Maryland State Standards for Mathematics: Grade 10

MD.A. Algebra Data Analysis

A.1. The student will demonstrate the ability to investigate, interpret, and communicate solutions to mathematical and real-world problems using patterns, functions, and algebra.

A.1.1. The student will analyze a wide variety of patterns and functional relationships using the language of mathematics and appropriate technology.

A.1.1.1. The student will recognize, describe, and/or extend patterns and functional relationships that are expressed numerically, algebraically, and/or geometrically.

A.1.1.2. The student will represent patterns and/or functional relationships in a table, as a graph, and/or by mathematical expression.

A.1.1.3. The student will apply addition, subtraction, multiplication, and/or division of algebraic expressions to mathematical and real-world problems.

A.1.1.4. The student will describe the graph of a non-linear function and discuss its appearance in terms of the basic concepts of maxima and minima, zeros (roots), rate of change, domain and range, and continuity.

A.1.2. The student will model and interpret real-world situations using the language of mathematics and appropriate technology.

A.1.2.1. The student will determine the equation for a line, solve linear equations, and/or describe the solutions using numbers, symbols, and/or graphs.

A.1.2.2. The student will solve linear inequalities and describe the solutions using numbers, symbols, and/or graphs.

A.1.2.3. The student will solve and describe using numbers, symbols, and/or graphs if and where two straight lines intersect.

A.1.2.4. The student will describe how the graphical model of a non-linear function represents a given problem and will estimate the solution.

A.1.2.5. The student will apply formulas and/or use matrices (arrays of numbers) to solve real-world problems.

A.3. The student will demonstrate the ability to apply probability and statistical methods for representing and interpreting data and communicating results, using technology when needed.

A.3.1. The student will collect, organize, analyze, and present data.

A.3.1.1. The student will design and/or conduct an investigation that uses statistical methods to analyze data and communicate results.

A.3.1.2. The student will use the measures of central tendency and/or variability to make informed conclusions.

A.3.1.3. The student will calculate theoretical probability or use simulations or statistical inferences from data to estimate the probability of an event.

A.3.2. The student will apply the basic concepts of statistics and probability to predict possible outcomes of real-world situations.

A.3.2.1. The student will make informed decisions and predictions based upon the results of simulations and data from research.

A.3.2.2. The student will interpret data and/or make predictions by finding and using a line of best fit and by using a given curve of best fit.

A.3.2.3. The student will communicate the use and misuse of statistics.

MD.G. Geometry

G.2. The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

G.2.1. The student will represent and analyze two- and three-dimensional figures using tools and technology when appropriate.

G.2.1.1. The student will analyze the properties of geometric figures.

G.2.1.2. The student will identify and/or verify properties of geometric figures using the coordinate plane and concepts from algebra.

G.2.1.3. The student will use transformations to move figures, create designs, and/or demonstrate geometric properties.

G.2.1.4. The student will construct and/or draw and/or validate properties of geometric figures using appropriate tools and technology.

G.2.2. The student will apply geometric properties and relationships to solve problems using tools and technology when appropriate.

G.2.2.1. The student will identify and/or verify congruent and similar figures and/or apply equality or proportionality of their corresponding parts.

G.2.2.2. The student will solve problems using two-dimensional figures and/or right-triangle trigonometry.

G.2.2.3. The student will use inductive or deductive reasoning.

G.2.3. The student will apply concepts of measurement using tools and technology when appropriate.

G.2.3.1. The student will use algebraic and/or geometric properties to measure indirectly.

G.2.3.2. The student will use techniques of measurement and will estimate, calculate, and/or compare perimeter, circumference, area, volume, and/or surface area of two-and three-dimensional figures and their parts.

MD.AII. Algebra II

AII.1. The student will develop, analyze, communicate, and apply models to real-world situations using the language of mathematics and appropriate technology.

AII.1.1. The student will model and interpret real-world situations, using the language of mathematics and appropriate technology.

AII.1.1.1. The student will determine and interpret a linear function when given a graph, table of values, essential characteristics of the function, or a verbal description of a real-world situation.

AII.1.1.2. The student will determine and interpret a quadratic function when given a graph, table of values, essential characteristics of the function, or a verbal description of a real-world situation.

AII.1.1.3. The student will determine and interpret an exponential function when given a graph, table of values, essential characteristics of the function, or a verbal description of a real-world situation.

AII.1.1.4. The student will be able to use logarithms to solve problems that can be modeled using an exponential function.

AII.1.2. Given an appropriate real-world situation, the student will choose an appropriate linear, quadratic, polynomial, absolute value, piecewise-defined, simple rational or exponential model and apply that model to solve the problem.

AII.1.3. The student will communicate the mathematical results in a meaningful manner.

AII.1.3.1. The student will describe the reasoning and processes used in order to reach the solution to a problem.

AII.1.3.2. The student will ascribe a meaning to the solution in the context of the problem and consider the reasonableness of the solution.

AII.2. Mathematical Concepts, Language, and Skills: The student will demonstrate the ability to analyze a wide variety of patterns and functional relationships using the language of mathematics and appropriate technology.

AII.2.1. The student will be familiar with basic terminology and notation of functions.

AII.2.1.1. The student will identify and use alternative representations of linear, piecewise-defined, quadratic, polynomial, simple rational and exponential functions.

AII.2.1.2. The student will identify the domain, range, the rule or other essential characteristics of a function.

AII.2.2. The student will perform a variety of operations and geometrical transformations on functions.

AII.2.2.1. The student will add, subtract, multiply, and divide functions.

AII.2.2.2. The student will find the composition of two functions and determine algebraically and/or graphically if two functions are inverses.

AII.2.2.3. The student will perform translations, reflections, and dilations on functions.

AII.2.3. The student will identify linear and nonlinear functions expressed numerically, algebraically, and graphically.

AII.2.4. The student will describe or graph notable features of a function using standard mathematical terminology and appropriate technology.

AII.2.5. The student will use numerical, algebraic, and graphical representations to solve equations and inequalities.

AII.2.6. The student will solve systems of linear equations and inequalities.

AII.2.7. The student will use the appropriate skills to assist in the analysis of functions.

AII.2.7.1. The student will add, subtract, multiply, and divide polynomial expressions.

AII.2.7.2. The student will perform operations on complex numbers.

AII.2.7.3. The student will determine the nature of the roots of a quadratic equation and solve quadratic equations of the form y = ax^2 + bx + c by factoring and the quadratic formula.

AII.2.7.4. The student will simplify and evaluate expressions with rational exponents.

AII.2.7.5. The student will perform operations on radical and exponential forms of numerical and algebraic expressions.

AII.2.7.6. The student will simplify and evaluate expressions and solve equations using properties of logarithms.

AII.2.8. The student will use literal equations and formulas to extract information.