New York Regents cheat sheet

Regents exams are New York State high school Regents examinations in subjects such as Algebra I, Geometry, Algebra II, Living Environment, Earth Science, Chemistry, Physics, Global History and Geography II, U.S. History and Government, and English Language Arts; each is written to the New York State Learning Standards for its subject.

Most Regents exams are scored on a 0-100 scale, and 65 is the score traditionally required for Regents credit; scores below 65 may still earn course credit locally under district policy, and appeals processes can allow a lower score to satisfy a graduation requirement in limited cases.

Many science and math Regents exams are composed of multiple parts, typically Part I multiple-choice and Parts II-IV constructed-response (short answer, extended response, and sometimes a lab-based or document-based section); point totals differ by subject, so always read the front cover for the number of questions and points.

A raw score is converted to the scaled 0-100 score using a conversion chart specific to each exam administration; raw-to-scale conversions vary by test date and subject, so a raw score from one administration does not map to the same scaled score in another.

On most Regents exams, a four-function or scientific calculator is permitted only for specified subjects (for example, Algebra I, Geometry, Algebra II, Chemistry, Physics, and Earth Science), and graphing calculators are allowed only where the exam's directions explicitly permit them.

Reference tables are provided for certain science exams (Earth Science Reference Tables, Chemistry Reference Tables, Physics Reference Tables); these contain constants, formulas, and data and must be used rather than memorized values when the exam supplies them.

The Global History and Geography II and U.S. History and Government exams include document-based questions (DBQs) that require citing evidence from provided documents plus outside knowledge; answers must reference the documents explicitly to earn credit.

For English Language Arts, the exam requires close reading of passages and text-based responses; claims and analyses must be supported with specific evidence from the texts rather than personal opinion alone.

Answers to constructed-response questions are scored with rubrics that award partial credit; showing work or citing evidence can earn points even when the final answer is incorrect, and leaving a question blank earns zero.

Algebra I: linear equations and inequalities, systems of equations, exponential functions, polynomials, factoring, quadratic equations, and functions; the quadratic formula is x = [-b ± sqrt(b^2 - 4ac)] / (2a), and the discriminant b^2 - 4ac determines the number of real solutions (positive: two, zero: one, negative: none).

Algebra I: slope formula m = (y2 - y1)/(x2 - x1); slope-intercept form y = mx + b; point-slope form y - y1 = m(x - x1); parallel lines have equal slopes, and perpendicular lines have slopes whose product is -1.

Geometry: distance formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2) and midpoint formula ((x1 + x2)/2, (y1 + y2)/2); the sum of interior angles of an n-gon is (n - 2)180 degrees.

Geometry: circle facts include central angle equals intercepted arc measure, inscribed angle equals half its intercepted arc, and the equation of a circle is (x - h)^2 + (y - k)^2 = r^2 with center (h, k) and radius r.

Geometry: volume formulas include cylinder V = pi r^2 h, cone V = (1/3)pi r^2 h, sphere V = (4/3)pi r^3, and pyramid V = (1/3)Bh; similar figures have equal corresponding angles and proportional corresponding sides.

Algebra II: function transformations follow y = a f(x - h) + k, where h shifts horizontally and k shifts vertically; the vertex form of a quadratic is y = a(x - h)^2 + k with vertex (h, k).

Algebra II: logarithm and exponent rules include log(ab) = log a + log b, log(a/b) = log a - log b, log(a^n) = n log a, and a^0 = 1 for a not equal to zero; exponential growth/decay is modeled by y = a(1 ± r)^t.

Algebra II: the unit circle gives exact trig values, such as sin 30 degrees = 1/2, cos 60 degrees = 1/2, sin 45 degrees = sqrt(2)/2, and tan 45 degrees = 1; the identity sin^2 x + cos^2 x = 1 holds for all x.

Statistics and probability: the mean is the sum of values divided by the count; the median is the middle value of an ordered data set; standard deviation measures spread, and a larger standard deviation means data are more spread out from the mean.

Living Environment: the cell theory states that all living things are made of cells, cells are the basic unit of structure and function, and new cells arise from existing cells; photosynthesis converts light energy, carbon dioxide, and water into glucose and oxygen, while cellular respiration releases energy from glucose.

Living Environment: DNA replication is semi-conservative; transcription makes mRNA from DNA, and translation at the ribosome builds proteins from amino acids according to codons; mutations can change protein structure and function.

Living Environment: natural selection requires variation, heritability, and differential reproductive success; evidence for evolution includes fossil records, comparative anatomy (homologous structures), and molecular similarities.

Living Environment: homeostasis maintains stable internal conditions through feedback; the immune system distinguishes self from nonself, and disruptions such as pathogens or environmental change can alter ecosystem stability.

Earth Science: the Earth Science Reference Tables provide the geologic time scale, mineral and rock identification properties, and the solar system data; the law of superposition states that in undisturbed sedimentary layers, older rock lies below younger rock.

Earth Science: plate tectonics explains earthquakes, volcanoes, and mountain building at convergent, divergent, and transform boundaries; the Richter scale measures earthquake magnitude, and seismic waves include P waves (fastest, compressional) and S waves (shear, cannot travel through liquids).

Earth Science: weather and climate are driven by unequal heating of Earth's surface; the Coriolis effect deflects moving air and water, and fronts mark boundaries between air masses; the greenhouse effect warms the atmosphere by trapping outgoing infrared radiation.

Chemistry: the periodic table organizes elements by increasing atomic number; groups share valence electron counts and similar chemical properties, and periods correspond to occupied electron shells; the mole is 6.02 x 10^23 particles.

Chemistry and Physics: balanced chemical equations conserve mass; pH below 7 is acidic, 7 is neutral, and above 7 is basic; in physics, Newton's second law is F = ma, work is W = Fd, and the speed of light is approximately 3.00 x 10^8 m/s.

U.S. History and Government: the Constitution establishes federalism, separation of powers, and checks and balances; the Bill of Rights (first ten amendments) protects individual liberties, and the amendment process requires two-thirds of Congress and three-fourths of the states.

U.S. History and Government: key turning points include the Declaration of Independence (1776), the Civil War and Reconstruction (1861-1877), industrialization and Progressive reforms, the New Deal response to the Great Depression, and the civil rights movement of the 1950s and 1960s.

U.S. History and Government: Supreme Court cases such as Marbury v. Madison (judicial review), Brown v. Board of Education (desegregation), and Miranda v. Arizona (rights of the accused) illustrate constitutional principles.

Global History and Geography II: major eras include the Neolithic Revolution, classical civilizations, the rise and spread of major world religions, the Age of Exploration, the Enlightenment and political revolutions, imperialism, the World Wars, the Cold War, and decolonization.

Global History and Geography II: geographic factors such as climate, access to water, and location shape settlement and trade; human rights documents such as the Universal Declaration of Human Rights (1948) reflect responses to atrocities and set international norms.

DBQ strategy: read the historical context and task first, then group documents by theme; each body paragraph should cite at least one document by number and connect it to outside historical knowledge to earn full credit.

English Language Arts: Regents reading passages require identifying central ideas, analyzing how an author develops a claim, and interpreting word choice and structure; responses must cite specific textual evidence, often with line numbers.

English Language Arts: the argument essay asks students to evaluate a claim using evidence from provided sources; a strong response states a clear position, acknowledges counterclaims, and uses source-based evidence rather than unsupported opinion.

English Language Arts: standard conventions matter in scoring; clear organization, transitions, and control of grammar and usage are rubric criteria, and textual analysis should explain how evidence supports the claim rather than merely summarizing the passage.