174 TExES Mathematics / Physical Science / Engineering 8 - 12 Exam

The TExES Mathematics / Physical Science / Engineering 8 - 12 Exam is a certification examination that is designed to determine if an individual has the knowledge necessary to teach mathematics, physical science, and engineering at the high school level within the Texas public school system. This exam assesses the individual's knowledge of a variety of mathematical topics, physics-related topics, engineering-related topics, the individual's understanding of the relationship that exists between the field of engineering and the fields of mathematics and physical science, and the teaching methods necessary to effectively teach these topics to students. This exam is required for an individual to become certified as an engineering teacher at the high school level within the state of Texas. The exam consists of 110 multiple-choice questions, 100 of which are scored and 10 that are not scored, that are related to the following areas:

Number Concepts (Approximately 5 questions)
Patterns and Algebra (Approximately 12 questions)
Geometry and Measurement (Approximately 7 questions)
Probability and Statistics (Approximately 5 questions)
Mathematical Processes and Perspectives (Approximately 3 questions)
Methods of Mathematical Instruction and Assessment (Approximately 3 questions)
Scientific Method, Scientific Inquiry, and Scientific Processes (Approximately 5 questions)
Physics (Approximately 13 questions)
Chemistry (Approximately 14 questions)
Methods of Science Instruction and Assessment (Approximately 3 questions)
The Engineering Method (Approximately 17 questions)
The Role and Responsibilities of an Engineer and the Role of Engineering in Society (Approximately 13 questions)

The exam-taker will be supplied with a Formula and Definitions Reference Sheet and a copy of the periodic table. The individual taking the exam may bring a graphing calculator to the exam as long as the calculator can be found on the list of approved brands and models for use on the TExES. It is important to note that some of the questions on the exam are extremely difficult to solve without the aid of a graphing calculator. The exam-taker will have fives hours to complete the exam and the exam will be scored on a scale of 100 - 300 with 240 set as the minimum score considered as passing for the exam. The Mathematics / Physical Science / Engineering 8 - 12 Exam is only offered in a paper-based format and the registration fee for the exam is $82. However, there may be other exams and fees in addition to this exam that are required in order for an individual to become certified as an entry-level high school mathematics, physical science, and engineering teacher within the state of Texas.

174 TExES Mathematics / Physical Science / Engineering 8 - 12 Exam Practice Questions

Sample Study Notes

1. Define mathematics, arithmetic, algebra, geometry, probability, statistics, trigonometry, calculus.

Answer:

Math explains the logic of numbers. All math concepts are built on addition, division, fractions and shapes; all mathematical relationships flow from these concepts. If students fail to grasp these basics, they are unable to apply applicable background knowledge when introduced to higher level math. The American Heritage College Dictionary defines mathematics as "the study of the measurement, properties and relationships of quantities using numbers and symbols." It is a formal science of structure, order and relationship, and is considered the basic language and foundation of all the other sciences. It is critical in the development of technology. It evolved from counting, measuring and describing shapes. Some areas of mathematics and their definitions:

ARITHMETIC: a system to count numbers using addition, subtraction, multiplication and division.
ALGEBRA: an abstract form of arithmetic using symbols to represent numbers.
GEOMETRY: the relationship of points, lines, angles, surfaces and solids.
PROBABILITY: the calculation of the chances that certain events will occur.
STATISTICS: the collection, organization and analysis of data.
TRIGONOMETRY: the relationship of the sides and angles of triangles.
CALCULUS: the limits, differentiation and integration of the functions of variables.

2. Discuss patterns and functions and equivalence and equations and what they represent.

Answer:
There are some basic concepts students need to understand in order to begin to think algebraically, so they can use what they "see" to make generalizations about "unknowns." Patterns and functions represent change and relationships. Repeating patterns show the same unit over and over again; in growth patterns, each unit is dependent upon the one before it, as well as its position in the pattern. The function is the relationship between values, e.g. the second depends on the first. Using concrete examples helps students visualize what the function is describing. As students begin to understand functional relationships, symbols can be used as abstract stand-ins for the relationships. Equivalence and balance are critical concepts in understanding algebraic equations. It is important for teachers to explain that the equal sign represents some type of relationship between the numbers and symbols on each side of the sign: if a calculation is performed on one side, the same calculation must be performed on the other side. Each side is equal; the equation must balance.

3. Define geometry and discuss some of its practical applications.

Answer:
The American Heritage College Dictionary defines geometry as investigation of "properties, measurements and relationships of points, lines, angles, surfaces and solids." Geometry developed from a practical need to determine land boundaries (survey), figure the size (area) of a field, measure the volume of a silo (cylinder), and determine the relative positions of three-dimensional objects in a defined space. Man's fascination with the stars and the heavens became the science of astronomy, which led to the development of trigonometry and its unique computational methods. Studying geometry helps students hone their spatial visualization skills, which helps them function better in the physical world. Points, lines, angles, surfaces and solids are all used in painting, sculpture and architecture. The artist must understand the relationship of these components in order to create in any medium. Various engineering disciplines use geometry to build bridges and dams, design freeway systems, mine for minerals and drill for oil. Geometry is used every day in many professions. Citing real-life examples makes the subject relevant to students' lives outside the classroom.

4. Discuss the importance of statistics.

Answer:
Statistics is the collection, organization and interpretation of data. The data can be facts or isolated bits of information, but it all relates in one way or another to a specific topic. This precise, analytical system is used to identify, study, and solve problems in many industries. Statistics can help people interpret events and make decisions in uncertain and difficult situations. Healthcare professionals, financial analysts, scientists, engineers and insurance actuaries all use statistics to infer relationships, measure interactions and predict outcomes among variables. Descriptive statistics is the foundation for the entire system. It is used to define and explain the basic components in a study. Exploratory statistics tries to figure out what the collected data is saying. This method involves averages and percentages, which are usually displayed on a graph or in a table. Since by definition it relies on information from previous experiments, this data is sometimes called secondary research. Confirmatory statistics is the method that applies general ideas and concepts to an issue or a problem in an effort to answer specific questions.

5. Discuss the Probability Theory.

Answer:
The Probability Theory is the study and analysis of random events, and especially whether those events can predict the behavior of a defined system. A probability is the numerical measure of the likelihood the event will happen. It is a number from zero (0) to one (1). Zero means it will definitely not happen, one means it definitely will happen and point five (0.5) means it is a draw, i.e. just as likely to happen as not happen. Probability is the possibility of an event happening or something being true. It is used to explain events that do not happen with any certainty. Probabilities must meet these general rules:

All probabilities must be a non-negative number.
The collection of all possible outcomes is equal to one (1).
If there are two possible outcomes that cannot happen at the same time (non-overlapping), the possibility that either outcome will happen is the total of the individual outcomes.

6. Explain why it is better to focus on the conceptual learning approach and use the procedural approach as a teaching tool.

Answer:
Experts agree that students need to know the definitions of terms, the applications of formulas, and the methods used to solve a problem. So even though studies have shown that using the procedural approach to teach math can actually inhibit understanding and prohibit integrating new concepts with previously learned data, the basics still need to be acquired during the study of the material. The question is when and how. Learning math necessarily entails improving reasoning ability, honing critical thinking skills, and discovering that these talents are applicable to other academic disciplines as well as to issues in the real world. To accomplish that goal, the teacher must design lesson plans, compose problems, and devise activities that require students to explain their thought process, compare methods and approaches, and justify results. With such instruction, students discover patterns and relationships and the activity becomes a meaningful learning experience rather than a rote exercise in memorization. Using this approach, students learn the definitions, formulas and methods as a natural outcome of understanding and integrating the new concepts.

7. Describe physics and define its core theories.

Answer:
Physics is a fundamental, experimental science: the study of matter, motion, energy, space and time. The goal of a physicist is to understand the natural world by formulating and testing hypotheses in an effort to develop scientific laws that predict other phenomena. Physics is one of the oldest sciences. Physicists specialize in either theoretical (the development of new theories) or experimental (testing theories and discovering new phenomena) research. Physics is divided into four disciplines: condensed matter physics; atomic, molecular, and optical physics; high-energy physics; and astronomy and astrophysics. Other sciences are complex applications of the laws of physics. The core theories of physics, as described in Webster's New Explorer Desk Encyclopedia, are:

CLASSICAL MECHANICS: the motion of objects
ELECTROMAGNETISM: interaction between charged particles
RELATIVITY: measurement changes in various states of motion
THERMODYNAMICS: relationships between heat, work, temperature and energy
QUANTUM MECHANICS: mathematical explanations of atomic and subatomic systems
OPTICS: production, propagation, changes and manipulation of light

8. Define these terms: motion, space and time.

Answer:
The following definitions are based on information from The American Heritage College Dictionary.

MOTION is "the act or process of changing position or place." It is the continuous change of an object's location as a result of force (lift, push or pull). It is explained as velocity (rate of speed), acceleration (increase in speed), displacement (the act of moving from its usual place), and time. Once an object is in motion, it acquires momentum (a measure of a body in motion).
SPACE is a fundamental quantity that describes the "expanse in which the solar system, stars, and galaxies exist, i.e., the universe." It is measured as the distance traveled by light in a vacuum.
TIME is "a non-spatial continuum in which events occur in apparently irreversible succession from the past through the present to the future." This is the view held by Immanuel Kant, who believed time is a measuring system devised by humans in an effort to sequence events. Sir Isaac Newton believed time is a fundamental, measurable dimension of the universe, in which events occur in a sequence.

9. Describe chemistry and explain a chemical reaction.

Answer:
Chemistry grew out of the practice of alchemy, a philosophical and spiritual discipline that investigated the possibility of transforming base metals into gold. Modern chemistry is the physical science that studies the composition, structure, properties and reactions of atoms, molecules, crystals and other aggregate matter by themselves or in relationship to each other. It is sometimes called the "central science" because it connects the other natural sciences. Chemistry studies matter in relation to energy (capacity to do work) and entropy (measurement of energy unable to do work) and the spontaneity of chemical reactions (changing of matter into one or more substances). Webster's New Explorer Desk Encyclopedia defines a chemical reaction as "any process in which substances are changed into different ones, with different properties." The reaction rearranges the chemical bonds of the atoms in each compound involved; however, the mass and number of atoms of each substance remains constant. Energy is either used or set free. The speed of the process varies depending upon the products involved. The sequence of a chemical reaction is called its mechanism.

10. Define scientific method, scientific inquiry, deductive and inductive reasoning.

Answer:

SCIENTIFIC METHOD: a set of procedures used to study natural phenomena. It provides guidelines with which to pose questions, analyze data and reach conclusions. It is used to investigate an event, gain knowledge or correct earlier conclusions about the occurrence and integrate the new information with previously learned data. Researchers pose hypotheses, and design experiments and studies to test them. The process must be objective, documented and shared with other researchers so the results can be verified by replicating the study in similar situations under the same conditions.
SCIENTIFIC INQUIRY: used to explore theories and develop explanations for natural phenomena. It has two functions: to provide a description of how something happens and to explain why the process succeeds or fails.
DEDUCTIVE REASONING: a process in which a specific conclusion logically follows from a general premise. If the premise is true, the conclusion is true. Deductive reasoning is used in mathematics.
INDUCTIVE REASONING: a process in which a universal conclusion is formed from considering an individual example. Inductive reasoning is the methodology of the natural and social sciences.

Last Updated: 03/15/2013

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