Basics in MathematicsLaajuus (3 ECTS)

Objective

The student is able to perceive the meaning and interpretation of mathematical expressions. The student knows how to use the Cartesian coordinate system to visualize pairs of numbers and how to plot elementary functions. The student can visualize also mentally the main features of the most important elementary functions.

The student is able to perform calculations with integers, fractional and decimal numbers. The student can simplify symbolic expressions composed of basic mathematical operations. The student is able to solve linear and quadratic equations, pairs of linear equations and most common types of equations containing roots, logarithms or exponentials. The student can plot elementary functions. The student can solve for the angles of a given triangle.

Content

Integers, basic algebraic operations and their rules. Fractions and calculations with fractions. Using letters as symbols of numbers. Basics rules of manipulating expressions that contain symbols and numbers. Basic rules for simplifying mathematical expressions. Decimal numbers and accuracy of calculations with decimal numbers. Roots and fractional powers. Solving linear equations and pair of linear equations. Solving simple equations containing roots. Coordinate system, straight line, parabola and other basic functions. Direct and inverse proportionality. Trigonometric functions solving the right angle. Exponential and logarithmic functions and related simple equations.

Solving more complicated equations. Complete solutions of simple trigonometric equations. General principles of solving exponential and logarithmic equations.

Qualifications

Secondary school mathematics