EDIEMS Diagnostic Evaluation Guide for Higher Secondary Education

Study Guide Structure and Methodology

The Study Guide for Diagnostic Evaluation at the Entrance of Higher Secondary Education (EDIEMS) is a comprehensive document designed by the Academic Sector Coordination (COSAC) under the Undersecretary of Higher Secondary Education (SEMS) in Mexico. It is intended to reinforce basic middle school learning, recover previous knowledge, and strengthen content essential for the transition to the upper secondary level. The guide is organized into sessions within specific formative fields. Each session concludes with essential content reviews, exercises, and questionnaires to verify learning. These sections are distinguished by visual icons: one representing evaluation questions to corroborate learning and another for recommended resources and additional materials for deeper study.

Students are encouraged to follow a specific eight-step methodology for the best use of this manual. This includes performing an exploratory reading, identifying each section, planning study and review sessions, determining specific study times and locations, having supporting materials on hand, ensuring comprehension of contents, taking brief breaks after every hour of study, and consulting teaching personnel at their respective institutions when doubts arise.

Natural Sciences: Matter and Its Corpuscular Model

Matter is defined as anything that has mass and volume, occupying a specific place in space. This essentially encompasses everything in the environment, from the human body to the oxygen in the air. The Corpuscular Model of Matter, or the particle model, postulates that all matter consists of extremely small particles—atoms, molecules, or ions—that are in constant motion. This model is vital for understanding the microscopic differences between elements, compounds, and mixtures.

Elements are pure substances represented by chemical symbols, usually consisting of one or two letters (the first always capitalized). The names of elements have diverse origins, such as Latin (Aurum for Gold, yielding its symbol $Au$), Greek (Cuprum for Copper, yielding its symbol $Cu$), Arabic (Kalium for Potassium, yielding its symbol $K$), or derived from geographical locations or names of famous scientists. Elements can exist in different states: solids (copper, gold), liquids (mercury, bromine), and gases (oxygen, nitrogen).

Compounds are pure substances constituted by more than one class of atoms chemically combined. They are represented by chemical formulas which indicate the symbols of the constituent elements and the quantity of their particles. For example, Water ($H_{2}O$) contains 2 hydrogen atoms and 1 oxygen atom. Compounds are classified by the number of elements: binary (two), ternary (three), or quaternary (four), and by type: organic or inorganic. Other examples include Sodium Chloride ($NaCl$), Sulfuric Acid ($H_{2}SO_{4}$), and Calcium Hydroxide ($Ca(OH)_{2}$).

Mixtures consist of the union of substances in variable quantities without being chemically combined, meaning each constituent retains its specific properties. Mixtures comprise a dispersant phase (the medium) and a dispersed phase (the substance in lesser proportion). Based on the size of the dispersed particles, mixtures are classified as homogeneous (uniform appearance, like air or soft drinks) or heterogeneous (visible phases, like salad, water with sand, or mud).

Properties of Matter

The characteristics used to identify and distinguish forms of matter are classified into extensive and intensive properties. Extensive properties depend on the amount of matter present. Significant examples include Mass, which is the amount of matter in a given space measured in kilograms ($kg$) and is an invariable property regardless of location (e.g., 1 kg of iron has the same mass on Earth as on Mars). Weight ($P$) is the measure of the gravitational force acting on a body and is proportional to mass; unlike mass, it varies by location (e.g., an object weighs less on the Moon than on Earth). The formula for weight is $P = m \times g$, where $g$ is the acceleration of gravity ($9.8\,m/s^{2}$). Volume refers to the space occupied by a body in any physical state, with the base unit being the cubic meter ($m^{3}$).

Intensive properties do not depend on the amount of matter but rather on its nature, making them useful for identifying substances. Density ($\rho$) relates mass to volume and remains constant for pure substances regardless of the sample size, though it can be affected by pressure and temperature. The formula is $\rho = \frac{m}{V}$. Temperature is the property determining the direction of heat flow, which always moves spontaneously from a body of higher temperature to one of lower temperature. The Boiling Point is the temperature at which a liquid becomes a gas, while the Fusion Point is the temperature at which a solid becomes a liquid.

The Periodic Table of Elements

The Periodic Table records the evolution of elemental classification, starting in 1789 with Antoine Lavoisier, who defined chemical elements and categorized them as metals, non-metals, gases, and rare earths. In 1829, Johann Dbereiner proposed the Law of Triads, showing relationships between atomic weights and properties. Dmitri Mendeléyev published a pivotal table in 1869 organizing 63 known elements by atomic mass and predicted the properties of undiscovered elements. In 1915, Henry Moseley consolidated the modern table by discovering the concept of the atomic number based on X-ray spectroscopy. Finally, John Newlands contributed the Law of Octaves, noting properties repeated every eight elements.

Modern elements are organized by atomic number ($Z$), representing the number of protons in the nucleus and defining the element's identity. The table consists of 7 horizontal rows called periods (indicating energy levels) and 18 vertical columns called groups (indicating similar chemical properties due to valence electron configurations). Significant families include Alkali Metals (Group 1), Alkaline Earth Metals (Group 2), Halogens (Group 17), and Noble Gases (Group 18). Transition Elements occupy groups 3 to 12 (Block B). Atomic Mass ($A$) is the total mass of an atom (protons plus neutrons), measured in Atomic Mass Units ($uma$) or Daltons ($Da$), where $1\,uma = 1.66 \times 10^{-24}\,g$. Valence is determined by the electrons in the outermost layer, which are used to form chemical bonds.

The Bohr Atomic Model and Configuration

In 1913, Niels Bohr proposed that electrons rotate in defined circular orbits called energy levels. Each level is at a fixed distance from the nucleus and has a specific maximum electron capacity determined by the formula $2n^{2}$, where $n$ is the level number (1 or K, 2 or L, 3 or M, etc.). Level 1 (K) holds 2 electrons; level 2 (L) holds 8; level 3 (M) holds 18; and level 4 (N) can hold 32. Electrons absorb energy to jump to a higher level and emit energy to jump to a lower one. In the fundamental state, electrons are at their lowest possible energy level. The Bohr model, often called the planetary model, explains the stability of matter and atomic spectra.

Bohr's postulates state that electrons orbit without radiating energy and only in orbits where the angular momentum is a multiple of Planck's constant ($h$). To calculate subatomic particles, the atomic number ($Z$) equals the number of protons ($p^{+}$) and, in a neutral atom, the number of electrons ($e^{-}$). The number of neutrons ($n^{0}$) is found using the mass number ($A$) rounded to an integer: $n^{0} = A - Z$. For example, Vanadium ($Z=23$, $A=50.94\sim51$) has 23 protons, 23 electrons, and $51 - 23 = 28$ neutrons. Electronic configuration involves distributing these electrons across energy levels following Bohr's capacity rules. For Strontium ($Z=38$), the distribution is Level 1: 2, Level 2: 8, Level 3: 18, and Level 4: 10.

Lewis Diagrams and Valence Electrons

Gilbert N. Lewis proposed that atoms combine to achieve a stable electronic configuration similar to a noble gas. Valence electrons are those found in the highest energy level (outermost layer) and are responsible for chemical bonding. The concept of valence as "combination power" was first mentioned by Edward Frankland in 1852. For instance, Sodium ($Na$) in Family IA has 1 valence electron, while Chlorine ($Cl$) in Family VIIA has 7.

Lewis diagrams represent these electrons as dots (or other signs) around the chemical symbol, which represents the nucleus and inner layers. The rules for these diagrams include writing the symbol, placing dots in cardinal positions (up, down, left, right), pairing them if more than four are present, and never exceeding 8 dots (the octet rule). Shared electron pairs form covalent bonds. Bonds can be: single (e.g., $NaCl$, where $Na$ cedes 1 electron), double (e.g., $O_{2}$, sharing two pairs), or triple (e.g., $N_{2}$, sharing three pairs).

Electronegativity and Bond Types

Electronegativity is the capacity of an atom to attract electrons in a chemical bond. It is a periodic property that generally increases from left to right across a period and from bottom to top within a group. Halogens (top right) like Fluorine ($F$) are highly electronegative, while Alkali metals (bottom left) like Cesium ($Cs$) have low electronegativity. Linus Pauling developed the relative electronegativity scale where Fluorine is $4.0$ and Cesium/Francium are $0.7$.

The difference in electronegativity ($\Delta EN$) predicts the bond type. If $\Delta EN$ is between $0$ and $0.4$, it is a non-polar or pure covalent bond (equitable sharing). If it is between $0.5$ and $1.6$, it is a polar covalent bond (inequitable sharing). If it is between $1.7$ and $3.3$, it is an ionic bond (electron transfer). For example, Carbon and Sulfur ($CS_{2}$) have $\Delta EN = 2.5 - 2.5 = 0$, forming a non-polar covalent bond. Cesium and Fluorine ($CsF$) have $\Delta EN = 4.0 - 0.7 = 3.3$, forming an ionic bond.

Ionic compounds consist of charged particles (cations and anions) joined by electrostatic forces, typically between a metal and a non-metal. They have high melting points and conduct electricity when dissolved or melted. Molecular compounds consist of atoms sharing electrons via covalent bonds between non-metals; they generally have lower melting and boiling points and do not conduct electricity.

Physics: Newton's Laws of Motion

Formulated in 1687, Newton's laws explain the relationship between forces and motion. The First Law (Law of Inertia) states that an object remains at rest or in uniform rectilinear motion unless acted upon by an external net force. Inertia is the resistance to change in motion, which increases with mass (e.g., a car passenger jerking forward during sudden braking). The Second Law (Fundamental Law of Dynamics) states that acceleration ($a$) is directly proportional to the net force ($F$) and inversely proportional to mass ($m$). This is expressed as $F = m \times a$. Force is measured in Newtons ($N$), mass in $kg$, and acceleration in $m/s^{2}$. The Third Law (Action and Reaction) states that for every action force exerted by object A on object B, there is a reaction force of equal magnitude and opposite direction exerted by B on A ($F_{A\rightarrow B} = -F_{B\rightarrow A}$). These forces occur simultaneously on different bodies and never cancel each other out.

Types of Motion

Motion is analyzed using velocity ($v$), which indicates speed and direction in $m/s$, and acceleration ($a$), which indicates the rate of change of velocity in $m/s^{2}$. Uniform Rectilinear Motion (MRU) occurs in a straight line at a constant velocity ($a=0$). The formula is $d = v \times t$. Uniformly Accelerated Rectilinear Motion (MRUA) occurs when velocity changes at a constant rate. Key formulas include: final velocity $v_{f} = v_{i} + (a \times t)$ and distance $d = (v_{i} \times t) + \frac{1}{2}a \times t^{2}$.

Uniform Circular Motion (MCU) describes a body rotating at a constant radius and speed. Despite constant speed, the changing direction creates centripetal acceleration ($a_{c}$). Relevant concepts include the Period ($T$), the time for one revolution in seconds; Frequency ($f = \frac{1}{T}$), revolutions per second in Hertz ($Hz$); Angular Velocity ($\omega$) in $rad/s$; and Tangential Velocity ($v = \omega \times r$). Centripetal acceleration is calculated as $a_{c} = \frac{v^{2}}{r}$. An example is a girl spinning a hula-hoop with a radius of $0.3\,m$ at $5\,Hz$, resulting in $v = 9.42\,m/s$ and $a_{c} = 295.78\,m/s^{2}$.

Energy and Its Conservation

Energy is the capacity of matter to produce work in forms like motion, light, or heat. Manifestations include Kinetic Energy ($E_{k}$), derived from motion, and Potential Energy ($E_{p}$), stored energy based on position. Mechanical Energy ($E_{m}$) is the sum: $E_{m} = E_{k} + E_{p}$. Kinetic energy is calculated as $E_{k} = \frac{1}{2}m \times v^{2}$. Gravitational Potential Energy is calculated as $E_{p} = m \times g \times h$, where $h$ is height and $g = 9.8\,m/s^{2}$. The Principle of Conservation of Energy states that in an isolated system, energy is neither created nor destroyed, only transformed. For a skater on a track, potential energy at the highest point transforms into kinetic energy at the lowest point, maintaining a constant total mechanical energy in the absence of friction.

Thermodynamics: Heat and Temperature

Heat and temperature are distinct concepts. Temperature is a measure of the average kinetic energy of the particles in a substance and is an intensive property. Heat is the transfer of thermal energy between bodies of different temperatures, always flowing from higher to lower until thermal equilibrium is reached. Standard units include Joules ($J$) and calories ($cal$), where $1\,cal = 4.184\,J$. The British Thermal Unit ($Btu$) equals $252\,cal$.

Temperature scales include: Fahrenheit, where water freezes at $32^{\circ}F$ and boils at $212^{\circ}F$; Celsius, where water freezes at $0^{\circ}C$ and boils at $100^{\circ}C$; and Kelvin (absolute scale), where $0\,K$ is absolute zero ($-273.15^{\circ}C$). Conversion formulas include: $K = {^{\circ}C} + 273.15$, ${^{\circ}F} = 1.8 \times {^{\circ}C} + 32$, and ${^{\circ}C} = \frac{{^{\circ}F} - 32}{1.8}$. For example, a recipe at $356^{\circ}F$ corresponds to $180^{\circ}C$.

Heat transfer occurs in three ways: Conduction, the propagation through solids via molecular collision (e.g., a metal rod in fire); Convection, the movement of heated fluids (liquids or gases) due to density changes (e.g., boiling water or wind); and Radiation, the propagation via electromagnetic waves, which can travel through a vacuum at $300,000\,km/s$ (e.g., sunlight).

Ethics and Human Principles

Ethics is a branch of philosophy orienting human conduct toward the good and social justice. Fundamental principles include Human Dignity (inherent value of every person, protected by Article 1 of the Mexican Constitution), Common Good (conditions allowing full development for all), Justice (constant attitude based on legality and equity), Liberty (the human capacity to act by individual will responsibly), and Integrity (coherence between thought, word, and action).

An ethical dilemma is a situation involving a choice between conflicting moral values where no perfect solution exists. Resolving a dilemma requires identifying the conflict, selecting a primary value as a guide, analyzing options, and making a choice that maintains logical coherence. For example, deciding whether to report a teammate's delay involves a conflict between loyalty and honesty/responsibility.

Identity and Citizenship

Personal identity is built from infancy through history/experiences, social interactions, talents/skills, interests, aspirations, and personality. It involves biological factors (genetics/temperament), family (primary socializer), social factors (friends/media), and cultural factors (language/traditions). Shared values like honesty, integrity, solidarity, empathy, respect, justice, equality, and tolerance are vital for social harmony.

Norms are rules of conduct ensuring social order and respect. These include family, school, and work rules, as well as Laws, which are formal written norms like the Political Constitution of the United Mexican States and Federal Laws. Institutions like the UN (and agencies like UNESCO/UNICEF), the CNDH, and the SEP are responsible for promoting a culture of peace and protecting human rights. Citizen participation includes social, community, political (voting), and citizen involvement to influence public decisions and ensure government accountability.

Mathematics: Arithmetic and Units

Mathematics involves sets like Integers ($\mathbb{Z}$), including positive/negative numbers and zero. Operations follow sign rules: same signs result in addition (retaining sign), different signs result in subtraction (retaining the sign of the larger absolute value). In multiplication/division, same signs yield positive results, while different signs yield negative results.

Fractions ($\frac{a}{b}$) represent parts of a whole. Sums and subtractions require a common denominator. Multiplication involves multiplying numerators by numerators and denominators by denominators ($\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$). Division involves multiplying by the reciprocal ($\frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}$). The Least Common Multiple (m.c.m.) is the smallest common multiple used to synchronize events. The Greatest Common Divisor (M.C.D.) is used to divide objects into the largest equal groups. Fundamental properties include Commutative ($A+B = B+A$), Associative ($(A+B)+C = A+(B+C)$), and Distributive ($A \times (B+C) = AB + AC$).

The International System of Units (SI) provides universal standards: meter ($m$) for length, kilogram ($kg$) for mass, second ($s$) for time, and cubic meter ($m^{3}$) for volume. Variations can be Direct (both variables increase together) or Inverse (one increases, the other decreases). Percentages are proportions based on 100, calculated as $\frac{\text{part}}{\text{total}} \times 100$. The Hierarchy of Operations dictates the order: 1. Grouping signs, 2. Exponents/Roots, 3. Multiplication/Division (left to right), 4. Addition/Subtraction (left to right).

Language and Communication

Text classification is based on communicative intention. Literary texts use creative, subjective language for aesthetic impact. Examples include: Narrative (relates real/imaginary events like novels/cuentos), Descriptive (presents features of objects/people), Dramatic (theater scripts based on dialogue), and Argumentative (persuades using reasoning/essays). Popular narratives include Comics, Myths, Legends, and Fables.

Drafting requires Connectors or Nexuses for coherence. Coordinative Nexuses join equal items (e.g., "and"), while Subordinative Nexuses join dependent items (e.g., "because"). Connectors can be structural (opening, continuity, closing) or semantic (addition, cause-effect, contrast, time, etc.). Writing clearly requires precise vocabulary, simple syntax, and correct punctuation. Coherency involves maintaining a global theme (global level) and logical connections within paragraphs (local level).

Reading analysis involves identifying the Main Idea (the central concept that has sense on its own) and Secondary Ideas (details that amplify, prove, or compare the central concept). A Summary uses the author's words to capture main points, whereas a Synthesis retrieves only essential information concisely. Graphic organizers like concept maps (sun, cloud, spider), synoptic charts, and comparison tables are visual tools used to simplify and order complex information.

Questions & Discussion

1. If an object has a mass of 50 kg and is accelerated at 3 m/s², what is the force? Response: Using Newton's Second Law, $F = m \times a$. Therefore, $F = 50\,kg \times 3\,m/s^{2} = 150\,N$.

2. What is the difference between a myth and a legend? Response: Myths have a sacred character, often involving gods and the creation of the world. Legends are based on real historical events or characters to which fantastic elements are added as part of a people's cultural identity.

3. How many groups and periods are in the current periodic table? Response: There are 18 groups (vertical columns) and 7 periods (horizontal rows).

4. What happens when an electron jumps from a lower energy level to a higher one? Response: According to the Bohr model, the electron absorbs energy.

5. If a car travels 285 km in 3 hours, how far will it travel in 12 hours at the same speed? Response: This is a direct proportionality problem. Using the rule of three: $K = \frac{12\,h \times 285\,km}{3\,h} = 1,140\,km$.

6. What is the value of 1 uma? Response: One atomic mass unit ($uma$) has a value of $1.66 \times 10^{-24}\,g$.