NY Regents Algebra II study guide
NY Regents Algebra II · Work through your exam, one topic at a time.
The Regents Examination in Algebra II is one of the high school Regents exams administered by the New York State Education Department through its Office of State Assessment, whose site navigation lists "Regents Exams" among New York's assessment programs. This page is an independent study resource for students preparing for that exam. It is not affiliated with, endorsed by, or produced by NYSED. Be aware of what could and could not be verified. Topics on this exam: Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability. The NY Regents Algebra II study guide has 5 sections and about 1,360 words.
01Number and Quantity
Algebra II extends the real number system to the complex numbers and treats radicals as rational exponents. Know that i = sqrt(-1), i^2 = -1, and powers of i cycle with period 4, so reduce the exponent modulo 4. Be able to add, subtract, multiply, and divide complex numbers; division uses the conjugate of the denominator, because (a+bi)(a-bi) = a^2+b^2 is real. A complex number a+bi has modulus sqrt(a^2+b^2).
300 words, about 2 min02Algebra
Algebra II emphasizes structure: rewriting expressions, factoring completely, and solving equations with justification. Be fluent with polynomial operations, special products, factoring by grouping, difference of squares, and sum/difference of cubes. The Remainder Theorem says the remainder when p(x) is divided by x-c is p(c); the Factor Theorem says x-c is a factor exactly when p(c) = 0. For rational expressions, factor first, record excluded values, then cancel.
270 words, about 1 min03Functions
A function assigns exactly one output to each input. Master function notation, domain and range, composition, inverses, and transformations. Domain restrictions come from denominators (nonzero), even roots (radicand nonnegative), and logarithms (argument positive). For f(g(x)), the inner function's output must lie in the outer function's domain, so combine restrictions.
270 words, about 1 min04Geometry
Algebra II geometry centers on conic sections, circles, and trigonometry. For a circle, complete the square to convert x^2+y^2+Dx+Ey+F = 0 into center-radius form (x-h)^2+(y-k)^2 = r^2; remember to add the same value to both sides for each variable. A parabola can be described by its focus and directrix: points are equidistant from both, which produces y-k = (1/(4p))(x-h)^2 for a vertical axis, where p is the directed distance from vertex to focus. In trigonometry, use radians unless degrees are specified; the unit circle gives signs by quadrant, and sin^2(theta)+cos^2(theta) = 1.
274 words, about 1 min05Statistics and Probability
Algebra II statistics focuses on interpreting data and using probability models. For a normal distribution, convert to a z-score z = (x-mu)/sigma; positive z means above the mean. Use the empirical rule (68-95-99.7) for approximate areas and a standard normal table for precise areas, remembering that tables usually give area to the left. For probability, use P(A or B) = P(A)+P(B)-P(A and B); for independent events, P(A and B) = P(A)P(B).
246 words, about 1 min