Grade 11 Math Practice

Introduce and perform operations with complex numbers, including addition, subtraction, multiplication, and division. Understand the concept of the imaginary unit 'i' and its properties.

Analyze the algebraic equations of conic sections (parabolas, ellipses, hyperbolas, and circles) and understand their properties, including vertices, foci, and axes of symmetry.

Solve exponential and logarithmic equations using properties of exponents and logarithms. This includes applying these concepts to real-world problems involving growth and decay.

Understand the concept of inverse functions, including how to find the inverse of a given function and determine if an inverse function exists. This involves graphical and algebraic approaches.

Apply the principle of mathematical induction to prove statements about integers, particularly for sequences, series, and properties of numbers. This involves understanding the base case and inductive step.

Learn to represent and manipulate data using matrices. This includes matrix addition, subtraction, scalar multiplication, and matrix multiplication, as well as understanding their applications.

Understand and work with parametric equations, which describe the coordinates of points on a curve as functions of a parameter. This includes converting between parametric and Cartesian forms.

Analyze and graph polynomial functions, including identifying roots, multiplicities, end behavior, and turning points. This includes understanding the relationship between the degree of a polynomial and its graphical features.

Understand the properties of rational functions, including finding vertical, horizontal, and slant asymptotes, and analyzing their behavior. This involves determining the domain and range and identifying holes in the graph.

Explore arithmetic and geometric sequences and series, including finding explicit and recursive formulas, calculating sums, and understanding convergence and divergence of infinite series.

Solve systems of equations that include non-linear equations, such as quadratic, exponential, or rational functions. This involves using substitution, elimination, and graphical methods.

Introduce vectors as quantities with both magnitude and direction. Learn to perform vector operations such as addition, subtraction, and scalar multiplication, and understand their geometric interpretation.

Understand the derivative as the instantaneous rate of change of a function, applying it to analyze motion, velocity, and acceleration from position functions.

Explore the concept of limits of functions as input values approach a certain number, understanding how to evaluate limits graphically and numerically.

Explore various probability distributions (e.g., binomial, normal) and apply them to model real-world phenomena and solve complex probability problems.

Develop and interpret statistical models, particularly linear and non-linear regression, to analyze relationships between variables and make predictions.

Utilize transformations (translations, rotations, reflections, dilations) as tools to prove geometric theorems and properties, focusing on congruence and similarity arguments.

Explore and prove theorems related to circles, including properties of tangents, secants, chords, inscribed angles, and central angles, and apply these to solve complex geometric problems.

Extend the understanding of trigonometric ratios (sine, cosine, tangent) to angles beyond acute angles using the unit circle, and apply these to solve problems involving right triangles and real-world scenarios.

This topic focuses on performing hypothesis tests for a single population mean, including understanding Type I and Type II errors and the power of a test.

Students will learn to formulate hypotheses, calculate test statistics, and interpret p-values to draw conclusions about population proportions.

This topic covers the construction and interpretation of confidence intervals for a single population mean, including the use of the t-distribution when the population standard deviation is unknown.

Students will learn to construct and interpret confidence intervals for a single population proportion, understanding the conditions for validity and the meaning of the confidence level.

Students will extend their understanding of inference to compare two population proportions using confidence intervals and hypothesis tests, considering scenarios with independent samples.

Apply trigonometric principles to solve real-world problems in physics and engineering, such as analyzing forces, projectile motion, and wave phenomena.

Analyze and graph transformations of sine, cosine, tangent, cotangent, secant, and cosecant functions, including amplitude, period, phase shifts, and vertical shifts.

Understand and apply the properties of inverse trigonometric functions (arcsin, arccos, arctan) to solve equations and evaluate expressions.

Apply the Law of Sines and the Law of Cosines to solve oblique triangles, finding unknown side lengths and angle measures.

Convert between rectangular and polar coordinates and understand how trigonometric functions are used to define and analyze curves in the polar plane.

Solve trigonometric equations using algebraic techniques and trigonometric identities, finding all solutions within a specified interval.

Prove and apply fundamental trigonometric identities, including Pythagorean, reciprocal, quotient, and sum/difference identities, to simplify expressions and solve equations.

Represent vectors using trigonometric concepts, including finding magnitudes and directions, and perform vector operations using trigonometric relationships.