📚

Algebra 1 Regents Exam Review Guide

Jun 2, 2025

Algebra 1 Regents Review - June 4, 2024

Overview

  • The Regents exam is based on the Next Generation Mathematics Learning Standards.
  • The review uses the June 2023 Algebra 1 Regents exam as a reference.
  • Common Core and Next Generation standards are similar.
  • One question is omitted due to updates in standards.
  • Supplementary problems are available on the emath instruction website.

Key Topics

Formula Sheet

  • Quadratic Formula: Essential for solving quadratic equations.
  • Slope Formula: Change in y divided by change in x.
  • Equations of Lines:
    • Slope-intercept form: y = mx + b.
    • Point-slope form: y - y₁ = m(x - x₁).
  • Exponential functions and sequences:
    • Compound interest.
    • Arithmetic and geometric sequences.
  • Interquartile Range (IQR) and outliers.

Multiple Choice Questions

Factoring & Simplifying

  1. Difference of Squares: Example: 9m² - 100.
  2. Rational vs. Irrational Numbers: Non-perfect squares result in irrational numbers.
  3. Substitution in Linear Equations: Verify if a point lies on a line.
  4. Polynomial Simplification: Distributing and combining like terms.

Sequence & Equations

  1. Arithmetic Sequence: Identify common difference and predict terms.
  2. Completing the Square: Recognize steps in solving quadratics by this method.

Functions & Graphs

  1. Exponential Growth: Recognize faster growth in exponential functions.
  2. Exponential Function Components: Understand each part's role.
  3. Conversions: Time and distance conversions without standard formulas.
  4. Polynomial Graphs: Recognize features like zeros and end behavior.

Solving & Evaluating

  1. Function Evaluation: Using function notation to substitute values.
  2. Unit Conversion: Items per unit of time.
  3. Exponent Rules: Apply operations on exponential expressions.
  4. Inequality Solutions: Solving systems of inequalities and testing solutions.

Free Response

Solving Equations

  1. Linear Equations: Solve using inverse operations and check solutions.
  2. Graphical Solutions: Understand intersection points of functions.
  3. Patterns and Sequences: Distinguish between linear and exponential growth.

Data & Statistics

  1. Box Plot Construction: Use five-number summary to plot data.
  2. Polynomial Expressions: Expanding and combining polynomials.

Functions & Systems

  1. Function Identification: Determine how to modify relations to become functions.
  2. Complete Factoring: Factor polynomials fully.
  3. Quadratic Formula: Solving quadratics with rounding.

Part 3 Problems

Graphing

  1. Graphing Functions: Plotting absolute value and quadratic functions to find intersections.

Rates of Change

  1. Analyzing Temperature Data: Identify intervals of increase and calculate average rate of change.
  2. Systems of Inequalities: Graphically solving and testing points for validity.
  3. Statistical Analysis: Linear regression and interpreting correlation coefficients.

Systems of Equations

  1. Word Problems with Systems: Set up and solve systems to find costs.

Supplementary Problems

Point-Slope Form

  • Writing equations in point-slope form using given points.

Identifying Outliers

  • Use IQR and given formulas to identify outliers in data sets.

Rationalizing Denominators

  • Simplify fractions by rationalizing denominators.

Solving Quadratic Systems

  • Use substitution or elimination to solve systems involving quadratics.

Conclusion

  • Emphasize careful review and use of time during the exam.
  • Importance of checking work and using calculator tools effectively.

Full transcript