YÖS Math, Most Common Topics (Algebra, Geometry, and Arithmetic)

If you’re studying for the YÖS Math section, you’ve probably noticed the hardest part isn’t the level of the questions, it’s knowing what to practice first so you don’t waste time. The good news is that YÖS Math tends to repeat the same core ideas across exams, so a smart plan beats random problem solving every time.

The YÖS (Yabancı Uyruklu Öğrenci Sınavı) is an entrance exam used for foreign students applying to Turkish universities, and in the centralized TR-YÖS format it focuses on math, geometry, and logic within a tight time limit. It’s designed to measure your problem-solving speed and accuracy, not advanced calculus.

In this post, you’ll get a practical, student-friendly list of the most frequently tested YÖS Math topics, plus simple study tips you can follow in English even if you’re new to Turkish-style exams. Topic weights can change by university and by exam format, but Algebra and Geometry usually take the biggest share of points, and Arithmetic shows up every time through ratios, numbers, and basic operations.

This guide is for students preparing in English who want a clear checklist, a study order that makes sense, and a way to track progress week by week without getting overwhelmed.

How the YÖS Math Section Works (Question Mix, Time, and What “Most Common” Means)

The YÖS Math section is less about advanced math and more about how well you can spot patterns, choose the right method fast, and avoid getting stuck. When students say “most common topics,” they usually mean the ideas that show up in many different question styles, not a fixed list with fixed percentages for every exam. Since YÖS formats can vary by university and by year, the smartest approach is to prepare for the areas that create the most question possibilities, then train your timing so you can actually use what you know under pressure.

If you want a broader picture of why Turkey attracts international students and how entry processes fit into that bigger system, this research overview provides helpful context: Internationalization in Turkish Higher Education.

Typical question distribution: why Algebra and Geometry come up the most

Algebra and geometry show up a lot because they act like “toolboxes,” not single topics. One algebra skill can be tested through equations, word problems, inequalities, functions, ratios, and patterns, even when the question looks different on the surface. Geometry works the same way because a single diagram can test angles, triangles, similarity, area, perimeter, circles, and basic coordinate ideas, all with small changes in the drawing.

That’s why “most common” often means this: these topics cover many sub-skills, and exam writers can remix them endlessly without making the questions feel repeated.

Here’s what that looks like in real questions, without solving anything:

• A typical Algebra question might ask you to form and solve an equation from words, such as, “The sum of two numbers is 36, and one is 4 more than the other, find the numbers,” or it might ask you to simplify an expression like 2(x - 3) + 5 and then plug in a value of x.
• A typical Geometry question might show a triangle with a few angles marked and ask for the missing angle, or it might show a circle with a chord and a tangent and ask for a specific angle or length using a known rule.

Even if you prefer one topic, it helps to treat algebra and geometry like your “main diet,” then use arithmetic as the daily habit that keeps you fast and accurate.

Time pressure and scoring: why topic choice affects your strategy

On YÖS-style exams, time is usually the real test. Two questions can be worth the same points, but one takes 20 seconds and the other takes three minutes plus a lucky guess. Your topic choices matter because some topics give faster points when you are under a clock, while others tend to pull you into longer work.

In general, you’ll find that:

• Fast wins often come from basic arithmetic (fractions, percent, ratio, quick comparisons) and straightforward algebra (one-step or two-step equations, clean substitutions, simple systems with clear numbers).
• Time traps often come from multi-step geometry (dense diagrams, multiple theorems at once, or problems where you must build the figure in your head before you can start), and from word problems with messy setup even when the math itself is easy.

A simple strategy that works for many students is to treat the section like a point-collection race, not a perfection test.

1. Scan and grab quick wins first, choosing questions where you already see the method after one read.
2. Mark the slow ones, especially geometry questions that require several steps or a full diagram rebuild.
3. Return later with a plan, because a hard question becomes easier when you come back calmer and can spot a shorter route.
4. Guess only when it makes sense, like eliminating choices or using estimation, since blind guessing can waste time without improving your score.

The goal is not to avoid hard topics, it’s to control when you face them, so your easiest points do not get left behind.

Most Common YÖS Algebra Topics to Master First

If you want faster points in YÖS Math, algebra is usually the best place to start because the same skills show up in many question types. When you can solve cleanly, simplify without slips, and write answers in the right form, you stop losing “easy” marks to small errors. Treat this section like building a reliable toolkit, not memorizing random tricks.

Photo by Karola G

Equations and inequalities (linear, quadratic, absolute value)

Most YÖS algebra questions reduce to one job: turn the problem into an equation or inequality, then solve it with clean steps. The better you get at this, the more “wordy” questions start feeling simple.

For single-variable linear equations, aim to solve in as few steps as possible, while keeping the work readable. A reliable habit is to clear parentheses first, combine like terms, then isolate the variable. For example, if you see 3(x - 2) + 5 = 2x + 1, expand carefully, collect x terms on one side, and constants on the other.

Systems show up too, but usually at a basic level. You do not need fancy methods, you just need control.

• Substitution works well when one equation is already solved for a variable, like y = 2x - 3.
• Elimination is fast when coefficients line up, or when you can multiply one equation to match terms.

With quadratic equations, the exam often expects you to recognize the quickest path. If the quadratic factors nicely, factoring is usually faster than a formula. If it does not factor cleanly, be ready to use completing the square or the quadratic formula, but only when needed.

Inequalities are where many students lose points because the solving steps feel familiar, but the answer format is different. Two rules matter most:

• When you multiply or divide by a negative number, the inequality sign flips.
• Your final answer should be written clearly as an interval or a set, depending on the choices.

For example, if your solution is x > 2, you should be comfortable writing it as an interval (2, ∞) if the question expects interval notation, or as a set {x | x > 2} if the question uses set-builder form.

Absolute value equations and inequalities are also common because they test logic and algebra at the same time. Build the habit of using cases:

• For |x - 3| = 5, use two cases: x - 3 = 5 and x - 3 = -5.
• For |x - 3| < 5, rewrite as a compound inequality: -5 < x - 3 < 5, then solve both sides.

One final step that saves points is checking solutions, especially for absolute value and rational expressions. A quick substitution can catch sign mistakes and “extra” solutions created by squaring both sides.

If you want a clean refresher on core algebra formulas and manipulation rules in one place, the formula pages in this Binghamton University PDF can help as a quick reference during review: MATH 220 course notes (PDF).

Exponents, radicals, and simplifying expressions without mistakes

This topic looks basic, but it is one of the biggest sources of lost marks because mistakes happen quietly. The goal is not to do hard exponent problems, it is to simplify fast and correctly.

Start with the exponent rules you actually use all the time:

• Product rule: a^m * a^n = a^(m+n)
• Quotient rule: a^m / a^n = a^(m-n) (when a ≠ 0)
• Power of a power: (a^m)^n = a^(mn)
• Negative exponents: a^-n = 1/a^n (when a ≠ 0)
• Fractional exponents: a^(1/2) = √a (for real-number settings where it applies)

Radicals are often about simplifying to the cleanest form. When you see something like √(50), you should quickly pull out perfect squares: √(50) = √(25*2) = 5√2. That kind of simplification shows up inside larger expressions, and it makes the next step easier.

Rationalizing is another common skill, usually at a basic level. You might need to rationalize a denominator like 1/√3 by multiplying top and bottom by √3, or handle a simple conjugate when you see terms like 1/(2 + √5).

Algebraic fractions are a frequent YÖS style because they test factoring and simplification in one line. Your safest routine is:

1. Factor everything (numerators and denominators).
2. Cancel only factors, not terms.

That last line is where many students slip. You can cancel x in (x(x+2))/x, but you cannot cancel the x in (x+2)/x+1 because it is not a factor of the whole numerator.

Typical pitfalls to watch for, even when you “know” the rules:

• Mixing addition and multiplication rules: √(a+b) ≠ √a + √b, and (a+b)^2 ≠ a^2 + b^2.
• Losing negative signs: (-3)^2 = 9, but -3^2 = -9 because the exponent applies first.
• Invalid operations: dividing by an expression that could be zero, or taking an even root of a negative number if the problem stays in real numbers.

A simple habit helps here: pause for half a second and ask, “Am I simplifying factors or terms?” That one check prevents a lot of avoidable errors.

Factoring and algebraic identities you actually use in YÖS

Factoring is the shortcut skill that makes other topics easier. It helps you solve quadratics quickly, simplify algebraic fractions, and spot patterns without long steps.

The patterns that show up most often are predictable, so you can train them until they feel automatic:

• Greatest common factor (GCF): ax + ay = a(x + y)
• Difference of squares: a^2 - b^2 = (a-b)(a+b)
• Perfect square trinomials: a^2 + 2ab + b^2 = (a+b)^2 and a^2 - 2ab + b^2 = (a-b)^2
• Simple grouping: ax + ay + bx + by = a(x+y) + b(x+y) = (a+b)(x+y)

In YÖS questions, factoring is rarely an end goal. It is usually a tool to finish something else faster.

Using factoring to solve equations:
If you reach something like x^2 - 5x = 0, factoring gives x(x - 5) = 0, then you apply the zero-product rule, so x = 0 or x = 5. This is faster than “moving terms around” without a plan.

Using factoring to simplify expressions and fractions:
When you have a fraction like (x^2 - 9)/(x - 3), recognizing x^2 - 9 as a difference of squares gives (x-3)(x+3)/(x-3), then it reduces to x+3 (with the restriction x ≠ 3). Those small restrictions matter because answer choices sometimes include the excluded value as a trap.

A good mental model is to think of factoring as finding a hidden zipper in the problem. Once you unzip it, the problem opens cleanly.

Functions and graphs (reading, not drawing masterpieces)

YÖS function questions often reward students who can read a function quickly, not students who can sketch perfect graphs. You should feel comfortable with function language, because it is a common way exams package algebra.

At the core, a function is just a rule that matches each input to one output. In question form, that means you will often do fast evaluation:

• If f(x) = 2x - 1, then f(3) = 2(3) - 1 = 5.
• If you see f(a+1) or f(2x), slow down and substitute the entire input with parentheses.

Domain and range also appear in simple forms. Most YÖS questions keep this practical:

• Watch for division by zero in expressions like f(x) = 1/(x-2), so x ≠ 2.
• Watch for square root restrictions like f(x) = √(x-5), so x ≥ 5 for real outputs.

Graph reading tends to focus on basic features you can spot quickly:

• Intercepts: where the graph crosses the axes, giving you x-intercepts (where y = 0) and the y-intercept (where x = 0).
• Slope: for straight lines, slope tells you rise over run, and it also tells you if the line increases or decreases.
• Increasing/decreasing: if the graph goes up as x increases, it is increasing, and if it goes down as x increases, it is decreasing.

A practical test-day approach is to treat graphs like maps. You are not painting a picture, you are collecting facts. Read what the graph is already telling you, then match it to the answer choices without overthinking the drawing.

Most Common YÖS Geometry Topics (2D Shapes, Triangles, and Circles)

In YÖS geometry, the diagram is your “data sheet.” If you train yourself to mark what you know (equal angles, parallel lines, radii, right angles), many questions stop feeling like puzzles and start feeling like short chains of rules. The most repeated topics are triangles, similarity, common quadrilaterals, and circle angle facts, because they create lots of question types with small changes.

Triangles and angle rules (the highest value geometry area)

Triangles are where YÖS geometry gives you the most points for the least memorization. Most triangle problems collapse into either one missing angle or one clean side ratio, as long as you stay calm and write down the basic rules.

Start with the angle rules you use constantly:

• Triangle angle sum: the three interior angles add to 180°, so if you know two angles, the third is immediate.
• Exterior angle rule: an exterior angle equals the sum of the two remote interior angles, and it also forms a linear pair with the adjacent interior angle (so they add to 180°).
• Straight line and around-a-point facts still matter in triangle diagrams, because many YÖS figures hide triangle angles inside bigger shapes.

Special right triangles are a must, because they turn “find the side” questions into quick pattern matching:

• 45-45-90 triangle: legs are equal, hypotenuse is leg·√2.
• 30-60-90 triangle: short leg is opposite 30°, long leg is short·√3, hypotenuse is 2·short.

A common YÖS trap is using the wrong side as the “short leg.” When you see a 30° angle, point to the side across from it first, then build the ratio from there.

Congruence ideas also show up, usually in a simple way. You do not need a full proof, but you should recognize the core idea: congruent triangles have equal corresponding sides and angles. In problem form, that often means:

• If two triangles match by given information (common ones are SSS, SAS, ASA, AAS, and HL for right triangles), then you can transfer lengths or angles across the diagram.
• Once you spot that transfer, the rest of the question often becomes basic angle sum or a quick subtraction.

If you want a solid checklist of triangle and angle topics that match what many students review in standard Geometry I, this Texas Tech University sheet is a useful reference: GEOM 1B Geometry I review sheet (PDF).

Similarity and ratios: the shortcut behind many YÖS geometry questions

Similarity is one of the best “time-saving” skills in YÖS geometry, because it replaces long calculations with proportional thinking. When two triangles are similar, they have the same shape but different sizes, so angles match and sides scale by a constant factor.

Here’s the core set of facts to keep ready:

• Corresponding angles are equal, so you can move angle values from one triangle to the other.
• Corresponding sides are proportional, so you can write a ratio like AB/DE = BC/EF = AC/DF.
• Scale factor (k): if one triangle is k times larger in side lengths, then:
  • Perimeter scales by k
  • Area scales by k²

That area rule is where YÖS likes to test focus. If the side scale factor is 3, the area does not triple, it becomes 9 times larger.

Spotting similarity quickly is a skill you can train. On YÖS-style diagrams, similarity often appears when:

• You can confirm AA similarity (two angles match), which is the fastest method.
• Parallel lines create equal angles (alternate interior angles, corresponding angles), then triangles “lock into” similarity without extra work.
• A smaller triangle sits inside a bigger one, sharing an angle and having another angle formed by a parallel line.

A simple routine helps: label the equal angles first, then write the matching vertex order (like △ABC ~ △DEF), then set up one clean proportion. When students get stuck, it’s usually because they wrote the ratio with mismatched sides.

For a clear explanation of similarity tied to dilations and scale factor (in plain, structured steps), this Ohio State University Ximera page is a strong refresher: Similarity (OSU Ximera).

Polygons and quadrilaterals (parallelogram, rectangle, trapezoid)

Quadrilateral questions feel easier when you treat them as “triangle questions in disguise.” Many YÖS problems split a four-sided figure with a diagonal, then test angles, congruence, or area using triangle tools.

The properties that show up the most are the ones that give quick deductions:

Parallelogram

• Opposite sides are parallel and equal.
• Opposite angles are equal, consecutive angles add to 180°.
• Diagonals bisect each other (they cut each other in half).

Rectangle

• All angles are 90°.
• Opposite sides are equal and parallel.
• Diagonals are equal and bisect each other.

Trapezoid

• One pair of opposite sides is parallel (the bases).
• Same-side interior angles along a leg add to 180° because of parallel lines.
• In an isosceles trapezoid, base angles are equal, and diagonals are equal.

For area, you do not need fancy moves, but you do need speed and the right formula:

• Parallelogram area: A = base·height
• Rectangle area: A = length·width
• Trapezoid area: A = ( (base1 + base2) / 2 ) · height

The common time-saver is choosing area and ratio methods instead of chasing lengths. For example, if two triangles share the same height, their areas are proportional to their bases, so you can compare areas with simple ratios and skip full computations. Another common shortcut is to compute a missing height from area, then use that height in a second step, rather than starting over with side lengths.

If you want a straight-to-the-point list of quadrilateral properties and angle facts, this chapter PDF is a helpful review source: Chapter 10 Quadrilaterals (PDF).

Circle questions (angles, tangents, chords, arc basics)

Circle questions in YÖS are usually about clean angle rules, plus one or two chord or tangent facts. They are not hard when your diagram is labeled well, but they punish messy thinking, especially when students mix angle measures (degrees) with arc lengths or line lengths.

Angle facts to keep ready:

• Central angle (at the center): its measure equals the measure of its intercepted arc (in degrees).
• Inscribed angle (vertex on the circle): its measure is half the measure of its intercepted arc.

A quick example that comes up often: if an arc is 80°, then an inscribed angle that intercepts it is 40°.

Tangents show up constantly, and the main rule is simple:

• A radius to the point of tangency is perpendicular to the tangent line, so it forms a 90° angle.

Chords and arcs are usually tested at a basic level, but the relationships matter:

• Equal chords subtend equal arcs (and equal central angles).
• A diameter drawn perpendicular to a chord bisects the chord (many problems use this to create equal segments).

On test day, labeling is everything. Write small angle marks, write the center point, and write 90° where a tangent meets a radius. Also keep units separate in your mind: degrees are for angles and arcs, units like cm are for segment lengths, and they are not interchangeable.

For a compact list of the circle definitions and theorems that show up in standard geometry courses (including tangent and chord rules), this Cerritos College PDF is a good one to review: Circle Definitions and Theorems (PDF).

Most Common YÖS Arithmetic and Number Topics (Fast Points if You Train Speed)

Arithmetic is where you can pick up fast, reliable points, as long as you stay organized and avoid sloppy errors. These questions usually do not require advanced math, but they do reward clean setups, quick conversions, and smart checking. If you practice these topics with a timer, you start seeing the same patterns again and again, and that’s when your speed improves without panic.

Fractions, decimals, percentages, and ratio proportion problems

A big share of YÖS arithmetic questions are really conversion questions in disguise. You might see a discount, a mixture, a class ratio, or a “part of a whole” story, but the core skill is the same: move between fractions, decimals, percents, and ratios without hesitation.

A few conversion habits save time right away:

• Fraction to decimal: divide numerator by denominator, then round only at the end if needed.
• Decimal to percent: move the decimal two places right, so 0.08 = 8%.
• Percent to decimal: move it two places left, so 35% = 0.35.
• Percent to fraction: write over 100 and reduce, so 12% = 12/100 = 3/25.

If you want a single-page refresher for these exact moves, this school handout is a clean reference: Math Rules Review.

For percent increase and decrease, treat it like a multiplier problem instead of a “formula hunt.”

• Increase by p% means multiply by 1 + p/100, so a 20% increase means multiply by 1.2.
• Decrease by p% means multiply by 1 - p/100, so a 15% decrease means multiply by 0.85.

This method stays fast even when numbers get messy, and it helps you avoid the common mistake of subtracting the percent from the wrong base.

For unit rate problems (cost per item, speed, work rate), keep your eyes on the “per 1” idea. If 6 notebooks cost 90 lira, you do 90/6 to get the cost per notebook, then scale up or down as needed. When answer choices look close, unit rate makes it easy to compare without extra steps.

For ratio and proportion setups, the biggest skill is writing the relationship correctly before you calculate. A practical way to stay consistent is to line up units and roles:

• If it’s “boys to girls,” keep it as boys over girls every time.
• If it’s “distance to time,” keep it as distance over time every time.

For example, if a:b = 3:5 and you learn b = 40, you can set b = 5k, so 5k = 40, then k = 8, then a = 3k = 24. That approach is usually faster than cross-multiplying, and it reduces sign and placement mistakes.

Before you bubble an answer, take two seconds for a reasonableness check with estimation. If 25% of a number is 80, then the full number should be around 320, since 25% is one-quarter. If your computed answer is 32 or 3,200, something went wrong, and you caught it early.

Number properties: primes, divisibility, GCD, LCM, remainders

Number properties show up as short questions with big payoff, especially when you know what to check first. The goal is not theory, it’s speed: spot structure, apply a rule, move on.

Start by memorizing the divisibility rules you will actually use:

• 2: last digit is even.
• 3: sum of digits is divisible by 3.
• 4: last two digits divisible by 4.
• 5: last digit 0 or 5.
• 9: sum of digits divisible by 9.
• 10: last digit 0.

These rules often appear in “which of these is divisible by…” questions, and they also help with factor finding when you need a quick GCD or LCM.

For GCD and LCM, the fastest method in most YÖS problems is prime factorization when numbers are not huge. Write each number as a product of primes, then:

• GCD: take the common primes with the smallest powers.
• LCM: take all primes with the largest powers.

If you need a quick conceptual refresher on divisibility and prime factorization, these lecture notes are clear and structured: Divisibility, Primes & Unique Factorization (UC Irvine).

Remainder questions look scary until you treat them like “leftovers.” A few practical patterns cover most exam styles:

• If a number is written as N = dq + r, then r is the remainder and it must satisfy 0 ≤ r < d.
• If you know N leaves remainder 2 when divided by 5, then N = 5k + 2, and that single line is often the whole setup.
• If the question asks for the remainder of a sum or product, stay calm and simplify the pieces, then recombine.

Common YÖS question types to train on repeat:

• “Smallest number” problems, like the smallest number that leaves a certain remainder with several divisors, which often uses LCM thinking.
• “How many multiples” questions, which usually reduce to counting multiples in a range using division and careful endpoints.
• Prime or composite traps, where you only need to test primes up to √n for a quick decision.

When you practice, keep your work clean and minimal, because the fastest remainder logic is often just one or two lines.

Sequences and patterns that appear in YÖS-style questions

Sequences show up in YÖS because they test two skills at once: pattern recognition and basic algebra. Most of the time, the math is simple, but you must write the first few terms clearly or you will chase the wrong idea.

Before using any formula, build this habit: write the first 3 to 5 terms neatly, then look for what changes. Many students try to guess the rule in their head and lose time when the pattern has a twist.

The two most common types are:

Arithmetic sequences (constant difference)
If each term increases by the same amount, it’s arithmetic. For example, 4, 7, 10, 13, ... has a common difference of 3. Basic tasks include finding a later term, finding the difference, or finding a missing middle term.

Geometric sequences (constant ratio)
If each term multiplies by the same number, it’s geometric. For example, 2, 6, 18, 54, ... multiplies by 3 each step. These questions often ask for a later term, or to identify the ratio from given terms.

Some YÖS pattern questions are not pure arithmetic or geometric, and that’s fine. A lot of them use simple mixed rules, such as:

• alternating operations (add, multiply, add, multiply),
• patterns in digits,
• repeating cycles in remainders.

When a sum is involved, keep it basic and avoid overthinking. If the sequence is arithmetic and you need a quick sum, pairing ends is often faster than writing a long expression. For example, the sum 1 + 2 + ... + 10 pairs to (1+10) + (2+9) + ..., giving five pairs of 11.

Your speed comes from discipline, not guessing. If you write terms clearly, label the difference or ratio, and only then choose a formula, these questions turn into steady points instead of time traps.

Probability, Statistics, and “Bonus” Topics That Still Show Up

Even if your main focus is algebra and geometry, YÖS-style exams still like to test quick thinking with probability, basic counting, and simple statistics. These questions often look easy, then steal points when you rush the setup or misread what the question counts. The good news is that most of them follow a few repeatable patterns, so you can train them like drills and collect fast marks.

Photo by Armando Are

Basic probability (simple events, independent events, complement)

At the YÖS level, probability is usually the same core idea: favorable outcomes over total outcomes, as long as all outcomes are equally likely. If you can list the sample space cleanly, you can usually solve the problem without any fancy steps.

A reliable way to think about it is this:

• Probability of event A: P(A) = (number of favorable outcomes) / (number of total outcomes)

So if you roll one fair die and want an even number, the favorable outcomes are {2,4,6} (3 outcomes) out of {1,2,3,4,5,6} (6 outcomes), so the probability is 3/6 = 1/2.

Independent events show up a lot because exams love repeated trials, like tossing a coin twice or drawing with replacement. Events are independent when one result does not change the other result, so you can multiply probabilities.

• Independent rule: P(A and B) = P(A)·P(B)

For example, getting Heads twice is (1/2)·(1/2) = 1/4, because the second flip does not care about the first flip.

Where many students lose time is “at least one” questions, because listing all the cases gets messy fast. The clean method is to use complements, which means you find the chance it does not happen, then subtract from 1.

• Complement rule: P(A^c) = 1 - P(A)
• At least one: P(at least one) = 1 - P(none)

Example you can reuse: if you flip a fair coin 3 times, the probability of at least one Head is 1 - P(no Heads). “No Heads” means all Tails, which is (1/2)^3 = 1/8, so the answer is 1 - 1/8 = 7/8. This method stays fast even when the number of trials grows.

If you want a clear, student-friendly reference for probability rules and notation, this handout explains the basics in plain language: Basic Probability: Key Definitions and Rules (CSU East Bay).

The biggest warning for probability questions is counting outcomes incorrectly, because one small counting mistake breaks everything. A few common traps show up often:

• Not checking “equally likely”: some word problems have outcomes with different chances, so “favorable over total” needs more care.
• Mixing up “and” vs “or”: “and” usually means multiply for independent events, while “or” often means add, but only after avoiding double-counting.
• Overcounting by listing sloppy cases: writing cases without a system can double-count the same outcome, especially with cards or digits.

A simple fix is to slow down and label what one “outcome” really is, such as an ordered pair like (first roll, second roll).

Counting basics (permutations, combinations) without heavy formulas

Counting is the quiet helper behind both probability and “how many ways” questions, and YÖS problems usually stay close to everyday logic. When you keep your counting organized, you avoid the two big mistakes: missing cases and counting the same case twice.

Start with the idea that works everywhere: the multiplication rule. If one step has m choices and the next step has n choices for each first choice, then the total outcomes are m·n. This is the same logic as outfits, passwords, and routes on a map.

A simple example: if you have 4 shirts and 3 pants, then you have 4·3 = 12 outfits, because each shirt can match with each pant.

Next, you decide whether order matters, because that single decision tells you which direction the problem goes.

• Order matters (arranging): “ABC” is different from “CBA,” so you count arrangements.
• Order does not matter (choosing): picking A and B is the same as picking B and A, so you count selections.

Everyday YÖS-style examples that match this idea:

• Arranging 5 students in a line is an order-matters problem, because who stands first matters.
• Choosing 3 students from 10 for a committee is an order-does-not-matter problem, because the set is what matters.

You do not need to obsess over formulas at first, because you can solve many problems with a clean, step-by-step count:

1. Decide what a single outcome looks like (a line, a team, a code).
2. Decide if order matters, then stick to that choice.
3. Use the multiplication rule for step-by-step building.
4. Use an organized list for small cases, especially when options are limited.

One more important note is that YÖS questions sometimes hide restrictions, like “no repetition,” “at least one vowel,” or “exactly two reds.” Those restrictions are where counting breaks, so you should rewrite them in your own words before counting.

For a deeper but still readable explanation of permutations vs combinations, this Whitman College section lays it out with examples: Combinations and permutations (Whitman College).

Reading graphs and simple statistics (mean, median, range)

Graph and statistics questions are usually about careful reading, not hard math, and they reward you when you stay strict with units and axes. Many mistakes happen because students read the picture but ignore what the labels actually say.

When you see a bar chart, look for categories and compare heights, then check if the bars represent counts, percentages, or something else. When you see a line graph, focus on change over time, then watch for uneven spacing on the time axis, because uneven spacing can trick your eyes.

A quick checklist that prevents most graph errors:

• Axes: confirm what each axis represents, including units.
• Scale: check if the scale jumps by 1, 2, 5, 10, or something else.
• Starting point: see if the y-axis starts at 0, because a truncated axis can exaggerate changes.
• Legend and labels: confirm you are reading the correct line or bar group.

For basic statistics, YÖS usually sticks to three measures: mean, median, and range, and each has its own “best use.”

Mean (average) is the sum of values divided by how many values there are, and it is easy to compute, but it can get pulled around by extreme values.

Median is the middle value when the data is ordered, and it stays stable when one value is very large or very small.

Range is the largest minus the smallest, and it tells you spread, but it ignores everything in the middle.

Outliers are the classic trap. If one student scored 100 and everyone else scored around 50, the mean rises even if most scores did not change, while the median might stay close to the typical score. If a question asks what represents the “typical” value, median is often the safer answer in the presence of an outlier.

A fast example to lock it in: for 2, 3, 3, 4, 20, the mean is (2+3+3+4+20)/5 = 32/5 = 6.4, but the median is 3, which feels more like the center of the list.

When you practice these, treat them like accuracy questions, because one missed axis unit or one skipped data point can turn an easy point into a wrong answer.

Conclusion

YÖS Math rewards smart priorities more than wide, random practice, so keep your focus on the areas that produce the most repeatable question types. Algebra should be your first anchor because it drives equations, simplification, functions, and many word problems. Geometry comes next, since triangles, similarity, and circles keep showing up in new diagrams, even when the rules stay the same. Keep arithmetic sharp every day because fractions, percent, ratio, and number properties are the easiest quick points when the clock is tight, then cover probability and basic stats as short drills so they don’t become surprise losses.

Topic mix can change by university and by year, so check your target school’s official pages and sample materials, and also keep an eye on ÖSYM updates for TR-YÖS, since the 2025 guide confirms a 40-question Math section within an 80-question, 100-minute exam.

Here’s a simple 3-step plan for next week: take one timed diagnostic using problems from an official source, then spend four days fixing your weakest two areas (one from algebra, one from geometry) while doing 15 minutes of arithmetic each day, then finish with two timed mixed sets and review every mistake with a short note you can reuse. For extra structure, use the Geometry I review from Texas Tech University (https://www.depts.ttu.edu/k12/current-students/forms/cbe-review-sheets/pdfs/geom1b.pdf) as your checklist.