MAT CLIL 3

X LO | Toruń | Poland

Programme for class 1

Real numbers [15h]

1.1.01. Natural numbers.
1.1.02. Integers. Rational numbers.
1.1.03. Irrational numbers.
1.1.04. Irrational numbers.
1.1.05. Decimal extension of a real numer.
1.1.06. The root of a nonnegative number.
1.1.07. The odd-degree root of a real number.
1.1.08. Powers with ineteger exponent.
1.1.09. Standard notation.
1.1.10. Approximations.
1.1.11. Percentages.

Language of mathematics [22h]

1.2.01. Sets.
1.2.02. Set operations.
1.2.03. Intervals.
1.2.04. Operations on intervals.
1.2.05. Solving inequalities.
1.2.06. Short multiplication formulas.
1.2.07. Application of algebraic transformations
1.2.08. Absolute value.
1.2.09. Absolute value properties.
1.2.10. Equations and inequalities with absolute value.
1.2.11. Absolute and relative approximation's error.

Linear function [19h]

1.3.01. Defining a function.
1.3.02. Linear functions and their graphs.
1.3.03. Properties of linear functions.
1.3.04. The equation of a straight line.
1.3.05. The gradient of a straight line.
1.3.06. Condition of perpendicularity of two lines.
1.3.0R. Linear functions - revision. CKE - exercises [pdf]
1.3.07. The system of linear equations.
1.3.08. Graphic interpretation of two linear equations with two unknowns.
1.3.09. Systems linear inequalities.
1.3.10. Applications of linear functions.

Functions [19h]

1.4.01. Domain and zeros of a function.
1.4.02. Graph of a function.
1.4.03. Monotonicity of functions.
1.4.04. Reading properties of a function from its graph.
1.4.05. Moving a function graph along the $x$ axis.
1.4.06. Moving a function graph along the $y$ axis.
1.4.07. Vectors in a coordinate system.
1.4.08. Moving a function graph with a vector.
1.4.09. Transforming a function graph by symmetry about the coordinate system axis
1.4.10. Other function graphs transformations.
1.4.11. Applications of functions.

Quadratic function [28h]

1.5.01. The graph of a function $f(x)=ax^2$.
1.5.02. Moving a graph the function $f(x)=ax^2$ with a vector.
1.5.03. Vertical and standard form of a quadratic function.
1.5.04. Quadratic equations.
1.5.05. Factored form of a quadratic function.
1.5.06. Equations reducible to quadratic equations.
1.5.0R. Quadratic functions - revision. CKE - exercises [pdf]
1.5.07. Quadratic inequalities.
1.5.08. Sets of equations.
1.5.09. Vieta's formulas.
1.5.10. Quadratic equations with parameters.
1.5.11. Applications of Quadratic functions.

Planimetry [23h]

1.6.01. Measures of angles in a triangle.
1.6.02. Congruent triangles.
1.6.03. Similar triangles.
1.6.04. Similar polygons.
1.6.05. Thales's theorem
1.6.06. Right triangles.
1.6.07. Trygonometric functions of acute angles.
1.6.08. Trygonometry - applications.
1.6.09. Solving right triangles.
1.6.10. Relations between trigonometric functions.
1.6.11. The area of a triangle.
1.6.11. The area of a quadrangle.

Analytic geometry [20h]

1.7.01. Distance between points in the coordinate system. The middle of a segment.
1.7.02. Distance between a point and a straight line
1.7.03. A circle in the coordinate system.
1.7.04. Two circles.
1.7.05. A circle and a straight line.
1.7.06. Systems of second degree equations.
1.7.07. A disc in the coordinate system.
1.7.08. Operations on vectors.
1.7.09. Vectors applications.
1.7.10. Dilation.
1.7.11. Line symmetry.
1.7.11. Central symmetry.