Intensive course in mathematics in the field of engineeringLaajuus (3 cr)

Objective

You are able to flexibly deal with expressions containing fractional numbers also in the symbolic form.

You are able to simplify mathematical expressions, to find a common factor and use the square of a binomial as well as the product of sum and difference.

You are familiar with basic formulas of powers and roots and you are able to use them effortlessly. You are also familiar with negative exponents.

You know thoroughly how to solve equations of first and second degree.

You area able to solve for a given variable in a formula.

You are able to solve a system of two linear equations and to create equations based on simple verbal problems.

You are familiar with mathematical functions and you are able to draw the graph of a line or a parabola.

You know the prerequisites for solving a right-angled triangle and you can carry out the solving process effortlessly.

Content

How do you carry out the basic calculations of fractional numbers?
How do you simplify expressions by removing parentheses, performing the multiplications and combining similar terms?
How do you perform mathematical operations for simplifying power and root expressions?
How do you factorizate a mathematical expression by using a common factor?
How are the formulas of the square of a binomial and the product of sum and difference work used?
How do you solve an equation of first degree and similar formulas?
What are the three forms of a quadratic equation and how can these be solved efficiently?
How do you define the slope, form the equation and draw the graph of a line?
How do you solve a system of two linear equations and present it graphically in the coordinate system?
How do you calculate the apex and zero positions of a parabola and draw the graph of it?
What are the right triangle definitions for trigonometry functions? How can the right triangle be solved?

Qualifications

passing the entrance examination of engineering studies

Accomplishment methods

Students are able to

use professional vocabulary systematically.
• They are able to carry out the basic calculations using fractional numbers, solve an equation of first and second degree, deal flexibly with expressions, form the equations and draw graphs of a line and a parabola and solve a right-angled triangle with varying given initial values.
• They are familiar with basic mathematical formulas which are the prerequisites for these tasks.