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

1. Areas of mathematics include:

A. Graphing
B. Algebra and Geometry
C. Analysis
D. Fiscal management

2. Which of the following is not a basic algebraic concept?

A. Patterns
B. Fractions
C. Equivalence
D. Balance

3. Geometry studies the relationship of:

A. Points and lines
B. Angles
C. Surfaces and solids
D. All of the above

4. Statistics is data that has been:

A. Collected
B. Monitored
C. Judged
D. Memorized

5. Probability Theory measures the likelihood of:

A. Rain
B. Something being true
C. Pluto being a planet
D. The end of the world

6. Teaching math using the procedural approach means:

A. Defining words and phrases
B. Explaining strategies
C. Providing precise methods
D. All of the above

7. The disciplines of physics are:

A. Functions
B. Reproduction
C. Anatomy and physiology
D. Astronomy and astrophysics

8. Which of the following terms is not used in physics?

A. Motion
B. Patterns and functions
C. Space
D. Time

9. Chemistry studies matter in relation to:

A. Energy
B. Evolution
C. Space
D. All of the above

10. Scientific method is used to:

A. Investigate crime
B. Predict the future
C. Integrate information
D. Follows a predictable path

ANSWER KEY EXAM 174

1. Answer: B

Mathematics is a formal science of structure, order and relationships and is considered the basic language and foundation of all the other sciences. It evolved from counting, measuring and describing shapes. Some areas 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 chance random 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. Answer: B

There are basic concepts in algebra that allow 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, i.e., the second depends on the first. Once functional relationships are understood, symbols are used as an abstract stand-in for the relationships. Equivalence and balance are critical concepts in understanding algebraic equations. 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 and they must balance.

3. Answer: D

The American Heritage College Dictionary defines geometry as the 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 where three-dimensional objects are placed and how they fit into a defined space. 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 by many professions.

4. Answer: A

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 various problems. Statistics can help people interpret events and make decisions in uncertain and difficult situations. Statistics infers relationships, measures interactions and predicts outcomes among variables. Descriptive statistics defines and explains the basic components in a study. Exploratory statistics tries to figure out what the collected data is saying. Confirmatory statistics applies general ideas and concepts to an issue or a problem in an effort to answer specific questions.

5. Answer: B

The Probability Theory is the study and analysis of random events and whether those events can predict the behavior of a defined system. It is the possibility of an event happening or something being true. It is used to explain events that do not happen with any certainty. 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; in other words, it has a fifty/fifty chance of happening.

6. Answer: C

Teaching math with a procedural approach or by direct instruction means defining terms and symbols, explaining formulas and giving students a step-by-step method to solve a problem. Definitions are exact and don't allow for creative examples or encourage critical thinking. The problem is solved "by the book." Most students acquire some level of proficiency but are usually unable to apply anything learned in math class in other academic areas or to situations outside of school. Experts agree students need to know the definitions of terms, how to apply formulas and understand the methods used to arrive at the answer to a problem. So even though studies have shown 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.

7. Answer: D

Physics is a fundamental, experimental science that studies matter, motion, energy, space and time and how they interact. Its goal 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. Humans have been trying to figure out how the world works since we started walking upright. 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.

8. Answer: B

These 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 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," i.e., a measuring system devised by humans (Immanuel Kant's view). Sir Isaac Newton believed time is a fundamental, measurable dimension of the universe in which events occur in a sequence.

9. Answer: A

Chemistry grew out of the practice known as 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 (the capacity to do work) and entropy (the measurement of energy unable to do work) and the spontaneity of chemical reactions (the changing of matter into one or more substances).

10. Answer: C

Scientific Method is 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 method rarely follows a predictable path. The testing of one hypothesis usually leads to other questions, which leads to the formation of other hypotheses.