New York Regents Mathematics (NYSED): the three-exam sequence, the credit structure, and how to study Algebra I, Geometry, and Algebra II

The New York State Regents Examinations in Mathematics are a sequence of three end-of-course exams, administered by the New York State Education Department (NYSED): Algebra I, Geometry, and Algebra II. They are built from the Next Generation Mathematics Learning Standards, New York's 2017 revision of the earlier Common Core standards. This page is the index for all three: it explains the sequence, the shared four-part structure, the reference sheet, how the raw score becomes a scale score, and how to study each course. The topic pages below carry the worked Regents-style questions.

The three-exam sequence

The three math Regents are designed to be taken in order, one course per year.

• Algebra I is normally taken in grade 9 and is the first Regents most students sit. For many students it is the single math Regents they must pass (a scale score of at least 65) to earn a Regents diploma, which makes it the highest-stakes math exam in the state.
• Geometry is normally taken in grade 10, after Algebra I. It is the most proof-heavy of the three and leans on transformations, similarity, trigonometry, circles, and coordinate methods.
• Algebra II is normally taken in grade 11. It is the most advanced course, extending Algebra I into polynomial, rational, radical, exponential, logarithmic, and trigonometric functions, and adding inferential statistics and probability.

Accelerated students often take Algebra I in grade 8 and finish Algebra II by grade 10. Each exam is offered in the January, June, and August administrations.

The shared four-part structure

All three math Regents use the same four-part design: 37 questions worth 86 credits total.

• Part I (questions 1 to 24) is multiple choice, four options each, no partial credit. It rewards fluent skills and quick reading of graphs and tables.
• Part II (questions 25 to 32) is short constructed response: each is worth 2 credits, and you must show work or give a brief explanation. A correct answer with no work usually earns only 1 of the 2 credits.
• Part III (questions 33 to 36) is 4-credit constructed response: multi-step problems that combine skills, such as a modeling task, a coordinate proof, or a statistics question with interpretation.
• Part IV (question 37) is a single 6-credit extended response: the longest, most demanding problem on the paper. In Geometry it is frequently a full proof; in Algebra I and Algebra II it is usually an extended modeling task.

A graphing calculator is required and may be used throughout. Because Parts II to IV award the method, you must present setups, substitutions, and justifications, not just a final number.

The Reference Sheet

Every math Regents includes a one-page High School Mathematics Reference Sheet at the front of the booklet. It is the same sheet across Algebra I, Geometry, and Algebra II, so a formula you need for one course may simply not be relevant to another. It provides:

• Customary unit conversions: for example $1$ foot $= 12$ inches, $1$ yard $= 3$ feet, $1$ pound $= 16$ ounces, $1$ pint $= 2$ cups, $1$ quart $= 2$ pints, $1$ gallon $= 4$ quarts.
• Core algebra and trig formulas: the Pythagorean theorem $a^2 + b^2 = c^2$; the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$; the area of a triangle $A = \frac{1}{2}ab\sin C$; the Law of Cosines $a^2 = b^2 + c^2 - 2bc\cos A$; the Law of Sines $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$; the relationship $1$ radian $= \frac{180}{\pi}$ degrees; the exponential model $A = A_0 e^{kt}$; the arithmetic sequence $a_n = a_1 + (n-1)d$; the geometric sequence $a_n = a_1 r^{n-1}$; and the finite geometric series $S_n = \frac{a_1 - a_1 r^n}{1 - r}$ for $r \neq 1$.
• Volume formulas: cylinder $V = \pi r^2 h$, cone $V = \frac{1}{3}\pi r^2 h$, sphere $V = \frac{4}{3}\pi r^3$, and pyramid $V = \frac{1}{3}Bh$.

The sheet is a support, not a substitute for understanding. Many essentials are not on it: the slope and distance formulas, the laws of exponents and logarithms, the probability rules, the z-score formula, and the trigonometric identities all have to be known. Knowing which formula fits a problem is the skill the exam tests.

Raw score, scale score, and the cut scores

Each exam is first scored to a raw score out of 86 credits. NYSED then converts that raw score to a scale score from 0 to 100 using a conversion chart published for that specific administration.

• A scale score of 65 is the standard passing score (Level 3) and counts toward a Regents diploma.
• A scale score of 85 is the mastery benchmark used for the Advanced Regents diploma with an honors or mastery designation.

The conversion is not linear, and the raw credits needed for a 65 or an 85 differ between administrations, which is why you should never assume a fixed raw cutoff. The scaling keeps the meaning of a 65 consistent even when one form is slightly harder than another.

How to study the math Regents

1. Master Part I skills until they are automatic. Half the credits (48 of 86) come from the 24 multiple-choice questions. Fast, accurate work on linear and quadratic skills, function reading, and basic statistics secures the largest block of credits.
2. Write like a grader on Parts II to IV. Show the setup, every algebraic step, and a sentence of interpretation where a context is involved. A bare correct answer loses method credit; correct method with a small slip still earns most of the credits.
3. Use the reference sheet, but know the gaps. Practice with the sheet in front of you so you know exactly what it gives. Memorize the slope and distance formulas, exponent and logarithm laws, probability rules, and trig identities that are not on it.
4. Work past papers under timed conditions. NYSED releases every exam with its scoring key and model responses. Working released papers is the single most effective preparation, because the question style and credit allocation are board-specific.
5. Connect the three courses. Algebra I functions reappear in Algebra II; coordinate methods bridge Algebra I and Geometry; the quadratic formula and sequences run through all three. Seeing the through-lines makes each new topic feel like an extension rather than a fresh start.

The courses, topic by topic

Each topic below has its own answer page with worked Regents-style questions (multiple choice and credit-based constructed response), plus an overview guide and a quiz for each module.

Algebra I.

• Expressions and equations: interpreting and rewriting expressions, polynomial operations and factoring, linear equations and inequalities, systems of equations and inequalities, solving quadratic equations.
• Functions and statistics: function notation and key features, linear and exponential models, quadratic functions and their graphs, one-variable statistics, two-variable data and regression.

Geometry.

• Congruence and proof: rigid motions and transformations, triangle congruence and CPCTC, geometric constructions, proofs about lines, angles, and triangles, parallelogram and quadrilateral proofs.
• Similarity, trigonometry, and circles: dilations and similarity, right triangle trigonometry, circles, angles, and segments, coordinate geometry and partitioning, volume and solids.

Algebra II.

• Polynomials and rationals: polynomial arithmetic and the Remainder Theorem, polynomial zeros and end behavior, rational expressions and equations, radicals and rational exponents, complex numbers and quadratics.
• Exponential, logarithmic, and trigonometric functions: exponential and logarithmic functions, solving exponential and logarithmic equations, radian measure and the unit circle, graphing sinusoidal functions, sequences and series.
• Statistics and probability: the normal distribution and z-scores, conditional probability and the probability rules, sampling and study design, regression and statistical inference.

For the official materials

NYSED publishes every Regents math exam, its scoring key, the conversion chart, and model student responses, along with the Reference Sheet and the educator guides, on its state assessment pages. Always study from the current released exams and the educator guide for each course, because the question style, the credit allocation, and the standards are specific to the New York Regents.