Grades
9th grade
Students develop deeper skills in algebra and geometry, including being introduced to functions, equations and inequalities, numerical sequences, and concepts of probability.
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- Definition of a quadratic functionStart
- Finding the value of a quadratic functionStart
- Finding the argument of a quadratic functionStart
- Determining whether a point belongs to a quadratic functionStart
- Creating a tableStart
- Branches of a quadratic functionStart
- Increasing and decreasing intervals of a quadratic functionStart
- Intersection point of the quadratic function with the Oy axisStart
- Finding the intersection point of a quadratic function with the Oy axisStart
- Zeros of a quadratic functionStart
- Finding the zeros of a quadratic functionStart
- Completing the square for a quadratic functionStart
- Finding the maximum or minimum value of a quadratic functionStart
- Vertex of a quadratic functionStart
- Finding the coordinates of the vertex of a quadratic functionStart
- Axis of symmetry of a parabolaStart
- Finding the equation of the axis of symmetry of a parabolaStart
- Graphing a quadratic functionStart
- Matching given quadratic function graphsStart
- Identifying the quadrants of a parabolaStart
- Finding the domain and range of a quadratic functionStart
- Constructing a function through pointsStart
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- Identifying irrational equationsStart
- Determining whether a root is an irrational equationStart
- Simple irrational equations 1Start
- Simple irrational equations 2Start
- Irrational equations in the form of productsStart
- Irrational equations with multiple rootsStart
- Irrational equations involving differences between rootsStart
- Irrational equations that can be reduced to quadratic equationsStart
- Complex irrational equations 1Start
- Complex irrational equations 2Start
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- Determining the solution of a system of equationsStart
- Solving systems of equations using substitutionStart
- Solving systems of equations using the addition methodStart
- Solving systems of equations using the reverse Vieta theoremStart
- Solving systems of equations using substitution of variablesStart
- Solving problems using systems of equationsStart
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- Identifying quadratic inequalitiesStart
- Reducing an inequality to a quadratic inequalityStart
- Finding the solution of a quadratic inequalityStart
- Solving quadratic inequalitiesStart
- Conditions of quadratic inequalitiesStart
- Solving quadratic inequalities using the graph of a quadratic functionStart
- Interval method for solving inequalitiesStart
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- Finding the value of a functionStart
- Finding the argument of a functionStart
- Determining if a point belongs to the graph of a functionStart
- Domain of a functionStart
- Finding the domain of a functionStart
- Range of a functionStart
- Increasing and decreasing functionsStart
- Finding the intervals where a function increases or decreasesStart
- Comparing numbers using function graphsStart
- Determining the evenness of a functionStart
- Determining the oddness of a functionStart
- Determining the evenness or oddness of a functionStart
- Determining the evenness or oddness of a function using its graphStart
- Drawing the graph of an even functionStart
- Drawing the graph of an odd functionStart
- Finding the equation of the symmetry axis of a functionStart
- Finding the center of symmetry of a function graphStart
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- Radian measure of an angleStart
- Comparing numbersStart
- Rotating a point around the origin by a positive angleStart
- Rotating a point around the origin by a negative angleStart
- Sine, cosine, tangent, and cotangent of an angleStart
- Calculating the value of an expressionStart
- Signs of sine, cosine, tangent, and cotangentStart
- Comparing the values of expressionsStart
- Relations between sine, cosine, tangent, and cotangentStart
- Trigonometric identitiesStart
- Sine, cosine, tangent, and cotangent of a negative angleStart
- Addition formulasStart
- Reduction formulasStart
- Double-angle formulasStart
- Sum and difference formulas for sineStart
- Sum and difference formulas for cosineStart
- Simplifying expressionsStart
- Simple trigonometric equationsStart
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- Methods for defining a sequenceStart
- Terms of a sequenceStart
- Finding terms of a sequenceStart
- Determining if a number is a term of a sequenceStart
- Identifying arithmetic progressionsStart
- Common difference of an arithmetic progressionStart
- Finding the unknown term of an arithmetic progressionStart
- Formula for the n-th term of an arithmetic progressionStart
- Determining the order of terms in an arithmetic progressionStart
- Properties of an arithmetic progressionStart
- Sum of the first n terms of an arithmetic progressionStart
- Identifying geometric progressionsStart
- Common ratio of a geometric progressionStart
- Finding the unknown term of a geometric progressionStart
- Formula for the n-th term of a geometric progressionStart
- Determining the order of terms in a geometric progressionStart
- Properties of a geometric progressionStart
- Sum of the first n terms of a geometric progressionStart
- Identifying infinite decreasing geometric progressionsStart
- Sum of an infinite decreasing geometric progressionStart
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- TranslationStart
- Translation: Determining coordinatesStart
- Symmetry with respect to the Ox-axisStart
- Symmetry with respect to the Ox-axis: Determining coordinatesStart
- Symmetry with respect to the Oy-axisStart
- Symmetry with respect to the Oy-axis: Determining coordinatesStart
- Axis of symmetryStart
- Central symmetryStart
- Drawing symmetry axesStart
- Number of symmetry axesStart
- RotationStart
- Rotation: Determining coordinatesStart
- Similarity transformationStart
- Filling in sentencesStart
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- Similar polygonsStart
- Properties of similar polygonsStart
- Finding the similarity coefficientStart
- Similar trianglesStart
- Similar triangles: Identifying elementsStart
- Properties of similar trianglesStart
- AA criterion for similarity of trianglesStart
- AA criterion for similarity of triangles: ProblemsStart
- SAS criterion for similarity of trianglesStart
- SAS criterion for similarity of triangles: ProblemsStart
- SSS criterion for similarity of trianglesStart
- SSS criterion for similarity of triangles: ProblemsStart
- Criterion 1 for similarity of right-angled trianglesStart
- Criterion 1 for similarity of right-angled triangles: ProblemsStart
- Criterion 2 for similarity of right-angled trianglesStart
- Criterion 2 for similarity of right-angled triangles: ProblemsStart
- Criterion 3 for similarity of right-angled trianglesStart
- Criterion 3 for similarity of right-angled triangles: ProblemsStart
- Applications of similarity criteriaStart
- Filling in sentencesStart
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- Sine, cosine, tangent, and cotangent of acute anglesStart
- Signs of sine, cosine, tangent, and cotangentStart
- Relations between sine, cosine, tangent, and cotangentStart
- Reduction formulasStart
- Simplifying expressionsStart
- Trigonometric functions in a triangleStart
- Trigonometric functions in a quadrilateralStart
- Calculating the area of a triangle using the sine of an angleStart
- Law of sinesStart
- Law of sines: ProblemsStart
- Law of sines in quadrilateralsStart
- Law of cosinesStart
- Law of cosines: ProblemsStart
- Law of cosines in quadrilateralsStart
- Solving trianglesStart
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- Inscribed polygonsStart
- Inscribed regular triangleStart
- Inscribed right-angled triangleStart
- Inscribed isosceles triangleStart
- Inscribed scalene triangleStart
- Inscribed quadrilateralStart
- Inscribed rectangleStart
- Inscribed squareStart
- Inscribed regular polygonStart
- Inscribed trapezoidStart
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- Circumscribed polygonsStart
- Circumscribed regular triangleStart
- Circumscribed right-angled triangleStart
- Circumscribed isosceles triangleStart
- Circumscribed scalene triangleStart
- Circumscribed quadrilateralStart
- Circumscribed squareStart
- Circumscribed rhombusStart
- Circumscribed regular polygonStart
- Circumscribed trapezoidStart
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