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New York State Regents Examinations Algebra I (Regents Examination) Syllabus
The Algebra I (Regents Examination) syllabus for New York State Regents Examinations in full: 6 chapters, 19 topics and 33 sub-topics, every one listed below, plus 54 Algebra I (Regents Examination) flashcards with answers.
Algebra I (Regents Examination) syllabus: all 6 chapters
Expand any chapter to see its topics and sub-topics.
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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
- Properties of Rational and Irrational Numbers
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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
- Solving Linear Equations and Inequalities
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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
- Function Concepts and Notation
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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
- Factoring and Solving Quadratics
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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
- Exponential Growth and Decay
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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
- Univariate Data
New York State Regents Examinations Algebra I (Regents Examination) flashcards — 54 questions with answers
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).
What is the sum of a rational number and an irrational number?
Always irrational.
What is the product of a nonzero rational number and an irrational number?
Always irrational.
Classify the number sqrt(16) and explain why.
Rational. sqrt(16) = 4, a whole number, which is rational.
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.
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.
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.
In the expression 5x^3 + 2x - 7, identify the terms, coefficients, and constant.
Terms: 5x^3, 2x, -7. Coefficients: 5 and 2. Constant: -7.
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).
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).
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.
What must you do to an inequality when you multiply or divide both sides by a negative number?
Reverse the inequality symbol.
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').
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.
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.
What is the formula for the slope between two points (x1,y1) and (x2,y2)?
m = (y2 - y1)/(x2 - x1).
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).
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.
What does the graph of x = 4 look like, and what is its slope?
A vertical line through x=4; its slope is undefined.
What are the three algebraic methods for solving a system of linear equations?
Graphing, substitution, and elimination (linear combination).
Show the other 34 Algebra I (Regents Examination) flashcards
What does the solution to a system of two linear equations represent graphically?
The point(s) of intersection of the two lines.
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.
How do you graph the solution region of a system of linear inequalities?
Graph each boundary line (dashed for < or >, solid for <= or >=), shade each solution half-plane, and the overlap is the solution.
In a real-world linear model y = mx + b, what do the slope and y-intercept represent?
The slope is the constant rate of change; the y-intercept is the initial value (when x=0).
What is the definition of a function?
A relation in which every input (x) is assigned exactly one output (y).
What does the notation f(3) = 7 mean?
When the input is 3, the function f produces an output of 7.
What is the vertical line test?
A graph represents a function if and only if no vertical line crosses it more than once.
What are the domain and range of a function?
Domain is the set of all possible input (x) values; range is the set of all possible output (y) values.
On a graph, how do you identify where a function is increasing, decreasing, or constant?
Reading left to right: increasing where it rises, decreasing where it falls, constant where it is horizontal.
What is a zero (x-intercept) of a function?
An input value where f(x)=0; the point where the graph crosses the x-axis.
What is the average rate of change of a function over [a,b]?
(f(b) - f(a))/(b - a), the slope of the line connecting the two endpoints.
What is the explicit (general) formula for an arithmetic sequence?
a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.
What is the explicit formula for a geometric sequence?
a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.
Why are sequences considered functions, and what is their domain?
Each term position maps to exactly one value; the domain is the positive integers (or whole numbers).
What is the recursive formula for an arithmetic sequence with common difference d?
a_1 given, and a_n = a_(n-1) + d.
How do you factor a difference of two squares, a^2 - b^2?
(a + b)(a - b).
How do you factor a trinomial of the form x^2 + bx + c?
Find two numbers that multiply to c and add to b; write as (x + p)(x + q).
What is the quadratic formula?
x = (-b +/- sqrt(b^2 - 4ac)) / (2a) for ax^2 + bx + c = 0.
What does the discriminant b^2 - 4ac tell you about a quadratic's roots?
Positive: two real roots; zero: one real (double) root; negative: no real roots.
What is the zero product property used in solving quadratics?
If a*b = 0, then a = 0 or b = 0; so set each factor equal to zero.
What are the coordinates of the vertex of a parabola y = ax^2 + bx + c?
x = -b/(2a), and y is found by substituting that x; the axis of symmetry is x = -b/(2a).
How does the sign of 'a' affect the graph of a parabola y = ax^2 + bx + c?
If a>0 it opens upward (minimum); if a<0 it opens downward (maximum).
What is the vertex form of a quadratic, and what does it reveal?
y = a(x - h)^2 + k, where (h, k) is the vertex.
For a projectile modeled by h(t) = -16t^2 + v0*t + h0, what does the vertex represent?
The maximum height reached and the time at which it occurs.
What is the general form of an exponential function, and the condition for growth vs decay?
y = a*b^x; growth if b>1, decay if 0<b<1, with a as the initial value.
In y = a(1+r)^t versus y = a(1-r)^t, what does r represent?
The growth rate (first) or decay rate (second) per time period, as a decimal.
How do you add or subtract polynomials?
Combine like terms (terms with the same variable and exponent).
State the product, quotient, and power laws of exponents.
x^a * x^b = x^(a+b); x^a / x^b = x^(a-b); (x^a)^b = x^(ab).
What do x^0 and x^(-n) equal (x not zero)?
x^0 = 1; x^(-n) = 1/x^n.
What measures of center and spread describe univariate data, and which is resistant to outliers?
Center: mean and median; spread: range, IQR, standard deviation. The median (and IQR) resist outliers.
On a scatter plot of bivariate data, what does the correlation coefficient r indicate?
The strength and direction of a linear relationship; r ranges from -1 to 1 (near 0 = weak, near +/-1 = strong).
What is the difference between correlation and causation?
Correlation means two variables move together; causation means one directly causes the other. Correlation does not imply causation.
In a two-way frequency table, what is a joint frequency versus a marginal frequency?
A joint frequency is a count in a single body cell (both categories); a marginal frequency is a row or column total.
What is a conditional relative frequency in a two-way table?
A cell count divided by its row or column total, showing the proportion within that category.
New York State Regents Examinations Algebra I (Regents Examination) FAQ
What is in the New York State Regents Examinations Algebra I (Regents Examination) syllabus?
New York State Regents Examinations Algebra I (Regents Examination) is split into 6 chapters: The Real Number System and Quantities, Linear Equations, Inequalities, and Systems, Functions, Quadratic Functions and Equations, Exponential Functions and Polynomials and Statistics and Data Analysis. Together they contain 19 topics and 33 sub-topics.
How many chapters are in New York State Regents Examinations Algebra I (Regents Examination)?
6 chapters, containing 19 topics and 33 sub-topics. The largest chapter is Linear Equations, Inequalities, and Systems, with 4 topics.
Are there flashcards for New York State Regents Examinations Algebra I (Regents Examination)?
Yes — a 54-card Algebra I (Regents Examination) deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.