Algebra 1 Regents Review - June 2024

Introduction

• Review for Algebra 1 Regents exam, first under the Next Generation Mathematics Learning Standards.
• Focus on June 2023 Algebra 1 Regents exam to prepare.
• Emphasizes understanding formula sheet provided during the exam.

Reference Sheet Overview

• Quadratic Equation & Formula: Used for solving zeros of a quadratic equation.
• Slope Formula: Change in y divided by change in x.
• Equation of a Line: Given in slope-intercept (y = mx + b) and point-slope form.
• Exponential Functions: Generic form y = a * b^x and compound interest formula.
• Sequences: Arithmetic and geometric sequence formulas.
• Interquartile Range & Outlier Formulas: New for evaluating data sets.

Exam Questions Overview

Multiple Choice

1. Factoring: Difference of squares (e.g., 9m² - 100).
2. Rational vs. Irrational Numbers: Identifying when expressions are irrational.
3. Linear Equations: Determine if a line passes through a given point by substitution.
4. Expression Simplification: Combining like terms.
5. Sequences: Calculate nth term in an arithmetic sequence.
6. Completing the Square: Process for solving quadratic equations.
7. Function Comparison: Evaluate which function has greatest value for x > 1.
8. Exponential Growth: Understanding parts of an exponential function (e.g., Bacteria growth).
9. Unit Conversion: Weekly to minutes item shipping calculation.
10. Graph Identification: Recognize function type (e.g., cubic) and its equation.
11. Function Evaluation: Calculate f(x) for given x using function notation.
12. Geometry & Algebra: Calculate volume changes with dimensional increases.
13. Exponent Rules: Apply exponent properties (e.g., a^x * a^y = a^(x+y)).
14. Inequalities: Determine minimum dimes needed for a monetary goal.
15. Formula Rearrangement: Solve for specific variable (e.g., trapezoid height).
16. Graph Transformations: Effects of multiplying function by constant.
17. Statistics: Analyze survey data using percentages.
18. Quadratic Solutions: Solve and understand solutions for quadratic equations.
19. Function Vertex: Determine if functions share the same vertex.
20. Function Domain: Understand domain of a quadratic function.
21. Removed Question: Not applicable under new standards.
22. Solving Inequalities: Algebraic solution for inequalities.
23. Polynomial Identification: Degree, leading coefficient, and constant term.
24. Real-World Domains: Determine reasonable domain for function based on context.

Free Response

25. Linear Equations with Decimals: Solve using algebraic methods.
26. Graph Zeros: Identify zeros from a graph and explain reasoning.
27. Sequence Analysis: Determine if sequence is arithmetic or exponential.
28. Box Plot Construction: Use five-number summary and construct plot.
29. Expression Simplification: Combine expressions into standard form.
30. Function Analysis: Modify relationships to become functions.
31. Polynomial Factoring: Factor completely using common techniques.
32. Quadratic Formula: Solve quadratic equation to nearest tenth.
33. Graphing Functions: Use graph to find points of intersection.
34. Data Analysis: Analyze temperature changes over time.
35. System of Inequalities: Graphically solve and analyze solutions.
36. Linear Regression: Analyze horse data with regression and correlation.
37. Systems of Equations: Solve real-world cost problems involving multiple purchases.

Supplementary Problems

1. Point-Slope Form: Use to find equation of line through two points.
2. Outlier Identification: Use interquartile range to identify outliers.
3. Systems of Equations: Solve system of parabola and line equations.
4. Rationalizing Denominators: Simplify fractions by rationalizing denominators.

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Final Advice

• Take your time during the exam, using all three hours if needed.
• Use your calculator effectively, verifying solutions where possible.
• Ensure graphing is accurate and label all parts.
• Review formula sheet and understand new topics like point-slope and outlier formulas.