Algebra, Functions, and Data Analysis (Virginia SOL)

Algebra and Functions (AF)

• AFDA.AF.1 Investigate linear, quadratic, and exponential function families algebraically and graphically, using transformations of parent functions.
• Recognize the graphs and equations of linear, quadratic, and exponential parent functions.
• Explain the transformation from a parent function given an equation or graph.
• Decide which function family best models a given representation, including in context.
• Write a linear, quadratic, or exponential equation from a graph using transformations.
• Use graphs or equations to solve contextual problems graphically and algebraically.
• Graph functions using transformations and verify with technology.
• Compare linear, quadratic, and exponential functions across graphs, tables, equations, and descriptions.
• AFDA.AF.2 Analyze characteristics of graphs of linear, quadratic, exponential, and piecewise-defined functions.
• From a graph, find the domain and range, including limits set by a context.
• Identify intervals on which a function is increasing, decreasing, or constant.
• From a graph, locate absolute maximum and minimum values.
• From a graph, find zeros and intercepts.
• Connect points on a graph with the corresponding function values.
• Describe the end behavior of a function from its graph.
• Identify horizontal and vertical asymptotes from a graph, where they exist.
• Describe and relate graph characteristics of the four function types, including in context.
• AFDA.AF.3 Model contextual optimisation problems with systems of linear equations or inequalities and solve them.
• Represent and interpret optimisation problems with systems of linear equations or inequalities.
• Solve systems of up to four equations or inequalities graphically, and algebraically where suitable.
• Identify the feasible region of a system of linear inequalities.
• Identify the coordinates of the vertices of a feasible region.
• Find and describe the maximum or minimum of a function over a feasible region.
• Check the validity of solutions and justify the reasonableness of answers or methods in context.

Data Analysis (DA)

• AFDA.DA.1 Apply the data cycle to bivariate scatterplots and fit linear, quadratic, or exponential curves of best fit.
• Formulate questions requiring bivariate data with two quantitative variables.
• Collect or acquire bivariate data from a representative sample.
• Create a scatterplot with technology and describe the relationship in context.
• Use data, scatterplots, or models to make predictions, decisions, and critical judgments.
• AFDA.DA.2 Apply the data cycle with an emphasis on designing and conducting experiments and observational studies.
• Formulate questions answerable with data and decide whether the data are quantitative or categorical.
• Describe and choose sampling methods: simple random, stratified, and cluster.
• Plan and conduct a study addressing control, randomisation, and experimental error.
• Collect or acquire data to answer a statistical question.
• Recognize data errors, missing values, or bias and decide how to handle them.
• Identify biased sampling methods.
• Given a study plan, identify sources of bias and ways to reduce them.
• Select and create visual representations of data.
• Apply appropriate statistical methods to analyze data.
• Communicate the study, data, analysis, and validity of conclusions.
• AFDA.DA.3 Calculate and interpret probabilities, including in context.
• Analyze, interpret, and predict outcomes using theoretical probability.
• Calculate conditional probabilities for dependent, independent, and mutually exclusive events.
• Calculate probabilities using Venn diagrams, tree diagrams, organized lists, two-way tables, or simulations.
• Interpret probabilities from simulations or experiments to make and justify decisions.
• Define and give examples of complementary, dependent, independent, and mutually exclusive events.
• Decide whether events are complementary, dependent, independent, or mutually exclusive.
• Compare and contrast permutations and combinations, including in context.
• Calculate permutations of n objects taken r at a time, without repetition.
• Calculate combinations of n objects taken r at a time, without repetition.
• AFDA.DA.4 Describe and apply properties of the normal distribution, including in context.
• Identify and describe the properties of a normal distribution.
• Decide when a normal distribution reasonably represents a data set.
• Describe how the mean and standard deviation affect the graph of a normal curve.
• Calculate and interpret a z-score given the mean and standard deviation.
• Compare two normally distributed data sets using standard normal curves and z-scores.
• Represent probability as area under the standard normal curve.
• Find probabilities under the standard normal curve using technology or a table.
• Investigate and relate normally distributed data sets to their descriptive statistics.