SC High School Discrete Math Curriculum

SC High School Discrete Math Curriculum

• CC.HSS.CP.B.9Use permutations and combinations to compute probabilities of compound events and solve problems.
  • Permutations
  • Combinations
  • Probability involving permutations and combinations
• CC.HSS.CP.A.1Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").
  • Introduction to probability
  • Organizing outcomes
  • Introduction to probability
  • Set notation
  • Set builder notation
  • Intersection and union of 2 sets
  • Intersection and union of 3 sets
• CC.HSS.CP.A.2Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
  • Probability of independent events
  • Multiplication rule for
  • Probability of independent events
• CC.HSS.CP.A.3Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
  • Conditional probability
• CC.HSS.CP.A.5Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
  • Comparing experimental and theoretical probability
• CC.HSS.MD.A.1Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
  • Probability distribution - histogram, mean, variance & standard deviation
• CC.HSS.MD.A.2Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
  • Properties of expectation
• CC.HSS.MD.A.3Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
  • Binomial distribution
  • Mean and standard deviation of binomial distribution
• CC.HSS.MD.B.7Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
  • Type 1 and type 2 errors
• CC.HSF.IF.A.1Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
  • Domain and range of a function
  • Function notation (advanced)
  • Identifying functions
• CC.HSF.IF.A.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
  • Function notation
  • Difference quotient: applications of functions
• CC.HSF.IF.A.3Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
  • Greatest common factors (GCF)
  • Introduction to sequences
  • Sigma notation
• CC.HSF.IF.B.5Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
  • Point of discontinuity
  • Even and odd functions
• CC.HSF.BF.A.2Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
  • Arithmetic sequences
  • Geometric sequences
  • Arithmetic series
  • Geometric series
  • Infinite geometric series
• CC.HSF.BF.B.4Find inverse functions.
  • Finding the quadratic functions for given parabolas
  • Inverse functions
• CC.HSF.LE.A.2Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
  • Graphing linear functions using table of values
• CC.HSA.SSE.B.4Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
  • Geometric series
  • Factor by taking out the greatest common factor
  • Factor by grouping
  • Factoring difference of squares: $x^2 - y^2$
• CC.HSN.VM.C.6Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
  • Notation of matrices
  • Adding and subtracting matrices
• CC.HSN.VM.C.9Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
  • Properties of matrix multiplication
• CC.HSN.VM.C.10Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
  • Zero matrix
  • Identity matrix
  • The determinant of a 2 x 2 matrix
  • The determinant of a 3 x 3 matrix (General & Shortcut Method)
  • The Inverse of a 2 x 2 matrix
• CC.HSN.VM.C.11Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
  • Transforming vectors with matrices
  • Transforming shapes with matrices
• CC.HSA.REI.C.8Represent a system of linear equations as a single matrix equation in a vector variable.
  • Representing a linear system as a matrix
  • Notation of matrices
  • Adding and subtracting matrices
  • Scalar multiplication of matrices
• CC.HSA.REI.C.9Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).
  • The Inverse of a 2 x 2 matrix
  • Solving linear systems using 2 x 2 inverse matrices
  • Matrix multiplication
  • The three types of matrix row operations
• CC.HSS.ID.A.2Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
  • Median and mode
  • Mean
  • Range and outliers
  • Center of a data set: mean, median, mode
  • Spread of a data set - standard deviation & variance
• CC.HSS.ID.A.3Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
  • Application of averages
  • Shapes of distributions
• CC.HSS.IC.A.1Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
  • Sampling methods
• CC.HSS.IC.B.3Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
  • Census and bias
• CC.HSS.IC.B.4Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
  • Margin of error
  • Confidence intervals to estimate population mean
  • Making a confidence interval
• CC.HSN.VM.A.1Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes.
  • Use sine ratio to calculate angles and sides (Sin = o / h)
  • Introduction to vectors
  • Magnitude of a vector
  • Direction angle of a vector
• CC.HSN.VM.A.2Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
  • Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
  • Scalar multiplication of vectors
  • Equivalent vectors
• CC.HSN.VM.B.4Add and subtract vectors.
  • Slope equation: $m = \frac{y_2-y_1}{x_2- x_1}$
  • Adding and subtracting vectors in component form
  • Operations on vectors in magnitude and direction form
• CC.HSN.VM.B.5Multiply a vector by a scalar.
  • Slope intercept form: y = mx + b
  • Unit vector