YÖS Exam Topics (Math, Geometry, Logic) and How to Study

If you’re applying to a Turkish university as an international student, the YÖS (Yabancı Uyruklu Öğrenci Sınavı) is one of the main exams you’ll hear about, because it helps schools measure if you’re ready for degree-level study. Students search for YÖS exam topics because the test isn’t about memorizing random facts, it’s about scoring well on the core skills universities care about most, math, geometry, and logic.

Right now, there are two routes: TR-YÖS (a centralized exam run by ÖSYM) and university YÖS exams (tests created and scheduled by each university). Even though dates, question counts, and small details can change by school, the topics are usually very similar across both routes, so your study plan can stay focused instead of scattered.

This post breaks the exam down into the key topic areas you’ll see most often, math, geometry, and logic (IQ style questions), then shows how to study them with practice that matches the exam format. It also explains what to double-check on official university pages before you register, so you don’t miss a language option, test center, or topic note listed by the school (for example, many universities post YÖS details on their international admissions pages, like https://www.istanbul.edu.tr/en/.).

What is the YÖS exam (TR-YÖS vs university YÖS) and why topics can vary

When people say “the YÖS exam,” they can mean two different things, and that’s exactly why YÖS exam topics sometimes look slightly different from one university to the next. In simple terms, YÖS is an entrance exam used by many Turkish universities to place international students, but the exam format depends on whether you take the centralized TR-YÖS or a university’s own YÖS.

Think of TR-YÖS as a common ruler that many schools can use, while a university YÖS is more like a custom ruler made by one school for its own needs. Both usually focus on the same core skills, but the balance, question style, and scoring rules can shift based on what the university wants to measure.

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TR-YÖS in 2025 to 2026 admissions: what changed and what stayed the same

For 2025 to 2026 admissions, the biggest shift is how often TR-YÖS is recognized across universities, since more schools now treat it as a standard option for international applicants. That recognition matters because it can simplify your planning, one exam score may work for several applications, instead of sitting separate tests with different rules.

At the same time, the older routes have not disappeared. Some universities still accept SAT scores, and some still run their own YÖS or use other admission pathways (such as certain diploma types or high school performance), especially for specific faculties or limited quotas. This mix is the main reason students feel confused when they compare “YÖS topics” online and see different answers.

What stayed the same is the practical reality that each university sets its own admission conditions and publishes them on its international admissions pages. You should treat every requirement list like a checklist, because small details can affect your plan, including accepted exams, minimum scores, language requirements, test dates, and document rules.

If you want a concrete example of how a university communicates TR-YÖS timelines and language options, you can see a typical announcement format on a Turkish university site like Karadeniz Technical University’s TR-YÖS application announcement.

Common YÖS exam sections you will see most often

Even when universities change the wrapper (TR-YÖS vs university YÖS), the core sections usually stay familiar because they test skills that predict success in first-year courses. In most YÖS formats, you’ll see a mix of math, geometry, and logic (IQ-style reasoning).

Here’s what each section is really measuring, with simple examples of what questions can look like:

• Math (basic to mid-level): This checks if you can work accurately under time pressure, using topics like arithmetic, fractions, ratios, equations, exponents, and basic functions. You might see questions like “If the price increases by 20% and then decreases by 20%, what happens to the final price?” or “Solve for x in a linear equation with fractions.”
• Geometry: This tests your visual reasoning and your comfort with shapes, angles, and measurement. Common areas include triangles, circles, polygons, similarity, perimeter, and area. You might get a diagram of intersecting lines and be asked to find an unknown angle, or a triangle where side ratios matter.
• Logic / IQ (reasoning): This checks pattern recognition and structured thinking, not memorized formulas. Expect number sequences, shape patterns, odd-one-out, basic probability-style reasoning, and word-free logic tables. A typical prompt might show a sequence like 2, 6, 12, 20, ? or a set of shapes that rotate or change by a rule.

Because universities can adjust the weight of each section, your safest approach is to master the shared core, then fine-tune based on the official guide for your target school, such as the kind of TR-YÖS info universities post on their admissions pages (example: Üsküdar University’s TR-YÖS 2025 applications page).

YÖS math topics you must know (the core of most exams)

If your goal is a strong YÖS score, math is the safest place to invest your time because it shows up everywhere, it repeats the same skills in different outfits, and it rewards accuracy under pressure. Think of YÖS math as a toolbox, not a chapter list, because the same tools (fractions, equations, ratios) get reused in arithmetic, algebra, and word problems.

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Numbers and operations: integers, fractions, decimals, ratios, and percent

This is the foundation that quietly decides your score, because even “easy” questions can fall apart if you rush signs, confuse percent with ratio, or mishandle fractions. Start with number properties (even/odd, prime, factors and multiples) and keep your rules straight for negatives, especially when parentheses show up.

You also need clean control over order of operations; a single missed bracket can flip the whole answer. When the exam asks you to estimate, rounding matters too, so practice rounding decimals, then checking if your estimate makes sense compared to the original value.

Ratios, proportions, and percent often look similar but behave differently. A ratio like 2:3 tells a relationship, a percent like 20% tells a part out of 100, and mixing them is a classic trap. When you see “increase by 20% then decrease by 20%,” remember it doesn’t return to the start, because the second change uses a new base.

Daily-life word problems usually package these skills in simple stories:

• Shopping: discounts, tax, unit price, “2 for 3” deals
• Sharing: splitting money, dividing a bill, ratio of ages
• Measurement: converting units, reading decimals, estimating totals

Common mistakes to watch for include careless sign errors (turning subtraction into addition), treating 0.25 as 25 instead of 25%, and forgetting that “percent of” means multiply, not divide.

Algebra basics: expressions, equations, inequalities, and functions

Algebra in YÖS is usually straightforward, but it tests if you can keep your work organized. You’ll simplify expressions by combining like terms and handling parentheses, for example turning 3(2x - 1) - (x + 4) into something cleaner before you solve anything. When exponents appear, they are often basic, but they punish sloppy arithmetic.

When a question says solve, it simply means “find the value(s) that make the statement true.” If 2x + 3 = 11, solving means finding the one number x that makes the left side equal the right side. The safest habit is doing the same operation to both sides, then checking your result by plugging it back in.

Expect lots of:

• Linear equations (including fractions): isolate x carefully, don’t multiply only one term by the denominator.
• Systems of equations (basic): two equations, two unknowns, often solved by substitution or elimination.
• Inequalities: solve like an equation, but remember the sign flip rule when multiplying or dividing by a negative.
• Absolute value basics: treat |x - 3| = 5 as two cases, because distance can be on either side.
• Functions (simple): evaluate values like f(2) given a rule such as f(x) = 2x - 1, which is just careful substitution.

If you want extra practice examples in the same “algebra fundamentals” style, a university worksheet set like this one can help you build speed and accuracy: Math 103 Practice Problems (CSUN).

Word problems and applied math: speed, work, mixtures, and basic probability

Word problems are where many students lose time, not because the math is hard, but because the translation step feels fuzzy. Your job is to turn a story into a small set of math facts, then solve those facts like a normal equation problem.

YÖS-style applied questions often repeat a few “greatest hits”:

• Speed, time, distance: use distance = speed × time, watch units (minutes vs hours), and treat “round trip” as two distances.
• Work problems: think in “job per hour” rates, so if A finishes in 6 hours, A’s rate is 1/6 job per hour.
• Mixtures: keep track of “amount of pure substance,” like salt or alcohol, not just total liquid.
• Percent and change in context: profit and loss, discounts, commissions, population changes.

A simple strategy that works well is to underline what the question asks for, then write a short “math sentence” before doing calculations, because it stops you from solving for the wrong variable.

Basic probability also shows up in a friendly form. You’ll usually see equally likely outcomes, like drawing a colored ball or choosing a number from a set. Remember probability = favorable outcomes / total outcomes, and double-check that you counted correctly. When counting is needed, focus on whether order matters (arrangements) or not (selections), because mixing those up is a common trap.

If you ever feel stuck on the wording, it helps to know how test writers use command words like “solve,” “evaluate,” and “simplify,” and this kind of academic glossary can clarify those terms: Glossary of Academic Terminology (Rice University).

YÖS geometry topics: shapes, angles, and quick diagram thinking

Geometry on the YÖS rewards calm, fast reading of diagrams. You don’t need fancy proofs, you need a small set of rules you can apply quickly, even when the figure looks messy. A good habit is to mark the diagram like a map: put tiny ticks on equal sides, add arc marks on equal angles, and write down angle sums you already know, before you start hunting for x.

Core geometry rules: triangles, polygons, circles, and angle relationships

Most YÖS geometry questions start with triangles, because triangles are the “atoms” of many shapes. Know triangle types and what they imply: equilateral means all sides equal and all angles are 60°, isosceles means base angles are equal, and right triangles trigger the Pythagorean theorem (a^2 + b^2 = c^2). In speed questions, look for common triples like 3-4-5 and 5-12-13 because they save time.

Similarity shows up a lot because it connects shapes to ratios. Two triangles are similar if their angles match (often the AA idea), and then their corresponding sides stay in the same ratio. Once you spot similarity, treat it like a scale model: if one side doubles, every matching side doubles too. A compact formula list like the “Useful formulas from geometry” section in Binghamton’s notes is a handy refresher: http://www2.math.binghamton.edu/lib/exe/fetch.php/people/mckenzie/math_220_course_notes_fall_2020_edition.pdf

Angle rules are where you can score easy points if you stay organized:

• Triangle sum: angles add to 180°.
• Linear pair: a straight line makes 180°, so adjacent angles add to 180°.
• Vertical angles: opposite angles are equal.
• Parallel lines with a transversal: alternate interior angles are equal, same-side interior angles add to 180°.

For polygons, remember the interior angle sum formula: (n - 2) × 180°, and each exterior angle (one at each vertex) adds up to 360° in total.

Circle basics are usually light but frequent: radius to diameter is r to 2r, a chord connects two points on the circle, and a tangent touches at one point and is perpendicular to the radius there. If you see a radius drawn to the tangent point, you can often lock in a 90° angle instantly.

Area, perimeter, volume, and coordinate geometry basics

YÖS geometry also tests measurement, and the fastest students treat formulas like short sentences. For perimeter, you’re just adding boundary lengths. For area, you’re counting “square units,” so always check if the question needs units or a numeric value.

Keep these core area and circumference facts ready:

• Rectangle: area A = lw, perimeter P = 2l + 2w.
• Triangle: A = (1/2)bh, even if the height is drawn outside.
• Parallelogram: A = bh (base times vertical height, not the slanted side).
• Trapezoid: A = (1/2)(b1 + b2)h.
• Circle: area A = πr^2, circumference C = 2πr.

When 3D shows up, it is usually straight volume:

• Prism: V = (base area) × height.
• Cylinder: V = πr^2h.

If you want a clean set of perimeter, circumference, and area notes to practice from, LSU’s geometry class notes are easy to scan: https://www.math.lsu.edu/Programs/DualEnrollment/PreDE/Geometry/ClassNotes

Coordinate geometry is often one quick calculation. The distance between (x1, y1) and (x2, y2) is √((x2 - x1)^2 + (y2 - y1)^2), and the midpoint is ((x1 + x2)/2, (y1 + y2)/2). A common YÖS trick is when the segment is horizontal or vertical, because distance becomes a simple absolute difference, no square root work needed.

To move faster, sketch a tiny coordinate grid, label points clearly, and compute differences first, because most mistakes come from sign errors, not hard math.

Logic and IQ topics in YÖS: patterns, sequences, and reasoning questions

YÖS logic and IQ questions reward calm thinking more than heavy math. When you train the right habits, these problems start to feel like quick puzzles, not scary mysteries. Your goal is to spot the rule, test it fast, then move on before you overthink it.

Sequences and patterns: number series and figure series

Number series questions usually follow a small set of repeatable rules, and the fastest way to solve them is to hunt for the simplest pattern first. Start with differences between terms, because many series are built by adding or subtracting a repeating step, like +3, +3, +3 or a step that grows, like +2, +4, +6, +8. If differences do not behave, check ratios (multiplying or dividing), which often signals a geometric pattern, like doubling each time.

You should also watch for alternating patterns, because many YÖS series switch between two rules. A common example looks like “add 5, then multiply by 2, then add 5, then multiply by 2,” which is easy once you split odd and even positions. Another frequent trick is a repeating cycle, where a short pattern repeats every 3 or 4 steps.

Figure series (visual patterns) work the same way, but the “math” is hidden inside shapes. Scan for one change at a time, such as:

• Count changes (number of sides, dots, lines, shaded parts).
• Position changes (moving one step clockwise each frame).
• Operation changes (adding a line, removing a corner, swapping shading).

A reliable approach is to write a tiny checklist in your head: differences, ratios, alternation, cycle, then mixed rules. When a rule almost fits but fails on one term, re-check for a hidden alternation before you abandon it.

Analytical reasoning: comparisons, ordering, and “if then” logic

Analytical reasoning in YÖS often feels like scheduling friends at a table, sorting heights, or ranking scores, and you win by staying organized. In ordering puzzles, treat each clue as a firm constraint, then build a clean order from strongest to weakest information. If the prompt says “A is taller than B, B is taller than C,” you can lock in A > B > C immediately, then place other people around that backbone.

Grouping and set logic shows up in simple forms, like placing students into two teams, or selecting items that match a rule. Here, the best habit is to track what must be true, and what cannot be true, because this narrows choices quickly.

Conditional statements (“if then”) sound harder than they are, as long as you read them like a rule on a door:

• If A, then B means whenever A happens, B must happen.
• It does not mean B forces A, so avoid that common trap.
• If A happens and B does not happen, the statement breaks, so that case is impossible.

When answers are multiple-choice, you do not always need a full solution. You can often eliminate options by checking one clue at a time and crossing out any choice that breaks it. If you want extra practice with structured puzzle thinking in a math-friendly style, Dartmouth’s puzzle collection is a solid way to build this skill without memorizing formulas: https://math.dartmouth.edu/news-resources/electronic/puzzlebook/book/book.pdf.

Spatial reasoning and puzzle style questions that appear in YÖS

Spatial reasoning questions test how well you can “move” shapes in your mind while staying accurate under time pressure. You will often see rotations, where a shape turns by 90 or 180 degrees, and mirror images, where left and right swap. A quick way to stay grounded is to pick one clear feature, like a dot or a shaded corner, then track only that feature through each move.

Another common format uses nets and simple 3D thinking, where a flat pattern folds into a cube or box. You do not need advanced geometry for this, but you do need a habit of checking which faces will touch after folding. If two squares share an edge in the net, they become adjacent faces, and opposite faces usually come from squares that never touch in the net.

You may also see puzzle styles like odd-one-out figures, completing a missing piece, or matching a rotated shape to its original. These reward pattern recognition, so repetition matters more than reading theory. When you practice, try to name the move you see (rotate, reflect, add, subtract, shift), because naming a rule makes it easier to repeat under stress.

If you like understanding why mental rotation practice helps over time, this Temple University paper gives useful context on spatial skills and rotation: https://sites.temple.edu/cognitionlearning/files/2021/08/Gunderson-Hildebrand-2021.pdf.

How to turn YÖS exam topics into a study plan that works

A YÖS plan works best when it matches your target schools and your current level. Instead of trying to study every topic “just in case,” you’re going to pick priorities, set a weekly rhythm, and use practice tests to steer what you do next. Think of it like building a house, you pour the foundation (basics), then you add floors (mixed practice), then you stress-test it (timed sets and full mocks).

Choose your target universities and confirm their requirements first

Before you build any schedule, lock down where you’re applying, because YÖS requirements can change by university and by program. Your first step is visiting each university’s official international admissions page and writing your findings into one checklist you can update.

Here’s what to verify, every time, on the official pages (not forums or old PDFs shared online):

• Accepted exam route: TR-YÖS, a university-run YÖS (if applicable), SAT, or another option.
• Minimum scores: the overall minimum and any program-specific minimums (medicine and engineering often set higher bars).
• Section weights or evaluation rules: some schools care more about quantitative reasoning, others emphasize math, and that changes how you split study time.
• Exam dates and application windows: note registration deadlines, test dates, result dates, and when applications open.
• Language options and test centers: check the available languages and locations, since that affects travel and planning.
• Score validity: confirm how long the score remains usable for applications.

Keep your checklist simple, with one row per university, then review it weekly until you register, because requirements and dates can get updated mid-season.

A simple weekly schedule: learn, drill, review, and full practice tests

A good YÖS week has four jobs: learn new skills, drill for speed, review to keep memory stable, and practice like the real exam. If you only learn, you stay slow, and if you only drill, your gaps stay hidden.

Use this template week and adjust time blocks to fit your life:

1. Day 1 (Learn + mini-check): Study one math topic and one geometry rule set, then do 15 to 25 mixed questions to confirm you understood.
2. Day 2 (Drill + logic pairing): Do focused math drills (like equations or ratios), then add a short logic set, so your brain switches gears like it will on test day.
3. Day 3 (Review + spaced repetition): Revisit formulas and key rules using short review notes, then solve 10 to 15 questions from older topics, so they don’t fade.
4. Day 4 (Geometry focus + mixed set): Work diagrams and angle rules, then do a mixed set combining geometry and logic, because visual focus can tire you fast.
5. Day 5 (Timed set): Do at least one timed set that feels uncomfortable but manageable, then review immediately while the mistakes are fresh.
6. Day 6 (Full practice test or half test): Simulate real conditions, no pauses, then score it and note timing problems.
7. Day 7 (Light review + reset): Fix weak spots, re-do missed questions, and plan next week.

If you want a simple structure for planning study days close to an exam, Cornell’s Learning Strategies Center has a clear model you can adapt without overcomplicating it: https://lsc.cornell.edu/how-to-study/studying-for-and-taking-exams/the-five-day-study-plan/

Practice test strategy: pacing, accuracy, and fixing mistakes fast

Practice tests should not be “score events,” they should be feedback sessions that tell you what to train next. After each timed set or full test, sort every missed question into one of three buckets, because each bucket needs a different fix.

• Concept error: you didn’t know the rule, formula, or method, so you need to relearn and then do targeted practice.
• Careless error: you knew how, but missed a sign, copied a number wrong, or rushed arithmetic, so you need better checking habits.
• Time pressure error: you understood it, but got stuck or moved too slowly, so you need pacing rules and repeated timed drills.

To make this useful, build a simple error log. For each missed question, write the topic, the error type, and one sentence on the correct method, then add one follow-up task (for example, “do 20 triangle angle questions,” or “practice two-step equations with fractions”). Rutgers has printable study templates that work well for tracking patterns like this, even if you keep the log in a notebook: https://knightbook.rutgers.edu/downloadable-templates/

Your pacing rule should be blunt: if a logic puzzle eats too much time, mark it and move on, because your score usually rises more from collecting easy and medium points than wrestling one hard question.

Common mistakes students make with YÖS topics and how to avoid them

Most YÖS score drops come from predictable habits, not “hard questions.” If you watch for these early, your plan becomes calmer and your results improve faster.

Skipping basics happens when you rush into advanced problems without clean control of fractions, ratios, and simple algebra steps, so build a short daily basics warm-up and treat it like brushing your teeth. Memorizing without practice shows up when you can recite a formula but freeze on a word problem, so you should always pair notes with questions right away. Ignoring geometry is another classic mistake, because geometry feels visual and “optional,” but it often gives quick points when your rules are sharp and your diagram reading is steady.

Logic creates its own trap: spending too long on one puzzle. A good rule is to attempt, test one clean idea, then skip if it still looks messy, because time lost there steals points elsewhere. The last big mistake is not training under time limits, since untimed practice can feel great while timed work falls apart.

If you want a helpful overview of how student errors form and how to respond to them, this Vanderbilt University resource explains error types in a practical way that fits test prep well: https://iris.peabody.vanderbilt.edu/wp-content/uploads/pdf_case_studies/ics_matherr.pdf

Conclusion

YÖS exam topics stay consistent in what they test, even when the exam route changes, math for accuracy and speed, geometry for clean diagram thinking, and logic for patterns and structured reasoning. On the math side, expect strong basics (numbers, ratios, equations, functions), plus common add-ons like probability, while geometry often returns to triangles, circles, area, and coordinate basics. Logic questions usually feel like IQ puzzles, sequences, rotations, folding, and ordering, where pacing matters as much as skill.

At the same time, exact details can vary by university, so treat every requirement list like a checklist, and confirm topics, question counts, and scoring rules on official pages before you commit your time.

If you want a simple next step, pick your target schools, write a one-page topic list for math, geometry, and logic, then start a weekly plan that includes timed sets and fast review, and keep your study habits steady like Cornell’s five-day plan suggests (https://lsc.cornell.edu/how-to-study/studying-for-and-taking-exams/the-five-day-study-plan/).