Overview
This lecture reviews the January 2025 Algebra 1 Regents Exam, walking through common question types and key strategies for solving them, including use of formula sheet, calculator techniques, and step-by-step solutions to representative problems.
Key Formula Sheet Topics
- The formula sheet provides: the quadratic formula, axis of symmetry, slope formula, equations of a line, arithmetic and geometric sequence formulas, compound interest, and methods to identify outliers and interquartile range.
- Most-used formulas on the exam: quadratic formula, arithmetic sequence formula, and slope formula.
Factoring, Equations, and Sequences
- Always check for a greatest common factor before factoring further.
- Factor differences of squares as (a + b)(a - b).
- To find the equation of a line given two points, use the slope formula and y = mx + b form.
- In geometric sequences, the common ratio is found by dividing consecutive terms.
- Arithmetic sequence nth term: first term + (n-1) × common difference.
Functions and Graph Interpretation
- The constant term in a polynomial is the term without a variable.
- In linear equations, the coefficient of x is the rate (slope); the constant is the set or starting fee.
- To determine the solution region for a system of inequalities, identify where shaded areas overlap and check for solid or dashed boundary lines.
- The domain of a graph is all valid input (x) values; open circles indicate excluded values.
Operations and Properties
- When subtracting polynomials, distribute the negative across all terms.
- Combine like terms to simplify expressions.
- Exponent rules: x^(a+b) = x^a × x^b.
- Addition property of equality: adding/subtracting the same value on both sides preserves equality.
Statistical and Data Analysis
- To find percent, divide the part by total and multiply by 100.
- Interquartile range (IQR) = Q3 − Q1.
- Mode is the most frequent value; median is the middle value.
- Use calculator’s statistical features for IQR and regression.
Problem-Solving Techniques
- Solve linear and quadratic equations by isolating the variable, using inverses, or applying the quadratic formula.
- When solving inequalities, reverse inequality sign when multiplying/dividing by a negative.
- Rationalize denominators by multiplying numerator and denominator by the radical in the denominator.
- For unit conversions, ensure units cancel appropriately.
Systems of Equations
- Set up equations based on totals (number of items and total value).
- Solve using elimination or substitution, being careful with units and coefficients.
- Interpret intersection point of graphed lines in word problems.
Regression and Correlation
- Use linear regression to model data: y = mx + b, rounding m and b as required.
- Correlation coefficient (r) close to 1 or -1 indicates strong linear fit; positive r means positive slope.
Key Terms & Definitions
- Quadratic Formula — Formula to solve ax² + bx + c = 0: x = [-b ± √(b²-4ac)]/2a.
- Slope Formula — m = (y2 - y1)/(x2 - x1), measures steepness of a line.
- Axis of Symmetry — Line x = -b/(2a) dividing a parabola into mirror images.
- Arithmetic Sequence Formula — an = a1 + (n-1)d; a1 = first term, d = common difference.
- Geometric Sequence — Sequence where each term is multiplied by a constant ratio.
- Constant Term — A term without variables in a polynomial.
- Domain — Set of all possible x-values (inputs) for a function.
- Interquartile Range (IQR) — Q3 minus Q1; measures middle 50% of data.
- Linear Regression — Best-fit line through data points; equation y = mx + b.
- Correlation Coefficient (r) — Measures strength and direction of a linear relationship.
Action Items / Next Steps
- Practice factoring, solving equations, and using the quadratic formula.
- Use your calculator for regression, sequence, and statistical problems as shown.
- Review the formula sheet and ensure you know when/how to apply each formula.
- Complete any assigned practice exams or problems from recent Regents tests.
- Get a good night's sleep and bring calculator and formula sheet to the exam.