X LO | Toruń | Poland
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Class 1
Class 3
Programme for class 2
2.1.
Polynomials [22h]
2.1.01. Polynomial degree and coefficients.
2.1.02. Adding and subtracting polynomials.
2.1.03. Multiplying polynomials.
2.1.04. Factoring polynomials (1).
2.1.05. Factoring polynomials (2).
2.1.06. Polynomial equations.
2.1.07. Dividing polynomials .
2.1.08. Equality of polynomials.
2.1.09. Bézout's theorem.
2.1.10. Integer and rational polynomial roots
2.1.11. Multiple roots of a polynomial.
2.1.12. Graph of a polynomial.
2.1.13. Polynomial inequalities .
2.1.14. Polynomials - applications.
2.2.
Rational functions [23h]
2.2.01. Inverse proportionality.
2.2.02. Graph of a function $f(x)=\frac{1}{x}$.
2.2.03. Moving graph of a function $f(x)=\frac{1}{x}$ with a vector.
2.2.04. Homographic function.
2.2.05. Transformations of a homographic function graph.
2.2.06. Multiplication and division of rational expressions.
2.2.07. Addition and subtraction of rational expressions.
2.2.08. Rational equations.
2.2.09. Rational inequalities
2.2.11. Rational function.
2.2.12. Equations and inequalities with absolute value.
2.2.13. Rational expressions - applications
2.2.14. Polynomials - applications.
2.2.
Trigonometric functions [29h]
2.3.01. Trigonometric functions of any angle.
2.3.02. Rotation angle.
2.3.03. Arc measure.
2.3.04. Periodic functions.
2.3.05. Graphs of sine and cosine functions.
2.3.06. Graphs of the functions tangent and cotangent.
2.3.07. Vector translation of a function graph.
2.3.08. Function graph transformations (1)
2.3.09. Function graph transformations (2)
2.3.10. Function graph transformations (3)
2.3.11. Trigonometric identities.
2.3.12. Trigonometric functions of sum and difference of angles.
2.3.13. Reduction formulas.
2.3.14. Trigonometric equations
2.3.15. Trigonometric inequalities
2.4.
Sequences [27h]
2.4.01. The concept of a sequence.
2.4.02. Defining sequences.
2.4.03. Monotonic sequences (1).
2.4.04. Recursive definition of a sequence.
2.4.05. Monotonic sequences (2).
2.4.06. Arithmetic sequence (1).
2.4.07. Arithmetic sequence (2).
2.4.08. Sum of the first $n$ terms of an arithmetic sequence.
2.4.09. Geometric sequence (1).
2.4.10. Geometric sequence (2).
2.4.11. Sum of the first $n$ terms of an geometric sequence.
2.4.12. Arithmetic and geometric sequence - word problems.
2.4.13. Compound Interest.
2.4.14. Limit of a sequence.
2.4.15. Improper limit of a sequence.
2.4.13. Calculating a limit of a sequence (1).
2.4.14. Calculating a limit of a sequence (2).
2.4.15. Geometric series.
2.5.
Calculus [29h]
2.5.01. The limit of a function at a point.
2.5.02. Calculating limits.
2.5.03. The one-sided limit of the function at a point.
2.5.04. Improper limits of the function.
2.5.05. The limit of a function at infinity.
2.5.06. Function continuity.
2.5.07. Continuous functions - properties.
2.5.R1.
Limits - revison [pdf]
2.5.08. Derivative of a function at a point.
2.5.09. Derivative function.
2.5.10. Operations on derivatives
2.5.11. Physical interpretation of the derivative.
2.5.12. Increasing and decreasing functions.
2.5.13. Function extrema
2.5.14. Maximum and minimum values of the function
2.5.15. Optimization issues.
2.5.16. Sketching a function graph.
2.5.R2.
Derivatives - revision. [pdf]
2.6.
Planimetry[16h]
2.6.01. Circumference and area of a disc.
2.6.02. Angles in a circle.
2.6.R1.
Arc, sector, angles in a circle [pdf]
2.6.03. The circle described on the triangle.
2.6.04. A circle inscribed in a triangle.
2.6.R2.
Triangles and Circles [pdf]
2.6.05. Convex quadrangles.
2.6.R3.
Quadrilaterals a [pdf]
2.6.06. The circle described on a quadrangle.
2.6.07. A circle inscribed in a quadrangle.
2.6.R4.
Quadrilaterals and Circles [pdf]
2.6.08. Sine theorem.
2.6.09. Cosine theorem.
2.6.R5.
Sine and cosine rules [pdf]