New York State Regents Examinations Algebra I (Regents Examination) Syllabus

Algebra I (Regents Examination) syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Algebra I (Regents Examination) in New York State Regents Examinations, not a summary of it.

1. 1

   The Real Number System and Quantities

   3 topics

   • Properties of Rational and Irrational Numbers
     • Sums and products of rational and irrational numbers
     • Classifying numbers
   • Units, Quantities, and Modeling
     • Choosing appropriate units and scale
     • Interpreting accuracy and level of precision
   • Algebraic Expressions and Structure
     • Interpreting parts of an expression (terms, factors, coefficients)
     • Rewriting expressions using equivalent forms
2. 2

   Linear Equations, Inequalities, and Systems

   4 topics

   • Solving Linear Equations and Inequalities
     • Equations in one variable
     • Compound and absolute-value contexts
   • Graphing Linear Functions
     • Slope, intercepts, and rate of change
     • Slope-intercept, point-slope, and standard form
   • Systems of Linear Equations and Inequalities
     • Solving by substitution and elimination
     • Graphing systems of inequalities
   • Modeling with Linear Relationships
     • Writing equations from real-world contexts
3. 3

   Functions

   3 topics

   • Function Concepts and Notation
     • Domain, range, and function evaluation
     • Interpreting function notation in context
   • Analyzing Functions from Graphs and Tables
     • Key features: intercepts, intervals, extrema, end behavior
     • Average rate of change over an interval
   • Sequences as Functions
     • Arithmetic and geometric sequences
     • Recursive and explicit definitions
4. 4

   Quadratic Functions and Equations

   3 topics

   • Factoring and Solving Quadratics
     • Factoring techniques (GCF, trinomials, difference of squares)
     • Quadratic formula and completing the square
   • Graphing Parabolas
     • Vertex, axis of symmetry, and zeros
     • Transformations and forms (standard, vertex, factored)
   • Modeling Quadratic Phenomena
     • Projectile and area problems
5. 5

   Exponential Functions and Polynomials

   3 topics

   • Exponential Growth and Decay
     • Comparing linear vs. exponential models
     • Interpreting growth/decay rates
   • Operations with Polynomials
     • Adding, subtracting, and multiplying polynomials
   • Laws of Exponents
     • Simplifying expressions with integer exponents
6. 6

   Statistics and Data Analysis

   3 topics

   • Univariate Data
     • Measures of center and spread
     • Comparing distributions and identifying outliers
   • Bivariate Data and Correlation
     • Scatter plots and lines of best fit
     • Correlation vs. causation; residuals
   • Two-Way Frequency Tables
     • Joint, marginal, and conditional frequencies

Algebra I (Regents Examination) flashcards for New York State Regents Examinations

22 of 54 cards from the Algebra I (Regents Examination) deck — real questions with worked answers.

1. What is the result of adding, subtracting, or multiplying two rational numbers?

   Always a rational number (the rationals are closed under +, -, x, and division by nonzero).

2. What is the sum of a rational number and an irrational number?

   Always irrational.

3. What is the product of a nonzero rational number and an irrational number?

   Always irrational.

4. Classify the number sqrt(16) and explain why.

   Rational. sqrt(16) = 4, a whole number, which is rational.

5. When checking a formula or computation, what does dimensional (unit) analysis verify?

   That the units on both sides of an equation match, confirming the quantities are combined correctly.

6. How do you convert 60 miles per hour into feet per second (unit setup)?

   Multiply by conversion factors: 60 mi/hr x (5280 ft/1 mi) x (1 hr/3600 s) = 88 ft/s.

7. In modeling, what is the difference between a quantity's measure and its level of accuracy (precision)?

   The measure is the value reported; precision refers to the smallest unit/decimal place used, limiting how exact the reported value is.

8. In the expression 5x^3 + 2x - 7, identify the terms, coefficients, and constant.

   Terms: 5x^3, 2x, -7. Coefficients: 5 and 2. Constant: -7.

9. What is a factor of an algebraic expression?

   A quantity being multiplied; in a product, each multiplicand is a factor (e.g., in 3(x+2), 3 and (x+2) are factors).

10. Rewriting P(1+r/n)^(nt) by viewing parts as a single quantity is an example of what skill?

    Interpreting expressions by their structure (seeing parts like (1+r/n) as a single entity to understand meaning).

11. What are the steps to solve a linear equation like 3(x-2)=12?

    Distribute: 3x-6=12; add 6: 3x=18; divide by 3: x=6.

12. What must you do to an inequality when you multiply or divide both sides by a negative number?

    Reverse the inequality symbol.

13. How is the solution to a one-variable inequality such as x>3 represented on a number line?

    An open circle at 3 with shading to the right (closed/filled circle if the symbol includes 'or equal to').

14. How do you solve a literal equation for a specified variable, e.g., solve A=lw for w?

    Isolate the variable using inverse operations: w = A/l.

15. What is the slope-intercept form of a linear equation, and what does each letter represent?

    y = mx + b, where m is the slope and b is the y-intercept.

16. What is the formula for the slope between two points (x1,y1) and (x2,y2)?

    m = (y2 - y1)/(x2 - x1).

17. What are the slopes of two lines that are (a) parallel and (b) perpendicular?

    Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals (product = -1).

18. What is the point-slope form of a linear equation?

    y - y1 = m(x - x1), where m is the slope and (x1,y1) is a point on the line.

19. What does the graph of x = 4 look like, and what is its slope?

    A vertical line through x=4; its slope is undefined.

20. What are the three algebraic methods for solving a system of linear equations?

    Graphing, substitution, and elimination (linear combination).

21. What does the solution to a system of two linear equations represent graphically?

    The point(s) of intersection of the two lines.

22. How many solutions does a linear system have if the lines are parallel versus the same line?

    Parallel (different intercepts): no solution. Same line: infinitely many solutions.

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