Pre-algebra at AIS-Salzburg is a general mathematics course which covers and reinforces basic mathematical terminology and procedures. Arithmetic processes are refined and reinforced as well as a wide range of mathematical concepts and terminology.
Algebra I lays the foundation for virtually all higher mathematics to be studied in the student’s academic future. In previous courses, students have used a letter to represent a number they seek to find. In Algebra I, however, the student is less concerned about what number the letter represents and will concentrate on the things that are true just because it is a number. Students will use expressions containing these letters to represent quantities in the real world. This will enable the student to predict such things as how high a bouncing ball is at a given point, how long it takes to reach a given height, and when it will be back down again. Particularly, students will learn to reduce complicated problems to simple ones, write expressions to represent a variable quantity in real-world situations, develop skills helpful in science classes, and learn operations with algebraic functions through rational expressions, multiplication and division, and addition and subtraction.
Geometry is the study of points, lines, shapes, and solids. The students will be engaged with fascinating theories concerning these which have been proven by mathematicians over thousands of years and learn to prove them themselves. The study of geometry develops the student’s spatial awareness and ability to think and imagine in 2 and 3 dimensions. Students will learn to draw diagrams accurately and construct shapes precisely using a compass. Course content includes the study of lines, points, and planes, angles, transformations, perimeter, area and volume, congruency and similarity, the Pythagorean Theorem. Finally students will be introduced to trigonometry.
The Algebra II course focuses primarily on the intermediate algebra level with the goal to evolve to circular and trigonometric functions and some advanced algebra. The ultimate unity of algebra and trigonometry will provide the foundation necessary for continuing on to precalculus and AP calculus in the following years. Major objectives for the course include the study of linear, quadratic, exponential, rational, and irrational functions and the ability to graph them by hand and on an automatic grapher; the ability to select a function and derive an equation that suits the information given within the problem; use of a variety of mathematical concepts to solve the same problem; and the ability to create mathematical models of phenomena in the real world.