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Algebra 2 Regents Review

Jun 23, 2025

Overview

This lecture provided a comprehensive review of Algebra 2 topics relevant for the Regents exam, including test format, core content areas (number systems, functions, algebra, trigonometry, statistics, and probability), and essential definitions, formulas, and strategies.

Regents Exam Format

  • Four main units: Number & Quantity (5–12%), Algebra (35–44%), Functions (30–40%), Statistics & Probability (14–21%).
  • 3 hours, 37 questions: 24 multiple choice (2 pts each), 8 short answer (2 pts each), 4 extended response (4 pts each), 1 final question (6 pts).
  • Raw scores converted to scaled scores; about 33% correct needed to pass.

Number & Quantity

  • Real numbers: rational (includes natural, whole, integers) and irrational (non-terminating, non-repeating).
  • Rationalizing denominators: multiply by conjugate to eliminate square roots.
  • Polynomial division: similar to long division; if remainder is zero, divisor is a factor.
  • Complex numbers: i = √(-1); complex numbers are in form a + bi.

Functions

  • A function passes the vertical line test: one y-value per x-value.
  • Domain: input values where function is defined; for rational, exclude values making denominator zero; for radicals, radicand ≥ 0.
  • Range: all possible output (y) values.
  • 1:1 functions: pass both vertical/horizontal line tests; onto: every y-value covered.
  • Compositions: f(g(x)); plug one function into another.
  • Inverses: swap x and y, solve for y.

Function Characteristics

  • End behavior: determined by highest degree and leading coefficient.
  • Multiplicity: number of times a factor repeats affects graph behavior.
  • Transformations: Horizontal (inside parentheses: shifts, stretches, reflections over y-axis), Vertical (outside: shifts, stretches, reflections over x-axis).
  • Remember: H.I.Y.A. “Horizontal Inside Y-axis”; V.X.V. “Vertical X-axis Vertical Outside”.

Algebra: Linear, Quadratic, Sequences

  • Slope: (y₂-y₁)/(x₂-x₁), rise over run.
  • Linear equations: y = mx + b (slope and y-intercept).
  • Three-variable systems: use elimination method; organize, eliminate variables step by step.
  • Quadratics: y = ax²+bx+c; use quadratic formula, axis of symmetry is -b/2a, discriminant decides number/type of roots.
  • Focus/directrix of parabolas: vertex form y = (x-h)²/(4p) + k; focus at (h, k+p), directrix at y = k-p.
  • Sequences: arithmetic (add/subtract) and geometric (multiply/divide); explicit vs. recursive formulas.

Trigonometry

  • Radians ↔ degrees: deg × π/180 = rad; rad × 180/π = deg.
  • Primary trig functions: sin (opposite/hypotenuse), cos (adjacent/hypotenuse), tan (opposite/adjacent).
  • Special triangles: memorize exact sin/cos/tan for 30°, 45°, 60°.
  • Unit circle: connects trig functions to (x, y) coordinates.
  • Inverse trig: arcsin, arccos, arctan to find angles.
  • Trig graphs: y = A sin(B(x–C)) + D; amplitude A, period 2π/B, phase shift C, vertical shift D.

Statistics & Probability

  • Study types: sample surveys, observational studies, controlled experiments; single/double blind.
  • Normal distribution: 68% within 1σ, 95% within 2σ, 99.7% within 3σ of mean.
  • Confidence intervals: mean ± z·(σ/√n); memorize z-values for 90%, 95%, 99% confidence.
  • Probability: P(A∪B) = P(A) + P(B) – P(A∩B); complements: P(not A) = 1 – P(A); independent/mutually exclusive events; conditional probability.

Key Terms & Definitions

  • Rational Number — A number that can be written as a fraction or repeating/terminating decimal.
  • Irrational Number — A non-repeating, non-terminating decimal (e.g., π, √2).
  • Amplitude — Half the distance between maximum and minimum y-values in a trig graph.
  • Frequency/Period — Frequency: cycles per unit; Period: length of one cycle (2π/frequency).
  • Quadratic Formula — x = [-b ± √(b²-4ac)]/(2a).
  • Discriminant — b² - 4ac; determines type and number of quadratic roots.
  • Standard Deviation (σ, s) — Measure of data spread around the mean.
  • Confidence Interval — Range estimating a population parameter, based on sample data.

Action Items / Next Steps

  • Memorize core formulas, properties, and z-values for confidence intervals.
  • Practice function transformations and trig identities.
  • Review calculator functions for regression and statistics (normCDF, LinSolve, sigma notation).
  • Complete recommended practice problems and review notes for each unit.

Full transcript