## Mathematics, advanced syllabus (MAA)

Sequence of completion:

Compulsory courses MAA1-MAA10 are completed in the order that the teacher recommends. Course MAA16 is a revision course at the beginning of upper secondary studies; the syllabus of basic education is revised and students are acquainted with studying advanced maths. Course MAA12 requires the completion of MAA7, MAA8 and MAA9. Courses MAA11, MAA13, MAA14 and MAA15 are to be completed in the third year. Possible independent course completion must be discussed with the teacher.

COMPULSORY COURSES

MAA1 Functions and equations

The contents of the course include, for example: calculating percentages, proportionality, concepts of power and square roots, examining power and exponential functions and solving different equations. Evaluated with a number grade.

MAA2 Polynomial functions

The course deals with polynomial functions, quadratic polynomial functions and the number of possible solutions, higher-order polynomial functions and polynomial inequalities. Students study products of polynomials and the binomial theorem. Polynomial calculation rules are revised. Evaluated with a number grade.

MAA3 Geometry

The course contents are: similarity of figures and bodies; sine and cosine rules; geometry of a circle, its parts and straight lines related to it; calculating lengths, angles, areas and volumes related to figures and bodies. Evaluated with a number grade.

MAA4 Analytical geometry

Students are expected to examine: equations of set points; for example, equations of straight lines, circles and parabolas as well as distance of a point from a straight line. Students also get practise in solving absolute value equations and inequalities and equation systems. Evaluated with a number grade.

MAA5 Vectors

The course includes studies on vectors and their properties and calculation rules points, distances and angles in two- and three-dimensional co-ordinate systems by means of vectors. Evaluated with a number grade.

MAA6 Probability and statistics

Students learn to illustrate different statistical distributions (discrete and continuous) and their parameters. They also study mathematical and statistical probability, combinatorics, rules for calculating probabilities, probability distributions, the expected value and normal distribution. Evaluated with a number grade.

MAA7 The derivative

The course comprises: rational equations and inequalities; limits, continuity and derivatives of functions. Students study differentiation of polynomial functions and of the products and quotients of functions; their use in examining the behaviour of polynomial functions and determining its extreme values as well as in determining the maximum and minimum of a rational function in connection with applied problems. Evaluated with a number grade.

MAA8 Radical and logarithmic functions

The course contents include: properties of radical, exponential and logarithmic functions and solving equations related to these, as well as derivatives. Studies also comprise inverse functions and derivation of composite functions. Evaluated with a number grade.

MAA9 Trigonometric functions and number sequences

Students are to study: trigonometric functions and their properties, equations and derivatives as well as number sequences. Evaluated with a number grade.

MAA10 Integral calculus

The course contents include: integral functions, integral functions of elementary functions, the definite integral and calculating areas and volumes. Evaluated with a number grade.

NATIONWIDE SPECIALISATION COURSES

MAA11 Number theory and logic

The course contents are: formalisation of statements, truth-values of statements, different principles of reasoning, the basic concepts of number theory: properties of prime numbers and the divisibility of integers. Evaluated with a number grade.

MAA12 Numerical and algebraic methods

The course includes, for example: the concepts of absolute and relative errors and, through these, the rules governing the accuracy of approximations; solving equations numerically through iteration; divisibility of polynomials; determining rates of change and areas numerically. Evaluated with a number grade.

MAA13 Advanced differential and integral calculus

The course places emphasis on consolidating and complementing students' skills in differential and integral calculations and examining the limits of functions and number sequences in infinity and improper integrals. Evaluated with a number grade.

SCHOOL-BASED SPECIALISATION COURSES

MAA14 Revision of basic mathematics (only in Finnish)

The content of the compulsory courses is revised, according to the needs and wishes of the students. Evaluated with a number grade. A 4 will not count towards the 75 courses.

MAA15 Preparing for the matriculation exam (only in Finnish)

The course prepares students for the matriculation exam. Assignments are based on former matriculation exam questions. Evaluated with a number grade. A 4 will not count towards the 75 courses.

MAA16 Revision of the first and the second courses

This course consists of revising topics from the first and the second courses: exponentials, polynomial expansion, polynomial factorisation, square roots, simultaneous equations, first, second and higher degree equations and inequalities. The course is aimed at those students who have not achieved the level they were aiming for. The course is held in the third period. Numerical grading. Grade 4 does not add to the total number of courses.

Course MAA16 is a revision course that revises contents of courses MAA1 and MAA 2. It is offered in the third period.

MAA17 = MAB7 Commercial mathematics

Students examine index numbers, cost, money transactions, tax and other calculations as well as mathematical models applicable to economic situations, using number sequence and sums. Evaluated with a number grade. A 4 will not count towards the 75 courses.

Changing from an advanced syllabus to a short syllabus:

The grades of advanced mathematics are accredited as follows: MAA1 = MAB1, MAA3 = MAB2, MAA6 = MAB5, MAA7 = MAB4 and MAA8 = MAB3. When changing from the advanced syllabus to the short one, you will have to discuss the change with the student counsellor.