Basics of MathematicsLaajuus (3 ECTS)

Objective

After completing the course the student is able to perform calculations with integers, fractions and decimal numbers. The student can simplify basic symbolic expressions. The student can solve linear and quadratic equations, pairs of linear equations, basic equations with radicals, and inequalities. The student can plot elementary functions. The student can solve right-angle triangles.

Content

Integers and fractions and their basic algebraic operations and rules. Basic rules of manipulating expressions that contain symbols and numbers. Basic rules for simplifying mathematical expressions. Roots and fractional powers. Solving linear equations and pairs of linear equations. Solving simple equations containing roots. Inequalities. Coordinate system, straight line, parabola and other basic functions. Direct and inverse proportionality. Trigonometric functions and the trigonometry of rectangular triangles.

Qualifications

Vocational school mathematics or short high school mathematics.

Assessment criteria, satisfactory (1)

The student can simplify simple numeric fractions. The student can simplify sums and products of polynomials. The student can extract a common factor. The student knows how to apply rules of signs. The student can simplify powers with integer exponentials. The student can solve simple linear equations. The student can sketch graphs of linear and quadratic functions. The student knows how to apply the Pythagorean formula.

Assessment criteria, good (3)

The student can apply the formulas for binomial products to factoring of polynomials. The student can simplify fractions involving symbolic expressions. The student is able to work with all types of powers and roots. The student can solve a pair of simultaneous equations. The student can solve problems that lead to proportionality, linear equations or pairs of simultaneous equations. The student can solve quadratic equations. The student can solve simple inequalities. The student can construct a linear function from given conditions. The student understands the meaning of the coefficient in the linear function. The student can analyze the properties of a quadratic function. The student can solve any part from a right-angle triangle.

Assessment criteria, excellent (5)

The student is especially confident and skillful in solving algebraic problems. The student can manage complicated rational expressions and he can calculate partial fractions. The students knows well the arithmetic properties and he can justify calculations based on those properties. The student can deduce the most important formulas and methods, such as the formula for solving a quadratic equation. The student can manage and report an applied problem that leads to a linear model.

Further information

The course can be completed without class attendance through an exam and/or other accomplishments, if the student has the necessary qualifications, e.g. based on the result of a diagnostic initial test or other evidence.