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Algebra II

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NY Algebra II Help: Master Concepts FastHelp

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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.

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.

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.

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).

NY.AII-A.APR.3

Identify zeros of polynomial functions when suitable factorizations are available.

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).

NY.AII-A.CED.1

Create equations and inequalities in one variable to represent a real-world context.

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.

NY.AII-A.REI.2

Solve rational and radical equations in one variable, identify extraneous solutions, and explain how they arise.

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.

NY.AII-A.REI.7b

Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

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.

NY.AII-F.IF.3

Recognize that a sequence is a function whose domain is a subset of the integers.

NY.AII-F.IF.6

Calculate and interpret the average rate of change of a function over a specified interval.

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).

NY.AII-F.BF.1a

Write a function that describes a relationship between two quantities.

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.

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.

NY.AII-F.BF.4a

Find the inverse of a one-to-one function both algebraically and graphically.

NY.AII-F.BF.6

Represent and evaluate the sum of a finite arithmetic or finite geometric series, using summation (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.

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).

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.

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.

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.

NY.AII-F.TF.5

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, horizontal shift, and midline.

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.

NY.AII-S.ID.4a

Recognize whether or not a normal curve is appropriate for a given data set.

NY.AII-S.ID.4b

If appropriate, determine population percentages using a graphing calculator for an appropriate normal curve.

NY.AII-S.ID.6a

Represent bivariate data on a scatter plot, and describe how the variables' values are related.

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.

NY.AII-S.IC.3

Recognize the purposes of and differences among surveys, experiments, and observational studies. Explain how randomization relates to each.

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.

NY.AII-S.IC.6a

Use the tools of statistics to draw conclusions from numerical summaries.

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.

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").

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.
Complete New York Algebra II Coverage

Algebra II Lessons

175

Video Explanations

1029

Practice Problems

2012

New York Standards

100% Aligned

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Complete Algebra II curriculum with video lessons, practice problems, step-by-step solutions, and progress tracking for every topic including complex numbers, polynomials, and trigonometry.

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