High School Advanced Topics (Nebraska Standards)

Number (N)

• MA.AT.N.1 Use estimation strategies and technology to reason and solve problems.
  • MA.AT.N.1.a Use domain and range to set a suitable graphing window.
  • MA.AT.N.1.b Compare radians and degrees and why graphing tools default to radians.
• MA.AT.N.2 Compare subsets of, and operate within, the complex number system.
  • MA.AT.N.2.a Do arithmetic with complex numbers.
  • MA.AT.N.2.b Show complex numbers and operations on the complex plane.
  • MA.AT.N.2.c Use complex numbers in polynomial identities and equations.
  • MA.AT.N.2.d Write numbers in bases such as binary and hexadecimal and convert to and from base 10.
  • MA.AT.N.2.e Explain modular arithmetic and its use in computer programming.
  • MA.AT.N.2.f Represent and model vector quantities.
  • MA.AT.N.2.g Do operations on vectors.
  • MA.AT.N.2.h Do matrix operations and use matrices in applications.
• MA.AT.N.3 Reason abstractly and quantitatively with units.
  • MA.AT.N.3.a Use vectors to show geometric relationships between complex numbers.

Algebra (A)

• MA.AT.A.1 Show and represent relationships with functions.
  • MA.AT.A.1.a Analyze and graph nonlinear functions and conic sections using key points and technology.
  • MA.AT.A.1.b Use the unit circle to define trig functions at multiples of 30° and 45° (π/6 and π/4).
  • MA.AT.A.1.c List the transformations that turn a parent function into a given function.
  • MA.AT.A.1.d Define the radian and how it relates to degrees.
• MA.AT.A.2 Use properties of operations with nonlinear expressions, equations and inequalities.
  • MA.AT.A.2.a Explain symmetry of functions and identify odd, even or neither.
  • MA.AT.A.2.b Analyze inverse functions algebraically and graphically, restricting domains when needed.
  • MA.AT.A.2.c Write equations of nonlinear functions from key points.
  • MA.AT.A.2.d Convert between radians and degrees.
  • MA.AT.A.2.e Use limits to describe behavior near asymptotes and removable discontinuities.
• MA.AT.A.3 Solve real problems using nonlinear functions and relations.
  • MA.AT.A.3.a Model real situations with nonlinear representations and technology.
  • MA.AT.A.3.b Model further real applications with nonlinear representations and technology.

Geometry (G)

• MA.AT.G.1 Identify attributes, use properties and theorems, and create two-dimensional shapes.
  • MA.AT.G.1.a Use the laws of sines and cosines to find unknown measures in triangles.
• MA.AT.G.2 Identify attributes, use properties and theorems, and create three-dimensional shapes.
  • MA.AT.G.2.a Identify the solid made by rotating a 2D figure about an axis.
  • MA.AT.G.2.b Identify the shape of a 2D cross-section of a solid.
  • MA.AT.G.2.c Use Cavalieri's principle to find volumes.
• MA.AT.G.3 Show and represent location, orientation and relationships on the coordinate plane.
  • MA.AT.G.3.a Identify symmetry in functions and link it to transformations.
  • MA.AT.G.3.b Describe translations with vectors.
  • MA.AT.G.3.c Find images and preimages under reflections in rational-slope lines through the origin, dilations, translations and combinations.
  • MA.AT.G.3.d Explain the focus–directrix construction of a parabola and derive its equation.
• MA.AT.G.4 Use geometric definitions and theorems to reason abstractly and quantitatively.
  • MA.AT.G.4.a Use known definitions and results in informal arguments.
  • MA.AT.G.4.b Tell apart empirical, example-based and deductive reasoning, and informal from formal reasoning.
  • MA.AT.G.4.c Weigh the effects of alternative definitions, e.g. for trapezoids.

Data (D)

• MA.AT.D.1 Pose questions and collect and organize data.
  • MA.AT.D.1.a Explain good practice in sample surveys, experiments and observational studies.
  • MA.AT.D.1.b Explain how randomization reduces confounding and lurking variables.
  • MA.AT.D.1.c Explain bias and confounding variables and how they affect conclusions.
  • MA.AT.D.1.d Explain how sampling distributions help estimate population parameters.
• MA.AT.D.2 Analyze data and interpret results.
  • MA.AT.D.2.a Decide when data are roughly normal and draw conclusions using the normal distribution.
  • MA.AT.D.2.b Build regression models for linear and nonlinear data, including transforming data to linearize it.
• MA.AT.D.3 Interpret and use probability ideas.
  • MA.AT.D.3.a Assign probabilities to payoffs and find expected values as means of distributions.
  • MA.AT.D.3.b Explain statistical significance and interpret it in context.
  • MA.AT.D.3.c Compare two groups, describe sampling variability and judge whether differences are significant.
  • MA.AT.D.3.d Use p-values to judge risk and make decisions.
  • MA.AT.D.3.e Use confidence intervals to estimate unknown population parameters.