United States · Common Core State Standards
11th Grade Mathematics
This course deepens the understanding of complex functions and mathematical modeling. Students explore non linear relationships and prepare for higher level calculus through rigorous analysis of patterns and structures.
Complex Systems and Polynomial Functions
Students investigate the behavior of higher degree polynomials and the necessity of complex numbers in solving equations. The unit focuses on the relationship between algebraic factors and graphical intercepts.
Expanding the real number system to include imaginary units for solving quadratic equations with no real roots.
Analyzing how the leading coefficient and degree of a polynomial dictate its long term growth and shape.
Using synthetic and long division to find roots and simplify complex algebraic expressions.
Rational and Radical Relationships
Exploring functions with variables in denominators and under radicals to understand domain restrictions and asymptotic behavior.
Identifying where functions fail to exist and how they behave as they approach those boundaries.
Developing techniques to isolate variables within radicals and identifying extraneous solutions.
Using rational functions to model situations where one value decreases as another increases.
Exponential and Logarithmic Growth
Investigating how quantities grow proportionally and how logarithms serve as the inverse operation to exponents.
Understanding logarithms as exponents and exploring their properties for simplifying expressions.
Applying exponential functions to model population growth, radioactive decay, and compound interest.
Applying shifts, stretches, and reflections to exponential and logarithmic graphs.
Trigonometric Functions and Periodic Motion
Extending right triangle trigonometry to the unit circle and periodic functions to model circular and wave motion.
Defining trigonometric ratios for all angles and transitioning from degrees to radians.
Modeling periodic phenomena using amplitude, period, phase shift, and midline.
Proving and applying fundamental identities to simplify expressions and solve equations.
Statistical Inference and Data Analysis
Using probability and statistics to make inferences about populations from samples and evaluate the validity of studies.
Understanding the properties of the bell curve and using z scores to determine probabilities.
Evaluating different methods of data collection and the impact of bias on conclusions.
Calculating how much a sample statistic is likely to differ from a population parameter.
Sequences, Series, and Limits
Exploring patterns in numbers through arithmetic and geometric progressions and introducing the concept of infinity.
Defining recursive and explicit formulas for patterns of addition and multiplication.
Calculating the total sum of a set of numbers using sigma notation and sum formulas.
Investigating when a sum of infinitely many terms results in a finite number.