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PRAXIS II General Mathematics Exam

This exam is for individuals who would like to be general mathematics instructors. You will be given two hours to complete this 120 question multiple choice exam. There are 20 pretest questions that will not be counted toward your score. There will be 12 questions on exceptionalities in mathematics, 29 questions on basic algebra, 17 questions on probability, statistics and applied mathematics; 26 questions on measurement and geometry along with 36 questions on basic skills and mathematical concepts.

Basic Skills and Mathematical Concepts
This section of the exam will assess your knowledge of inductive and deductive reasoning, mathematics and everyday life, problem solving strategies, computation methods, calculator usage, problem-solving, primes, factors, multiplication, addition, subtraction, division, rounding numbers, identifying integers, real number properties, ratios, and patterns and relationships.

Measurement and Geometry
This section of the exam will assess your knowledge of angles, polygons, points, lines, rays, segments, parts of triangles, Pythagorean theory, geometric solids, volume, perimeter, and calculation of measurements with various instruments.

Statistics, Probability and Applied Mathematics
This section of the exam will assess your knowledge of income and expenditure, credit costs, savings accounts, checking accounts, comparison shopping, profit margin, discounts, sales tax, salaries, commissions, income tax, payroll deductions, the fundamental counting principle; probability of single and multiple events; calculation of the mean median or mode range for a set of data and, interpretation of bar, circle and line graphs.

Algebra One
This section of exam also assess your knowledge of quadric equations, radical expressions, linear equations, the equation of a line, polynomials, factors, operations, rational expressions, monomials, Cartesian and linear graphs, and word problems.

Exceptionalities in the Mathematics Program
This section of the exam will assess your knowledge of the reading skills required by students to succeed in mathematics, student reading deficits at each grade level, support services for students with disabilities, and legal considerations of educating exceptional students.

PRAXIS II General Mathematics Practice Questions

1. Which of the following is not an area of mathematics?

A. Geometry
B. Algebra
C. Geography
D. Calculus

2. Geometry is the measurement and relationship of:

A. points and lines
B. angles
C. surfaces and solids
D. All of the above

3. Which of the following is not part of the conceptual learning approach?

A. Rote memorization
B. Explaining thought processes
C. Comparing methods
D. Justifying results

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

A. Patterns
B. Cosine
C. Functions
D. Balance

5. Common financial terms include:

A. credit
B. savings account
C. interest
D. All of the above

Answer Key For General Mathematics

1. Answer: C

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 especially 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 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: D

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 where three-dimensional objects are placed and how they fit into 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 hones students' 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. Citing real life examples makes the subject relevant to students' lives outside the classroom.

3. Answer: A

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 show using the procedural approach to teach math can actually inhibit understanding and prohibit integrating new concepts with previously learned data if not balanced with a conceptual understanding, the basics still need to be acquired during process-oriented study of the material. The question is when and how.

One of the functions of learning math is improving reasoning ability, honing critical thinking skills, and discovering these talents are applicable in all academic disciplines as well as issues in the real world. To accomplish that goal using the conceptual approach, the instructor designs lesson plans, composes problems, and devises activities that require students to explain their thought process, compare methods and approaches, and justify results. Students discover patterns and relationships, and the activity becomes a meaningful learning experience rather than a rote exercise in memorization. Using this approach, students can learn the definitions, formulas, and methods as a natural outcome of understanding and integrating the new concepts.

4. Answer: B

There are 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; i.e., 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 an abstract stand-in for the relationships.

Equivalence and balance are critical concepts in understanding algebraic equations. It is important teachers explain the equal sign represents some type of relationship between the numbers and symbols on each side of the sign, and 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.

5. Answer: D

INCOME is the total of all earnings in a specific time period including, but not limited to, wages, salaries, profits, interest, etc.

EXPENSE (also known as expenditure) is the cost paid in exchange for an item or service.

CREDIT enables the borrower (debtor) to postpone payment while taking immediate possession of an item by agreeing to make payments to the lender (creditor) over a specific period of time.

SAVINGS ACCOUNTS contain funds that earn interest and cannot be used directly as money, meaning they are not accessible by writing a check or visiting an ATM.

INTEREST (simple or compound) is a fee paid by the financial institution for the use of funds held in various types of accounts.

CHECKING ACCOUNTS (also known as transactional or demand accounts) provide convenient, immediate access to funds currently deposited in that account. They are not used to save funds and usually do not earn interest.