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Grade 11 Math Courses - NY Curriculum

Discover Grade 11 Math in NY, featuring Algebra II. This course builds on previous concepts, introducing complex numbers, advanced functions, and trigonometry to prepare students for higher-level mathematics.

NY Grade 11 Math Curriculum - Algebra II

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ID
Math Standard Description
StudyPug Topic
NY.AII-N.RN.1
Explore how the meaning of rational exponents follows from extending the properties of integer exponents.
Convert between radicals and rational exponents
Exponents: Product rule (a^x)(a^y) = a^(x+y)
Exponents: Division rule: a^x / a^y = a^(x-y)
Exponents: Power rule: (a^x)^y = a^(xy)
Exponents: Negative exponents
Exponents: Zero exponent: a^0 = 1
Exponents: Rational exponents
NY.AII-N.RN.2
Convert between radical expressions and expressions with rational exponents using the properties of exponents.
Solving for exponents
Operations with radicals
Conversion between entire radicals and mixed radicals
Converting radicals to mixed radicals
Converting radicals to entire radicals
Adding and subtracting radicals
Multiplying and dividing radicals
Rationalize the denominator
Evaluating and simplifying radicals
NY.AII-N.CN.1
Know there is a complex number i such that i^2 = –1, and every complex number has the form a + bi with a and b real.
Understanding the number systems
Introduction to imaginary numbers
NY.AII-N.CN.2
Use the relation i^2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
Combining the exponent rules
Complex numbers and complex planes
Adding and subtracting complex numbers
Multiplying and dividing complex numbers
NY.AII-A.SSE.2
Recognize and use the structure of an expression to identify ways to rewrite it.
Polynomial components
Simplifying rational expressions and restrictions
Applications of polynomials
Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
NY.AII-A.SSE.3
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
Common factors of polynomials
Adding and subtracting rational expressions
Evaluating polynomials
Using algebra tiles to factor polynomials
Solving polynomial equations
NY.AII-A.APR.2
Apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
Greatest common factors (GCF)
Remainder theorem
Polynomial long division
Polynomial synthetic division
NY.AII-A.APR.3
Identify zeros of polynomial functions when suitable factorizations are available.
Factoring polynomials: x^2 + bx + c
Characteristics of polynomial graphs
Factor theorem
Rational zero theorem
NY.AII-A.APR.6
Rewrite rational expressions in different forms: Write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x).
Applications of polynomial functions
Solving polynomial inequalities
Fundamental theorem of algebra
NY.AII-A.CED.1
Create equations and inequalities in one variable to represent a real-world context.
Introduction to linear equations
Solving rational equations
Solving exponential equations using exponent rules
NY.AII-A.REI.1b
Explain each step when solving rational or radical equations as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Combination of both parallel and perpendicular line equations
Applications of inequalities
What is linear programming?
NY.AII-A.REI.2
Solve rational and radical equations in one variable, identify extraneous solutions, and explain how they arise.
Evaluating and simplifying radicals
Solving radical equations
Square and square roots
Cubic and cube roots
NY.AII-A.REI.4b
Solve quadratic equations by: i) inspection, ii) taking square roots, iii) factoring, iv) completing the square, v) the quadratic formula, and vi) graphing. Write complex solutions in a + bi form.
Solving quadratic equations by factoring
Solving quadratic equations by completing the square
Using quadratic formula to solve quadratic equations
Multiplying and dividing radicals
Rationalize the denominator
NY.AII-A.REI.7b
Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
System of linear-quadratic equations
Nature of roots of quadratic equations: The discriminant
Applications of quadratic equations
Solving quadratic inequalities
NY.AII-A.REI.11
Given the equations y = f(x) and y = g(x): i) recognize that each x-coordinate of the intersection(s) is the solution to the equation f(x) = g(x); ii) find the solutions approximately using technology to graph the functions or make tables of values; iii) find the solution of f(x) < g(x) or f(x) ≤ g(x) graphically; and iv) interpret the solution in context.
Graphing linear functions using table of values
Graphing exponential functions
Graphing logarithmic functions
The inverse of 3 x 3 matrices with matrix row operations
The inverse of 3 x 3 matrix with determinants and adjugate
NY.AII-F.IF.3
Recognize that a sequence is a function whose domain is a subset of the integers.
Greatest common factors (GCF)
Introduction to sequences
Sigma notation
NY.AII-F.IF.4b
For a function that models a relationship between two quantities: i) interpret key features of graphs and tables in terms of the quantities; and ii) sketch graphs showing key features given a verbal description of the relationship.
Word problems of graphing linear functions
Characteristics of quadratic functions
Relationship between two variables
Understand relations between x- and y-intercepts
Combining transformations of functions
Reflection across the y-axis: y = f(-x)
Reflection across the x-axis: y = -f(x)
Transformations of functions: Horizontal stretches
Transformations of functions: Vertical stretches
NY.AII-F.IF.6
Calculate and interpret the average rate of change of a function over a specified interval.
Rate of change
Direct variation
NY.AII-F.IF.7
Graph functions and show key features of the graph by hand and using technology when appropriate.
Graphing linear functions using a single point and slope
Graphing quadratic functions: General form VS. Vertex form
Graphing exponential functions
Graphing logarithmic functions
Graphing from slope-intercept form y=mx+b
Graphing transformations of exponential functions
Sine graph: y = sin x
Cosine graph: y = cos x
Tangent graph: y = tan x
Cotangent graph: y = cot x
Secant graph: y = sec x
Cosecant graph: y = csc x
NY.AII-F.IF.8
Write a function in different but equivalent forms to reveal and explain different properties of the function.
Slope intercept form: y = mx + b
General form: Ax + By + C = 0
Point-slope form: y - y_1 = m(x - x_1)
Converting from general to vertex form by completing the square
Adding functions
Subtracting functions
Multiplying functions
Dividing functions
Operations with functions
NY.AII-F.IF.9
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
Parallel and perpendicular lines in linear functions
Graphs of rational functions
Inequalities of combined functions
NY.AII-F.BF.1a
Write a function that describes a relationship between two quantities.
Applications of linear relations
Finding an exponential function given its graph
Finding a logarithmic function given its graph
NY.AII-F.BF.2
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Arithmetic sequences
Geometric sequences
Arithmetic series
Geometric series
Infinite geometric series
NY.AII-F.BF.3b
Using f(x) + k, k f(x), f(kx), and f(x + k): i) identify the effect on the graph when replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); ii) find the value of k given the graphs; iii) write a new function using the value of k; and iv) use technology to experiment with cases and explore the effects on the graph. Include recognizing even and odd functions from their graphs.
Transformations of quadratic functions
Transformations of functions: Horizontal translations
Transformations of functions: Vertical translations
NY.AII-F.BF.4a
Find the inverse of a one-to-one function both algebraically and graphically.
Finding the quadratic functions for given parabolas
Inverse functions
NY.AII-F.BF.5a
Understand inverse relationships between exponents and logarithms algebraically and graphically.
Product rule of logarithms
Solving exponential equations with logarithms
What is a logarithm?
Converting from logarithmic form to exponential form
Evaluating logarithms without a calculator
Common logarithms
Natural log: ln
Evaluating logarithms using change-of-base formula
Converting from exponential form to logarithmic form
NY.AII-F.BF.6
Represent and evaluate the sum of a finite arithmetic or finite geometric series, using summation (sigma) notation.
Sigma notation
NY.AII-F.BF.7
Explore the derivation of the formulas for finite arithmetic and finite geometric series. Use the formulas to solve problems.
Arithmetic series
Geometric series
NY.AII-F.LE.2
Construct a linear or exponential function symbolically given: i) a graph; ii) a description of the relationship; and iii) two input-output pairs (include reading these from a table).
Graphing linear functions using table of values
NY.AII-F.LE.4
Use logarithms to solve exponential equations, such as ab^ct = d (where a, b, c, and d are real numbers and b > 0) and evaluate the logarithm using technology.
Quotient rule of logarithms
Combining product rule and quotient rule in logarithms
Evaluating logarithms using logarithm rules
NY.AII-F.LE.5
Interpret the parameters in a linear or exponential function in terms of a context.
Exponential growth and decay by a factor
Finance: Compound interest
Continuous growth and decay
Logarithmic scale: Richter scale (earthquake)
Logarithmic scale: pH scale
Logarithmic scale: dB scale
Finance: Future value and present value
NY.AII-F.TF.1
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
Converting between degrees and radians
Trigonometric ratios of angles in radians
Radian measure and arc length
NY.AII-F.TF.2
Apply concepts of the unit circle in the coordinate plane to calculate the values of the six trigonometric functions given angles in radian measure.
Unit circle
NY.AII-F.TF.5
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, horizontal shift, and midline.
Graphing transformations of trigonometric functions
Determining trigonometric functions given their graphs
NY.AII-F.TF.8
Prove the Pythagorean identity sin^2(θ) + cos^2(θ) = 1. Find the value of any of the six trigonometric functions given any other trigonometric function value and when necessary find the quadrant of the angle.
Pythagorean identities
NY.AII-S.ID.4a
Recognize whether or not a normal curve is appropriate for a given data set.
Organizing data
Introduction to normal distribution
Normal distribution and continuous random variable
Z-scores and random continuous variables
NY.AII-S.ID.4b
If appropriate, determine population percentages using a graphing calculator for an appropriate normal curve.
Organizing data
Introduction to normal distribution
Normal distribution and continuous random variable
Z-scores and random continuous variables
NY.AII-S.ID.6a
Represent bivariate data on a scatter plot, and describe how the variables' values are related.
Reading and drawing line graphs
Bivariate, scatter plots and correlation
NY.AII-S.IC.2
Determine if a value for a sample proportion or sample mean is likely to occur based on a given simulation.
Sampling distributions
Rare event rule
NY.AII-S.IC.3
Recognize the purposes of and differences among surveys, experiments, and observational studies. Explain how randomization relates to each.
Census and bias
NY.AII-S.IC.4
Given a simulation model based on a sample proportion or mean, construct the 95% interval centered on the statistic (+/- two standard deviations) and determine if a suggested parameter is plausible.
Margin of error
Confidence intervals to estimate population mean
Making a confidence interval
NY.AII-S.IC.6a
Use the tools of statistics to draw conclusions from numerical summaries.
Influencing factors in data collection
NY.AII-S.IC.6b
Use the language of statistics to critique claims from informational texts. For example, causation vs correlation, bias, measures of center and spread.
Influencing factors in data collection
NY.AII-S.CP.1
Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").
Introduction to probability
Organizing outcomes
Set notation
Set builder notation
Intersection and union of 2 sets
Intersection and union of 3 sets
NY.AII-S.CP.7
Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.
Addition rule for "OR"

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