PHUMA: Integrated admission foundations: spanish, math, biology, formal, social

Lengua española: comprensión, gramática y expresión

Comprensión y análisis de textos: tema, tesis, estructura y modalización

El bloque de comprensión y análisis parte siempre de un texto -de ordinario una columna o un artículo de opinión, aunque también puede aparecer un fragmento ensayístico o narrativo- y comprueba tres cosas: si has entendido lo que dice, si sabes cómo está construido y si reconoces los recursos verbales que lo sostienen. La respuesta debe estar anclada en el texto: cada afirmación se justifica con una cita breve o una paráfrasis reconocible.

Tema y resumen se evalúan distinto

• Tema: formulación breve del asunto central; un sintagma nominal puede ser útil, pero deben seguirse las instrucciones concretas. Ejemplo: «La desconfianza hacia las noticias digitales».
• Resumen: reformulación fiel y condensada (con la extensión que indique la tarea), sin copiar fragmentos literales, sin opinión y sin ejemplos; solo las ideas principales en su orden.

Tesis, argumentos y estructura

La tesis es la idea que el autor defiende; puede estar explícita o sugerirse mediante una ironía. Los argumentos más frecuentes en la prensa son de autoridad (cita de un experto), de ejemplificación, de datos o estadísticas, de causa-efecto, de analogía y de experiencia personal. Según dónde aparezca la tesis, la estructura es analizante o deductiva (tesis al principio), sintetizante o inductiva (tesis al final), encuadrada (tesis inicial que se recupera en el cierre) o paralela (sin tesis única, con ideas coordinadas).

Modalización y funciones del lenguaje

La subjetividad se manifiesta en la primera persona, en verbos de opinión («creo», «sostengo»), en adjetivos valorativos, en sufijos apreciativos y en modalizadores («sin duda», «quizá», «es evidente que»). Reconoce también la función apelativa (interrogaciones retóricas, segunda persona, imperativos) y la poética (el lenguaje se exhibe en títulos y juegos de palabras).

Ejemplo razonado

Un texto que empieza «Nunca tuvimos tanta información disponible ni tan pocas herramientas para comprobarla» admite el tema «La paradoja de la abundancia informativa sin verificación»; «La información digital» sería demasiado vago. El resumen debe recoger la idea central; una anécdota solo se conserva si resulta indispensable para entenderla. La tesis -la abundancia no garantiza conocimiento- se apoya en la antítesis como procedimiento de apertura y se desarrolla después con argumentos de causa-efecto.

Errores que restan

• Convertir la formulación del tema en un resumen desordenado, sin seguir la consigna.
• Copiar tres líneas literales y presentarlas como resumen.
• Introducir valoración propia donde se pide objetividad.
• No reconocer la dimensión argumentativa de un texto que defiende una tesis, aunque combine exposición y argumentación.
• Ignorar los conectores, que son la prueba material de la estructura.

Expresión escrita: adecuación, coherencia y cohesión en el texto exigido

La pregunta de expresión escrita pide un texto completo -artículo de opinión, carta al director, columna, reseña o texto expositivo-argumentativo- con la extensión que señale la consigna sobre el asunto del texto previo o sobre una cuestión cercana. Se evalúan la adecuación a la tipología y al registro, la coherencia de la argumentación, la cohesión y la corrección normativa; la valoración concreta depende de los criterios publicados para la tarea.

Planificar antes de escribir

Dedica tres o cuatro minutos a un esquema: tesis en una línea, dos argumentos distintos entre sí y una concesión. Un texto de cuatro párrafos (entrada con tesis, argumento, contraargumento matizado, cierre) demuestra estructura; un bloque único de texto, no.

Cohesión y registro

• Conectores variados y precisos: «además», «sin embargo», «por consiguiente», «en la medida en que», «si bien», «de ahí que».
• Referencia interna mediante sinónimos, hiperónimos y pronombres; evita repetir el mismo sustantivo.
• Registro: elige trato y vocabulario según el género y el destinatario. El tuteo no es incorrecto por sí mismo; en una carta formal a un desconocido puede resultar inadecuado.
• Sintaxis variada: alterna enunciados largos con otros breves; evita encadenar subordinadas sin controlar sus relaciones y referentes.

Ejemplo razonado

Enunciado ficticio de práctica: «Redacta un artículo de opinión (150-200 palabras) sobre el uso del móvil en las aulas». Esquema: tesis -regular, no prohibir en abstracto-; argumento de causa-efecto (la notificación interrumpe la atención sostenida); argumento de ejemplificación (centros que limitan el aparato a tareas concretas y mejoran la convivencia); concesión (el móvil como herramienta didáctica puntual); cierre que retoma la tesis. Si el borrador inicial dice «El móvil es malo y hay que quitarlo», la reformulación útil es: «Prohibirlo sin más resulta tentador, pero también contraproducente: sin reglas claras, el conflicto se traslada al recreo». El cambio añade conector concesivo, matiz y una consecuencia; eso es lo que sube la nota.

Errores que restan

• Escribir por debajo del mínimo exigido o duplicar el máximo.
• Texto sin tesis reconocible: solo opiniones sueltas.
• Mezclar tipologías (una narración donde se pedía argumentación).
• Olvidar el título cuando la tipología lo requiere.
• Usar la primera persona en cada frase («yo pienso», «yo creo») en lugar de construir argumentos.
• Descuidar tildes, comas y concordancia: el corrector lo computa.

Reflexión gramatical y léxica: funciones, subordinadas y valores de «se»

La reflexión gramatical y léxica se formula sobre una oración o un par de oraciones del propio texto: clasificar la oración, identificar el tipo de subordinada y su función, explicar un «se», señalar perífrasis o localizar un uso léxico. No basta con etiquetar: hay que demostrar la etiqueta con una prueba.

Pruebas sintácticas que hay que citar

• Sujeto: concordancia con el verbo («Los vecinos protestaron / El vecino protestó»).
• CD: conmutación por «lo, la, los, las» («Compró el pan» → «Lo compró»).
• CI: conmutación por «le, les» («Escribió a su madre» → «Le escribió»).
• Atributo: con verbos copulativos y conmutación por «lo» invariable («Era médica» → «Lo era»).
• Complemento predicativo: puede concordar con el sujeto o el CD. Combina concordancia y estructura; la sustitución aislada por «así» no distingue por sí sola un predicativo de un complemento de modo.
• Complemento de régimen: preposición exigida por el verbo, conmutable por «de eso / en eso».

Oración compuesta

Coordinadas (copulativas, adversativas, disyuntivas, explicativas), yuxtapuestas y subordinadas. Sustantivas: conmutables por «esto», funcionan como sujeto, CD, CRég, atributo, CN o CC («Me molesta que llegues tarde»). Adjetivas o de relativo: pueden modificar un antecedente expreso; también existen relativas libres sin antecedente expreso. Analiza la función del relativo dentro de su oración y distingue, cuando corresponda, especificativas y explicativas. Adverbiales propias: lugar, tiempo y modo (conmutables por «allí», «entonces», «así»). Impropias: causales, finales, condicionales, concesivas, consecutivas y comparativas.

Valores de «se» y perífrasis

«Se» puede ser reflexivo, recíproco, pasiva refleja (verbo en tercera persona con sujeto paciente: «Se venden pisos»), impersonal (sin sujeto, con verbos intransitivos o con persona: «Se vive bien aquí»), uso aspectual o concordado («Se comió el pastel»), distinto del dativo ético o marca de verbo pronominal. Las perífrasis son modales (obligación, probabilidad) o aspectuales (ingresiva, incoativa, durativa, reiterativa, terminativa).

Ejemplo razonado

«Le pidieron que cerrara la puerta enseguida». Oración compuesta por subordinación. «Le» es CI (→ «Le pidieron eso»). La subordinada «que cerrara la puerta enseguida» conmuta por «lo»: «Lo pidieron»; por tanto es sustantiva de CD. Dentro de ella, «la puerta» es CD y «enseguida» CC de tiempo. El error habitual es llamarla adverbial por empezar con «que».

Errores que restan

• Identificar la subordinada sin decir qué función cumple respecto de la principal.
• Confundir «que» conjunción con «que» relativo (comprueba si hay antecedente).
• Llamar CD a un CI por el leísmo, o al revés.
• Confundir pasiva refleja con impersonal: busca el sujeto y la concordancia.
• Definir el léxico sin contexto: «sinónimo» exige comprobar la equivalencia en la oración.

Mathematical foundations: algebra, functions, ratios and data

Algebra, functions, equations and data in explicit models

Algebraic Operations

What this domain tests

The Algebraic operations domain tests whether you can rewrite expressions accurately and recognize structure before calculating. The subject methods include polynomial arithmetic, factoring, rational expressions, exponent laws, radicals, and complex numbers. Most errors come from illegal cancellation or from ignoring restrictions on variables.

Polynomials and factoring

• Add and subtract by combining like terms; multiply each term of one polynomial by each term of the other. For nonzero polynomials over the real numbers, the degree of their product is the sum of their degrees.
• Memorize special products: $(a\pm b)^2=a^2\pm 2 ab+b^2$, $(a+b)(a-b)=a^2-b^2$, and $a^3\pm b^3=(a\pm b)(a^2\mp ab+b^2)$.
• Factoring strategy: greatest common factor first, then grouping, difference of squares, sum or difference of cubes, or trinomial trial. State the coefficient domain: a factorization over integers need not be complete over the real or complex numbers.

Rational expressions and exponents

• Cancel factors, never terms: $\frac{x+2}{2}$ cannot become $x+1$.
• For $x^{m/n}$, take the $n$th root and raise to the $m$; negative exponents move the factor across the fraction bar.
• State excluded values where a denominator is zero before simplifying. Simplifying does not restore them.

Radicals and complex numbers

• Simplify radicals by extracting perfect-power factors; rationalize denominators using conjugates.
• Since $i^2=-1$, add and subtract complex numbers componentwise, multiply as binomials and replace $i^2$, and divide by multiplying numerator and denominator by the conjugate.

Worked example

Simplify $\frac{x^2-4}{x^2-x-6}\cdot\frac{x^2-9}{x+2}$ and list restrictions.

Factor: $\frac{(x-2)(x+2)}{(x-3)(x+2)}\cdot\frac{(x-3)(x+3)}{x+2}$. Before canceling, note $x\ne 3$ and $x\ne-2$. Canceling $(x+2)$ and $(x-3)$ leaves $\frac{(x-2)(x+3)}{x+2}$, with $x\ne 3,-2$. Check $x=0$: the original equals $\left(\frac{-4}{-6}\right)\left(\frac{-9}{2}\right)=-3$, and the simplified expression equals $\frac{(-2)(3)}{2}=-3$.

Traps that cost marks

• Writing $(a+b)^2=a^2+b^2$ and omitting the middle term $2 ab$.
• Canceling a term shared by numerator and denominator rather than a common factor.
• Forgetting that a simplified rational expression keeps the original domain restrictions.
• Applying a negative exponent only to the coefficient, as in treating $(2 x)^{-2}$ as $2 x^{-2}$.

Equations and Inequalities

What this domain tests

The Equations and inequalities domain tests solving and interpreting solution sets: linear and quadratic equations, rational and radical equations, absolute value, systems, and inequalities. These exercises combine both algebraic solutions and correct interval notation, including excluded values.

Linear equations and systems

• Solve linear equations by applying inverse operations to both sides. An identity is true for all values; a contradiction has no solution.
• For systems, substitution or elimination gives an ordered pair. Parallel distinct lines produce no solution; the same line produces infinitely many solutions. Always check the ordered pair in both original equations.

Quadratic equations

• Write in standard form $ax^2+bx+c=0$. Use factoring and the zero product property, the square root property, completing the square, or the quadratic formula.
• The discriminant $b^2-4 ac$ determines the type of roots: positive gives two distinct real roots, zero gives one repeated real root, and negative gives two complex conjugate roots.
• For $ax^2+bx+c=0$, the sum of roots is $-b/a$ and the product is $c/a$.

Inequalities and absolute value

• Multiplying or dividing an inequality by a negative number reverses its direction.
• For $k>0$, $|X|<k$ means write $-k<X<k$; and for $k>0$, $|X|>k$ means write $X<-k$ or $X>k$.
• For rational inequalities, find critical values from numerator and denominator, test intervals on a sign chart, and exclude zeros of the denominator. Use a bracket at a numerator zero only if the inequality allows equality and the expression is defined there.

Radical and rational equations

• Squaring both sides can introduce extraneous solutions, so every candidate must be checked in the original equation.

Worked example

Solve $\sqrt{2 x+3}=x$.

Square both sides: $2 x+3=x^2$, so $x^2-2 x-3=0$, which factors as $(x-3)(x+1)=0$. Candidates are $x=3$ and $x=-1$. Check $x=3$: $\sqrt{9}=3$, valid. Check $x=-1$: $\sqrt{1}=1$, but the right side is $-1$, so it is extraneous. The solution set is ${3}$. Squaring erased the sign information that the check restores.

Traps that cost marks

• Forgetting to reverse an inequality after multiplying or dividing by a negative.
• Using a closed interval at a value that makes a denominator zero.
• Dividing both sides by a variable and losing the solution where that variable equals zero.
• Skipping the check after squaring a radical equation.

Functions and Their Properties

What this domain tests

The Functions and their properties domain tests the function concept across algebraic and graphical representations: notation, domain and range, composition, inverses, transformations, and basic behavior of parent functions. Useful practice includes questions that combine two ideas, such as finding the domain of a composition.

Domain and range

• The domain is the set of allowed inputs. Exclude values that make a denominator zero and, for even roots, values that make the radicand negative.
• The range is the set of outputs. Use the graph, vertex, asymptotes, or end behavior to determine it.
• Express domains and ranges in interval notation, using parentheses at excluded values and infinities.

Composition and inverses

• $(f\circ g)(x)=f(g(x))$. Its domain requires $x$ in the domain of $g$ and $g(x)$ in the domain of $f$.
• An inverse exists only for a one-to-one function; the horizontal line test detects whether each output has a unique input.
• To find an inverse, swap $x$ and $y$ and solve for $y$. The domain and range of $f$ and $f^{-1}$ interchange, and $f(f^{-1}(x))=x$ on the appropriate domain.

Transformations and parent graphs

• $y=f(x-h)+k$ shifts the graph $h$ units right and $k$ units up.
• $y=af(x)$ stretches vertically when $|a|>1$ and compresses when $0<|a|<1$; negative $a$ reflects across the $x$-axis.
• $y=f(-x)$ reflects across the $y$-axis. Apply transformations in a consistent order, handling horizontal shifts and scalings inside the argument carefully.

Worked example

Find the inverse of $f(x)=\frac{2 x+1}{x-3}$.

Write $y=\frac{2 x+1}{x-3}$ and swap: $x=\frac{2 y+1}{y-3}$. Multiply: $x(y-3)=2 y+1$, so $xy-3 x=2 y+1$. Collect $y$ terms: $xy-2 y=3 x+1$, hence $y(x-2)=3 x+1$ and $y=\frac{3 x+1}{x-2}$. Thus $f^{-1}(x)=\frac{3 x+1}{x-2}$, with $x\ne 2$. The original function excludes $x=3$ from its domain, and its inverse excludes $x=2$ from its domain, matching the range restriction.

Traps that cost marks

• Assuming $f(g(x))=g(f(x))$; composition is generally not commutative.
• Ignoring the inner function's domain when finding the domain of a composition.
• Reading $f^{-1}(x)$ as $1/f(x)$ rather than as inverse notation.
• Confusing horizontal and vertical line tests, or shifting a graph in the wrong direction.

Algebra, functions and data in stated models

Translate a numerical story into a model before manipulating symbols. Identify the variable and its unit, the fixed quantities, and any restrictions such as whole-number counts or nonnegative time. A fixed joining fee plus a monthly charge has the formC=b+mx. The intercept represents the initial charge and the slope the change per additional month in that stated model. A line may fit a classroom example without describing every real membership contract or every future observation.

For an inequality, interpret the boundary phrase carefully. At least includes the threshold and gives a greater-than-or-equal relation; at most includes it with a less-than-or-equal relation. Check a candidate in the original story after solving. A negative number of tickets may solve an algebraic equation but fail the count restriction. For two equations, a common solution must satisfy both; parallel distinct lines do not share a point, while two forms of the same line describe one common set.

Functions assign each permitted input exactly one output. Their tables, graphs, formulas and verbal descriptions emphasize different properties. Distinguish an input restriction from an output range, an intercept from a rate of change, and a zero from a point where the function is undefined. In a quadratic model, identify what the vertex represents and whether it lies in the allowed domain. A mathematical vertex outside a supplied time interval need not be an attainable physical maximum.

Data questions add another layer of interpretation. Compute the mean from sum divided by count; use the ordered middle observation or pair for the median. An extreme observation can affect the mean differently from the median. Compare a spread measure when two groups have the same center, and check whether a graph changes its scale or begins above zero. A scatterplot association can suggest a pattern without proving that one variable causes the other. The sample, method and possible confounding variables matter.

For example, a fee modelC=40+25 m with budget 215 gives 40+25 m<=215, hence m<=7. If months must be nonnegative whole numbers, the permitted counts are 0 through 7. The original inequality and 25 m<=175 describe the same feasible set; a question claiming they are different answers would be defective. This check illustrates why equivalent algebraic forms and units must be evaluated before accepting a proposed multiple-choice key.

Biological foundations: cells, molecules, inheritance and evidence

Module 2: Biomolecules - Water, Carbohydrates, Lipids, Proteins and Enzymes

Biochemistry relates water, carbohydrates, lipids and proteins to biological functions. Interpret structure, chemical bonds and supplied observations. This is shared conceptual practice rather than a claim about an official module or paper.

Water

Water is dipolar, so it forms hydrogen bonds: high specific heat capacity and high latent heat of vaporisation (thermal stability, cooling by sweating), cohesion and surface tension (xylem transport), a good solvent for ions and polar molecules, and ice floating because it is less dense than liquid water.

Carbohydrates and lipids

Monosaccharides (trioses to hexoses; α- and β-glucose differ only in the position of the –OH on carbon 1) join by condensation, forming glycosidic bonds, to give disaccharides (maltose, sucrose, lactose) and polysaccharides. Starch (amylose helix plus branched amylopectin) stores energy in plants, glycogen is more branched for animals, cellulose is unbranched β-1,4 chains held by hydrogen bonds into microfibrils for strength. Reducing sugars (all monosaccharides, maltose, lactose) reduce Benedict's solution; sucrose is non-reducing. Triglycerides form by condensation of glycerol with three fatty acids into ester bonds; saturated chains pack tightly, cis-unsaturated chains commonly kink and reduce close packing; trans configurations behave differently. Phospholipids are amphipathic and build bilayers.

Proteins and enzymes

Amino acids join through peptide bonds. Protein primary structure is sequence; secondary alpha-helices and beta-sheets involve backbone hydrogen bonding; tertiary structure depends on several interactions and quaternary structure joins subunits. Fibrous and globular describe broad structural patterns rather than universally separate functions. Most enzymes are proteins, while some RNA molecules also catalyze reactions. Catalysts lower an activation barrier without changing the reaction equilibrium. Rate depends on temperature, substrate, enzyme amount and assay conditions. High temperature can destabilize a protein; pH can change protonation and binding without necessarily causing unfolding. Denaturation usually disrupts the folded state rather than cleaving every peptide bond. In a simple reversible competitive model apparent Km increases while Vmax is unchanged. In a pure noncompetitive model Vmax decreases while Km is unchanged. Those kinetic patterns do not uniquely identify an atomic binding pocket. Cofactors can support catalytic activity.

Worked example

A supplied food-test dataset reports no reducing-sugar signal from sucrose before hydrolysis and a positive signal afterward, with suitable positive and negative controls. Hydrolysis can release glucose and fructose, explaining the changed observation. Interpret the recorded chemistry rather than treating this paragraph as an operating procedure. Appropriate assay conditions and controls matter: a negative result can reflect a failed assay as well as absence of the target compound.

Traps that cost marks

Avoid calling every polysaccharide reducing, confusing alpha- and beta-glucose linkages, or treating enzymes as organisms that are killed. A declining measured rate can reflect substrate depletion, pH effects, inhibition or instability; inspect the supplied conditions before assigning a cause. A typical glycerophospholipid has two fatty-acid tails and a phosphate-containing head, unlike a triacylglycerol with three fatty acids.

Module 1: Cell Biology - Ultrastructure, Membranes and Cell Division

Cell biology links organelle structure with function, membrane exchange and cell division. This chapter reviews shared foundations and interprets supplied water-potential data. It does not assert a target paper structure or marking scheme.

Organelles: structure fits function

Prokaryotic cells lack a membrane-bound nucleus. Bacteria commonly have a nucleoid, 70S ribosomes and a peptidoglycan wall, but wall-less bacteria exist; archaeal walls do not contain peptidoglycan. Plasmids and flagella occur in some cells, not all. Eukaryotes compartmentalise functions: nucleus with chromatin and nucleolus; mitochondria with inner membrane and matrix; chloroplasts with thylakoids and stroma in photosynthetic cells; rough and smooth ER; Golgi apparatus and ribosomes. A typical plant cell additionally has a cellulose wall and a large vacuole. A structure should be identified by its actual features rather than assuming every member has every listed organelle.

Membranes and transport

The fluid mosaic model describes a lipid bilayer with proteins and, in suitable cells, sterols, glycoproteins and glycolipids. Cholesterol is characteristic of many animal membranes; sterol composition differs among organisms. Simple diffusion moves suitable molecules down a chemical gradient. Osmosis is net water movement down water potential across a selectively permeable membrane. Facilitated diffusion uses proteins without direct ATP hydrolysis; carrier-mediated flux can saturate. Primary active transport can use ATP directly, while secondary transport uses an electrochemical gradient maintained by another energy-dependent process. The mammalian sodium-potassium pump moves three sodium ions out and two potassium ions in per ATP in its ordinary cycle. Sodium-coupled glucose uptake illustrates secondary transport. Vesicular transport uses energy. Surface area, diffusion distance, gradients and permeability together influence exchange.

Mitosis and the cell cycle

Interphase: G1 growth, S DNA replication, G2 organelle replication. Prophase - chromosomes condense, spindle forms, nuclear envelope breaks down. Metaphase: spindle microtubules attach through kinetochores at centromeric regions and chromosomes align at the equator. Anaphase - centromeres divide and sister chromatids move to opposite poles. Telophase - nuclei reform and chromosomes decondense. Cytokinesis is by cleavage furrow in animals, cell plate in plants. Mitosis maintains genetic constancy for growth, repair and asexual reproduction.

Worked example

A plant cell has solute potential -1200 kPa and pressure potential +400 kPa, giving water potential -800 kPa. In an external solution at -900 kPa, initial net water movement is out because -800 is higher than -900. As water leaves, pressure and solute concentration can change. The initial comparison does not prove complete plasmolysis: a new equilibrium may retain positive pressure. Distinguish a direction predicted by initial potentials from a final cellular condition that requires further information.

Traps that cost marks

Common errors include adding potentials with inconsistent signs, describing osmosis without comparing water potentials, and confusing centromeres with centrioles. Mitosis normally preserves the starting chromosome complement; it does not automatically turn every cell into a haploid or diploid product. DNA replication precedes chromosome separation. Specify whether an active transport step uses ATP directly or a pre-existing electrochemical gradient.

Module 3: Genetics - DNA, Gene Expression, Meiosis and Inheritance

Genetics traces the storage, replication and expression of information, chromosome behavior and inheritance probabilities. Use explicit organism, ploidy and dominance assumptions. Shared practice does not establish a current official module or paper format.

DNA structure and replication

Nucleotides: deoxyribose, phosphate, and a base - purines adenine and guanine, pyrimidines thymine and cytosine. Nucleotides link 3′–5′ by phosphodiester bonds into two antiparallel strands; A pairs with T by two hydrogen bonds, G with C by three. Replication is semi-conservative: helicase unwinds, each strand acts as a template, DNA polymerase adds nucleotides 5′→3′, the leading strand is continuous while the lagging strand forms Okazaki fragments joined by ligase. Meselson–Stahl's density-gradient experiment supports this.

Gene expression

The code is a triplet, degenerate, non-overlapping and (nearly) universal, with AUG the usual start and UAA/UAG/UGA stop codons in the standard code; alternative initiation and code exceptions exist. Transcription: RNA polymerase makes mRNA from the template strand; eukaryotic mRNA is spliced to remove introns. Translation: mRNA binds a ribosome, tRNA anticodons pair with codons, peptide bonds form between amino acids, and the polypeptide is released at a stop codon.

Meiosis and inheritance

Meiosis I separates homologous chromosomes and meiosis II separates sister chromatids. A standard diploid-cell model gives four haploid products, though not all become equivalent functional gametes. Crossing over and independent assortment can create variation. An Aa by Aa cross gives a 3:1 phenotype expectation only with complete dominance and suitable viability assumptions. Aa by aa gives a 1:1 expectation; AA by aa does not. Codominance and multiple alleles require different genotype-to-phenotype rules. In a conventional XY model, an X-linked locus can be hemizygous in males; sex-determination systems differ among organisms. A 9:3:3:1 expectation requires an AaBb by AaBb cross, independent assortment, complete dominance at both loci and the stated viability model. Nearby linked loci often yield excess parental combinations in an informative test cross.

Worked example

A supplied informative fly test cross gives 41 grey-normal, 39 ebony-vestigial, 10 grey-vestigial and 9 ebony-normal offspring. Under the stated parental-phase and viability assumptions, the parental total is 80 and recombinant total 19, suggesting linkage rather than a 1:1:1:1 model. The observed recombinant frequency is 19/99, about 19.2 percent. Treating this percentage as a map distance is a short-interval approximation; undetected multiple crossovers can make actual genetic distance larger. The observation estimates a frequency, not a universally exact physical distance or an assumption-free genetic map.

Traps that cost marks

Confusing the template strand with the coding strand. Saying DNA polymerase works 3′→5′. Giving genotype ratios where gamete or phenotype ratios are asked. Using a test cross with anything other than a homozygous recessive. Assuming independent assortment for linked genes. Forgetting that crossing over occurs in prophase I, not anaphase.

Metabolismo celular: catabolismo y anabolismo, respiración, fotosíntesis, enzimas

Esta revisión relaciona rutas metabólicas, compartimentos celulares, transferencia de electrones y modelos enzimáticos. Los balances se interpretan con los supuestos indicados, sin atribuir un número fijo universal de ATP ni una estructura oficial de examen.

Enzimas

Las enzimas reducen la barrera de activación. Vmax depende de la cantidad de enzima en el modelo; Km es un parámetro cinético y no equivale universalmente a una constante de afinidad. En el modelo competitivo reversible sencillo aumenta Km aparente sin cambiar Vmax. En el modelo no competitivo puro disminuye Vmax sin cambiar Km. Un patrón cinético no demuestra por sí solo una localización de unión; la regulación alostérica puede producir varios patrones. También existen modificación covalente y retroinhibición.

Catabolismo

Glucólisis en el citosol: glucosa → 2 piruvato, 2 ATP netos y 2 NADH. El piruvato se descarboxila a acetil-CoA (2 NADH). Ciclo de Krebs: dos vueltas por glucosa, con 6 NADH, 2 FADH₂, 2 ATP y CO₂. Cadena respiratoria en la membrana interna y quimiosmosis: el gradiente de protones mueve la ATP sintasa y el aceptor final es el O₂, que forma agua. Algunos modelos modernos aproximan 2,5 ATP por NADH y 1,5 por FADH2 en condiciones eucariotas determinadas. El rendimiento real depende del acoplamiento, las lanzaderas y otros costes; los valores 3 y 2 pertenecen a una contabilidad histórica y no son universales.

Anabolismo

Fotosíntesis: fase luminosa en tilacoides, con fotólisis del agua (origen del O₂), transporte de electrones por los fotosistemas II y I y fotofosforilación, que producen ATP y NADPH. Fase oscura o ciclo de Calvin en el estroma: fijación por la RuBisCO, reducción y regeneración de la ribulosa-1,5-bifosfato, consumiendo ATP y NADPH. Quimiosíntesis: bacterias que oxidan compuestos inorgánicos para reducir CO₂.

Ejemplo resuelto

Un conjunto de datos suministrado presenta la misma Vmax y una Km aparente diez veces mayor con inhibidor. En el modelo reversible sencillo es compatible con competencia y predice que aumentar sustrato reduce el efecto. No demuestra que el inhibidor ocupe un bolsillo atómico idéntico. Una Vmax menor podría corresponder a inhibición mixta u otros cambios, no solo a no competitiva pura. La falta de recuperación después de un lavado tampoco prueba por sí sola irreversibilidad: deben considerarse el tiempo, la eliminación incompleta y la estabilidad de la enzima.

Errores que cuestan puntos

Colocar la glucólisis en la mitocondria, olvidar que el O₂ liberado procede del agua y no del CO₂, confundir el ciclo de Calvin con el de Krebs, contar ATP brutos en vez de netos en la glucólisis y creer que la fermentación produce ATP en grandes cantidades (la reducción fermentativa regenera NAD+ y permite continuar la glucólisis, donde se obtiene ATP por fosforilación a nivel de sustrato).

Scientific Inquiry, Methodology, and the Nature of Science

Experimental Reasoning

Items here ask you to design, critique, and interpret investigations, and to tell scientific claims apart from pseudoscientific ones. The content is process and reasoning, not vocabulary recall.

Core rules and concepts

• A hypothesis is a testable, falsifiable statement about a relationship; a theory is a broad, repeatedly supported explanatory framework (cell theory, evolution by natural selection); a law states a consistent regularity, often mathematically. Science supports or fails to support claims - it does not "prove" them.
• The independent variable is manipulated by the researcher; the dependent variable is measured; controlled variables are held constant; the control group receives no treatment, a placebo, or a baseline condition.
• Random assignment can reduce systematic allocation bias and supports causal inference in a well-designed experiment. Observational association alone does not establish causation; additional design, assumptions and evidence are needed for causal interpretation.
• Accuracy is closeness to the true value; precision is reproducibility. Random error degrades precision; systematic error (miscalibrated instrument, biased thermometer) degrades accuracy.
• Replication and adequate sample size reduce the chance that a result reflects random variation; descriptive statistics (mean, standard deviation) summarize data, while inferential statistics (t-test, chi-square) test hypotheses.
• Deduction moves from a general principle to a specific prediction; induction builds general patterns from specific observations.

Worked example

A student counts oxygen bubbles released per minute by Elodea at five distances from a lamp and concludes that light intensity drives photosynthesis. Distance is the independent variable; bubble rate is the dependent variable. Controls that must be held constant include water temperature, dissolved CO₂ (bicarbonate concentration), plant mass, and counting interval. The design has a confound: an incandescent lamp also heats the water, so temperature, not light, could explain the trend. Fixing it requires a heat filter or water bath, plus independently replicated observations and a justified sample-size choice, reporting variation alongside means. Three replicates can illustrate a calculation but are not a universal guarantee of sufficient power. Even then the defensible conclusion is that light intensity is associated with increased photosynthetic rate in this system - a claim about a sample, not proof of a universal law.

Traps that cost marks

Calling a hypothesis a theory, or saying a result "proves" a hypothesis. Confusing the control group with controlled variables. Accepting causation from correlation. Ignoring a confound such as temperature, pH, or time of day. Treating a single trial as evidence. Forgetting that the sample must be representative before results are generalized.

Microbiología, inmunología y biotecnología: virus, bacterias, respuesta inmunitaria, aplicaciones biotecnológicas

Esta revisión relaciona estructura microbiana, defensa inmunitaria y métodos de análisis de ADN. Se interpretan modelos celulares y datos suministrados; no se ofrecen diagnósticos, dosis, decisiones de tratamiento ni normas sanitarias extranjeras.

Virus y bacterias

Los virus son entidades acelulares con genoma de ADN o ARN, cápside y, en algunos casos, envuelta. Los ciclos lítico y lisogénico describen determinados bacteriófagos, no todos los virus. Los retrovirus utilizan transcripción inversa y pueden integrar ADN viral. Muchas bacterias poseen pared de peptidoglicano, pero existen bacterias sin pared; plásmidos, flagelos y endosporas no son universales. La estructura de una bacteria concreta debe leerse en los datos. Conjugación, transformación y transducción son mecanismos distintos de transferencia genética horizontal.

Inmunidad

Innata: barreras, pH, complemento, fagocitos, células NK e inflamación; reconoce patrones mediante receptores y no utiliza la memoria clonal clásica de linfocitos B y T; la inmunidad entrenada evita reducirla a una ausencia absoluta de memoria. Adaptativa: linfocitos B → células plasmáticas → anticuerpos (IgG, IgM, IgA, IgE, IgD); los linfocitos T auxiliares CD4 reconocen antígeno en MHC II y activan a B y a CD8; los T citotóxicos CD8 destruyen células infectadas presentadas por MHC I. Selección clonal, memoria y respuesta secundaria más rápida y con mayor título, sobre todo de IgG.

Biotecnología

Las enzimas de restricción reconocen secuencias determinadas y pueden producir extremos cohesivos o romos; no todas las enzimas reconocen el mismo tipo de secuencia. Las ligasas unen enlaces del esqueleto del ADN. Los vectores permiten estudiar secuencias introducidas en sistemas adecuados. PCR, electroforesis y secuenciación responden preguntas diferentes: amplificación de una región, comparación de fragmentos y orden de bases. En una comparación convencional de ADN lineal en el mismo gel, los fragmentos pequeños suelen migrar más lejos; la conformación y el sistema importan. Una banda no demuestra por sí sola identidad de secuencia ni expresión funcional. La ingeniería genética requiere comprobar tanto el cambio previsto como su efecto en el modelo estudiado.

Ejemplo resuelto

Partimos de una sola molécula de ADN y aplicamos PCR. En el modelo ideal de duplicación perfecta, tras 5 ciclos el número sería 2^5 = 32 y tras 20 ciclos aproximadamente 1,05 millones. El razonamiento es multiplicativo porque cada ciclo duplica cada molécula, hasta que la fase exponencial se satura al agotarse cebadores o dNTP. Si la muestra inicial tuviera 10 moléculas, tras 5 ciclos habría 320 copias.

Errores que cuestan puntos

Afirmar que los antibióticos matan virus, olvidar que los virus solo se replican dentro de una célula, tratar IgM e IgG como un diagnóstico binario de fase: una respuesta secundaria sistémica suele mostrar aumento de anticuerpos de alta afinidad, pero el isotipo depende del contexto y creer que los linfocitos T producen anticuerpos.

Biotechnology: interpreting DNA evidence and model controls

Biotechnology questions should distinguish what a method measures from what an investigator hopes to infer. A DNA sequence, an amplified fragment, a gene-expression estimate and a phenotype are different forms of evidence. A method can be useful without answering every biological question about the organism from which a sample came.

PCR amplifies a selected DNA region using template-dependent DNA synthesis. At a conceptual level, strands separate, primers associate with complementary regions, and a polymerase extends new DNA. A useful ideal counting model assumes every starting target molecule doubles in each cycle: N equals N0 times two to the power n. Twenty starting target copies after four perfectly efficient cycles would give 320 copies. This arithmetic is a supplied idealization; real amplification efficiency, reagent depletion and detection limits prevent unlimited exact doubling. No particular operating temperatures, primer sequences or experimental protocol are implied by this conceptual description.

Controls separate possible explanations. A no-template control checks whether a signal can appear without the intended template, for example through contamination. A known positive control checks that the detection process can work. A separate extraction control may reveal losses or inhibition introduced before amplification. A failed control changes which conclusions are defensible; it cannot be repaired by simply calling every unexpected band a new biological discovery.

Gel electrophoresis separates molecules according to their behavior in a defined matrix and electric field. Under a conventional comparison of linear double-stranded DNA fragments, smaller fragments generally travel farther through the same gel. A size marker helps estimate fragment length. Equal apparent band lengths do not establish identical sequences, and band brightness is not automatically an exact count unless the measurement has been calibrated. Molecular conformation and the experimental system can alter migration.

Sequencing identifies nucleotide order, while a gene-expression measurement concerns RNA or its derived signal. Reverse transcription can convert RNA into a DNA form for subsequent analysis; amplifying genomic DNA alone does not show that a gene was actively expressed. Interpretation requires specifying the sampled material and comparison conditions.

Genetic engineering changes DNA, potentially by adding, deleting or altering sequences. A sequence change does not guarantee a particular phenotype: regulation, gene interactions and environmental conditions matter. Verification therefore connects the intended genetic change with suitable expression and phenotype evidence. In school practice, use supplied harmless model datasets and distinguish a proposed explanation from a demonstrated mechanism.

Formal reasoning from explicit premises

Formal reasoning from explicit premises

A reasoning question supplies a model, not necessarily a report of how the real world works. Identify its stated premises and the exact conclusion before applying background knowledge. If a passage says every member of group A belongs to B, it establishes inclusion in that direction. It does not establish that every member of B belongs to A. A diagram or small counterexample can help keep the direction clear.

Quantifiers and existence

All, some and none make different claims. All engineers use a specified tool and no user of that tool lacks a stated skill together imply that no engineer lacks that skill, within the supplied model. However, all A are B and some B are C do not by themselves imply that some A are C. The B members in C may lie outside A. A universal statement does not always establish that its subject class has a member, so do not silently turn all into some.

Conditions and alternatives

If P then Q makes P sufficient for Q and Q necessary for P in the stated implication. It does not prove the converse. If the model says an event moves indoors if rain continues, an indoor event is not proof of rain: there may be another reason. A valid contrapositive is if not Q then not P. Keep and, or, only if and unless distinct, and state any interpretation needed for an ambiguous everyday use of or. Do not invent a condition that the text has not supplied.

Cases and counterexamples

For a must-follow question, try to construct a permitted case where the proposed conclusion is false. One such case refutes necessity. For a possibility question, one coherent case can establish consistency, but it does not establish that the outcome must happen. In a number pattern, explain the intended simple rule and verify every supplied pair; do not claim a finite list has only one unrestricted mathematical continuation.

Explain the inferential step

Write the premises, the relation used and the conclusion in a short chain. A persuasive story or familiar technical setting cannot replace that chain. When a passage quotes a fictional policy, use it only for the reasoning exercise and never transfer it into a real legal, clinical, laboratory or professional procedure. If essential information is absent, identify the missing link. Clear reasoning includes knowing when the evidence supports a limited conclusion and when it does not determine one.

Social evidence, institutions and collaborative problem solving

Social evidence, institutions and collaborative problem solving

Social questions combine information about people, institutions and collective choices. Begin by identifying what the source actually supplies: a survey, a historical account, a legal extract, a map, an economic model or an opinion. These sources answer different kinds of questions. A description of a fictional community is not a current national statistic, and a passage about one institution does not establish the rules of another country.

Read a social claim carefully

Separate a factual claim, a value judgment and a proposed explanation. A statement that attendance decreased is different from a claim that participants are irresponsible or that a new timetable caused the decrease. Define what was measured, over what period and among whom. In a survey, identify the population and sample, the question wording, the response count and the missing observations. A percentage alone may conceal a small or selected sample.

Use comparisons with appropriate limits

Compare like quantities using the same units, definitions and time period. A change in recorded cases may reflect reporting, classification or access rather than a change of the same size in the underlying activity. Maps require a legend, scale and defined geographic boundary. A historical sequence can establish that one event preceded another without proving that it was the only cause. Consider competing explanations and distinguish the evidence for each.

Institutions and primary records

Identify an institution's documented role before assigning it a power or responsibility. Current membership counts, officeholders, eligibility, legal procedures and public-program conditions require current primary records. They are not inferred from a familiar organization name. In this independent foundation material, unverified Honduran statutory, agency and current political details remain open rather than being replaced with another country's law. A supplied excerpt can be analyzed on its own terms without claiming that it reproduces the whole current legal framework.

Collaborative decisions

State the shared problem in observable terms, invite relevant evidence, identify alternatives and compare them against explicit criteria. Record decisions and responsibilities without turning a disagreement into an unsupported claim about another person's motive. A small trial can test an explanation before a large change is adopted. Revisit the result and explain what remains uncertain. These methods support social analysis and teamwork; they do not certify a complete national syllabus, a legal interpretation or a measured personal trait from one recognition question.