How to Prepare for EXANI-II Math: A 12-Week Study Plan

One of the sample questions in CENEVAL's official guide for the EXANI-II gives three polynomials, $A = x - 3$, $B = 3x^{3} - x^{2}$ and $C = -4x^{2} + 2x$, and asks for $B + 2C - A$. Careful work gives $3x^{3} - 9x^{2} + 3x + 3$, option A. The guide then explains the two wrong options, and neither is random: one comes from a slip with the distributive property, the other from a slip with the sign rules. Let the 2 reach only the first term of C, for instance, and the x term comes out as $x$ instead of $3x$ while every other term stays correct. That exact answer is one of the three options.

That is the exam in miniature: three options per question and, if the guide's samples are typical, wrong answers built from predictable mistakes. The EXANI-II (Examen Nacional de Ingreso a la Educación Superior) is the admission exam Mexican universities contract from CENEVAL to assess applicants who have finished upper-secondary school. Mathematics runs through it in two layers: Pensamiento matemático (mathematical thinking), which every candidate answers, and subject modules that depend on the degree you apply for. This guide covers the format, the scoring, and a 12-week plan.

Where the Math Is on the EXANI-II

The EXANI-II is one long sitting, not a set of separate papers. This is CENEVAL's current structure, from its official EXANI-II page:

Area	Questions	Counts toward the global score
Subject module 1	24	Yes
Subject module 2	24	Yes
Comprensión lectora (reading comprehension)	30	Yes
Redacción indirecta (indirect writing)	30	Yes
Pensamiento matemático	30	Yes
Scored subtotal (five areas)	138
English as a foreign language	30	No, diagnostic only
Total	168

Mathematics appears twice: in Pensamiento matemático, which everyone answers, and possibly in the two subject modules, depending on what your university assigns.

A few rules hold across the whole exam. Every question is multiple choice with three options. About 10 percent more questions are added as pilot items, plus two control questions, and none of these are scored, so treat every question as if it counts. The whole exam is one session of at most 4.5 hours. The one exception to the two-module layout is Premedicina (pre-medicine), a single 48-question module that cannot be combined with another.

The institution also decides how you sit the exam: on paper, online at a site it designates, or from home (Examen desde casa). Everything here describes CENEVAL's current structure, so if you are preparing for the EXANI-II in 2027, confirm your modules and modality in your university's convocatoria, the call for applicants each institution publishes with its own dates, venues and costs. There is no single national exam date.

One warning about prep material. Older books and some websites still describe areas called Pensamiento analítico (analytical thinking) and Estructura de la lengua (language structure), which belong to the previous version of the exam. Because Pensamiento matemático existed in that version too, an outdated book can look current at a glance, so check its areas against the table above.

Pensamiento Matemático: 18 Questions of Understanding, 12 of Modeling

CENEVAL defines Pensamiento matemático as the ability to recognize and use mathematics in daily life, drawing on arithmetic, algebra, geometry, statistics and probability to formulate and solve problems in varied contexts. The official temario (syllabus) splits the 30 questions between two subareas, with three themes in each.

Comprensión de lo matemático (understanding mathematics): 18 questions. Sentido numérico (number sense) covers linear inequalities, simplifying algebraic expressions, trigonometric ratios, area, standard deviation and the arithmetic mean. Conexiones (connections) covers ratios and proportions, the graphical interpretation of linear equations, axes of symmetry, estimating trajectories, frequencies, and the classical probability of simple events. Estimación (estimation) covers the laws of exponents, percentage, units of measure as a standard of comparison, and sample space.

Matematización (mathematization, or modeling): 12 questions. Desarrollo de usos (developing uses) covers graphing second-degree equations, the graphical behavior of quadratic functions, trigonometric relations, graphical representation of information, and measures of central tendency and dispersion. Lenguaje matemático (mathematical language) covers polynomials and systems of linear equations in two and three unknowns. Resignificaciones (reinterpretations) covers tabular linear variation and measures of position: deciles, quartiles and percentiles.

Notice what the list leaves out: no limits, no derivatives, no logarithms, and, with every question multiple choice, nothing to prove. Calculus appears only in the Cálculo diferencial e integral module, for the programs that assign it. Much of the difficulty is in the setting. CENEVAL's definition is about mathematics in everyday situations, so expect topics to arrive inside a context rather than as bare exercises, and expect the first step to be recognizing which tool the situation calls for.

If percentages still feel like a formula you look up, the percentages guide rebuilds them around one idea. The ratios and proportions guide covers scaling, the exponents guide shows why the exponent laws hold, the inequalities guide explains why the sign flips when you multiply by a negative, and the trigonometry guide turns sine and cosine into coordinates you can picture. With 18 of the 30 questions testing understanding, the plan below opens with number sense.

Your Modules Are Chosen for You

The second layer of EXANI-II math depends on your degree program, and you do not choose it. CENEVAL offers 18 módulos de conocimientos disciplinares (subject-knowledge modules), 16 specific and two general, and each institution selects two according to the program. CENEVAL's own example is a Civil Engineering applicant whose institution assigns Cálculo diferencial e integral (differential and integral calculus) and Física (physics). Another university, or another program at the same one, can assign a different pair.

Four of the specific modules are mathematics through and through, 24 questions each.

Aritmética (arithmetic). Fourteen questions on principles of real numbers, from fractions, decimals, signs and powers to scientific notation, prime factors, divisibility, least common multiple and greatest common divisor. Ten on problems with rational numbers: ratio and proportion, percentage, arithmetic and geometric progressions, proportional sharing, simple interest and the rule of three.

Cálculo diferencial e integral. Twelve differential questions: limits, derivatives (by definition and for trigonometric, exponential, logarithmic and polynomial functions), tangent lines, and physical applications including optimization. Twelve integral questions: methods of integration and definite integrals for area, volume and motion.

Probabilidad y estadística (probability and statistics). Twelve statistics questions: population and sample, types of variables, frequencies with their tables and graphs, mean, median, mode, variance, standard deviation and percentiles. Twelve probability questions: sample space, set theory, permutations, counting techniques, axioms and distributions.

Matemáticas financieras (financial mathematics). Fourteen questions on basic financial elements (ratios, direct and inverse proportion, percentages and discounts, sequences and series) and ten on simple interest, including amortization and investments.

If your program assigned calculus, the derivatives guide builds derivatives up from slope, and the integrals guide treats integrals as accumulation, the idea behind the area, volume and motion questions. For probability and statistics, start with the statistics guide and the guide to permutations and combinations.

So read your university's convocatoria before planning anything, and if it does not name your modules, ask the institution: CENEVAL says only the institutions can give details about the content of their exam. The modules are 48 of the 138 scored questions, a little over a third. Preparing calculus for a program that assigned Matemáticas financieras, or the reverse, costs weeks you do not have.

No Penalty, Three Options: Answer Everything

CENEVAL's scoring rule fits on one line: a correct answer earns 1 point, a wrong answer 0, and there is no penalty for wrong answers or unanswered questions. A blank and a wrong guess cost the same, so a blank is never the better choice.

Three options make guessing unusually productive. A blind guess is right one time in three. Rule out one option you know is wrong, a sign that cannot be right or a value outside any sensible range, and the guess becomes a coin toss. Partial knowledge turns directly into expected points.

Results come back on the Índice Ceneval (CENEVAL's score index), a scale from 700 to 1,300. According to CENEVAL's description of the results report, you receive a global score and a score for each area on that scale, based on your number of correct answers. The report also breaks out each subarea, so Comprensión de lo matemático and Matematización come back separately.

That leaves the question many students search for: how many correct answers is 1,000 points? CENEVAL answers with a design principle rather than a table. The exam is built so that most applicants at the same sitting land near 50 percent correct, which corresponds to 1,000 points. So 1,000 means roughly half right, by design.

CENEVAL issues no pass or fail, only the score. Each university sets its own admission criteria, so the same score can be enough for one program and short for another.

A Basic Calculator Changes Less Than You Think

The EXANI-II allows a calculator with basic functions, which the guide calls a calculadora simple, and no other support material or electronic device. That takes care of tedious arithmetic: long division, decimals, 16 percent of a price. It does not touch the mathematics.

The sample question is all brackets and signs, and no key on a basic calculator writes this line for you:

$$3x^{3} - x^{2} + 2(-4x^{2} + 2x) - (x - 3) = 3x^{3} - 9x^{2} + 3x + 3$$

The same goes for the rest of Matematización. A system in two or three unknowns needs a choice between substitution and elimination. The graph of a quadratic function needs you to know where the vertex and the roots come from. A chart or frequency table needs reading before it needs arithmetic. The calculator can only check numbers you have already set up correctly.

Two habits follow. Practice from the first week with the same kind of basic calculator you will use on exam day. And keep estimating in your head: Estimación is one of the official themes, and a quick estimate catches a mistyped number faster than retyping the calculation. If quadratic graphs are a weak spot, the quadratic equations guide connects the equation to its parabola; for systems, see the systems of equations guide.

Diagnose Before You Plan

Before starting the plan, sit one timed set of 30 questions spread across the Pensamiento matemático topic list, in about 45 minutes, with only a basic calculator. If one of your modules is mathematical, add a 24-question set for it. Start with official material: the Guía para el sustentante (CENEVAL's candidate guide) has sample items with an explanation of every option, and CENEVAL's exam page also lists a Guía Interactiva EXANI-II among its support materials. For volume, use practice books or an online simulador (practice test) whose areas match the current exam.

The score matters less than the error map. Sort every miss into five bins: concept gaps, method gaps, arithmetic slips, reading problems, and time problems.

Each bin needs its own fix. Concept gaps need explanation and simple examples. Method gaps need worked examples, then reproduction from a blank page. Arithmetic slips need slower, checked work and the estimating habit. Reading problems need you to restate what the question asks before looking at the options, because a well-built wrong option is often the right answer to a slightly different question. Time problems need timed mixed sets, but only once the mathematics is secure.

The 12-Week Study Plan

Five two-week blocks, then two weeks of rehearsal. End every session with ten minutes of mixed questions from earlier blocks. Short daily sets hold skills in place far better than occasional long sessions, which is the idea behind spaced repetition for math practice.

Weeks 1 and 2: number sense. Percentages and percent change, ratios and proportions, the laws of exponents, units of measure, and linear inequalities, all from the 18-question Comprensión de lo matemático subarea. Practice them inside everyday situations, the way CENEVAL frames the area.

Weeks 3 and 4: the algebra language. Simplifying algebraic expressions, operations with polynomials, systems of linear equations in two and three unknowns, graphs of linear equations, and tabular linear variation. Write out every bracket and every sign; that is where the sample question's wrong options come from.

Weeks 5 and 6: geometry and trigonometry. Area, axes of symmetry, trigonometric ratios and relations, and the graphs of quadratic functions: vertex, roots, and which way the parabola opens. Sketch before you calculate.

Weeks 7 and 8: data and chance. The mean, dispersion and standard deviation, quartiles, deciles and percentiles, frequencies and graphs of data, sample spaces, and the classical probability of simple events. Write the sample space down before counting anything.

Weeks 9 and 10: your two assigned modules. For a math module, work through its official subareas in proportion to their question counts: 14 and 10 for Aritmética, 12 and 12 for Cálculo diferencial e integral. If neither module is mathematical, keep a short Pensamiento matemático set running daily while you prepare them.

Weeks 11 and 12: full rehearsals. Complete timed sessions in your modality, every area included, every question answered. Review each rehearsal for as long as it took, redo missed problems from a blank page a day later, then freeze the routine. No new topics in the final days.

Exam-Day Pacing for a 4.5-Hour Session

The official numbers give you a pace: 168 questions, plus about 10 percent in pilot items and two control items, come to roughly 187 items. Over 270 minutes, that is just under a minute and a half per item on average. That is our arithmetic, not a CENEVAL figure. At that rate, the 30 Pensamiento matemático questions get a little over 40 minutes.

The average hides wide variety. A percentage can take thirty seconds; a system of three equations can take four minutes. Where your modality lets you move back through the exam, work in two passes. On the first, answer everything you can do quickly, and when a question stalls you past two minutes, eliminate what you can, pick the best remaining option, and move on. On the second, return to your guesses. Never leave a blank: a guess you never revisit still beats an empty answer.

If your institution uses Examen desde casa, prepare the setup as seriously as the mathematics. CENEVAL states that if a power or internet failure interrupts a home session, the lost time cannot be restored and the exam cannot be rescheduled. Check your computer and connection against CENEVAL's published requirements well ahead, and sit at least one rehearsal on the same machine, in the same room, at the same time of day.

Where Math Zen Fits

Math Zen has an EXANI-II exam path covering the arithmetic, algebra, functions, geometry, trigonometry, sequences, probability and statistics behind Pensamiento matemático. Its adaptive difficulty keeps each topic at the level you can currently handle and sends more practice to the topics you miss. If your university assigned the calculus module, you can add Math Zen's limits, derivatives and integrals topics alongside the path. It does not reproduce the exam's three-option format, so pair it with official material and timed sets; the EXANI-II exam page summarizes the format in one place.

The Bottom Line

EXANI-II math comes in two layers: 30 Pensamiento matemático questions that every candidate answers, split 18 and 12 between understanding and modeling, and two 24-question modules your university assigns, some of them entirely mathematical. Every question has three options, a wrong answer costs nothing, a basic calculator is allowed, and scores land on the Índice Ceneval between 700 and 1,300, with 1,000 near half right by design. Read your convocatoria first, diagnose before you plan, rebuild the core topics in two-week blocks, give your modules their own two weeks, and finish with full rehearsals in your modality. Twelve weeks of that is enough to walk in knowing what each kind of question will ask, with the habit of answering every one.