities, numerical sequences, and concepts of probability.
lesson 1
Quadratic function- 1. Definition of a quadratic function
- 2. Finding the value of a quadratic function
- 3. Finding the argument of a quadratic function
- 4. Determining whether a point belongs to a quadratic function
- 5. Creating a table
- 6. Branches of a quadratic function
- 7. Increasing and decreasing intervals of a quadratic function
- 8. Intersection point of the quadratic function with the Oy axis
- 9. Finding the intersection point of a quadratic function with the Oy axis
- 10. Zeros of a quadratic function
- 11. Finding the zeros of a quadratic function
- 12. Completing the square for a quadratic function
- 13. Finding the maximum or minimum value of a quadratic function
- 14. Vertex of a quadratic function
- 15. Finding the coordinates of the vertex of a quadratic function
- 16. Axis of symmetry of a parabola
- 17. Finding the equation of the axis of symmetry of a parabola
- 18. Graphing a quadratic function
- 19. Matching given quadratic function graphs
- 20. Identifying the quadrants of a parabola
- 21. Finding the domain and range of a quadratic function
- 22. Constructing a function through points
lesson 2
Irrational equations- 1. Identifying irrational equations
- 2. Determining whether a root is an irrational equation
- 3. Simple irrational equations 1
- 4. Simple irrational equations 2
- 5. Irrational equations in the form of products
- 6. Irrational equations with multiple roots
- 7. Irrational equations involving differences between roots
- 8. Irrational equations that can be reduced to quadratic equations
- 9. Complex irrational equations 1
- 10. Complex irrational equations 2
lesson 3
Systems of equations- 1. Determining the solution of a system of equations
- 2. Solving systems of equations using substitution
- 3. Solving systems of equations using the addition method
- 4. Solving systems of equations using the reverse Vieta theorem
- 5. Solving systems of equations using substitution of variables
- 6. Solving problems using systems of equations
lesson 4
Inequalities- 1. Identifying quadratic inequalities
- 2. Reducing an inequality to a quadratic inequality
- 3. Finding the solution of a quadratic inequality
- 4. Solving quadratic inequalities
- 5. Conditions of quadratic inequalities
- 6. Solving quadratic inequalities using the graph of a quadratic function
- 7. Interval method for solving inequalities
lesson 5
Systems of inequalitieslesson 6
Properties of functions- 1. Finding the value of a function
- 2. Finding the argument of a function
- 3. Determining if a point belongs to the graph of a function
- 4. Domain of a function
- 5. Finding the domain of a function
- 6. Range of a function
- 7. Increasing and decreasing functions
- 8. Finding the intervals where a function increases or decreases
- 9. Comparing numbers using function graphs
- 10. Determining the evenness of a function
- 11. Determining the oddness of a function
- 12. Determining the evenness or oddness of a function
- 13. Determining the evenness or oddness of a function using its graph
- 14. Drawing the graph of an even function
- 15. Drawing the graph of an odd function
- 16. Finding the equation of the symmetry axis of a function
- 17. Finding the center of symmetry of a function graph
lesson 7
Elements of trigonometry- 1. Radian measure of an angle
- 2. Comparing numbers
- 3. Rotating a point around the origin by a positive angle
- 4. Rotating a point around the origin by a negative angle
- 5. Sine, cosine, tangent, and cotangent of an angle
- 6. Calculating the value of an expression
- 7. Signs of sine, cosine, tangent, and cotangent
- 8. Comparing the values of expressions
- 9. Relations between sine, cosine, tangent, and cotangent
- 10. Trigonometric identities
- 11. Sine, cosine, tangent, and cotangent of a negative angle
- 12. Addition formulas
- 13. Reduction formulas
- 14. Double-angle formulas
- 15. Sum and difference formulas for sine
- 16. Sum and difference formulas for cosine
- 17. Simplifying expressions
- 18. Simple trigonometric equations
lesson 8
Sequences. Progressions- 1. Methods for defining a sequence
- 2. Terms of a sequence
- 3. Finding terms of a sequence
- 4. Determining if a number is a term of a sequence
- 5. Identifying arithmetic progressions
- 6. Common difference of an arithmetic progression
- 7. Finding the unknown term of an arithmetic progression
- 8. Formula for the n-th term of an arithmetic progression
- 9. Determining the order of terms in an arithmetic progression
- 10. Properties of an arithmetic progression
- 11. Sum of the first n terms of an arithmetic progression
- 12. Identifying geometric progressions
- 13. Common ratio of a geometric progression
- 14. Finding the unknown term of a geometric progression
- 15. Formula for the n-th term of a geometric progression
- 16. Determining the order of terms in a geometric progression
- 17. Properties of a geometric progression
- 18. Sum of the first n terms of a geometric progression
- 19. Identifying infinite decreasing geometric progressions
- 20. Sum of an infinite decreasing geometric progression
lesson 9
Probability theory and elements of mathematical statisticslesson 10
Geometric transformations in the plane- 1. Translation
- 2. Translation: Determining coordinates
- 3. Symmetry with respect to the Ox-axis
- 4. Symmetry with respect to the Ox-axis: Determining coordinates
- 5. Symmetry with respect to the Oy-axis
- 6. Symmetry with respect to the Oy-axis: Determining coordinates
- 7. Axis of symmetry
- 8. Central symmetry
- 9. Drawing symmetry axes
- 10. Number of symmetry axes
- 11. Rotation
- 12. Rotation: Determining coordinates
- 13. Similarity transformation
- 14. Filling in sentences
lesson 11
Similar polygons- 1. Similar polygons
- 2. Properties of similar polygons
- 3. Finding the similarity coefficient
- 4. Similar triangles
- 5. Similar triangles: Identifying elements
- 6. Properties of similar triangles
- 7. AA criterion for similarity of triangles
- 8. AA criterion for similarity of triangles: Problems
- 9. SAS criterion for similarity of triangles
- 10. SAS criterion for similarity of triangles: Problems
- 11. SSS criterion for similarity of triangles
- 12. SSS criterion for similarity of triangles: Problems
- 13. Criterion 1 for similarity of right-angled triangles
- 14. Criterion 1 for similarity of right-angled triangles: Problems
- 15. Criterion 2 for similarity of right-angled triangles
- 16. Criterion 2 for similarity of right-angled triangles: Problems
- 17. Criterion 3 for similarity of right-angled triangles
- 18. Criterion 3 for similarity of right-angled triangles: Problems
- 19. Applications of similarity criteria
- 20. Filling in sentences
lesson 12
Relations between the sides and angles of a triangle- 1. Sine, cosine, tangent, and cotangent of acute angles
- 2. Signs of sine, cosine, tangent, and cotangent
- 3. Relations between sine, cosine, tangent, and cotangent
- 4. Reduction formulas
- 5. Simplifying expressions
- 6. Trigonometric functions in a triangle
- 7. Trigonometric functions in a quadrilateral
- 8. Calculating the area of a triangle using the sine of an angle
- 9. Law of sines
- 10. Law of sines: Problems
- 11. Law of sines in quadrilaterals
- 12. Law of cosines
- 13. Law of cosines: Problems
- 14. Law of cosines in quadrilaterals
- 15. Solving triangles
lesson 13
Vectorslesson 14
Circumference and circlelesson 15
Polygon inscribed in a circlelesson 16
Polygon circumscribed around a circle- 1. Circumscribed polygons
- 2. Circumscribed regular triangle
- 3. Circumscribed right-angled triangle
- 4. Circumscribed isosceles triangle
- 5. Circumscribed scalene triangle
- 6. Circumscribed quadrilateral
- 7. Circumscribed square
- 8. Circumscribed rhombus
- 9. Circumscribed regular polygon
- 10. Circumscribed trapezoid