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Statistics A.11. The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve real-world problems, using mathematical models. Mathematical models will include linear and quadratic functions.
Functions A.7. The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including A.7.a) determining whether a relation is a function. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
A.7.d) x- and y-intercepts.
A.8. The student, given a situation in a real-world context, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
Equations and Inequalities A.4. The student will solve multistep linear and quadratic equations in two variables, including A.4.a) solving literal equations (formulas) for a given variable.
A.4.d) solving multistep linear equations algebraically and graphically.
A.4.e) solving systems of two linear equations in two variables algebraically and graphically.
A.5. The student will solve multistep linear inequalities in two variables, including A.5.a) solving multistep linear inequalities algebraically and graphically.
A.6. The student will graph linear equations and linear inequalities in two variables, including A.6.a) determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined.
Expressions and Operations A.1. The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables.
A.2. The student will perform operations on polynomials, including A.2.a) applying the laws of exponents to perform operations on expressions.
A.2.b) adding, subtracting, multiplying, and dividing polynomials.
VA.AFDA.Algebra, Functions, and Data Analysis
Algebra, Functions, and Data Analysis
Data Analysis AFDA.6. The student will calculate probabilities. Key concepts include AFDA.6.b) dependent and independent events.
AFDA.6.d) counting techniques (permutations and combinations).
AFDA.8. The student will design and conduct an experiment/survey. Key concepts include AFDA.8.b) sampling technique.
AFDA.8.d) data collection.
AFDA.8.e) data analysis and reporting.
Algebra and Functions AFDA.1. The student will investigate and analyze function (linear, quadratic, exponential, and logarithmic) families and their characteristics. Key concepts include
Statistics AII.10. The student will identify, create, and solve real-world problems involving inverse variation, joint variation, and a combination of direct and inverse variations. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
AII.12. The student will compute and distinguish between permutations and combinations and use technology for applications.
Functions AII.7. The student will investigate and analyze functions algebraically and graphically. Key concepts include AII.7.c) x- and y-intercepts.
Expressions and Operations AII.2. The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve real-world problems, including writing the first n terms, finding the nth term, and evaluating summation formulas. Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
VA.AII/T.Algebra II and Trigonometry
Algebra II and Trigonometry
Statistics AII/T.10. The student will identify, create, and solve real-world problems involving inverse variation, joint variation, and a combination of direct and inverse variations. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
AII/T.12. The student will compute and distinguish between permutations and combinations and use technology for applications.
Functions AII/T.7. The student will investigate and analyze functions algebraically and graphically. Key concepts include AII/T.7.c) x- and y-intercepts.
Expressions and Operations AII/T.2. The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve real-world problems, including writing the first n terms, finding the nth term, and evaluating summation formulas. Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
DM.13. The student will apply the formulas of combinatorics in the areas of DM.13a). the Fundamental (Basic) Counting Principle;
DM.13c). permutations and combinations; and
Three-Dimensional Figures G.14. The student will use similar geometric objects in two- or three-dimensions to G.14.a) compare ratios between side lengths, perimeters, areas, and volumes.
G.14.d) solve real-world problems about similar geometric objects.
Reasoning, Lines, and Transformations G.2. The student will use the relationships between angles formed by two lines cut by a transversal to G.2.a) determine whether two lines are parallel.
G.2.b) verify the parallelism, using algebraic and coordinate methods as well as deductive proofs.
G.2.c) solve real-world problems involving angles formed when parallel lines are cut by a transversal.
G.3. The student will use pictorial representations, including computer software, constructions, and coordinate methods, to solve problems involving symmetry and transformation. This will include G.3.a) investigating and using formulas for finding distance, midpoint, and slope.
G.3.b) applying slope to verify and determine whether lines are parallel or perpendicular.
G.3.c) investigating symmetry and determining whether a figure is symmetric with respect to a line or a point.
Polygons and Circles G.11. The student will use angles, arcs, chords, tangents, and secants to G.11.b) solve real-world problems involving properties of circles.
MA.6. The student will use mathematical induction to prove formulas and mathematical statements.
MA.9. The student will investigate and identify the characteristics of exponential and logarithmic functions in order to graph these functions and solve equations and real-world problems. This will include the role of e, natural and common logarithms, laws of exponents and logarithms, and the solution of logarithmic and exponential equations. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
VA.PS.Probability and Statistics
Probability and Statistics
PS.1. The student will analyze graphical displays of univariate data, including dotplots, stemplots, and histograms, to identify and describe patterns and departures from patterns, using central tendency, spread, clusters, gaps, and outliers. Appropriate technology will be used to create graphical displays.
PS.11. The student will identify and describe two or more events as complementary, dependent, independent, and/or mutually exclusive.
PS.12. The student will find probabilities (relative frequency and theoretical), including conditional probabilities for events that are either dependent or independent, by applying the Law of Large Numbers concept, the addition rule, and the multiplication rule.
PS.15. The student will identify random variables as independent or dependent and find the mean and standard deviations for sums and differences of independent random variables.
PS.2. The student will analyze numerical characteristics of univariate data sets to describe patterns and departures from patterns, using mean, median, mode, variance, standard deviation, interquartile range, range, and outliers.
PS.3. The student will compare distributions of two or more univariate data sets, analyzing center and spread (within group and between group variations), clusters and gaps, shapes, outliers, or other unusual features.
PS.4. The student will analyze scatterplots to identify and describe the relationship between two variables, using shape; strength of relationship; clusters; positive, negative, or no association; outliers; and influential points.
PS.5. The student will find and interpret linear correlation, use the method of least squares regression to model the linear relationship between two variables, and use the residual plots to assess linearity.
PS.8. The student will describe the methods of data collection in a census, sample survey, experiment, and observational study and identify an appropriate method of solution for a given problem setting.
PS.9. The student will plan and conduct a survey. The plan will address sampling techniques (e.g., simple random, stratified) and methods to reduce bias.