South Carolina flagSouth Carolina: Algebra 2 with Probability Math Standards

29 standards · 4 domains

DATA, PROBABILITY, AND STATISTICAL REASONING

  • A2P.DPSR.1.1 Describe events as subsets of a sample space using characteristics or categories of the outcomes, or as unions, intersections, or complements of other events.
  • A2P.DPSR.1.2 Explain whether two events, A and B, are independent if and only 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.
  • A2P.DPSR.1.3 Determine whether 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 in mathematical and real-world situations.
  • A2P.DPSR.1.4 Recognize and explain the concepts of conditional probability and independence.
  • A2P.DPSR.2.1 Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A and interpret the answer in terms of the model.
  • A2P.DPSR.2.2 Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B) and interpret the answer in terms of the model.
  • A2P.DPSR.2.3 Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)*P(B|A) = P(B)*P(A|B) and interpret the answer in terms of the model.
  • A2P.DPSR.2.4 Use permutations and combinations to determine the number of possible outcomes in a sample space.

MEASUREMENT, GEOMETRY, AND SPATIAL REASONING

  • A2P.MGSR.1.1 Build the unit circle for sine and cosine functions using right triangle definitions.
  • A2P.MGSR.1.2 Use models of periodic phenomena to evaluate and analyze the graph of sine and cosine functions.

NUMERICAL REASONING

  • A2P.NR.1.1 Understand that there is an imaginary unit i such that i^2 = -1 and explain the structure of a complex number as a + bi, where a and b are real.
  • A2P.NR.1.2 Add, subtract, and multiply complex numbers.
  • A2P.NR.2.1 Perform operations with matrices including addition, subtraction, and scalar multiplication.

PATTERNS, ALGEBRA, AND FUNCTIONAL REASONING

  • A2P.PAFR.1.1 Graph, identify roots, and analyze quadratic functions in mathematical and real-world situations.
  • A2P.PAFR.1.2 Solve quadratic inequalities that model mathematical and real-world situations.
  • A2P.PAFR.1.3 Graph and analyze polynomial functions in mathematical and real-world situations.
  • A2P.PAFR.1.4 Solve polynomial inequalities that model mathematical and real-world situations.
  • A2P.PAFR.1.5 Recognize perfect squares and perfect cubes and use them to describe the structure of polynomials.
  • A2P.PAFR.2.1 Graph rational and radical functions and describe their key features. Limit to square roots and cube roots only.
  • A2P.PAFR.2.2 Perform arithmetic operations on rational expressions, including problems in context, and express rational expressions in irreducible form.
  • A2P.PAFR.2.3 Create and solve rational and radical equations in one variable, including those that model real-life situations, and verify solutions to identify extraneous solutions if they appear.
  • A2P.PAFR.3.1 Create, solve, and graph exponential functions, including those that model real-life situations.
  • A2P.PAFR.3.2 Find the sum of the terms of arithmetic and geometric sequences.
  • A2P.PAFR.4.1 Identify the effect on the graph of replacing f(x) by kf(x), f(x)+k, f(x-k), f(kx) for any real number k including multiple transformations; write an equation of a transformed parent function given its graph. Extend to equations involving rational, polynomial, radical, exponential, and piecewise.
  • A2P.PAFR.5.1 Graph piecewise functions and describe their key features.
  • A2P.PAFR.5.2 Solve linear absolute value inequalities.
  • A2P.PAFR.6.1 Find the inverse of functions and verify graphically.
  • A2P.PAFR.6.2 Calculate and interpret the average rate of change of the function over a specified interval, given a function in graphical, symbolic, or numerical form.
  • A2P.PAFR.6.3 Use linear programming to solve systems of equations and inequalities by addressing the constraints that arise in real-world situations.