Algebra I

Real released Regents questions on writing a one-variable equation from a situation and solving linear equations — distributing, combining like terms, variables on both sides, and fractional or decimal coefficients.

Real released Regents questions on rearranging a formula to solve for a specified variable — transforming formulas from science, geometry, and finance by isolating one letter in terms of the others.

Real released Regents questions on solving a linear inequality and reading its solution on a number line — watch the direction of the symbol and whether the endpoint is open or closed.

Real released Regents questions on solving systems algebraically — linear systems by substitution and elimination, and linear-quadratic systems whose solutions are the points where a line meets a parabola.

Real released Regents questions on graphing a linear inequality as a half-plane and solving a system of linear inequalities — testing whether a point is a solution and reading the overlapping solution region.

Real released Regents questions on adding, subtracting, and multiplying polynomials — distribute carefully, combine like terms, and write the result in standard form.

Real released Regents questions on factoring expressions completely — pull out the greatest common factor, recognize a difference of two squares, factor trinomials, and combine the methods.

Real released Regents questions on solving quadratics — factoring, the square-root method, completing the square, and the quadratic formula. Multiple choice is checked instantly; the show-your-work problems are self-scored against the official NYSED rubric.

Real released Regents questions on what makes a relation a function, finding domain and range, the practical domain in a context, and comparing two functions given as tables, graphs, or equations.

Real released Regents questions on function notation — evaluating f(x) at a value — and on shifting a function's graph.

Real released Regents questions on reading what a graph means — relating a graph to the event it models (speed or distance over time) and naming key features like where a function increases, decreases, is constant, or reaches a maximum.

Real released Regents questions on the features of a parabola — its zeros (x-intercepts), its vertex and minimum or maximum from vertex form, and what a quadratic model's numbers mean in context.

Real released Regents questions on linear functions — slope as a rate of change, average rate of change over an interval, interpreting slope and intercept in context, and writing the equation of a line.

Real released Regents questions on telling linear and exponential models apart — linear functions change by a constant amount, exponential functions by a constant ratio.

Real released Regents questions on reading an exponential model y = a·bᵗ — its initial value, and the growth or decay rate hidden in the base (0.75 is a 25% decay, not 75%).

Real released Regents questions on arithmetic and geometric sequences — find the common difference or ratio, the nth term, and recursive or explicit rules.

Real released Regents questions on data and statistics — compare data sets by center and spread, find a linear regression and correlation coefficient, tell correlation from causation, and read a two-way table.

Real released Regents questions on classifying numbers as rational or irrational and reasoning about closure — what you get when you add or multiply rationals and irrationals.