# The Long Mathematics Syllabus (MAA)

The long mathematics program is aimed at providing students with the mathematical skills necessary for professional and higher education, and for general everyday use. The coursework in long mathematics will provide the opportunity for the student to utilize the mathematical concepts and processes thereby learning to understand the nature of mathematical information. The tuition will seek to provide students with a clear understanding of the importance of mathematics in the development of society, and how it applies to everyday life situations and in science and technology.

### MAA2 Polynomial Functions and Equations

This course focuses on solving polynomial equations of various degrees and inequalities both mechanically and in practical applications.
Keskeiset sisällöt: Applying polynomial products and the binomial expansion. Using polynomial functions, factorizing second degree equations and solving polynomial equations and inequalities.

### MAA3 Geometry

This course involves interpreting and describing two dimensional figures and three- dimensional objects. Solving geometrical problems using the properties of various figures and solids.
Keskeiset sisällöt: Using the properties of similar figures, the sine and cosine rule, the circle, Pythagoras’ theorem and oblique triangle trigonometry, finding and calculating lengths, angles, areas and volumes of various figures and solids.

### MAA4 Vectors

This course deals with applying two and three dimensional vectors for solving a variety of problems.
Keskeiset sisällöt: basic properties of vectors, vector subtraction and multiplication, component vectors and scalar product, solving systems of equations, vector lines and planes in space.

### MAA5 Analytic Geometry

This course focuses on understanding and applying analytic geometry both geometrically and algebraically.
Keskeiset sisällöt: sets of points as equations, using equations with reference to points, lines, circles and parabolas, solving absolute value equations and inequalities, distance from a line to a point.

### MAA6 Differential Calculus

This course deals with understanding and applying differential calculus of polynomial and rational functions to solve a variety of both theoretical and practical application problems.
Keskeiset sisällöt: rational equations and inequalities, the limiting value of a function, continuity and the derivative, the derivative of polynomial functions, including the product and quotient rule, examining polynomials for determining maximum and minimum values.

### MAA7 Trigonometric Functions

This course focuses on examining and applying the properties of trigonometric functions and equations including the derivative of these functions.
Keskeiset sisällöt: angles and radians, the unit circle, symmetry and periodicity of trigonometric functions, solving trigonometric equations, derivative of composite functions, derivative of trigonometric functions.

### MAA8 Root and Logarithm Functions

This course involves applying and solving root, exponential and logarithmic functions and equations, including the derivative of these functions.
Keskeiset sisällöt: exponent laws, root functions and equations, exponential functions and equations, logarithmic functions and equations, derivative of root, exponential and logarithmic functions.

### MAA9 Integral Calculus

This course focuses on using integral functions and evaluating integrals by integration and applying this for solving a variety of problems.
Keskeiset sisällöt: functions and its integral, the definite integral, calculating areas and volumes.

### MAA10 Probability and Statistics

This course involves calculating the probability of events and organizing, interpreting and analyzing the distribution of statistical information.
Keskeiset sisällöt: discrete and continuous statistical distributions, interpreting statistical
data, laws of probability classical and statistical, permutations and combinations, discrete and continuous probability distributions, the expected value, normal distribution.