NY Regents Algebra II study plan

Factor polynomials of degree three and four using grouping, difference of squares, and sum or difference of cubes

Solve quadratic equations by factoring, completing the square, and the quadratic formula, and state what the discriminant reveals about the roots

Simplify, multiply, and divide rational expressions while listing every restricted domain value

Solve rational equations and reject extraneous solutions by checking in the original equation

Rewrite radical expressions as rational exponents and convert rational exponents back to radical form

Add, subtract, multiply, and divide complex numbers, and simplify powers of i

Solve radical equations and verify each solution algebraically

Apply the Remainder and Factor Theorems to divide polynomials and identify all zeros

Solve systems containing one linear and one quadratic equation

Evaluate and interpret function notation for linear, quadratic, and piecewise-defined functions

Determine domain and range from equations and from stated algebraic restrictions

Sketch vertical and horizontal shifts, stretches, compressions, and reflections of parent functions

Construct inverse functions algebraically and verify them by composition

Compose two functions and state the domain of the resulting composite function

Convert between exponential and logarithmic form and apply logarithm properties to expand and condense expressions

Solve exponential equations using logarithms, including base e and the natural logarithm

Write and solve exponential growth and decay models from described situations

Compute average rate of change over an interval and contrast linear with exponential growth

Graph sine and cosine functions and identify amplitude, period, and midline

Write the equation of a circle in standard form by completing the square

Identify center, radius, vertex, focus, and directrix from equations of circles and parabolas, then graph them accurately

Apply the distance and midpoint formulas to coordinate-geometry problems

Derive and use the equation of a parabola given its focus and directrix

Compute volumes of solids and apply similarity ratios to scale lengths, areas, and volumes

Compute and interpret z-scores and apply the empirical rule to estimate areas under a normal curve

Distinguish sample surveys, experiments, and observational studies and identify sources of bias

Calculate conditional probabilities from two-way frequency tables and test whether two events are independent

Write and evaluate arithmetic and geometric sequences using both explicit and recursive formulas

Evaluate sums written in sigma notation for arithmetic and geometric series

Fit and interpret linear, quadratic, and exponential regression models to data described in words

Interpret correlation coefficients, residuals, and the difference between correlation and causation

Calculate expected value for a discrete probability distribution and interpret it in context

Interpret margin of error and confidence level in the context of a reported survey

Solve probability problems involving unions, intersections, and complements

Complete two timed full-length practice exams under test-day conditions

Classify every missed item by domain and by error type (concept, computation, or misread)

Re-teach the three weakest topics from the error log by writing fresh worked examples

Apply reference-sheet formulas from memory without prompting