# Free study guides Canonical: https://duckyhelper.com/learn/ Updated: 2026-10-01 Free study guides, one topic per page. Each guide explains the idea in plain words, works through real examples step by step, and ends with practice questions you can check yourself. ## [Algebra 1](https://duckyhelper.com/learn/algebra-1/) - [How to solve multi-step equations](https://duckyhelper.com/learn/algebra-1/solving-equations/): Solve multi-step equations with parentheses, fractions and variables on both sides. Step-by-step worked examples, common mistakes and 5 practice questions. - [How to solve and graph inequalities](https://duckyhelper.com/learn/algebra-1/inequalities/): Solve and graph linear inequalities, including compound and/or inequalities. Learn exactly when to flip the sign, with worked examples and 5 practice questions. - [How to solve absolute value equations and inequalities](https://duckyhelper.com/learn/algebra-1/absolute-value/): Solve absolute value equations and inequalities step by step: isolate, split into two cases, check for extraneous answers. Worked examples and practice. - [How to find the slope of a line](https://duckyhelper.com/learn/algebra-1/slope/): Find the slope of a line from two points, a graph or an equation. Zero vs undefined slope, parallel and perpendicular slopes, worked examples and practice. - [Slope-intercept form and how to write the equation of a line](https://duckyhelper.com/learn/algebra-1/slope-intercept-form/): Write the equation of a line in slope-intercept, point-slope and standard form. From a point and a slope, two points, or a parallel line, with worked examples. - [How to solve systems of equations](https://duckyhelper.com/learn/algebra-1/systems-of-equations/): Solve systems of equations by graphing, substitution and elimination. Step-by-step examples, no solution vs infinitely many, word problems and practice. - [Functions, function notation, domain and range](https://duckyhelper.com/learn/algebra-1/functions/): What a function is, how to read and evaluate f(x), and how to find domain and range from an equation, table or graph. Worked examples and 5 practice questions. - [Exponent rules and how to use them](https://duckyhelper.com/learn/algebra-1/exponent-rules/): All the exponent rules in one place, why they work, and how to simplify expressions with negative and zero exponents. Worked examples and 5 practice questions. - [How to simplify square roots and radicals](https://duckyhelper.com/learn/algebra-1/simplifying-radicals/): Simplify square roots step by step: pull out perfect squares, add and multiply radicals, and rationalize the denominator. Worked examples and practice. - [Adding, subtracting and multiplying polynomials](https://duckyhelper.com/learn/algebra-1/polynomials/): How to add, subtract and multiply polynomials, including FOIL and the special products like (a + b)^2. Step-by-step examples, common mistakes and practice. - [How to factor polynomials](https://duckyhelper.com/learn/algebra-1/factoring/): Factor polynomials step by step: greatest common factor, trinomials (even when a is not 1), grouping and difference of squares. Worked examples and practice. - [How to solve quadratic equations](https://duckyhelper.com/learn/algebra-1/solving-quadratics/): Solve quadratic equations by factoring, square roots and the quadratic formula, and use the discriminant to count solutions. Worked examples and practice. ## [Algebra 2](https://duckyhelper.com/learn/algebra-2/) - [Complex numbers and the imaginary unit i](https://duckyhelper.com/learn/algebra-2/complex-numbers/): How to add, subtract, multiply and divide complex numbers, simplify powers of i, and solve quadratics with complex roots. Worked examples and practice. - [Completing the square](https://duckyhelper.com/learn/algebra-2/completing-the-square/): How to complete the square to solve quadratics, write vertex form and find a circle's center and radius. Step-by-step examples and 5 practice questions. - [Dividing polynomials](https://duckyhelper.com/learn/algebra-2/polynomial-division/): How to divide polynomials by long division and synthetic division, and use the remainder and factor theorems. Step-by-step examples and 5 practice questions. - [Rational expressions and equations](https://duckyhelper.com/learn/algebra-2/rational-expressions/): How to simplify, multiply, divide, add and subtract rational expressions, and solve rational equations without keeping extraneous solutions. With practice. - [Transformations of functions](https://duckyhelper.com/learn/algebra-2/function-transformations/): How shifts, stretches and reflections change a graph, why f(x - h) moves right, and what order to apply them in. Worked examples and 5 practice questions. - [Inverse functions](https://duckyhelper.com/learn/algebra-2/inverse-functions/): How to find the inverse of a function, check it by composition, read it on a graph, and restrict the domain when needed. Worked examples and practice. - [Logarithms](https://duckyhelper.com/learn/algebra-2/logarithms/): What a logarithm is, the product, quotient and power rules, change of base, and how to solve exponential and log equations. Worked examples and practice. - [Sequences and series](https://duckyhelper.com/learn/algebra-2/sequences-and-series/): Formulas for the nth term and the sum of arithmetic and geometric sequences, plus infinite geometric series, with worked examples and 5 practice questions. ## [Biology](https://duckyhelper.com/learn/biology/) - [Cell organelles and their functions](https://duckyhelper.com/learn/biology/cell-organelles/): Cell organelles and what they do: nucleus, ribosomes, ER, Golgi, mitochondria, chloroplasts and more, plus plant vs animal vs bacteria cells and practice. - [Enzymes](https://duckyhelper.com/learn/biology/enzymes/): How enzymes work: activation energy, the active site, induced fit, and how temperature, pH and inhibitors change enzyme activity. Data examples and practice. - [Cellular respiration](https://duckyhelper.com/learn/biology/cellular-respiration/): Cellular respiration step by step: glycolysis, the citric acid cycle and the electron transport chain, where each happens, fermentation and practice. - [Photosynthesis](https://duckyhelper.com/learn/biology/photosynthesis/): Photosynthesis explained step by step: the overall equation, light-dependent reactions, the Calvin cycle, where each happens, and worked counting examples. - [Mitosis vs meiosis](https://duckyhelper.com/learn/biology/mitosis-vs-meiosis/): Mitosis vs meiosis compared: purpose, phases, chromosome numbers and genetic variation, with a side-by-side chart, counting examples and 5 practice questions. - [DNA replication](https://duckyhelper.com/learn/biology/dna-replication/): DNA replication step by step: helicase, primase, DNA polymerase and ligase, leading vs lagging strands, base pairing and semiconservative copying. - [Transcription and translation](https://duckyhelper.com/learn/biology/transcription-and-translation/): Transcription and translation step by step: DNA to mRNA to protein, reading codons, the codon chart and mutations. Worked examples and practice questions. - [How to do Punnett squares](https://duckyhelper.com/learn/biology/punnett-squares/): How to do Punnett squares: monohybrid, test cross, dihybrid 9:3:3:1 and sex-linked crosses, with genotype and phenotype ratios explained and practice. - [Natural selection](https://duckyhelper.com/learn/biology/natural-selection/): Natural selection explained: variation, inheritance, overproduction and survival, with antibiotic resistance, population data and Hardy-Weinberg practice. - [Food webs and energy pyramids](https://duckyhelper.com/learn/biology/food-webs-and-energy-pyramids/): Food chains, food webs, trophic levels and energy pyramids explained, with the 10% rule, trophic level transfer efficiency calculations and practice questions. - [The immune system basics](https://duckyhelper.com/learn/biology/immune-system/): Immune system basics: barriers, inflammation and phagocytes (innate), B cells, T cells and antibodies (adaptive), memory and vaccines, with a comparison table. ## [Chemistry](https://duckyhelper.com/learn/chemistry/) - [How to balance chemical equations](https://duckyhelper.com/learn/chemistry/balancing-chemical-equations/): Balance chemical equations step by step: count atoms, change only coefficients, handle fractions and polyatomic ions. 4 worked examples and 5 practice problems. - [Types of chemical reactions](https://duckyhelper.com/learn/chemistry/types-of-chemical-reactions/): The 5 types of chemical reactions: synthesis, decomposition, single and double replacement, combustion. How to spot each, predict products, and practice. - [The mole and molar mass](https://duckyhelper.com/learn/chemistry/mole-and-molar-mass/): What a mole is, how to find molar mass, and how to convert grams, moles and particles. Worked examples with units, common mistakes and 5 practice problems. - [Stoichiometry: how much reacts and how much forms](https://duckyhelper.com/learn/chemistry/stoichiometry/): Learn stoichiometry in three steps: grams to moles, mole ratio, moles to grams. Worked examples with every unit shown, common mistakes and 5 practice problems. - [How to find the limiting reactant](https://duckyhelper.com/learn/chemistry/limiting-reactant/): Find the limiting reactant and excess reactant step by step, then the product amount and leftover. Worked examples in moles and grams plus 5 practice problems. - [How to calculate percent yield](https://duckyhelper.com/learn/chemistry/percent-yield/): How to calculate percent yield: find the theoretical yield with stoichiometry, then divide actual by theoretical. Worked examples and 5 practice problems. - [Molarity and dilution](https://duckyhelper.com/learn/chemistry/molarity-and-dilution/): Molarity is moles of solute per liter of solution. Learn the molarity formula, M1V1 = M2V2 for dilutions, worked examples with units and 5 practice problems. - [The ideal gas law: PV = nRT](https://duckyhelper.com/learn/chemistry/ideal-gas-law/): Use the ideal gas law PV = nRT and the combined gas law. Which R to use, converting to kelvins, worked examples with units and 5 practice problems with answers. - [How to write electron configurations](https://duckyhelper.com/learn/chemistry/electron-configuration/): Write electron configurations step by step: filling order, noble gas shorthand, ions, Hund's rule and the Cr and Cu exceptions, plus 5 practice questions. - [Periodic trends](https://duckyhelper.com/learn/chemistry/periodic-trends/): Periodic trends made simple: atomic radius, ionization energy, electronegativity and ion size, the reason for each, real data and 5 practice questions. - [Ionic vs covalent bonds](https://duckyhelper.com/learn/chemistry/ionic-vs-covalent-bonds/): Ionic vs covalent bonds: electron transfer vs sharing, the electronegativity difference rule, a properties table, ionic formulas and 5 practice questions. - [How to draw Lewis structures](https://duckyhelper.com/learn/chemistry/lewis-structures/): Draw Lewis structures in 6 steps: count valence electrons, connect atoms, fill octets, add multiple bonds, check formal charge. Plus 5 practice questions. - [VSEPR theory and molecular shapes](https://duckyhelper.com/learn/chemistry/vsepr-molecular-shapes/): Predict molecular shape with VSEPR: count electron groups and lone pairs, read the shapes chart, find bond angles and polarity, then try 5 practice questions. - [Acids, bases and pH](https://duckyhelper.com/learn/chemistry/acids-bases-and-ph/): Acids, bases and the pH scale: pH = -log[H3O+], pOH, strong vs weak acids, conjugate pairs and pH significant figures, with examples and 5 practice problems. ## [Essay Writing](https://duckyhelper.com/learn/essay-writing/) - [How to write a thesis statement](https://duckyhelper.com/learn/essay-writing/thesis-statement/): How to write a strong thesis statement: a specific claim someone could argue with, plus your reasons. Weak vs strong examples, a simple formula and practice. - [How to outline an essay](https://duckyhelper.com/learn/essay-writing/essay-outline/): How to write an essay outline: start with your thesis, give each body paragraph one point with evidence, then plan the ending. Template and practice. - [How to write an introduction paragraph](https://duckyhelper.com/learn/essay-writing/introduction-paragraph/): How to write an essay introduction: a specific hook, just enough background, and a clear thesis at the end. Weak vs strong openings, examples and practice. - [How to write a body paragraph](https://duckyhelper.com/learn/essay-writing/body-paragraphs/): How to write a strong body paragraph: a topic sentence, evidence, an explanation of what the evidence proves, and a link back. Example and 5 practice items. - [How to write a conclusion paragraph](https://duckyhelper.com/learn/essay-writing/conclusion-paragraph/): How to write an essay conclusion: restate your thesis in new words, pull your points together, and show why they matter. What to avoid, examples and practice. - [Transition words for essays](https://duckyhelper.com/learn/essay-writing/transition-words/): Transition words for essays grouped by what they do: add, contrast, give an example, show cause, order steps, conclude. How to use them well, plus practice. - [Citing sources: MLA vs APA basics](https://duckyhelper.com/learn/essay-writing/citing-sources-mla-vs-apa/): MLA vs APA citation basics: in-text citations, Works Cited vs References, and a book and a webpage cited both ways. Current editions: MLA 9 and APA 7. - [How to write an argumentative essay](https://duckyhelper.com/learn/essay-writing/argumentative-essay/): How to write an argumentative essay: a debatable thesis, one reason per paragraph with evidence, a fair counterargument and rebuttal, and a strong ending. - [How to write a compare and contrast essay](https://duckyhelper.com/learn/essay-writing/compare-and-contrast-essay/): How to write a compare and contrast essay: pick two subjects, find a point, write a thesis, and organize block or point by point. Examples and practice. - [How to write a college application essay](https://duckyhelper.com/learn/essay-writing/college-application-essay/): The seven 2026-27 Common App essay prompts, quoted word for word, plus how to pick one, find your story, and write it in your own voice. With practice. ## [Geometry](https://duckyhelper.com/learn/geometry/) - [Angles, parallel lines and polygon angle sums](https://duckyhelper.com/learn/geometry/angles-and-parallel-lines/): Corresponding, alternate interior and same-side angles, triangle angle sums, exterior angles and polygon angle sums. Worked examples and 5 practice questions. - [Triangle congruence: SSS, SAS, ASA, AAS and HL](https://duckyhelper.com/learn/geometry/triangle-congruence/): How to prove triangles congruent with SSS, SAS, ASA, AAS and HL, why SSA fails, what CPCTC means, and a two-column proof. Worked examples and practice. - [Similar triangles and scale factor](https://duckyhelper.com/learn/geometry/similar-triangles/): How to prove triangles similar (AA, SAS, SSS), set up proportions that work, and scale areas and volumes. Worked examples and 5 practice questions. - [The Pythagorean theorem](https://duckyhelper.com/learn/geometry/pythagorean-theorem/): Use the Pythagorean theorem to find any side of a right triangle, spot triples, classify triangles with the converse and find distances. With practice. - [Special right triangles: 45-45-90 and 30-60-90](https://duckyhelper.com/learn/geometry/special-right-triangles/): The side ratios for 45-45-90 and 30-60-90 triangles, where they come from, and how to use them, including rationalizing. Worked examples and practice. - [Right triangle trigonometry and SOHCAHTOA](https://duckyhelper.com/learn/geometry/right-triangle-trigonometry/): Use sine, cosine and tangent (SOHCAHTOA) to find sides and angles of right triangles, with inverse trig, angles of elevation and cofunctions. With practice. - [Circle theorems: angles, chords, tangents and arcs](https://duckyhelper.com/learn/geometry/circle-theorems/): Central and inscribed angles, arcs, chords and tangents, plus arc length and sector area in degrees. Clear rules, worked examples and 5 practice questions. ## [Grammar](https://duckyhelper.com/learn/grammar/) - [Comma rules](https://duckyhelper.com/learn/grammar/commas/): The comma rules that matter most, in plain words: before and or but, after intro words, in lists, around extra information. Examples and 5 practice questions. - [When to use a semicolon](https://duckyhelper.com/learn/grammar/semicolons/): When to use a semicolon, in plain words: between two related sentences, before however or therefore, and in lists that already have commas. With practice. - [How to use a colon](https://duckyhelper.com/learn/grammar/colons/): How to use a colon: after a complete sentence to introduce a list, an example or an explanation. When not to use one, plus colon vs semicolon, with practice. - [Apostrophe rules](https://duckyhelper.com/learn/grammar/apostrophes/): Apostrophe rules in plain words: one owner, many owners, children's, contractions, and why plurals and its never take one. Examples and 5 practice questions. - [Subject-verb agreement](https://duckyhelper.com/learn/grammar/subject-verb-agreement/): Subject-verb agreement in plain words: find the real subject, then match the verb. Tricky cases: of phrases, and, or, each, there is. With 5 practice questions. - [Pronoun-antecedent agreement](https://duckyhelper.com/learn/grammar/pronoun-antecedent-agreement/): How to make pronouns agree with the nouns they replace: singular or plural, clear reference, no switching person. Examples, common mistakes and practice. - [Misplaced and dangling modifiers](https://duckyhelper.com/learn/grammar/misplaced-and-dangling-modifiers/): What misplaced and dangling modifiers are, how to spot them, and the two ways to fix them. Clear examples, common mistakes and 5 practice questions. - [Parallel structure](https://duckyhelper.com/learn/grammar/parallel-structure/): What parallel structure is and how to fix lists, comparisons and paired words like not only and but also so every part matches. Examples and 5 practice items. - [Run-on sentences, comma splices and fragments](https://duckyhelper.com/learn/grammar/run-on-sentences-and-fragments/): How to spot and fix run-on sentences, comma splices and sentence fragments, with the four ways to join two sentences and clear examples. 5 practice items. - [Who vs whom](https://duckyhelper.com/learn/grammar/who-vs-whom/): When to use who and when to use whom, with the he or him test, whoever vs whomever, and examples. Plus 5 practice questions with answers explained. - [Its vs it's](https://duckyhelper.com/learn/grammar/its-vs-its/): Its vs it's explained simply: it's means it is or it has, its shows ownership. The one-second test, examples, common mistakes and 5 practice questions. - [Affect vs effect](https://duckyhelper.com/learn/grammar/affect-vs-effect/): Affect vs effect made simple: affect is usually a verb, effect is usually a noun. The quick test, the two rare uses, examples and 5 practice questions. - [Verb tense](https://duckyhelper.com/learn/grammar/verb-tense/): Verb tenses in plain words: past, present, future, the perfect tenses, staying consistent, and present tense for literature. Examples and 5 practice items. - [Active vs passive voice](https://duckyhelper.com/learn/grammar/active-vs-passive-voice/): Active vs passive voice explained: how to spot passive voice, how to change it to active, and when passive is the better choice. Examples and 5 practice items. - [Capitalization rules](https://duckyhelper.com/learn/grammar/capitalization/): Capitalization rules for students: proper nouns, titles before names, family words, school subjects, seasons, directions and regions. Examples and practice. ## [Physics](https://duckyhelper.com/learn/physics/) - [Unit conversion and significant figures](https://duckyhelper.com/learn/physics/unit-conversion-and-significant-figures/): Convert units with conversion factors, count significant figures, and round answers for multiplication and addition. Rules, worked examples and practice. - [The kinematics equations](https://duckyhelper.com/learn/physics/kinematics-equations/): The four kinematics equations for constant acceleration, how to pick one, sign rules and free fall. Worked examples with units and 5 practice problems. - [Projectile motion](https://duckyhelper.com/learn/physics/projectile-motion/): Solve projectile motion by splitting it into horizontal and vertical parts. Horizontal and angled launches, range, max height and 5 practice problems. - [Newton's laws of motion](https://duckyhelper.com/learn/physics/newtons-laws-of-motion/): Newton's three laws of motion in plain words: inertia, F = ma and action-reaction pairs. Examples with weight, net force and elevators, plus practice. - [How to draw free body diagrams](https://duckyhelper.com/learn/physics/free-body-diagrams/): Draw free body diagrams step by step: which forces to include, how to label them, ramps and angled pulls, then use F = ma. Worked examples and practice. - [Friction: static and kinetic](https://duckyhelper.com/learn/physics/friction/): Static vs kinetic friction, the coefficient of friction and how to tell if an object moves. Worked examples with units, a coefficient table and practice. - [Circular motion and centripetal force](https://duckyhelper.com/learn/physics/circular-motion/): Uniform circular motion explained: centripetal acceleration v²/r, centripetal force, period, flat curves and loops. Worked examples and 5 practice problems. - [Work and energy](https://duckyhelper.com/learn/physics/work-and-energy/): Work, kinetic and potential energy, the work-energy theorem, conservation of energy and power. Formulas with units, worked examples and practice problems. - [Momentum and collisions](https://duckyhelper.com/learn/physics/momentum-and-collisions/): Momentum p = mv, impulse, conservation of momentum, and elastic vs inelastic collisions. Worked examples with units and signs, plus 5 practice problems. - [Density and buoyancy](https://duckyhelper.com/learn/physics/density-and-buoyancy/): Density ρ = m/V, why things float or sink, and Archimedes' principle for buoyant force. Worked examples with units, common mistakes and 5 practice problems. - [Waves: wavelength, frequency and speed](https://duckyhelper.com/learn/physics/waves/): Wave basics in plain words: wavelength, frequency, period, amplitude and v = fλ, transverse vs longitudinal waves. Worked examples and 5 practice problems. - [Ohm's law and simple circuits](https://duckyhelper.com/learn/physics/ohms-law-and-circuits/): Ohm's law V = IR, series and parallel resistors, and electric power, explained simply. Worked circuit examples with units and 5 practice problems. ## [SAT Math](https://duckyhelper.com/learn/sat-math/) - [Linear equations in one variable on the SAT](https://duckyhelper.com/learn/sat-math/linear-equations/): How to solve linear equations in one variable on the SAT, plus no solution and infinitely many solutions questions. Worked examples and 5 practice questions. - [Linear functions and slope on the SAT](https://duckyhelper.com/learn/sat-math/linear-functions/): Find and interpret slope and intercepts on the SAT from points, tables, graphs and word problems. Worked examples, common traps and 5 practice questions. - [Systems of linear equations on the SAT](https://duckyhelper.com/learn/sat-math/systems-of-equations/): Solve SAT systems of linear equations by substitution, elimination or Desmos, and spot no solution and infinitely many solutions fast. 5 practice questions. - [Linear inequalities on the SAT](https://duckyhelper.com/learn/sat-math/linear-inequalities/): Solve linear inequalities, turn word problems into inequalities, and check points in systems of inequalities on the SAT. Worked examples, 5 practice questions. - [Percentages on the SAT](https://duckyhelper.com/learn/sat-math/percentages/): Solve SAT percent questions with multipliers: percent of, percent change, discounts and tax, reverse percents and repeated changes. Examples and practice. - [Ratios, rates, proportions and units on the SAT](https://duckyhelper.com/learn/sat-math/ratios-rates-and-units/): Solve SAT ratio, rate, proportion and unit conversion questions by tracking units, including the area conversion trap. Examples and 5 practice questions. - [Equivalent expressions on the SAT](https://duckyhelper.com/learn/sat-math/equivalent-expressions/): Rewrite SAT expressions by distributing, factoring, using exponent rules and adding fractions, then match coefficients. Examples and 5 questions. - [Functions and function notation on the SAT](https://duckyhelper.com/learn/sat-math/functions/): Evaluate f(x), read functions from graphs and tables, compose f(g(x)) and shift graphs on the SAT. Worked examples, common traps and 5 practice questions. - [Quadratics on the SAT](https://duckyhelper.com/learn/sat-math/quadratics/): Solve SAT quadratics by factoring or the quadratic formula, find the vertex, and count real solutions with the discriminant. Examples and 5 practice questions. - [Exponential growth and decay on the SAT](https://duckyhelper.com/learn/sat-math/exponential-functions/): Write and read SAT exponential growth and decay models: growth factor, percent rate, doubling time and changing the time unit. Examples and 5 questions. - [Nonlinear equations and systems on the SAT](https://duckyhelper.com/learn/sat-math/nonlinear-equations-and-systems/): Solve SAT radical, absolute value and rational equations, and line plus parabola systems, without falling for extraneous solutions. Examples and 5 questions. - [Mean, median and spread on the SAT](https://duckyhelper.com/learn/sat-math/statistics/): Find mean, median and range on the SAT, compare standard deviations, use the total trick, and see how outliers move each measure. Examples and 5 questions. - [Probability and two-way tables on the SAT](https://duckyhelper.com/learn/sat-math/probability/): Answer SAT probability questions with two-way tables: find the right total, handle "given that" conditional probability, and combine events. With practice. - [Scatterplots, margin of error and study design on the SAT](https://duckyhelper.com/learn/sat-math/scatterplots-and-inference/): Read lines of best fit and residuals, use margin of error, and judge what a sample or experiment can prove on the SAT. Worked examples and 5 practice questions. - [Lines, angles and triangles on the SAT](https://duckyhelper.com/learn/sat-math/lines-angles-and-triangles/): The angle and triangle facts the SAT uses again and again: parallel lines, triangle sums, isosceles and similar triangles. Examples and 5 practice questions. - [Area and volume on the SAT](https://duckyhelper.com/learn/sat-math/area-and-volume/): Use the SAT reference sheet for area and volume, work backward to a missing length, and scale shapes correctly. Worked examples and 5 practice questions. - [Right triangles and trigonometry on the SAT](https://duckyhelper.com/learn/sat-math/right-triangles-and-trigonometry/): Right triangle trig for the SAT: SOHCAHTOA, special right triangles, sin x = cos(90 - x) and radians. Worked examples, common traps and 5 practice questions. - [Circles on the SAT](https://duckyhelper.com/learn/sat-math/circles/): Solve SAT circle questions: read the circle equation, complete the square to find center and radius, and find arc length and sector area in degrees or radians. - [How to use Desmos on the SAT](https://duckyhelper.com/learn/sat-math/desmos-calculator/): How to use the built-in Desmos calculator on the digital SAT: systems, parabolas, regressions, statistics and equivalence checks, and when it is slower. - [The hardest SAT math question types, and how to beat them](https://duckyhelper.com/learn/sat-math/hardest-questions/): The question types that make SAT math hard: hidden constants, no-solution systems, discriminants, circles, percent chains and tangent lines, with practice. ## [SAT Reading and Writing](https://duckyhelper.com/learn/sat-reading-writing/) - [How the SAT Reading and Writing section works](https://duckyhelper.com/learn/sat-reading-writing/how-the-section-works/): How the digital SAT Reading and Writing section works: 54 questions, two 32-minute adaptive modules, four domains, question order and how scoring works. - [SAT Words in Context questions](https://duckyhelper.com/learn/sat-reading-writing/words-in-context/): How to answer SAT Words in Context questions: find the clue in the passage, predict your own word, then match it. Worked examples and 5 practice questions. - [SAT text structure and purpose questions](https://duckyhelper.com/learn/sat-reading-writing/text-structure-and-purpose/): How to answer SAT main purpose, sentence function and overall structure questions. Name what the text does with a verb, then match. Examples and practice. - [SAT cross-text connections questions](https://duckyhelper.com/learn/sat-reading-writing/cross-text-connections/): How to answer SAT cross-text connections questions: sum up each text in one line, find where they meet, and answer as the author of the other text would. - [SAT central ideas and details questions](https://duckyhelper.com/learn/sat-reading-writing/central-ideas-and-details/): How to answer SAT central ideas and details questions: find the point most sentences support, avoid too narrow or too broad choices, and prove details. - [SAT command of evidence: textual](https://duckyhelper.com/learn/sat-reading-writing/command-of-evidence-textual/): How to answer SAT textual evidence questions: which finding would support or weaken a claim, and which quotation best illustrates it. Examples and practice. - [SAT command of evidence: quantitative (graphs and tables)](https://duckyhelper.com/learn/sat-reading-writing/command-of-evidence-quantitative/): How to answer SAT Reading and Writing graph and table questions: read the claim first, then find the exact data that proves it. Worked examples and practice. - [SAT inference questions](https://duckyhelper.com/learn/sat-reading-writing/inferences/): How to answer SAT inference questions that ask which choice most logically completes the text. Follow the chain of facts and avoid going too far. - [SAT punctuation: Boundaries questions](https://duckyhelper.com/learn/sat-reading-writing/boundaries-punctuation/): The punctuation rules the digital SAT tests in Boundaries questions: semicolons, colons, comma splices, however, and pairs of commas. Examples and practice. - [SAT grammar: Form, Structure, and Sense](https://duckyhelper.com/learn/sat-reading-writing/form-structure-and-sense/): The SAT grammar rules in Form, Structure, and Sense: subject-verb agreement, pronouns, verb forms and tense, modifiers, and possessives. Examples and practice. - [SAT rhetorical synthesis (notes) questions](https://duckyhelper.com/learn/sat-reading-writing/rhetorical-synthesis/): How to answer SAT rhetorical synthesis (student notes) questions: read the goal first, list what it needs, and pick the sentence that does that job. - [SAT transitions questions](https://duckyhelper.com/learn/sat-reading-writing/transitions/): How to answer digital SAT transitions questions: name the link between two sentences, then pick the one word that fits. Worked examples and 5 practice items. - [SAT poetry and literature passages](https://duckyhelper.com/learn/sat-reading-writing/poetry-and-literature-passages/): How to read poems and older fiction on the digital SAT: use the intro line, find the speaker and the shift, decode old words, and answer from the lines. - [Pacing the SAT Reading and Writing section](https://duckyhelper.com/learn/sat-reading-writing/pacing-and-time-management/): How to pace the digital SAT Reading and Writing section: about 71 seconds a question, a time budget by domain, checkpoints, and when to mark and move on. - [How to improve your SAT Reading and Writing score](https://duckyhelper.com/learn/sat-reading-writing/how-to-improve-your-score/): A study plan for the SAT Reading and Writing section: take a timed practice test, sort every miss by skill and reason, fix the biggest group first, repeat. ## Get DuckyHelper Free to start. 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