This exam is designed for individuals, who would like teach mathematics at the middle school level. You will be given two hours to complete this 55 multiple-choice and numeric entry questions exam. There will be 34 questions regarding arithmetic and algebra with the 21 other questions being about geometry and data.

Discrete Mathematics, Statistical Concepts, Probability and Data

In this section of the exam you will be required to solve problems by: finding and interpreting common measures of dispersion, standard deviation, outliers, range and spread of data; finding and interpreting common measures of central tendency such as mean, median and mode. You will also be asked to solve probability problems by using counting techniques, by using geometric probability, and solve probability problems that involve finite sample spaces. Your ability to analyze data in charts, line bars, circles, histograms, tables, graphs, scatterplots, stemplots, and draw conclusions from that data.

Functions and their Graphs

This section of the exam will assess your knowledge of algebraic expressions, equations, domain values in ranges of a function, usage of a mathematical model for two different situations, and notations and functions. You will also be given a set of conditions and required to identify if a graph in the plane is the graph of a function. Your ability to utilize a graph and to choose an equation to represent the graph will be assessed. Questions regarding sketching a graph representing exponential or quadratic function, absolute value, step, or linear function will also be assessed.

Measurement and Geometry

You will be required to solve problems in metric and English systems in this section of the exam. Your ability to solve problems regarding the properties of polygons in the plane, points, lines, translations, rotations, reflections, angles, sectors, arcs, circles, squares, rectangles, trapezoid’s, parallelograms, triangles, perpendicular lines, and two and three dimensional objects will be assessed in this portion of the exam. Your ability to compute the parameter and area of circles, triangles, quadrilaterals and regions within these figures and; compute the surface area and volume of spheres, solids, cylinders, cones, prisms and the combination of these figures will be assessed. Questions regarding the application of the Pythagorean theorem to solve problems that include isosceles and equilateral triangles will be included in this section of the exam.

Basic Algebra and Mathematics

In this section of the exam you will be required to solve and graph linear equations and inequalities with one or two variables, solve and graph nonlinear algebraic equations, solve equations and inequalities involving absolute value, solve quadratic equation problems, and determine line equations. Problems that require solving algebraic expression and problems that include formulas, equations, adding, subtracting, multiplying, and dividing polynomials, and algebraic fractions will be included in this section of the exam. Your knowledge of standard algebraic operations that involve negative exponents, fractional exponents, radicals, exponents, and complex numbers will be included in this section of the exam. Addition, subtraction, multiplication, and division of rational numbers, identification of basic mathematical operations, identification of the multiplicative and additive in versus of a number, and the order and finite set of real numbers will be included in this section of the exam. Your knowledge of classification of real numbers, complex, rational, or irrational, decimals, powers, roots, and exponents will be assessed in this section of the exam. Number system operation, counting numbers, factors, divisibility, multiples, ratio, proportion, and percentages will also be included in this section of the exam.

Problem Solving Exercises

Questions in the section of the exam will assess your understanding of the learning of mathematical content and learning to think in a mathematical manner. The following topics will be covered in a section of the exam: mathematical problem-solving, mathematical reasoning and proof, mathematical connections, mathematical representation, and the usage of technology. Mathematical problem solving questions will assess your ability to solve mathematical problems, and apply mathematics to solve problems in other contexts. In the mathematical reasoning and proof section you will be asked to utilize serious reasoning and proof methods, create and investigate mathematical conjectures, and create and evaluate mathematical proofs and arguments. Under the mathematical connections section you will be asked to connect mathematical ideas, apply mathematics in the context of other areas, and show an understanding of the interrelationship between mathematical ideas. Under the mathematical representation category you will be asked to apply and translate mathematical representations to solve problems. Your ability to use mathematical representations for modeling and interpretation of social, physical, and mathematical phenomena will be assessed. Your ability to create and utilize representations for the organization, recording, and communication of mathematical ideas will also be included in this section of the exam. In the use of technology section your ability to use technology to solve problems will be assessed.