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A.A.1. Relations and Functions: Analyze functions and relations (e.g. polynomial, absolute value, rational, radical, logarithmic, exponential, algebraic, piece-wise, and step functions). A.A.1.1. Demonstrate an understanding of the concept of a function, use function notation, evaluate a function, determine whether or not a given relation is a function and determine whether or not a given function is one-to-one. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
A.A.1.10. Collect and analyze data to make predictions and to investigate scatterplots and to determine the equation for a curve of best fit including linear, power, exponential, and logarithmic functions.
A.A.1.11. Connect the relationships among the solution of an equation, zero of a function, x-intercept of a graph and the factors of a polynomial expression.
A.A.1.12. Find the x and y-intercepts of a function if they exist.
A.A.1.13. Identify, distinguish between, and describe the characteristics of the following functions in tabular, verbal, graphical or symbolic form: polynomial, power, absolute value, rational, radical, logarithmic, exponential, algebraic, piecewise, and step. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
A.A.4. Polynomial Functions: Model and analyze polynomial functions. Solve polynomial equations. A.A.4.1. Perform operations on polynomial expressions.
A.A.4.2. Analyze and calculate permutations, combinations, and other systematic counting methods.
A.A.5. Radical Functions: Model and analyze radical functions. Solve radical equations. A.A.5.1. Find equivalent expressions using the properties of rational exponents.
A.A.7. Logarithmic and Exponential Functions: Model and analyze logarithmic and exponential functions. Solve logarithmic and exponential equations. A.A.7.4. Graph and analyze exponential and logarithmic functions. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
A.A.8. Matrices, Systems of Equations and Inequalities: Analyze and apply various methods to graph and solve systems of equations and inequalities. A.A.8.2. Solve systems of linear equations in two or three variables algebraically, graphically, and/or with matrix algebra.
A.A.8.3. Analyze an inconsistent system of equations.
A.A.9. Sequences and Series: Analyze and evaluate sequences and series. A.A.9.1. Define, recognize, and discriminate among arithmetic, geometric and other sequences and series. Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
A.A.9.5. Generate and describe other recursive sequences such as factorials and the Fibonacci sequence. Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
OR.A.D.Advanced Discrete Mathematics
Advanced Discrete Mathematics
A.D.1. Set Theory: Operate with sets and use set theory to solve problems. A.D.1.3. Use Venn diagrams to explore relationships and patterns, and to make arguments about relationships between sets.
A.D.5. Combinatorics and Discrete Probability: Understand and apply fundamental counting techniques in solving combinatorial and probability problems. A.D.5.1. Produce all combinations and permutations of sets.
A.D.5.2. Calculate the number of combinations and permutations of sets of m items taken n at a time.
A.D.5.3. Apply basic fundamental counting principles such as The Pigeonhole Principle, Multiplication Principle, Addition Principle, and Binomial Theorem to practical problems.
A.D.5.4. Solve probability problems such as conditional probability, probability of simple events, mutually exclusive events, and independent events
A.D.6. Sequences and Series: Analyze and evaluate sequences and series. A.D.6.1. Define, recognize, and discriminate among arithmetic, geometric and other sequences and series. Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
A.D.6.5. Generate and describe other recursive sequences such as factorials and the Fibonacci sequence. Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
A.D.7. Recurrence, Recursion and Induction: Understand and apply recurrence, recursive, and inductive methods to solve problems. A.D.7.3. Use mathematical induction to prove recurrence relations and concepts in number theory such as sums of infinite integer series, divisibility statements, and parity statements.
A.D.7.4. Use mathematical induction to analyze the validity of an iterative algorithm.
A.D.7.5. Describe arithmetic and geometric sequences recursively. Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
A.D.8. Logic: Understand the fundamentals of propositional logic, arguments, and methods of proof. A.D.8.7. Appropriately select and use methods of deductive, inductive, and indirect proof and determine whether a short proof is logically valid.
A.S.1. Exploratory Data: Analyze summary measures of sets of data. A.S.1.1. Construct, interpret, and summarize numerical characteristics of univariate data sets to describe patterns and departure from patterns, using measures of center, spread, and position.
A.S.1.3. Explore bivariate data by analyzing patterns, correlation, linearity, least-squares regression line, residual plots, outliers, influential points, and transformations to achieve linearity.
A.S.1.4. Explore categorical data using frequency tables and bar charts; investigating marginal, joint and conditional relative frequencies; and by comparing distributions.
A.S.2. Sampling and Experimentation: Plan, conduct, and analyze well-designed methods of data collection. A.S.2.1. Describe the methods of data collection. Evaluate how appropriate each method is relative to the purposes of various types of inquires and hypotheses under investigation given various population distributions.
A.S.2.2. Plan, analyze, and conduct a survey, and/or observational study; describe characteristics of a well-designed and well-conducted survey; explore various sampling methods including investigating sources of bias.
A.S.2.3. Plan, analyze, and conduct an experiment; describe characteristics and components of a well-designed and well-conducted experiment; explore various methods of experimental designs; and associated sources of bias and confounding.
A.S.2.4. Explore the generalizability of results and types of conclusions that can be drawn from observational studies, experiments, and surveys. Understand when each method is most appropriate, and explain the differences between the three methods.
A.S.3. Anticipating Patterns: Understand how probability can be applied as a tool used for anticipating what the distribution of data should look like under a given model. A.S.3.1. Analyze probability by exploring such topics as ''Law of Large Numbers,'' addition and multiplication rule, conditional probability and independence, discrete random variables and their probability distributions, simulations of random behavior and mean, standard deviation, and learn how to select appropriate linear transformations of a random variable.
A.S.3.2. Explore the independence versus dependence of two random variables. Determine the mean and standard deviation for sum or difference of independent random variables.
A.S.4. Statistical Inference: Estimate population parameters and test hypotheses. A.S.4.5. Understand how to read the results of a regression, and use this to make predictions of future events with a stated confidence.
H.1A. Algebra and Numeracy: Demonstrate a deep understanding of real numbers and algebraic symbols by fluently creating, manipulating, computing with, and determining equivalent expressions, both numeric and symbolic. H.1A.3. Express square roots in equivalent radical form and their decimal approximations when appropriate. Quiz, Flash Cards, Worksheet, Game & Study Guide Real numbers
H.1A.4. Develop, identify, and/or justify equivalent algebraic expressions, equations, and inequalities using the properties of exponents, equality and inequality, as well as the commutative, associative, inverse, identity, and distributive properties. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
H.2A. Algebra: Use linear equations and functions to represent relationships and solve linear equations, linear inequalities, systems of linear equations, and systems of linear inequalities. H.2A.1. Identify, construct, extend, and analyze linear patterns and functional relationships that are expressed contextually, numerically, algebraically, graphically, in tables, or using geometric figures. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
H.2A.2. Given a rule, a context, two points, a table of values, a graph, or a linear equation in either slope intercept or standard form, identify the slope of the line, determine the x and/or y intercept(s), and interpret the meaning of each.
H.2A.7. Write, use, and solve linear equations and inequalities using graphical and symbolic methods with one or two variables. Represent solutions on a coordinate graph or number line.
H.2A.8. Solve systems of two linear equations graphically and algebraically, and solve systems of two linear inequalities graphically.
H.3A. Algebra: Use quadratic and exponential equations and functions to represent relationships. H.3A.4. Given a quadratic or exponential function, interpret and analyze the relationship between the independent and dependent variables, and evaluate the function for specific values of the domain. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
H.1G. Geometry: Apply properties of two-dimensional figures. H.1G.1. Identify, apply, and analyze angle relationships among two or more lines and a transversal to determine if lines are parallel, perpendicular, or neither.
H.1G.2. Apply theorems, properties, and definitions to determine, identify, and justify congruency or similarity of triangles and to classify quadrilaterals.
H.1G.3. Apply theorems of corresponding parts of congruent and similar figures to determine missing sides and angles of polygons.
H.1G.5. Determine the missing dimensions, angles, or area of regular polygons, quadrilaterals, triangles, circles, composite shapes, and shaded regions.
H.2G. Geometry: Apply properties of three-dimensional solids. H.2G.1. Identify, classify, model, sketch, and label representations of three-dimensional objects from nets and from different perspectives.
H.2G.2. Identify and apply formulas for surface area and volume of spheres; right solids, including rectangular prisms and pyramids; cones; and cylinders; and compositions thereof. Solve related context-based problems.
H.3G. Geometry: Transform and analyze figures. H.3G.1. Recognize and identify line and rotational symmetry of two-dimensional figures.
H.3G.2. Identify and perform single and composite transformations of geometric figures in a plane, including translations, origin-centered dilations, reflections across either axis or y = +/- x, and rotations about the origin in multiples of 90 degrees.
H.3G.3. Apply a scale factor to determine similar two- and three-dimensional figures, are similar. Compare and compute their respective areas and volumes of similar figures.
H.3G.4. Apply slope, distance, and midpoint formulas to solve problems in a coordinate plane.
H.1S. Data Analysis: Analyze and interpret empirical data. H.1S.1. Given a context, determine appropriate survey methods, analyze the strengths and limitations of a particular survey, observational study, experiment, or simulation, and the display of its data.
H.1S.4. Use or construct a scatter plot for a given data set, determine whether there is a (n) linear, quadratic, exponential, or no trend. If linear, determine if there is a positive or negative correlation among the data; and, if appropriate, sketch a line of best fit, and use it to make predictions.
H.1S.5. Construct, analyze, and interpret tables, scatter plots, frequency distributions, and histograms of data sets.
H.2S. Probability: Apply basic principles of probability. H.2S.1. Identify, analyze, and use experimental and theoretical probability to estimate and calculate the probability of simple events.
H.2S.2. Determine the sample space of a probability experiment.
H.2S.3. Compute and interpret probabilities for independent, dependent, complementary, and compound events using various methods (e.g., diagrams, tables, area models, and counting techniques).