NY Regents Algebra I study plan

Classify real numbers into subsets (natural, whole, integer, rational, irrational) and justify each classification with a counterexample when needed.

Simplify radical expressions and apply the laws of exponents, including rational exponents, with 90% accuracy on 20 mixed problems.

Convert between radical and rational exponent forms and evaluate numerical expressions without a calculator.

Use units to solve multi-step dimensional-analysis problems and interpret the reasonableness of results.

Solve multi-step linear equations and inequalities, including those with variables on both sides and absolute value, showing each inverse operation.

Rearrange formulas and literal equations for a specified variable in at least 10 varied contexts.

Solve systems of two linear equations by graphing, substitution, and elimination, and classify the system as consistent, inconsistent, or dependent.

Translate word problems into linear equations or inequalities and interpret the solution in context.

Factor quadratic expressions completely, including difference of squares and trinomials with a leading coefficient other than 1.

Solve quadratic equations by factoring, completing the square, and the quadratic formula, and choose the most efficient method for a given equation.

Identify key features of quadratic functions from equations and graphs: vertex, axis of symmetry, intercepts, and direction of opening.

Interpret function notation and evaluate functions for given inputs, including from tables and graphs.

Distinguish among linear, quadratic, and exponential functions using tables, graphs, and equations, and justify the choice with rate-of-change reasoning.

Write recursive and explicit rules for arithmetic and geometric sequences and connect them to linear and exponential models.

Sketch and interpret piecewise and absolute value functions, including domain and range restrictions.

Evaluate and interpret average rate of change over an interval for a given function.

Apply the Pythagorean theorem and its converse to solve right-triangle problems, including those in three-dimensional figures.

Use distance, midpoint, and slope formulas to classify quadrilaterals on the coordinate plane.

Perform and describe transformations (translations, reflections, rotations, dilations) on the coordinate plane and identify lines of symmetry.

Calculate perimeter and area of composite figures and use volume formulas for prisms, cylinders, pyramids, and cones.

Compute and compare measures of center (mean, median) and spread (range, interquartile range, standard deviation) for data sets, including the effect of outliers.

Construct and interpret box plots, histograms, and two-way frequency tables, and calculate joint, marginal, and conditional relative frequencies.

Evaluate statistical studies for bias, sampling method, and causation versus correlation.

Solve geometric probability problems involving area models and use the addition and multiplication rules for probability.

Fit a linear or exponential regression to bivariate data using technology or by hand, interpret the correlation coefficient, and make predictions.

Solve probability problems involving independent and dependent events, including conditional probability, and verify using Venn diagrams or tree diagrams.

Review algebraic manipulation skills (factoring, solving equations) in the context of statistics problems, such as finding a missing data value given a mean.

Interpret the slope and intercept of a regression line in the context of the data.

Complete two full-length practice exams under timed conditions, simulating the Regents format and scoring guide.

Identify and rework the five most frequently missed problem types across all domains using targeted review.

Create a one-page formula and concept sheet from memory and verify it against a reference sheet.

Practice test-taking strategies: pacing, eliminating answer choices, and checking reasonableness of answers.