Mississippi flagMississippi: Algebra III Math Standards

46 standards · 5 domains

ALGEBRA

  • AIII.A.8 Determine characteristics of graphs of parent functions (domain/range, increasing/decreasing intervals, intercepts, symmetry, end behavior, and asymptotic behavior).
  • AIII.A.9 Determine the end behavior of polynomial functions.
  • AIII.A.10 Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^2 + y^2)^2 = (x^2 – y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples.
  • AIII.A.11 Verify the Binomial Theorem by mathematical induction or by a combinatorial argument.
  • AIII.A.12 Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.
  • AIII.A.13 Write rational expressions in simplest form. (For example (x^3 – x^2 – x + 1)/(x^3 + x^2 – x – 1) = (x – 1)/(x + 1).
  • AIII.A.14 Decompose a rational function into partial fractions.
  • AIII.A.15 Determine asymptotes and holes of rational functions, explain how each was found, and relate these behaviors to continuity.
  • AIII.A.16 Add, subtract, multiply and divide rational expressions.
  • AIII.A.17 Solve polynomial and rational inequalities. Relate results to the behavior of the graphs.
  • AIII.A.18 Find the composite of two given functions and find the inverse of a given function. Extend this concept to discuss the identity function f(x) = x.
  • AIII.A.19 Simplify complex algebraic fractions (with/without variable expressions and integer exponents) to include expressing (f(x+h)-f(x))/h as a single simplified fraction when f(x) = 1/1-x for example.
  • AIII.A.20 Find the possible rational roots using the Rational Root Theorem.
  • AIII.A.21 Find the zeros of polynomial functions by synthetic division and the Factor Theorem.
  • AIII.A.22 Graph and solve quadratic inequalities.

FUNCTIONS

  • AIII.F.23 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
  • AIII.F.24 Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
  • AIII.F.25 Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
  • AIII.F.26 Verify by composition that one function is the inverse of another.
  • AIII.F.27 Read values of an inverse function from a graph or a table, given that the function has an inverse.
  • AIII.F.28 Produce an invertible function from a non-invertible function by restricting the domain.
  • AIII.F.29 Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
  • AIII.F.30 Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x, π+x, and 2π–x in terms of their values for x, where x is any real number.
  • AIII.F.31 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
  • AIII.F.32 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
  • AIII.F.33 Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
  • AIII.F.34 Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.
  • AIII.F.35 Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
  • AIII.F.36 Prove the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

GEOMETRY

  • AIII.G.37 Graph piecewise defined functions and determine continuity or discontinuities.
  • AIII.G.38 Describe the attributes of graphs and the general equations of parent functions (linear, quadratic, cubic, absolute value, rational, exponential, logarithmic, square root, cube root, and greatest integer).
  • AIII.G.39 Explain the effects of changing the parameters in transformations of functions.
  • AIII.G.40 Predict the shapes of graphs of exponential, logarithmic, rational, and piece-wise functions, and verify the prediction with and without technology.
  • AIII.G.41 Relate symmetry of the behavior of even and odd functions.
  • AIII.G.42 Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
  • AIII.G.43 Prove the Laws of Sines and Cosines and use them to solve problems.
  • AIII.G.44 Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

NUMBER AND QUANTITY

  • AIII.NQ.1 Express sequences and series using recursive and explicit formulas.
  • AIII.NQ.2 Evaluate and apply formulas for arithmetic and geometric sequences and series.
  • AIII.NQ.3 Calculate limits based on convergent and divergent series.
  • AIII.NQ.4 Evaluate and apply infinite geometric series.
  • AIII.NQ.5 Extend the meaning of exponents to include rational numbers.
  • AIII.NQ.6 Simplify expressions with fractional exponents to include converting from radicals.
  • AIII.NQ.7 Factor algebraic expressions containing fractional exponents.

STATISTICS AND PROBABILITY

  • AIII.SP.45 Analyze expressions in summation and factorial notation to solve problems.
  • AIII.SP.46 Prove statements using mathematical induction.