Algebra and geometryLaajuus (3 ECTS)

Objective

The student will be able to calculate the value of a given expression and to simplify expressions, to solve simple equations and pairs of equations, use the coordinate system in presenting points and graphs of simple functions. The student will be familiar with the basic concepts of geometry is will be able to employ them in one-, two- and three-dimensional problems.

The student will understand three-dimensionality and its two-dimensional presentation. The student will be able to draw projections, find out the surface area of a body, draw axonometric drawings, draw an axonometric structural section, be able to solve the points of inflection of surfaces by using altitude lines and to draw an ellipsis in a number of ways.

Content

Number fields. Calculation rules. Expressions with letters. The value of an expression. Simplifying expressions. Polynomials. Power and root. Linear and quadratic equations. Linear pair of equations. Root equations. Inverse and direct proportionality. The coordinate system. Graphs for linear and quadratic polynomials. Trigonometry. Plane geometry. Space geometry.

Line types and using them. Polyhedra and intersections of polyhedra. Memory triangles. Cavalier projection, military projection, isometric orthogonal projection, isometric projection. Structural section in an isometric projection, the golden section. The real length of a line by turning it downward and parallel to vertical plane. The surface area of a body. Altitude lines and graphs. Ellipsis.

Assessment criteria, satisfactory (1)

The student is able to calculate the value of an expression, to simplify simple algebraic and trigonometric expressions, form and solve simple algebraic and trigonometric equations, use the coordinate system and calculate area and volume.

Assessment criteria, good (3)

The student is able to calculate the value of an expression requiring unit conversions, to simplify algebraic and trigonometric equations, to form and solve algebraic and trigonometric equations, use various types of coordinate systems and to scale plane areas and bodies.

Assessment criteria, excellent (5)

The student is able to calculate the value of a complex expression, form and solve demanding algebraic and trigonometric equations, use various types of coordinate systems and coordinate conversions, scale plane areas and bodies determined in various ways.