Indiana: Finite Mathematics Math Standards
27 standards · 5 domains
MATRICES
- FM.MA.1 Add, subtract, and multiply matrices of appropriate dimensions (i.e. up to 3x3 matrices). Multiply matrices by scalars. Calculate row and column sums for matrix equations.
- FM.MA.2 Understand 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.
- FM.MA.3 Understand the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
- FM.MA.4 Solve problems represented by matrices using row-reduction techniques and properties of matrix multiplication, including identity and inverse matrices.
- FM.MA.5 Use matrices to solve real-world problems that can be modeled by a system of equations (i.e. up to 3 linear equations) in two or three variables using technology.
- FM.MA.6 Build and use matrix representations to model polygons, transformations, and computer animations.
NETWORKS
- FM.N.1 Use networks, traceable paths, tree diagrams, Venn diagrams, and other pictorial representations to find the number of outcomes in a problem situation.
- FM.N.2 Optimize networks in different ways and in different contexts by finding minimal spanning trees, shortest paths, and Hamiltonian paths including real-world problems.
- FM.N.3 Use critical-path analysis in the context of scheduling problems and interpret the results.
- FM.N.4 Construct and interpret directed and undirected graphs, decision trees, networks, and flow charts that model real-world contexts and problems.
- FM.N.5 Use graph-coloring techniques to solve problems.
- FM.N.6 Construct vertex-edge graph models involving relationships among a finite number of elements. Describe a vertex-edge graph using an adjacency matrix. Use vertex-edge graph models to solve problems in a variety of real-world settings.
OPTIMIZATION
PROBABILITY
- FM.P.1 Use Markov chains to solve problems with and without technology.
- FM.P.2 Understand and use the addition rule to calculate probabilities for mutually exclusive and non mutually exclusive events
- FM.P.3 Understand and use the multiplication rule to calculate probabilities for independent and dependent events. Understand 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.
- FM.P.4 Understand the multiplication counting principle, permutations, and combinations; use them to solve real-world problems. Use simulations with and without technology to solve counting and probability problems.
- FM.P.5 Calculate the probabilities of complementary events.
- FM.P.6 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
- FM.P.7 Analyze decisions and strategies using probability concepts. Analyze probabilities to interpret odds and risk of events.
- FM.P.8 Describe 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.
- FM.P.9 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
- FM.P.10 Use the relative frequency of a specified outcome of an event to estimate the probability of the outcome and apply the law of large numbers in simple examples.