8th grade
Students learn the basic concepts of algebra and geometry. They become familiar with square roots, exponents with rational indices, and quadratic equations. Additionally, they are introduced to quadrilaterals, basic concepts of trigonometry, and the Pythagorean theorem.
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lesson 1
Algebraic fractions -
lesson 2
Hyperbola -
lesson 3
Square root and cube root -
lesson 4
n-th roots -
lesson 5
Powers with rational exponents -
lesson 6
Concept of inequalities -
lesson 7
Linear inequalities -
lesson 8
System of linear inequalities
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lesson 9
Absolute value of a number. Equations and inequalities with absolute value -
lesson 10
Approximate calculations -
lesson 11
Quadratic equations -
lesson 12
Reduced quadratic equations. Vieta's theorem.- 1 . Finding reduced quadratic equations
- 2 . "Reducing a quadratic equation to a reduced quadratic equation"
- 3 . "Finding the sum and product of the roots of a reduced quadratic equation"
- 4 . "Finding the roots of a reduced quadratic equation using the selection method"
- 5 . Factoring a quadratic trinomial into linear factors
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lesson 13
Equations reducible to quadratic equations -
lesson 14
Data analysis -
lesson 15
Quadrilaterals- 1 . Polygons
- 2 . Properties of interior angles of polygons
- 3 . Properties of external angles of polygons
- 4 . Parallelogram and its properties
- 5 . Angles in a parallelogram
- 6 . Signs of a parallelogram
- 7 . Rectangle and its properties
- 8 . Angles in a rectangle
- 9 . Square and its properties
- 10 . Angles in a square
- 11 . Rhombus and its properties
- 12 . Angles in a rhombus
- 13 . Trapezium and its types
- 14 . Angles in a trapezoid
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lesson 16
Thales' theorem and its applications
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lesson 17
Trigonometric functions of an acute angle -
lesson 18
Pythagoras' theorem -
lesson 19
Trigonometric identities- 1 . Fundamental trigonometric identity
- 2 . Trigonometric identities
- 3 . Additional angles
- 4 . "Calculation of sine, cosine, tangent and cotangent of an angle of 30 degrees"
- 5 . "Calculation of sine, cosine, tangent and cotangent of an angle of 45 degrees"
- 6 . "Calculation of sine, cosine, tangent and cotangent of an angle of 60 degrees"
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lesson 20
Solving right triangles -
lesson 21
Coordinate system in a plane -
lesson 22
Vectors in a plane- 1 . Vector concept
- 2 . Vector coordinates
- 3 . Multiplying a vector by a number
- 4 . Vector addition
- 5 . Opposite vectors
- 6 . Vector subtraction
- 7 . Finding the length of a vector
- 8 . Dot product of vectors
- 9 . Equality of vectors
- 10 . Collinearity of vectors
- 11 . Triangle rule
- 12 . Parallelogram rule
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lesson 23
Area -
lesson 24
Angles in a circle- 1 . Circle. Radius, diameter and chord
- 2 . The relative position of a straight line and a circle
- 3 . Tangent to a circle
- 4 . The relative position of two circles
- 5 . Central angle
- 6 . Degree measure of arc
- 7 . Inscribed angle
- 8 . Angle between tangent and chord
- 9 . Angles formed by the intersection of two chords
- 10 . "The angle between two secants drawn from the same point outside the circle"
- 11 . Properties of two tangents drawn from one point to a circle
- 12 . Chord of a circle
- 13 . Diameter of circle