Integrated Algebra II (from 2028-29) (Maryland MCCRS)

Number and Operation Sense – NOS.A: Rational exponents

• IA2.NOS.A.1 Use properties of exponents to write equivalent expressions with radicals and rational exponents.

Number and Operation Sense – NOS.B: The complex number system

• IA2.NOS.B.2 Write complex numbers in standard form and use them for solutions of quadratics that have no real solutions.

Algebraic Thinking – AT.A: Structure in expressions

• IA2.AT.A.1 Rewrite and interpret quadratic expressions to show their key properties.
  • a. Factor to find zeros and explain what they mean in context.
  • b. Complete the square to find and interpret a maximum or minimum.
  • c. Compare standard, factored and vertex forms and when each is most useful.
• IA2.AT.A.2 Use the Zero Product Property on factored polynomials of degree 3 or more to find zeros and sketch graphs.
• IA2.AT.A.3 Add, subtract and multiply polynomials to rewrite and analyze relationships, including binomial times trinomial.

Algebraic Thinking – AT.B: Equations and systems

• IA2.AT.B.4 Create and solve one-variable quadratic equations with methods suited to their form.
  • a. Write quadratic equations for relationships between quantities.
  • b. Choose and justify a solving method and interpret the solution in context.
  • c. Write complex solutions in the form a + bi.
• IA2.AT.B.5 Solve one-variable equations with a single radical, explain extraneous solutions and check answers in context.
• IA2.AT.B.6 Create, solve and analyze systems of a linear and a quadratic equation in context.
  • a. Write a linear-quadratic system for a relationship.
  • b. Solve exactly and approximately with algebra, graphs or tables.
  • c. Interpret the solutions in context.
• IA2.AT.B.7 Use technology to solve systems mixing linear, exponential, quadratic and/or radical equations and interpret them.

Algebraic Thinking – AT.C: Reason about functions

• IA2.AT.C.8 Calculate or estimate and interpret average rates of change of exponential, quadratic and radical functions.
• IA2.AT.C.9 Compare two quadratic functions given in different ways.
• IA2.AT.C.10 Analyze and compare how different families of functions behave.
  • a. Compare patterns of change and key features of linear, quadratic, exponential, higher polynomial and radical functions.
  • b. Analyze how the number and type of solutions vary across families and how graphs show this.

Algebraic Thinking – AT.D: Model with functions

• IA2.AT.D.11 Write a quadratic function to model a description, table or graph.
• IA2.AT.D.12 Represent and interpret quadratic functions with tables and graphs in context.
  • a. Make tables and graphs and identify key features such as intercepts, symmetry, extrema, domain and range.
  • b. Relate the key features to the situation.
  • c. Justify that a quadratic model fits by analyzing trends and predictions.
• IA2.AT.D.13 Find and interpret inverses of quadratic and exponential functions algebraically and graphically.
  • a. Restrict the domain of a quadratic so it is one-to-one and write its inverse as a square root function.
  • b. Write the inverse of an exponential function as a logarithm and evaluate logarithms.
  • c. Graph a function and its inverse and analyze their features and symmetry about y = x.
  • d. Interpret inverse functions in context.
• IA2.AT.D.14 Represent and interpret polynomial (degree 3 or more) and radical functions with tables and graphs in context.
  • a. Make tables and graphs of polynomial functions and identify key features.
  • b. Make tables and graphs of radical functions and identify key features, including domain limits.
  • c. Relate the key features of these functions to the context.
• IA2.AT.D.15 Analyze how transformations change a function in vertex form and what they mean in context.
  • a. Identify how the graph changes under each transformation, find k from a graph and name the transformation.
  • b. Explain what each transformation means by linking the structure to the quantities.

Geometric Reasoning – GR.A: Transformations and similarity

• IA2.GR.A.1 Use coordinates to describe how dilations change plane figures, including the effect of scale factor and center.
• IA2.GR.A.2 Use similarity transformations to decide and justify whether triangles are similar.
  • a. Find a sequence of transformations that maps one triangle onto another.
  • b. Justify similarity with congruent angles and proportional sides.
• IA2.GR.A.3 Use properties of similar triangles to solve geometry problems in context.
• IA2.GR.A.4 Use properties of similarity transformations to establish the AA criterion.

Geometric Reasoning – GR.B: Right triangle relationships

• IA2.GR.B.5 Use similarity of right triangles to define sine, cosine and tangent of acute angles.
• IA2.GR.B.6 Justify the side relationships in special right triangles.
  • a. Use reasoning such as splitting an equilateral triangle or a square to explain them.
  • b. Describe the constant side ratios and how they relate to the angles.
• IA2.GR.B.7 Use trig ratios, the Pythagorean theorem and special right triangles to solve right triangles in context.

Geometric Reasoning – GR.C: Circles and their properties

• IA2.GR.C.8 Use similarity to develop formulas for arc length, radian measure and sector area.
  • a. Show with similarity that arc length is proportional to the radius.
  • b. Find radian measure as the ratio of arc length to radius.
  • c. Apply the sector area formula with radians.
• IA2.GR.C.9 Write the equation of a circle from its center and radius and read the center and radius from an equation.

Geometric Reasoning – GR.D: Model with geometry

• IA2.GR.D.10 Use shapes, their measures and properties to represent real objects and solve modeling and design problems.
• IA2.GR.D.11 Rearrange geometric formulas to isolate and interpret a quantity of interest.

Reasoning with Data, Statistics and Probability – DS.A: Statistical inquiry

• IA2.DS.A.1 Evaluate and improve study designs and analyze claims based on data critically.
  • a. Assess limits of a sample or design for bias, randomness and representativeness.
  • b. Propose changes to sampling or data collection to make results more valid.
  • c. Identify possible bias or misuse in collecting, showing or modeling data.
  • d. Recognize when correlation is wrongly taken as causation.

Reasoning with Data, Statistics and Probability – DS.B: Describe, analyze and compare data

• IA2.DS.B.2 Show two-variable data on a scatter plot and describe the relationship.
  • a. Fit a quadratic, higher-degree polynomial or radical function and use it to solve problems.
  • b. Judge the fit visually and analytically for the data and context.
• IA2.DS.B.3 Build and interpret two-way frequency tables to analyze association between categorical variables.
  • a. Use the tables to decide whether events are independent.
  • b. Approximate conditional probabilities and relate them to independence.