{"id":17400,"date":"2026-05-04T12:00:00","date_gmt":"2026-05-04T10:00:00","guid":{"rendered":"https:\/\/newsite.finki.ukim.mk\/announcements\/soopshtenie-za-podgotvitelna-nastava-po-matematika-za-drzhavna-matura\/"},"modified":"2026-05-04T12:00:00","modified_gmt":"2026-05-04T10:00:00","slug":"soopshtenie-za-podgotvitelna-nastava-po-matematika-za-drzhavna-matura","status":"publish","type":"announcement","link":"https:\/\/finki.ukim.mk\/en\/announcements\/soopshtenie-za-podgotvitelna-nastava-po-matematika-za-drzhavna-matura\/","title":{"rendered":"Announcement on preparatory mathematics classes for the State Matura"},"content":{"rendered":"<div>\n<div>\n<h3>Free Online Preparatory Mathematics Classes for the State Matura Examination<\/h3>\n<\/div>\n<div>\n<p><strong>Dear Secondary-School Graduates and Future Students,<\/strong><\/p>\n<p>The Faculty of Computer Science and Engineering (FCSE) is pleased to announce <strong>FREE online preparatory classes in MATHEMATICS<\/strong> for the external examination subject <strong>MATHEMATICS<\/strong> within the State Matura examination, during the period <strong>9 May 2026 \u2013 3 June 2026<\/strong>.<\/p>\n<p>The classes will be delivered by FCSE professors and teaching assistants.<\/p>\n<p>The preparatory classes are organised to help secondary-school graduates\u2014our future students\u2014achieve the best possible results in the Mathematics examination for the State Matura, which will be held on <strong>6 June 2026<\/strong>.<\/p>\n<p>The preparatory classes will comprise <strong>57 teaching hours<\/strong> (<strong>42 hours of core instruction + 15 hours of supplementary instruction<\/strong>), distributed evenly across <strong>13 days<\/strong> and will cover all content prescribed by the Mathematics Examination Programme for the State Matura in general and vocational secondary education, which includes the following five areas:<\/p>\n<ul>\n<li><strong>AREA 1:<\/strong> MATHEMATICAL LOGIC AND SETS <strong>(weighting: 7%)<\/strong><\/li>\n<li><strong>AREA 2:<\/strong> REAL AND COMPLEX NUMBERS <strong>(weighting: 12%)<\/strong><\/li>\n<li><strong>AREA 3:<\/strong> ALGEBRA <strong>(weighting: 40%)<\/strong><\/li>\n<li><strong>AREA 4:<\/strong> GEOMETRY <strong>(weighting: 34%)<\/strong><\/li>\n<li><strong>AREA 5:<\/strong> TRIGONOMETRY <strong>(weighting: 7%)<\/strong><\/li>\n<\/ul>\n<div>\n<p>For all questions concerning the preparatory classes, secondary-school graduates may contact us at the following email address: <\/p>\n<\/div>\n<div>\n<p>In the event of difficulty signing in to Microsoft Teams, please try joining while signed out, using an incognito browser window.<\/p>\n<\/div>\n<div>\n<p>To receive announcements and materials from the preparatory classes, please register using the following form.<\/p>\n<p><a href=\"https:\/\/forms.office.com\/Pages\/ResponsePage.aspx?id=e8TK8LPiG06lL0h9LZliiIsrU4KqDQtCn9MvF2BSluRUMUIwTUVHRkw1MzVKSEZNMU1JMjZDTzY4WS4u\" rel=\"noopener noreferrer\" target=\"_blank\">Registration for Preparatory Classes <\/a><\/p>\n<p>Preparatory-class materials are available at the following link: <a href=\"https:\/\/finkiukim-my.sharepoint.com\/:f:\/g\/personal\/webadmin_finki_ukim_mk\/IgBI16HrkoJEQ6YR9TKwIZsCAU8-kyx46NFaSZsAE6P2kps?e=p8zYwT\" rel=\"noopener noreferrer\" target=\"_blank\">Preparatory-Class Materials<\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div>\n<div>\n<h3>Class Schedule<\/h3>\n<\/div>\n<div>\n<p>Classes will be held according to the following schedule:<\/p>\n<table>\n<thead>\n<tr>\n<th>Date<\/th>\n<th>Date<\/th>\n<th>Day<\/th>\n<th>Teaching Hours<\/th>\n<th>Start Time \/ Link<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Session 1<\/td>\n<td>09.05.2026<\/td>\n<td>Saturday<\/td>\n<td>5 hours<\/td>\n<td><strong>10:00<\/strong><br \/><a href=\"https:\/\/teams.microsoft.com\/l\/meetup-join\/19%3ameeting_Yjk2ZTE0N2MtZWJhMi00ZGMwLThhMTYtYTI3ZWRlZGRhOWQ3%40thread.v2\/0?context=%7b%22Tid%22%3a%22f0cac47b-e2b3-4e1b-a52f-487d2d996288%22%2c%22Oid%22%3a%2282532b8b-0daa-420b-9fd3-2f17605296e4%22%7d\" rel=\"noopener noreferrer\" target=\"_blank\">Join on Microsoft Teams<\/a><\/td>\n<\/tr>\n<tr>\n<td>Session 2<\/td>\n<td>12.05.2026<\/td>\n<td>Tuesday<\/td>\n<td>3 hours<\/td>\n<td><strong>15:00<\/strong><br \/><a href=\"https:\/\/teams.microsoft.com\/l\/meetup-join\/19%3ameeting_NjVjMmNlY2YtNjRmMi00Y2Q5LWE4N2YtY2QzZTA5NDExNGEx%40thread.v2\/0?context=%7b%22Tid%22%3a%22f0cac47b-e2b3-4e1b-a52f-487d2d996288%22%2c%22Oid%22%3a%2282532b8b-0daa-420b-9fd3-2f17605296e4%22%7d\" rel=\"noopener noreferrer\" target=\"_blank\">Join on Microsoft Teams<\/a><\/td>\n<\/tr>\n<tr>\n<td>Session 3<\/td>\n<td>14.05.2026<\/td>\n<td>Thursday<\/td>\n<td>3 hours<\/td>\n<td><strong>15:00<\/strong><br \/><a href=\"https:\/\/teams.microsoft.com\/l\/meetup-join\/19%3ameeting_OThhOGVkYjgtMTAzZC00OTYwLTg5ZmItZDhkZmI3ZGM5NDA0%40thread.v2\/0?context=%7b%22Tid%22%3a%22f0cac47b-e2b3-4e1b-a52f-487d2d996288%22%2c%22Oid%22%3a%2282532b8b-0daa-420b-9fd3-2f17605296e4%22%7d\" rel=\"noopener noreferrer\" target=\"_blank\">Join on Microsoft Teams<\/a><\/td>\n<\/tr>\n<tr>\n<td>Session 4<\/td>\n<td>16.05.2026<\/td>\n<td>Saturday<\/td>\n<td>5 hours<\/td>\n<td><strong>10:00<\/strong><br \/><a href=\"https:\/\/teams.microsoft.com\/l\/meetup-join\/19%3ameeting_MThkZjU3ODgtZTM2My00ZWNhLWJhZjgtY2VhMDU2ZWUyN2Zi%40thread.v2\/0?context=%7b%22Tid%22%3a%22f0cac47b-e2b3-4e1b-a52f-487d2d996288%22%2c%22Oid%22%3a%2282532b8b-0daa-420b-9fd3-2f17605296e4%22%7d\" rel=\"noopener noreferrer\" target=\"_blank\">Join on Microsoft Teams<\/a><\/td>\n<\/tr>\n<tr>\n<td>Session 5<\/td>\n<td>19.05.2026<\/td>\n<td>Tuesday<\/td>\n<td>3 hours<\/td>\n<td><strong>16:00<\/strong><br \/><a href=\"https:\/\/teams.microsoft.com\/l\/meetup-join\/19%3ameeting_NmU5NzliZTgtNjcxZS00YWFiLTk3YTktMDcxZmFjNGZlYWIy%40thread.v2\/0?context=%7b%22Tid%22%3a%22f0cac47b-e2b3-4e1b-a52f-487d2d996288%22%2c%22Oid%22%3a%2282532b8b-0daa-420b-9fd3-2f17605296e4%22%7d\" rel=\"noopener noreferrer\" target=\"_blank\">Join on Microsoft Teams<\/a><\/td>\n<\/tr>\n<tr>\n<td>Session 6<\/td>\n<td>21.05.2026<\/td>\n<td>Thursday<\/td>\n<td>3 hours<\/td>\n<td><strong>15:00<\/strong><br \/><a href=\"https:\/\/teams.microsoft.com\/l\/meetup-join\/19%3ameeting_OTc3NmYwN2YtNDhmNi00Mjc3LWE3OGEtZjljYzQxOTkwMzRl%40thread.v2\/0?context=%7b%22Tid%22%3a%22f0cac47b-e2b3-4e1b-a52f-487d2d996288%22%2c%22Oid%22%3a%2282532b8b-0daa-420b-9fd3-2f17605296e4%22%7d\" rel=\"noopener noreferrer\" target=\"_blank\">Join on Microsoft Teams<\/a><\/td>\n<\/tr>\n<tr>\n<td>Session 7<\/td>\n<td>23.05.2026<\/td>\n<td>Saturday<\/td>\n<td>5 hours<\/td>\n<td><strong>10:00<\/strong><br \/><a href=\"https:\/\/teams.microsoft.com\/l\/meetup-join\/19%3ameeting_YjliY2Q4NTAtODJmNy00NTJiLWFiNTAtYjljYTA2ZDA1ZTA1%40thread.v2\/0?context=%7b%22Tid%22%3a%22f0cac47b-e2b3-4e1b-a52f-487d2d996288%22%2c%22Oid%22%3a%2282532b8b-0daa-420b-9fd3-2f17605296e4%22%7d\" rel=\"noopener noreferrer\" target=\"_blank\">Join on Microsoft Teams<\/a><\/td>\n<\/tr>\n<tr>\n<td>Session 8<\/td>\n<td>26.05.2026<\/td>\n<td>Tuesday<\/td>\n<td>5 hours<\/td>\n<td><strong>12:00<\/strong><br \/><a href=\"https:\/\/teams.microsoft.com\/l\/meetup-join\/19%3ameeting_ODI0NTQwYWQtOWQ2Zi00YTdiLTk4YzEtMmE1M2M0OWZmYTZh%40thread.v2\/0?context=%7b%22Tid%22%3a%22f0cac47b-e2b3-4e1b-a52f-487d2d996288%22%2c%22Oid%22%3a%2282532b8b-0daa-420b-9fd3-2f17605296e4%22%7d\" rel=\"noopener noreferrer\" target=\"_blank\">Join on Microsoft Teams<\/a><\/td>\n<\/tr>\n<tr>\n<td>Session 9<\/td>\n<td>28.05.2026<\/td>\n<td>Thursday<\/td>\n<td>5 hours<\/td>\n<td><strong>10:00<\/strong><br \/><a href=\"https:\/\/teams.microsoft.com\/l\/meetup-join\/19%3ameeting_ZDhhY2JiMGItYzg2OC00N2Y4LWJjMzgtZWViZjliZjRmNjgz%40thread.v2\/0?context=%7b%22Tid%22%3a%22f0cac47b-e2b3-4e1b-a52f-487d2d996288%22%2c%22Oid%22%3a%2282532b8b-0daa-420b-9fd3-2f17605296e4%22%7d\" rel=\"noopener noreferrer\" target=\"_blank\">Join on Microsoft Teams<\/a><\/td>\n<\/tr>\n<tr>\n<td>Session 10<\/td>\n<td>30.05.2026<\/td>\n<td>Saturday<\/td>\n<td>5 hours<\/td>\n<td><strong>10:00<\/strong><br \/><a href=\"https:\/\/teams.microsoft.com\/l\/meetup-join\/19%3ameeting_ODYyNTE0ZmItMWJiMi00NzA4LThhZmEtOGQ4YzdmNDdkOWYy%40thread.v2\/0?context=%7b%22Tid%22%3a%22f0cac47b-e2b3-4e1b-a52f-487d2d996288%22%2c%22Oid%22%3a%2282532b8b-0daa-420b-9fd3-2f17605296e4%22%7d\" rel=\"noopener noreferrer\" target=\"_blank\">Join on Microsoft Teams<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>A further <strong>15 hours<\/strong> (<strong>3 days \u00d7 5 hours<\/strong>) will be held to solve problems submitted by participants during the classes, according to the following schedule:<\/p>\n<table>\n<thead>\n<tr>\n<th>Date<\/th>\n<th>Date<\/th>\n<th>Day<\/th>\n<th>Teaching Hours<\/th>\n<th>Start Time \/ Link<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Session 11<\/td>\n<td>01.06.2026<\/td>\n<td>Monday<\/td>\n<td>5 hours<\/td>\n<td><strong>11:00<\/strong><br \/><a href=\"https:\/\/teams.microsoft.com\/l\/meetup-join\/19%3ameeting_MzEwODU5MjMtNGE5NS00NTA1LWJiNDUtZjAwZDRhNGRlOThh%40thread.v2\/0?context=%7b%22Tid%22%3a%22f0cac47b-e2b3-4e1b-a52f-487d2d996288%22%2c%22Oid%22%3a%2282532b8b-0daa-420b-9fd3-2f17605296e4%22%7d\" rel=\"noopener noreferrer\" target=\"_blank\">Join on Microsoft Teams<\/a><\/td>\n<\/tr>\n<tr>\n<td>Session 12<\/td>\n<td>02.06.2026<\/td>\n<td>Tuesday<\/td>\n<td>5 hours<\/td>\n<td><strong>11:00<\/strong><br \/><a href=\"https:\/\/teams.microsoft.com\/l\/meetup-join\/19%3ameeting_NzBlYWNhOWMtYzk3NC00Y2E2LTg4ZmMtMTY3MzI1MTQxMzA2%40thread.v2\/0?context=%7b%22Tid%22%3a%22f0cac47b-e2b3-4e1b-a52f-487d2d996288%22%2c%22Oid%22%3a%2282532b8b-0daa-420b-9fd3-2f17605296e4%22%7d\" rel=\"noopener noreferrer\" target=\"_blank\">Join on Microsoft Teams<\/a><\/td>\n<\/tr>\n<tr>\n<td>Session 13<\/td>\n<td>03.06.2026<\/td>\n<td>Wednesday<\/td>\n<td>5 hours<\/td>\n<td><strong>10:00<\/strong><br \/><a href=\"https:\/\/teams.microsoft.com\/l\/meetup-join\/19%3ameeting_MTE1M2VjNmQtNWM2Mi00ZTM1LTg4YjEtY2I1YWYwZmU5Yzkz%40thread.v2\/0?context=%7b%22Tid%22%3a%22f0cac47b-e2b3-4e1b-a52f-487d2d996288%22%2c%22Oid%22%3a%2282532b8b-0daa-420b-9fd3-2f17605296e4%22%7d\" rel=\"noopener noreferrer\" target=\"_blank\">Join on Microsoft Teams<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div>\n<div>\n<h3>Mathematics Examination Programme for the State Matura<\/h3>\n<\/div>\n<div>\n<p>The Mathematics Examination Programme for the State Matura is provided below.<\/p>\n<h4><strong>A. CONTENT<\/strong><\/h4>\n<h4><strong>AREA 1: MATHEMATICAL LOGIC AND SETS<\/strong><\/h4>\n<p><strong>1. MATHEMATICAL LOGIC<\/strong><\/p>\n<ul>\n<li>The concept of a proposition<\/li>\n<li>Logical operations (negation, conjunction, disjunction, implication and equivalence)<\/li>\n<li>Compound propositions<\/li>\n<li>Laws of logic (commutative, associative and distributive laws; implication replacement; law of non-contradiction; law of the excluded middle; De Morgan\u2019s laws; modus ponens; modus tollens; and hypothetical syllogism)<\/li>\n<\/ul>\n<p><strong>2. SETS<\/strong><\/p>\n<ul>\n<li>The concepts of a set and a subset<\/li>\n<li>Methods of defining sets<\/li>\n<li>Operations on sets<\/li>\n<li>Laws governing operations on sets<\/li>\n<\/ul>\n<h4><strong>AREA 2: REAL AND COMPLEX NUMBERS<\/strong><\/h4>\n<p><strong>1. NUMBERS<\/strong><\/p>\n<ul>\n<li>Natural numbers<\/li>\n<li>Integers<\/li>\n<li>Rational numbers<\/li>\n<li>Real numbers<\/li>\n<li>Complex numbers<\/li>\n<\/ul>\n<p><strong>2. OPERATIONS ON NUMBERS<\/strong><\/p>\n<ul>\n<li>Natural numbers<\/li>\n<li>Integers<\/li>\n<li>Rational numbers<\/li>\n<li>Real numbers<\/li>\n<li>Complex numbers<\/li>\n<\/ul>\n<p><strong>3. PROPORTIONALITY OF QUANTITIES<\/strong><\/p>\n<ul>\n<li>Ratios and proportions; direct and inverse proportionality<\/li>\n<li>Simple and compound rule of three<\/li>\n<li>Percentage calculations: percentage, below one hundred and above one hundred<\/li>\n<li>Proportional division<\/li>\n<li>Percentage calculations: of one hundred, below one hundred and above one hundred<\/li>\n<li>Interest calculations<\/li>\n<\/ul>\n<h4><strong>AREA 3: ALGEBRA<\/strong><\/h4>\n<p><strong>1. ALGEBRAIC RATIONAL EXPRESSIONS<\/strong><\/p>\n<ul>\n<li>Powers with natural-number exponents<\/li>\n<li>Integral rational expressions: monomials and polynomials<\/li>\n<li>Fractional rational expressions<\/li>\n<\/ul>\n<p><strong>2. LINEAR EQUATIONS AND LINEAR INEQUALITIES<\/strong><\/p>\n<ul>\n<li>Linear equations in one unknown<\/li>\n<li>Linear inequalities in one unknown<\/li>\n<\/ul>\n<p><strong>3. LINEAR FUNCTIONS, SYSTEMS OF LINEAR EQUATIONS AND SYSTEMS OF LINEAR INEQUALITIES<\/strong><\/p>\n<ul>\n<li>Real-valued functions<\/li>\n<li>Linear functions<\/li>\n<li>Systems of two linear equations in two unknowns<\/li>\n<li>Systems of two linear inequalities in one unknown<\/li>\n<\/ul>\n<p><strong>4. QUADRATIC EQUATIONS AND QUADRATIC FUNCTIONS<\/strong><\/p>\n<ul>\n<li>Incomplete and complete quadratic equations<\/li>\n<li>Nature of the solutions of a quadratic equation<\/li>\n<li>Vieta\u2019s formulas and their application<\/li>\n<li>The concept of a quadratic function<\/li>\n<li>Graphs of elementary quadratic functions<\/li>\n<li>Canonical form of a quadratic function; vertex of a parabola<\/li>\n<\/ul>\n<h4><strong>AREA 4: GEOMETRY<\/strong><\/h4>\n<p><strong>1. GEOMETRIC FIGURES IN THE PLANE<\/strong><\/p>\n<ul>\n<li>Basic geometric figures<\/li>\n<li>Rays, line segments and half-planes<\/li>\n<li>Circumference and circle<\/li>\n<li>Angles and types of angles<\/li>\n<li>Polygonal lines and polygons<\/li>\n<li>Vectors; operations on vectors<\/li>\n<\/ul>\n<p><strong>2. PERIMETER AND AREA OF PLANE FIGURES<\/strong><\/p>\n<ul>\n<li>The concepts of perimeter and area<\/li>\n<li>Perimeter and area of rectangles, triangles, quadrilaterals and regular polygons<\/li>\n<li>Circumference of a circle and length of a circular arc<\/li>\n<li>Area of a circle and parts of a circle<\/li>\n<\/ul>\n<p><strong>3. GEOMETRIC SOLIDS<\/strong><\/p>\n<ul>\n<li>Points, lines and planes<\/li>\n<li>Geometric solids<\/li>\n<li>Polyhedra and solids of revolution<\/li>\n<li>Intersections of geometric solids with a plane<\/li>\n<\/ul>\n<p><strong>4. SURFACE AREA AND VOLUME OF GEOMETRIC SOLIDS<\/strong><\/p>\n<ul>\n<li>The concepts of surface area and volume of a solid<\/li>\n<li>Prisms<\/li>\n<li>Pyramids<\/li>\n<li>Cylinders<\/li>\n<li>Cones<\/li>\n<li>Spheres<\/li>\n<\/ul>\n<h4><strong>AREA 5: TRIGONOMETRY<\/strong><\/h4>\n<p><strong>1. TRIGONOMETRIC FUNCTIONS IN A RIGHT-ANGLED TRIANGLE<\/strong><\/p>\n<ul>\n<li>Measurement of angles (degrees and radians)<\/li>\n<li>Concept and definition of the trigonometric functions of an acute angle<\/li>\n<li>Trigonometric functions of complementary angles<\/li>\n<li>Values of the trigonometric functions of the angles 30\u00b0, 45\u00b0 and 60\u00b0<\/li>\n<li>Fundamental trigonometric identities<\/li>\n<li>Solving a right-angled triangle<\/li>\n<\/ul>\n<\/div>\n<\/div>","protected":false},"featured_media":15124,"template":"","class_list":["post-17400","announcement","type-announcement","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/finki.ukim.mk\/en\/wp-json\/wp\/v2\/announcement\/17400","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/finki.ukim.mk\/en\/wp-json\/wp\/v2\/announcement"}],"about":[{"href":"https:\/\/finki.ukim.mk\/en\/wp-json\/wp\/v2\/types\/announcement"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/finki.ukim.mk\/en\/wp-json\/wp\/v2\/media\/15124"}],"wp:attachment":[{"href":"https:\/\/finki.ukim.mk\/en\/wp-json\/wp\/v2\/media?parent=17400"}],"curies":[{"name":"WordPress","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}