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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.
- 9-11.9.2.1.1 Understand the definition of a function. Use functional notation and evaluate a function at a given point in its domain.
- 9-11.9.2.1.2 Distinguish between functions and other relations defined symbolically, graphically or in tabular form.
- 9-11.9.2.1.3 Find the domain of a function defined symbolically, graphically or in a real-world context.
- 9-11.9.2.1.4 Obtain information and draw conclusions from graphs of functions and other relations.
- 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.
- 9-11.9.2.1.8 Make qualitative statements about the rate of change of a function, based on its graph or table of values.
- 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.
- Checkpoint opportunity

- 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.
- 9-11.9.2.2.1 Represent and solve problems in various contexts using linear and quadratic functions.
- 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.
- Checkpoint opportunity

- 9-11.9.2.3 Generate equivalent algebraic expressions involving polynomials and radicals; use algebraic properties to evaluate expressions.
- 9-11.9.2.3.2 Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree.
- 9-11.9.2.3.3 Factor common monomial factors from polynomials, factor quadratic polynomials, and factor the difference of two squares.
- 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.
- 9-11.9.2.3.7 Justify steps in generating equivalent expressions by identifying the properties used. Use substitution to check the equality of expressions for some particular values of the variables; recognize that checking with substitution does not guarantee equality of expressions for all values of the variables.
- Checkpoint opportunity

- 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.
- 9-11.9.2.4.4 Represent relationships in various contexts using systems of linear inequalities; solve them graphically. Indicate which parts of the boundary are included in and excluded from the solution set using solid and dotted lines.
- 9-11.9.2.4.6 Represent relationships in various contexts using absolute value inequalities in two variables; solve them graphically.
- Checkpoint opportunity

### 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.
- Checkpoint opportunity

- 9-11.9.4.2 Explain the uses of data and statistical thinking to draw inferences, make predictions and justify conclusions.
- 9-11.9.4.2.2 Identify and explain misleading uses of data; recognize when arguments based on data confuse correlation and causation.
- 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.
- Checkpoint opportunity

- 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.
- Checkpoint opportunity