11th Grade Mathematics

Students will define the imaginary unit 'i' and simplify expressions involving square roots of negative numbers.

Students will perform addition, subtraction, multiplication, and division of complex numbers, including using complex conjugates.

Students will solve quadratic equations that yield complex roots using the quadratic formula and completing the square.

Students will identify the degree and leading coefficient of polynomial functions and relate them to the function's end behavior.

Students will sketch polynomial graphs by identifying real roots, their multiplicity, and the resulting behavior at the x-axis.

Students will perform long division of polynomials to find quotients and remainders.

Students will use synthetic division as a shortcut for polynomial division and apply the Remainder Theorem.

Students will apply the Factor Theorem to determine if a binomial is a factor of a polynomial and to find polynomial roots.

Students will use the Rational Root Theorem to identify potential rational roots of polynomial equations.

Students will understand the Fundamental Theorem of Algebra and its implications for the number of complex roots.

Students will apply Descartes' Rule of Signs to determine the possible number of positive and negative real roots of a polynomial.

Students will combine various techniques (factoring, theorems, synthetic division) to find all roots of polynomial equations.

Students will apply polynomial functions to model real-world situations and interpret their solutions.

Students will identify and graph vertical asymptotes of rational functions based on their denominators.

Students will determine and graph horizontal or slant asymptotes of rational functions based on degree comparison.

Students will identify and analyze holes (removable discontinuities) in the graphs of rational functions.

Students will solve rational equations by finding common denominators and identifying extraneous solutions.

Students will solve rational inequalities using sign analysis and interval notation.

Students will simplify radical expressions involving nth roots and rational exponents.

Students will solve equations containing a single radical term, ensuring to check for extraneous solutions.

Students will solve equations involving two or more radical terms, requiring multiple steps of isolation and squaring.

Students will graph square root and cube root functions, identifying their domain, range, and transformations.

Students will distinguish between direct and inverse variation and write equations to model these relationships.

Students will model situations involving joint and combined variation, writing and solving relevant equations.

Students will apply rational functions to solve real-world problems involving rates, work, and concentrations.

Students will use radical functions to model real-world phenomena such as physics formulas or geometric relationships.

Students will define and graph exponential functions, identifying key features like intercepts and asymptotes.

Students will explore the mathematical constant 'e' and its role in natural exponential and logarithmic functions.

Students will understand logarithms as the inverse of exponential functions and graph basic logarithmic functions.

Students will apply the product, quotient, and power rules of logarithms to expand and condense logarithmic expressions.

Students will use the change of base formula to evaluate logarithms with any base and convert between bases.

Students will solve exponential equations by equating bases, taking logarithms, or using graphical methods.

Students will solve logarithmic equations by using properties of logarithms and converting to exponential form.

Students will apply exponential functions to model real-world scenarios such as population growth, radioactive decay, and financial investments.

Students will calculate compound interest and understand the concept of continuous compounding using the formula A=Pe^rt.

Students will graph exponential functions by applying vertical and horizontal shifts, stretches, and reflections.

Students will graph logarithmic functions by applying vertical and horizontal shifts, stretches, and reflections.

Students will explore real-world applications of logarithms, such as pH, Richter scale, and decibels.

Students will use regression techniques to find exponential and logarithmic models that best fit given data sets.

Students will define angles in standard position, identify coterminal angles, and convert between degrees and radians.

Students will define trigonometric ratios (sine, cosine, tangent) using the unit circle for all angles.

Students will use reference angles to find trigonometric values for any angle and identify values for quadrantal angles.

Students will graph sine and cosine functions, identifying and applying transformations related to amplitude and period.

Students will graph sine and cosine functions, incorporating phase shifts and vertical shifts (midlines).

Students will use sine and cosine functions to model real-world periodic phenomena such as tides, temperature, or Ferris wheels.

Students will prove and apply fundamental trigonometric identities, including reciprocal, quotient, and Pythagorean identities.

Students will use algebraic manipulation and fundamental identities to verify more complex trigonometric identities.

Students will solve trigonometric equations for solutions within a given interval and for general solutions.

Students will define and evaluate inverse trigonometric functions, understanding their restricted domains and ranges.

Students will apply the Law of Sines to solve oblique triangles, including ambiguous cases.

Students will define basic probability concepts, calculate probabilities of simple and compound events, and understand sample spaces.

Students will calculate conditional probabilities and determine if events are independent using formulas and two-way tables.

Students will calculate permutations and combinations to determine the number of possible arrangements or selections.

Students will calculate and interpret mean, median, mode, range, interquartile range, and standard deviation.

Students will understand the properties of the normal distribution, calculate z-scores, and use them to find probabilities.

Students will evaluate different sampling methods and identify potential sources of bias in data collection.

Students will distinguish between experimental and observational studies and understand the principles of experimental design.

Students will understand the basic concepts of statistical inference, including population parameters and sample statistics.

Students will explore sampling distributions and understand the implications of the Central Limit Theorem.

Students will construct and interpret confidence intervals for population proportions.

Students will construct and interpret confidence intervals for population means.

Students will understand the basic framework of hypothesis testing, including null and alternative hypotheses.

Students will perform significance tests for population proportions and interpret p-values.

Students will define sequences, identify patterns, and write explicit and recursive formulas for various sequences.

Students will identify arithmetic sequences, find the nth term, and calculate the sum of arithmetic series.

Students will identify geometric sequences, find the nth term, and calculate the sum of finite geometric series.

Students will use sigma notation to represent series and evaluate sums of finite series.

Students will apply arithmetic and geometric series to solve real-world problems, including financial applications.

Students will determine if an infinite geometric series converges or diverges and calculate the sum of convergent series.

Students will intuitively understand the concept of a limit by examining function behavior as x approaches a value or infinity.

Students will evaluate limits as x approaches infinity and relate them to horizontal asymptotes of functions.

Students will define continuity and identify different types of discontinuities in functions.

Students will explore Pascal's Triangle and use the Binomial Theorem to expand binomials raised to a power.

Students will be introduced to the principle of mathematical induction and use it to prove mathematical statements.