Illinois State Standards for Mathematics: Grade 12

IL.6. Number Sense: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.

6.A. Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings.

6.A.5. Perform addition, subtraction and multiplication of complex numbers and graph the results in the complex plane.

6.B. Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships.

6.B.5. Identify, represent and apply numbers expressed in exponential, logarithmic and scientific notation using contemporary technology.

6.C. Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers.

6.C.5. Determine the level of accuracy needed for computations involving measurement and irrational numbers.

6.D. Solve problems using comparison of quantities, ratios, proportions and percents.

6.D.5. Solve problems involving loans, mortgages and other practical applications involving geometric patterns of growth.

IL.7. Estimation and Measurement: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.

7.A. Measure and compare quantities using appropriate units, instruments and methods.

7.A.5. Apply nonlinear scales (e.g., Richter, decibel, pH) to solve practical problems.

7.B. Estimate measurements and determine acceptable levels of accuracy.

7.B.5. Estimate perimeter, area, volume, and capacity of irregular shapes, regions and solids and explain the reasoning supporting the estimate.

7.C. Select and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.

7.C.5a. Use dimensional analysis to determine units and check answers in applied measurement problems.

7.C.5b. Determine how changes in one measure may affect other measures (e.g., what happens to the volume and surface area of a cube when the side of the cube is halved).

IL.8. Algebra and Analytical Methods: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.

8.A. Describe numerical relationships using variables and patterns.

8.A.5. Solve mathematical problems involving recursive patterns and use models that employ such relationships.

8.B. Interpret and describe numerical relationships using tables, graphs and symbols.

8.B.5. Use functions including exponential, polynomial, rational, parametric, logarithmic, and trigonometric to describe numerical relationships.

8.C. Solve problems using systems of numbers and their properties.

8.C.5. Use polynomial, exponential, logarithmic and trigonometric functions to model situations.

8.D. Use algebraic concepts and procedures to represent and solve problems.

8.D.5. Formulate and solve nonlinear equations and systems including problems involving inverse variation and exponential and logarithmic growth and decay.

IL.9. Geometry: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.

9.A. Demonstrate and apply geometric concepts involving points, lines, planes and space.

9.A.5. Use geometric figures and their properties to solve problems in the arts, the physical and life sciences and the building trades, with and without the use of technology.

9.B. Identify, describe, classify and compare relationships using points, lines, planes and solids.

9.B.5. Construct and use two- and three-dimensional models of objects that have practical applications (e.g., blueprints, topographical maps, scale models).

9.C. Construct convincing arguments and proofs to solve problems.

9.C.5a. Perform and describe an original investigation of a geometric problem and verify the analysis and conclusions to an audience.

9.C.5b. Apply physical models, graphs, coordinate systems, networks and vectors to develop solutions in applied contexts (e.g., bus routing, areas of irregular shapes, describing forces and other physical quantities).

9.D. Use trigonometric ratios and circular functions to solve problems.

9.D.5. Analyze and solve problems involving periodic patterns (e.g., sound waves, tide variations) using circular functions and communicate results orally and in writing.

IL.10. Data Analysis and Probability: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.

10.A. Organize, describe and make predictions from existing data.

10.A.5. Construct a statistics-based presentation, individually and as members of a team, to communicate and justify the results of a project.

10.B. Formulate questions, design data collection methods, gather and analyze data and communicate findings.

10.B.5. Design a statistical experiment to answer a question about a realistic situation, conduct the experiment, use statistics to interpret the data, and communicate the results, individually and as members of a team.

10.C. Determine, describe and apply the probabilities of events.

10.C.5a. Compute conditional probabilities and the probabilities of independent events.

10.C.5b. Compute probabilities in counting situations involving permutations and combinations.

10.C.5c. Make predictions using probabilities associated with normally distributed events.