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New York 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

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1029

Practice Problems

1911

New York Standards

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

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