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### 9-11.9.2 Algebra

- 9-11.9.2.1 Understand the concept of function, and identify important features of functions and other relations using symbolic and graphical methods where appropriate.
- 9-11.9.2.1.3 Find the domain of a function defined symbolically, graphically or in a real-world context.
- 9-11.9.2.1.5 Identify the vertex, line of symmetry and intercepts of the parabola corresponding to a quadratic function, using symbolic and graphical methods, when the function is expressed in the form f(x) = ax
^{2}+ bx + c, in the form f(x) = a(x – h)^{2}+ k, or in factored form. - 9-11.9.2.1.6 Identify intercepts, zeros, maxima, minima and intervals of increase and decrease from the graph of a function.
- 9-11.9.2.1.7 Understand the concept of an asymptote and identify asymptotes for exponential functions and reciprocals of linear functions, using symbolic and graphical methods.
- 9-11.9.2.1.9 Determine how translations affect the symbolic and graphical forms of a function. Know how to use graphing technology to examine translations.

- 9-11.9.2.2 Recognize linear, quadratic, exponential and other common functions in real-world and mathematical situations; represent these functions with tables, verbal descriptions, symbols and graphs; solve problems involving these functions, and explain results in the original context.
- 9-11.9.2.2.2 Represent and solve problems in various contexts using exponential functions, such as investment growth, depreciation and population growth.
- 9-11.9.2.2.3 Sketch graphs of linear, quadratic and exponential functions, and translate between graphs, tables and symbolic representations. Know how to use graphing technology to graph these functions.
- 9-11.9.2.2.4 Express the terms in a geometric sequence recursively and by giving an explicit (closed form) formula, and express the partial sums of a geometric series recursively.
- 9-11.9.2.2.5 Recognize and solve problems that can be modeled using finite geometric sequences and series, such as home mortgage and other compound interest examples. Know how to use spreadsheets and calculators to explore geometric sequences and series in various contexts.
- 9-11.9.2.2.6 Sketch the graphs of common non-linear functions such as f(x)= the square root of x, f(x) = |x|, f(x)= 1/x, f(x) = x
^{3}, and translations of these functions, such as f(x) = the square root of (x-2) + 4. Know how to use graphing technology to graph these functions.

- 9-11.9.2.3 Generate equivalent algebraic expressions involving polynomials and radicals; use algebraic properties to evaluate expressions.
- 9-11.9.2.3.1 Evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified points in their domains.
- 9-11.9.2.3.2 Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree.
- 9-11.9.2.3.4 Add, subtract, multiply, divide and simplify algebraic fractions.
- 9-11.9.2.3.5 Check whether a given complex number is a solution of a quadratic equation by substituting it for the variable and evaluating the expression, using arithmetic with complex numbers.
- 9-11.9.2.3.6 Apply the properties of positive and negative rational exponents to generate equivalent algebraic expressions, including those involving nth roots.

- 9-11.9.2.4 Represent real-world and mathematical situations using equations and inequalities involving linear, quadratic, exponential, and nth root functions. Solve equations and inequalities symbolically and graphically. Interpret solutions in the original context.
- 9-11.9.2.4.1 Represent relationships in various contexts using quadratic equations and inequalities. Solve quadratic equations and inequalities by appropriate methods including factoring, completing the square, graphing and the quadratic formula. Find non-real complex roots when they exist. Recognize that a particular solution may not be applicable in the original context. Know how to use calculators, graphing utilities or other technology to solve quadratic equations and inequalities.
- 9-11.9.2.4.2 Represent relationships in various contexts using equations involving exponential functions; solve these equations graphically or numerically. Know how to use calculators, graphing utilities or other technology to solve these equations.
- 9-11.9.2.4.3 Recognize that to solve certain equations, number systems need to be extended from whole numbers to integers, from integers to rational numbers, from rational numbers to real numbers, and from real numbers to complex numbers. In particular, non-real complex numbers are needed to solve some quadratic equations with real coefficients.
- 9-11.9.2.4.5 Solve linear programming problems in two variables using graphical methods.
- 9-11.9.2.4.6 Represent relationships in various contexts using absolute value inequalities in two variables; solve them graphically.
- 9-11.9.2.4.7 Solve equations that contain radical expressions. Recognize that extraneous solutions may arise when using symbolic methods.
- 9-11.9.2.4.8 Assess the reasonableness of a solution in its given context and compare the solution to appropriate graphical or numerical estimates; interpret a solution in the original context.

### 9-11.9.4 Data Analysis & Probability

- 9-11.9.4.1 Display and analyze data; use various measures associated with data to draw conclusions, identify trends and describe relationships.
- 9-11.9.4.1.1 Describe a data set using data displays, including box-and-whisker plots; describe and compare data sets using summary statistics, including measures of center, location and spread. Measures of center and location include mean, median, quartile and percentile. Measures of spread include standard deviation, range and inter-quartile range. Know how to use calculators, spreadsheets or other technology to display data and calculate summary statistics.
- 9-11.9.4.1.2 Analyze the effects on summary statistics of changes in data sets.
- 9-11.9.4.1.3 Use scatterplots to analyze patterns and describe relationships between two variables. Using technology, determine regression lines (line of best fit) and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions.
- 9-11.9.4.1.4 Use the mean and standard deviation of a data set to fit it to a normal distribution (bell-shaped curve) and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets and tables to estimate areas under the normal curve.

- 9-11.9.4.2 Explain the uses of data and statistical thinking to draw inferences, make predictions and justify conclusions.
- 9-11.9.4.2.1 Evaluate reports based on data published in the media by identifying the source of the data, the design of the study, and the way the data are analyzed and displayed. Show how graphs and data can be distorted to support different points of view. Know how to use spreadsheet tables and graphs or graphing technology to recognize and analyze distortions in data displays.
- 9-11.9.4.2.3 Design simple experiments and explain the impact of sampling methods, bias and the phrasing of questions asked during data collection.

- 9-11.9.4.3 Calculate probabilities and apply probability concepts to solve real-world and mathematical problems.
- 9-11.9.4.3.1 Select and apply counting procedures, such as the multiplication and addition principles and tree diagrams, to determine the size of a sample space (the number of possible outcomes) and to calculate probabilities.
- 9-11.9.4.3.2 Calculate experimental probabilities by performing simulations or experiments involving a probability model and using relative frequencies of outcomes.
- 9-11.9.4.3.3 Understand that the Law of Large Numbers expresses a relationship between the probabilities in a probability model and the experimental probabilities found by performing simulations or experiments involving the model.
- 9-11.9.4.3.4 Use random numbers generated by a calculator or a spreadsheet, or taken from a table, to perform probability simulations and to introduce fairness into decision making.
- 9-11.9.4.3.5 Apply probability concepts such as intersections, unions and complements of events, and conditional probability and independence, to calculate probabilities and solve problems.
- 9-11.9.4.3.6 Describe the concepts of intersections, unions and complements using Venn diagrams. Understand the relationships between these concepts and the words AND, OR, NOT, as used in computerized searches and spreadsheets.
- 9-11.9.4.3.7 Understand and use simple probability formulas involving intersections, unions and complements of events.
- 9-11.9.4.3.8 Apply probability concepts to real-world situations to make informed decisions.
- 9-11.9.4.3.9 Use the relationship between conditional probabilities and relative frequencies in contingency tables.