Nebraska flagNebraska: High School Advanced Topics Math Standards

44 standards · 4 domains

ALGEBRA

  • AT.A.1.a Analyze and graph nonlinear functions (trigonometric, rational, higher-order polynomials, logarithmic, and piecewise) and relations (conic sections) using their points of interest and graphing technology.
  • AT.A.1.b Use the unit circle to define the trigonometric functions on multiples of known angles (positive and negative multiples of 30 and 45 degrees or pi/6 and pi/4).
  • AT.A.1.c Given a function, list the sequence of algebraic transformations that changes a parent function to the given function.
  • AT.A.1.d Define the radian unit of measure and its relationship with degrees.
  • AT.A.2.a Explain symmetry of functions and determine whether a function is odd, even, or neither.
  • AT.A.2.b Represent, interpret, and analyze inverses of functions algebraically and graphically using domain restrictions when necessary.
  • AT.A.2.c Write equations of nonlinear functions (trigonometric, rational, higher-order polynomials, logarithmic and piecewise) using points of interest of the function.
  • AT.A.2.d Convert between radian and degree measures of an angle.
  • AT.A.2.e Use limits to describe the behavior of a function near its asymptotes and removable discontinuities.
  • AT.A.3.a Analyze and model authentic situations using various non-linear representations and relations with appropriate technology.
  • AT.A.3.b Analyze and model authentic application situations using various non-linear representations and relations with appropriate technology.

DATA

  • AT.D.1.a Explain what constitutes good practice in designing a sample survey, an experiment, and an observational study.
  • AT.D.1.b Explain the use of randomization to reduce the influence of confounding or lurking variables.
  • AT.D.1.c Explain issues of bias and confounding variables in a study and their implications for interpretation.
  • AT.D.1.d Demonstrate knowledge of the role sampling distributions play in the estimation of an unknown population parameter through the use of appropriate sampling techniques.
  • AT.D.2.a Determine when a data set can be reasonably said to be normally distributed and draw conclusions about the data from the associated normal distribution.
  • AT.D.2.b Use technology to develop regression models for linear and non-linear data to predict unobserved outcomes. Apply algebraic transformations to non-linear data to generate a linearized data set and employ linear regression techniques to analyze the non-linear data set.
  • AT.D.3.a Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. Interpret the expected value as the mean of a probability distribution.
  • AT.D.3.b Communicate what constitutes statistical significance. Interpret statistical significance in the context of a situation and answer investigative questions appropriately.
  • AT.D.3.c Use data to compare two groups, describe sample variability, and decide if differences between parameters are significant based on the statistics.
  • AT.D.3.d Use probability as a tool for assessing risk and for informed decision making by computing and interpreting P-values.
  • AT.D.3.e Use confidence intervals to estimate an unknown population parameter.

GEOMETRY

  • AT.G.1.a Apply the Law of Sines and the Law of Cosines to find unknown measures in triangles.
  • AT.G.2.a Determine the three-dimensional object created by rotating or revolving a two-dimensional object about an axis.
  • AT.G.2.b Determine the shape of a two-dimensional cross-section of a three-dimensional object.
  • AT.G.2.c Use Cavalieri’s Principle to determine volume of three-dimensional figures.
  • AT.G.3.a Identify symmetry properties of a function (e.g., axis of symmetry of a parabola) and know the connection between its symmetry properties and specific transformations.
  • AT.G.3.b Recognize that translations can be described in terms of vectors.
  • AT.G.3.c Find the images and preimages of transformations of a point, shape, or relation on the coordinate plane, where transformations include the following compositions: reflections about lines of any rational slope passing through the origins, delations about the origin by any positive scale factor, and translations.
  • AT.G.3.d Explain the focus-directrix construction of a parabola and derive the equation of a parabola from focus and directrix for a parabola whose axis of symmetry is a coordinate axis.
  • AT.G.4.a Use known definitions and results in informal argumentation to construct logical arguments.
  • AT.G.4.b Distinguish between empirical reasoning, examples, and deductive reasoning, as well as informal and formal reasoning.
  • AT.G.4.c Evaluate the deductive consequences of alternative definitions of known objects (e.g., whether a trapezoid is defined as a quadrilateral with exactly one pair of parallel sides or defined as at least one pair of parallel sides).

NUMBER

  • AT.N.1.a Use domain and range restrictions to apply an appropriate viewing window while using graphing technology.
  • AT.N.1.b Compare and contrast radians and degrees as measures of angles and the reason graphing utilities tend to use radians as the default setting.
  • AT.N.2.a Perform arithmetic operations with complex numbers.
  • AT.N.2.b Represent complex numbers and their operations in the complex plane.
  • AT.N.2.c Use complex numbers in polynomial identities and equations.
  • AT.N.2.d Represent quantities using bases other than decimal such as binary (base 2) or hexadecimal (base 16) and convert numbers to and from base 10.
  • AT.N.2.e Explain modular arithmetic and its role in computer programming.
  • AT.N.2.f Represent and model vector quantities.
  • AT.N.2.g Perform operations on vectors.
  • AT.N.2.h Perform operations on matrices and use matrices in applications.
  • AT.N.3.a Use vectors to communicate the geometric relationships between complex numbers in the complex plane.