Grade 11 Mathematics

Distinguishing between functions and relations using mapping diagrams, graphs, and sets of ordered pairs, focusing on the definition of a function.

Understanding and applying function notation to evaluate expressions and interpret function values in context.

Determining the domain and range of various functions from graphs, equations, and real-world scenarios.

Identifying and graphing common parent functions (linear, quadratic, absolute value, square root, cubic) and their key features.

Applying vertical and horizontal translations to parent functions and understanding their effect on the graph and equation.

Investigating the effects of vertical and horizontal stretches and compressions on the graphs of functions.

Understanding reflections across the x-axis and y-axis and their impact on function equations and graphs.

Applying multiple transformations (translations, stretches, reflections) in sequence to graph and write equations of functions.

Determining the inverse of a function graphically and understanding the symmetry about y=x.

Finding the inverse of linear, quadratic, and simple rational functions algebraically.

Understanding and evaluating composite functions, and using composition to verify inverses.

Defining, graphing, and evaluating piecewise functions, including step functions.

Identifying different function families (linear, quadratic, exponential, etc.) from data and applying them to real-world modeling.

Reviewing and mastering various polynomial factoring techniques (GCF, trinomials, difference of squares, grouping) essential for rational expressions.

Defining rational expressions, identifying restrictions on variables, and simplifying basic expressions.

Performing multiplication and division on rational expressions, including complex fractions.

Finding common denominators and performing addition and subtraction of rational expressions.

Solving equations involving rational expressions and checking for extraneous solutions.

Applying rational equations to solve real-world problems such as work-rate, distance-rate-time, and mixture problems.

Solving inequalities involving rational expressions and interpreting solutions graphically.

Reviewing standard, vertex, and factored forms of quadratic functions and their graphical properties (vertex, axis of symmetry, intercepts).

Mastering solving quadratic equations using factoring and the square root property.

Using the method of completing the square to solve quadratic equations and convert standard form to vertex form.

Applying the quadratic formula to solve equations and using the discriminant to determine the nature of roots.

Introducing imaginary numbers, complex numbers, and performing basic operations (addition, subtraction, multiplication) with them.

Solving quadratic equations that yield complex conjugate roots using the quadratic formula.

Finding the intersection points of lines and parabolas using both algebraic (substitution/elimination) and graphical methods.

Solving quadratic inequalities algebraically and graphically, expressing solutions using interval notation.

Applying quadratic functions to solve real-world optimization problems (e.g., maximizing area, projectile motion).

Reviewing and mastering the laws of exponents for integer powers, including zero and negative exponents.

Extending the laws of exponents to rational powers and converting between radical and exponential forms.

Graphing basic exponential functions (y=a*b^x) and identifying key features like intercepts, asymptotes, and growth/decay.

Applying transformations (translations, stretches, reflections) to exponential functions and writing their equations.

Applying exponential functions to real-world scenarios such as population growth, radioactive decay, and compound interest.

Solving exponential equations by equating bases and introducing the concept of logarithms.

Defining logarithms as the inverse of exponential functions and converting between logarithmic and exponential forms.

Reviewing SOH CAH TOA and solving for unknown sides and angles in right triangles.

Defining angles in standard position, understanding positive and negative angles, and identifying coterminal angles.

Introducing the unit circle, radian measure, and determining exact trigonometric values for special angles.

Calculating trigonometric ratios for angles beyond the first quadrant using reference angles and the unit circle.

Applying the Sine Law to solve for unknown sides and angles in non-right triangles, including the ambiguous case.

Applying the Cosine Law to solve for unknown sides and angles in non-right triangles.

Graphing the parent sine and cosine functions and identifying their amplitude, period, and midline.

Applying transformations (amplitude, period, phase shift, vertical shift) to sine and cosine functions.

Using sinusoidal functions to model real-world periodic phenomena such as tides, temperatures, and sound waves.

Introducing fundamental trigonometric identities (reciprocal, quotient, Pythagorean) and using them to simplify expressions.

Solving basic trigonometric equations over a specified interval and finding general solutions.

Graphing tangent, cotangent, secant, and cosecant functions and identifying their asymptotes and key features.

Defining sequences, identifying patterns, and distinguishing between finite and infinite sequences.

Defining arithmetic sequences, finding the common difference, and deriving explicit and recursive formulas.

Calculating the sum of finite arithmetic series using summation notation and formulas.

Defining geometric sequences, finding the common ratio, and deriving explicit and recursive formulas.

Calculating the sum of finite geometric series and introducing the concept of infinite geometric series.

Applying arithmetic and geometric sequences to understand simple and compound interest calculations.

Using series to calculate the future value of annuities and the present value of loans.

Defining basic probability concepts, sample spaces, and calculating probabilities of simple events.

Distinguishing between permutations and combinations and applying formulas to count arrangements and selections.

Calculating conditional probabilities and determining if events are independent using formulas and two-way tables.

Reviewing measures of central tendency and spread, and creating various graphical representations of data.