# Praxis II Middle School mathematics Exam by ETS

The exam is aimed for those individuals, who wants to teach mathematics at the middle school level. Two hours will be provided, to complete 40 multiple choice questions and 3 short answer questions. A graphing calculator may be used in this exam. There will be 10 M. C. Q covering discrete mathematics, statistical concepts, probability and data, 8 questions covering graphs and their functions, 10 questions covering measurements and geometry, and 12 questions covering basic algebra and mathematics. The multiple-choice questions will comprise 67% of the total grade and the short answer questions will comprise 33% of the total grade.

- Discrete Mathematics, Statistical Concepts, Probability and Data: In this section, you need to solve problems by: Finding and interpreting common measures of dispersion, standard deviation, outliers, range and spread of data; finding and interpreting basic measures of central tendency like mean, median and mode. Questions may 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 analyse data in charts, line bars, circles, histograms, tables, graphs, scatterplots, stemplots and make conclusions from data.
- Functions and their Graphs: This section will test your knowledge of algebraic expressions, equations, domain values in ranges of a function, use of a mathematical model for two different situations, 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 use a graph and to choose an equation representing the graph will be tested. Questions pertaining to sketching a graph representing exponential or quadratic function, absolute value, step or linear function will also be tested.
- Measurement and Geometry: You need to solve problems in metric and English systems in this section. Your ability and understanding to solve problems pertaining to the properties of polygons in the plane, points, lines, translations, rotations, reflections, angles, sectors, arcs, circles, squares, rectangles, trapezoid's, parallelograms, triangles, perpendicular lines, two and three dimensional objects will be tested in this section. Your ability to calculate 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 combination of these figures will be tested. Questions pertaining to the application of the Pythagorean theorem to solve problems that focus isosceles and equilateral triangles will be covered in this section.
- Basic Algebra and Mathematics: You need to solve and graph linear equations and in-equalities with 1 − 2 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 cover formulas, equations, adding, subtracting, multiplying, and dividing polynomials, and algebraic fractions will be included in this section. Your knowledge of standard algebraic operations that involve negative exponents, fractional exponents, radicals, exponents and complex numbers will be included in this section. 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. Your knowledge of classification of real numbers, complex, rational or irrational, decimals, powers, roots and exponents will be tested in this section. Number system operation, counting numbers, factors, divisibility, multiples, ratio, proportion and percentages will be covered in this section.
- Problem Solving Exercises: This section will test your understanding of the learning of mathematical content and learning to think in a mathematical manner. The topics will be covered in a section are: Mathematical problem-solving, mathematical reasoning and proof, mathematical connections, mathematical representation and the use of technology. Mathematical problem solving questions will test 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 need 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 knowledge to use mathematical representations for modeling and interpretation of social, physical and mathematical phenomena will be tested. Your ability to create and use representations for the organization, recording and communication of mathematical ideas will also be included in this section. In the use of technology section your ability to use technology to solve problems will be tested.