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<rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom"><channel><title>YSR Studies blog</title><link>https://ysrstudies.com/blog/</link><description>Study guides that start with the evidence.</description><language>en</language><atom:link href="https://ysrstudies.com/blog/feed.xml" rel="self" type="application/rss+xml"/><item><title>How to write a lab report: the sections, what goes in each, and a marked example (a pendulum measures g)</title><link>https://ysrstudies.com/blog/writing/how-to-write-a-lab-report/</link><guid isPermaLink="true">https://ysrstudies.com/blog/writing/how-to-write-a-lab-report/</guid><description>How to write a lab report, section by section: what the marker checks in each, with a pendulum experiment worked from the raw times to g and its error.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Writing</category></item><item><title>Comma splices, run-on sentences, fragments and the passive voice: the four sentence faults and their repairs</title><link>https://ysrstudies.com/blog/writing/comma-splice/</link><guid isPermaLink="true">https://ysrstudies.com/blog/writing/comma-splice/</guid><description>A comma splice is two sentences joined by a comma alone. Three ways to mend it, then the run-on, the fragment and the passive voice, each broken and fixed.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Writing</category></item><item><title>Citing sources: MLA vs APA side by side, the annotated bibliography, and avoiding plagiarism</title><link>https://ysrstudies.com/blog/writing/mla-vs-apa/</link><guid isPermaLink="true">https://ysrstudies.com/blog/writing/mla-vs-apa/</guid><description>MLA 9 and APA 7 side by side: a book, an article and a web page in both styles, in-text citations, the annotated bibliography, and where plagiarism begins.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Writing</category></item><item><title>Logical fallacies: the fifteen a student meets, each with a sentence that commits it and the honest version</title><link>https://ysrstudies.com/blog/writing/logical-fallacies/</link><guid isPermaLink="true">https://ysrstudies.com/blog/writing/logical-fallacies/</guid><description>Fifteen logical fallacies, each in a sentence that commits it and the honest version that makes the same point, plus the counterargument paragraph.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Writing</category></item><item><title>Ethos, pathos and logos: the three appeals with examples, and the rhetorical analysis essay</title><link>https://ysrstudies.com/blog/writing/ethos-pathos-logos/</link><guid isPermaLink="true">https://ysrstudies.com/blog/writing/ethos-pathos-logos/</guid><description>Ethos, pathos and logos in one line each, three passages that use them, how to tell them apart, and how to write the rhetorical analysis essay.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Writing</category></item><item><title>Transition words, topic sentences and paragraph structure: how a paragraph holds together</title><link>https://ysrstudies.com/blog/writing/transition-words-and-paragraphs/</link><guid isPermaLink="true">https://ysrstudies.com/blog/writing/transition-words-and-paragraphs/</guid><description>Transition words grouped by the move they make, the topic sentence that gives a paragraph one job, and a paragraph with no topic sentence repaired.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Writing</category></item><item><title>Thesis statements: arguable, focused, and the test that tells a claim from a topic</title><link>https://ysrstudies.com/blog/writing/thesis-statement/</link><guid isPermaLink="true">https://ysrstudies.com/blog/writing/thesis-statement/</guid><description>A thesis statement is one sentence a reader could disagree with. The three-question test, six weak theses fixed, and when a three-part thesis helps.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Writing</category></item><item><title>Redox reactions: oxidation numbers, balancing by half reactions, a galvanic cell&#x27;s voltage and what an electrolytic cell deposits</title><link>https://ysrstudies.com/blog/science/redox-and-galvanic-cells/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/redox-and-galvanic-cells/</guid><description>Redox worked end to end: oxidation numbers by rule, balancing in acid by half reactions, a galvanic cell’s voltage, and Faraday’s law for electrolysis.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>How to calculate pH: strong acids, weak acids, buffers and the titration curve, worked in the order a test asks them</title><link>https://ysrstudies.com/blog/science/ph-and-buffers/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/ph-and-buffers/</guid><description>How to calculate pH in order: a strong acid by the log, a weak acid by Ka and an ICE table, a buffer by Henderson–Hasselbalch, then the titration curve.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>Equilibrium and Le Chatelier&#x27;s principle: Kc, the ICE table solved line by line, Ksp, and which way the system shifts and why</title><link>https://ysrstudies.com/blog/science/equilibrium-and-le-chateliers-principle/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/equilibrium-and-le-chateliers-principle/</guid><description>Equilibrium worked: the Kc expression, an ICE table solved to the end, Ksp from a solubility, and Le Chatelier’s principle for each change with the reason.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>Enthalpy, Hess&#x27;s law and calorimetry: the bookkeeping of heat, worked three ways on one screen</title><link>https://ysrstudies.com/blog/science/enthalpy-and-hesss-law/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/enthalpy-and-hesss-law/</guid><description>Enthalpy worked three ways: a coffee-cup calorimeter with q = mcΔT, Hess&#x27;s law by adding equations, and enthalpies of formation. The sign error named.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>The gas laws and PV = nRT: the units that make it work, the one rearrangement, and a gas produced by a reaction</title><link>https://ysrstudies.com/blog/science/ideal-gas-law/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/ideal-gas-law/</guid><description>The ideal gas law PV = nRT worked with matching units: kelvin, kilopascals and R = 8.314. One rearrangement, the gas from a reaction, and the wrong line.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>Electronegativity, polarity and intermolecular forces: the chain from a bond&#x27;s electronegativity difference to a molecule&#x27;s boiling point</title><link>https://ysrstudies.com/blog/science/electronegativity-and-intermolecular-forces/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/electronegativity-and-intermolecular-forces/</guid><description>Electronegativity difference names the bond, the shape decides if the molecule is polar, and polarity picks the intermolecular force. Three liquids ranked.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>Lewis structures: the counting method that always works, with formal charge and resonance worked on the nitrate ion</title><link>https://ysrstudies.com/blog/science/lewis-structures/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/lewis-structures/</guid><description>How to draw Lewis structures by counting first: valence electrons, skeleton, octets, then double bonds. Nitrate worked with formal charges and resonance.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>The endocrine system, hormones, the kidney and the nephron: control by chemistry</title><link>https://ysrstudies.com/blog/science/endocrine-system-and-the-kidney/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/endocrine-system-and-the-kidney/</guid><description>How hormones work, the ones SBI4U asks for, and the nephron traced from filtrate to urine with its volumes, ADH and aldosterone placed where they act.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>Homeostasis, negative feedback, the nervous system and the action potential</title><link>https://ysrstudies.com/blog/science/homeostasis-and-the-nervous-system/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/homeostasis-and-the-nervous-system/</guid><description>Homeostasis as a five-part feedback loop traced on body temperature, then the action potential traced from −70 mV to the peak and back, the ions in order.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>Mitosis vs meiosis: the stages side by side, and the three differences that get tested</title><link>https://ysrstudies.com/blog/science/mitosis-vs-meiosis/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/mitosis-vs-meiosis/</guid><description>Mitosis and meiosis traced side by side on one human cell, chromosome and chromatid counts at every stage, and the three differences tests ask, named.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>Punnett squares, dihybrid crosses and Mendelian ratios, worked and checked</title><link>https://ysrstudies.com/blog/science/punnett-squares/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/punnett-squares/</guid><description>How to do a Punnett square: a monohybrid cross, then a dihybrid cross worked to 9:3:3:1 and checked with the product rule, the two ratios told apart.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>DNA replication, transcription and translation: from the double helix to a protein</title><link>https://ysrstudies.com/blog/science/dna-to-protein/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/dna-to-protein/</guid><description>DNA structure and replication, then one twelve-base gene traced through transcription and translation to a peptide, the template-strand error named.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>Macromolecules, protein structure and enzymes: active sites, induced fit, inhibition</title><link>https://ysrstudies.com/blog/science/enzymes-and-macromolecules/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/enzymes-and-macromolecules/</guid><description>The four macromolecules and their bonds, the four levels of protein structure, and one enzyme&#x27;s cycle traced to the rate graph with both inhibitions.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>Photosynthesis: the light-dependent reactions and the Calvin cycle, and how it mirrors respiration</title><link>https://ysrstudies.com/blog/science/photosynthesis/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/photosynthesis/</guid><description>Photosynthesis in two stages: the light reactions split water and load ATP and NADPH; the Calvin cycle fixes three CO₂ per G3P, every count traced.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>Electron configuration and periodic trends: the filling order, the exceptions, and what the table tells you without a chart</title><link>https://ysrstudies.com/blog/science/electron-configuration/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/electron-configuration/</guid><description>Electron configuration worked for iron and its ions: the filling order, Hund’s rule, why 4s empties before 3d, the Cr and Cu exceptions, the four trends.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>Cellular respiration: glycolysis, the Krebs cycle, the electron transport chain, and the ATP count</title><link>https://ysrstudies.com/blog/science/cellular-respiration/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/cellular-respiration/</guid><description>One glucose traced through glycolysis, the Krebs cycle and the electron transport chain with every count, and why the ATP total reads 30 to 32 or 36 to 38.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>The double slit, diffraction gratings, the photoelectric effect and time dilation: the four ideas of modern physics</title><link>https://ysrstudies.com/blog/science/light-and-modern-physics/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/light-and-modern-physics/</guid><description>What the double slit experiment shows, its fringe spacing worked with units, a grating’s angles, the photoelectric ledger in eV, time dilation at 0.80c.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>Coulomb&#x27;s law, electric fields, electric potential, magnetic fields and the right-hand rule</title><link>https://ysrstudies.com/blog/science/electric-and-magnetic-fields/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/electric-and-magnetic-fields/</guid><description>Coulomb&#x27;s law worked with units converted, the electric field and potential that follow, and the right-hand rule on a proton in a magnetic field.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>Work, kinetic and potential energy, the work–energy theorem, and power</title><link>https://ysrstudies.com/blog/science/work-energy-and-power/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/work-energy-and-power/</guid><description>Work, kinetic and potential energy and the work–energy theorem, worked on one skier down a hill and across the flat, by energy and then by forces.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>Momentum, impulse and collisions: elastic, inelastic, and two dimensions</title><link>https://ysrstudies.com/blog/science/momentum-and-impulse/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/momentum-and-impulse/</guid><description>Momentum p = mv, impulse as the change in momentum, and conservation worked on one crash with signs: the shared speed, the energy lost, the force.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>Centripetal force, circular motion and universal gravitation: one idea, three questions</title><link>https://ysrstudies.com/blog/science/centripetal-force-and-gravitation/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/centripetal-force-and-gravitation/</guid><description>Centripetal force is the net force toward the centre, not a new force. One satellite orbit worked with units: speed, period and g up there.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>Free-body diagrams, Newton&#x27;s laws, friction and inclines: the one method for every force problem</title><link>https://ysrstudies.com/blog/science/free-body-diagrams/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/free-body-diagrams/</guid><description>How to draw a free-body diagram and turn it into Newton’s second law, worked on a box sliding down a 30° incline with friction, every force in newtons.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>The kinematics equations: which one to use, worked line by line on a projectile</title><link>https://ysrstudies.com/blog/science/kinematics-equations/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/kinematics-equations/</guid><description>The five kinematics equations, the rule that picks one (the missing quantity), and a projectile off a cliff worked with units and the sign error named.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>Functional groups and IUPAC naming: the twelve groups in one table, naming in five steps on one molecule, and the isomers of one formula counted</title><link>https://ysrstudies.com/blog/science/functional-groups/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/functional-groups/</guid><description>The twelve functional groups in one table, IUPAC naming in five steps worked on one alcohol with the numbering trap, and the isomers of C₄H₁₀O counted.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>Rate laws, reaction order, activation energy and the Arrhenius equation, worked on one table of data and two temperatures</title><link>https://ysrstudies.com/blog/science/rate-laws-and-activation-energy/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/rate-laws-and-activation-energy/</guid><description>Rate laws from a table of initial rates, the reaction order and the rate constant&#x27;s units, then activation energy from two temperatures by Arrhenius.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>Stoichiometry: one reaction taken from balancing through moles, the mole ratio, limiting reactant and percent yield</title><link>https://ysrstudies.com/blog/science/stoichiometry/</link><guid isPermaLink="true">https://ysrstudies.com/blog/science/stoichiometry/</guid><description>Stoichiometry in five steps on one reaction: balance, grams to moles, the mole ratio, the limiting reactant, percent yield, the wrong line at each step.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Science explained</category></item><item><title>u-substitution and integration by parts: the one question that chooses between them, the LIATE order for u, and two examples worked line by line</title><link>https://ysrstudies.com/blog/math/u-substitution-and-integration-by-parts/</link><guid isPermaLink="true">https://ysrstudies.com/blog/math/u-substitution-and-integration-by-parts/</guid><description>u-substitution or integration by parts: one question decides. Each worked line by line, the du scaling and the sign students drop, LIATE, and two siblings.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Math explained</category></item><item><title>L&#x27;Hôpital&#x27;s rule and the Mean Value Theorem: when each applies, one example of each worked, and the hypothesis students skip</title><link>https://ysrstudies.com/blog/math/lhopitals-rule-and-the-mean-value-theorem/</link><guid isPermaLink="true">https://ysrstudies.com/blog/math/lhopitals-rule-and-the-mean-value-theorem/</guid><description>L’Hôpital’s rule and the Mean Value Theorem: the hypothesis to check first, one example of each worked line by line, and the case where each theorem fails.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Math explained</category></item><item><title>Implicit differentiation and related rates: the one idea behind both, worked on a curve and on the ladder problem</title><link>https://ysrstudies.com/blog/math/implicit-differentiation-and-related-rates/</link><guid isPermaLink="true">https://ysrstudies.com/blog/math/implicit-differentiation-and-related-rates/</guid><description>Implicit differentiation and related rates as one idea: the chain rule with a hidden variable. A curve and the ladder problem worked, the skipped step.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Math explained</category></item><item><title>Limits: what they are, how to find them from a table, a graph and the algebra, the limit laws, and what to do when you get 0/0</title><link>https://ysrstudies.com/blog/math/limits/</link><guid isPermaLink="true">https://ysrstudies.com/blog/math/limits/</guid><description>Limits explained three ways: a table of values, the graph and the algebra. The limit laws, what 0/0 means, factoring and rationalising, one example worked.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Math explained</category></item><item><title>The chain rule: inside, outside, and the inner derivative students forget, with ln x and eˣ worked</title><link>https://ysrstudies.com/blog/math/chain-rule/</link><guid isPermaLink="true">https://ysrstudies.com/blog/math/chain-rule/</guid><description>The chain rule as a habit: outside, inside, times the inside&#x27;s derivative. One example worked, the forgotten factor named, with ln x and e^x.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Math explained</category></item><item><title>Product and quotient rules: one example worked line by line for each, and the sign error in the quotient rule that costs the mark</title><link>https://ysrstudies.com/blog/math/product-and-quotient-rules/</link><guid isPermaLink="true">https://ysrstudies.com/blog/math/product-and-quotient-rules/</guid><description>The product rule and the quotient rule, each worked line by line, the subtraction order students reverse, and a sibling problem to try with its answer.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Math explained</category></item><item><title>Derivative rules: the complete list, when each one applies, one example worked line by line, and the two rules students confuse</title><link>https://ysrstudies.com/blog/math/derivative-rules/</link><guid isPermaLink="true">https://ysrstudies.com/blog/math/derivative-rules/</guid><description>Every derivative rule on one page: power, product, quotient, chain, exponential, log and trig, with when each applies and one example worked line by line.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Math explained</category></item><item><title>Trig identities: the eight you derive, the rest you look up, the double-angle formulas, and how to solve a trig equation without losing a solution</title><link>https://ysrstudies.com/blog/math/trig-identities/</link><guid isPermaLink="true">https://ysrstudies.com/blog/math/trig-identities/</guid><description>Trig identities grouped by origin: Pythagorean, quotient, reciprocal and compound-angle, with the double angles derived; one proof and one equation worked.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Math explained</category></item><item><title>Confidence intervals, p-values and hypothesis tests: one of each computed by hand, and what every sentence of the result does and does not mean</title><link>https://ysrstudies.com/blog/math/confidence-intervals-and-p-values/</link><guid isPermaLink="true">https://ysrstudies.com/blog/math/confidence-intervals-and-p-values/</guid><description>A 95 % confidence interval, a t-test and a chi-square test computed by hand, and the two sentences students get wrong about intervals and p-values, fixed.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Math explained</category></item><item><title>The normal distribution and z-scores: the sketch, the table, and the three questions every normal-curve problem turns out to be</title><link>https://ysrstudies.com/blog/math/normal-distribution-and-z-scores/</link><guid isPermaLink="true">https://ysrstudies.com/blog/math/normal-distribution-and-z-scores/</guid><description>The normal distribution and z-scores on one mean and standard deviation: the area below, the area between, the value at a percentile, the table misread.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Math explained</category></item><item><title>Describing data by hand: mean, median, mode, variance and standard deviation, quartiles, the box plot and the histogram, all from one set of eight numbers</title><link>https://ysrstudies.com/blog/math/standard-deviation/</link><guid isPermaLink="true">https://ysrstudies.com/blog/math/standard-deviation/</guid><description>Standard deviation by hand on eight numbers, with the mean, median, mode, variance, quartiles and box plot from the same data, and when to divide by n − 1.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Math explained</category></item><item><title>Matrices: how to multiply them, the 3×3 determinant, and Gaussian elimination to reduced row echelon form, each worked line by line</title><link>https://ysrstudies.com/blog/math/matrices/</link><guid isPermaLink="true">https://ysrstudies.com/blog/math/matrices/</guid><description>Matrix multiplication entry by entry, the 3×3 determinant by cofactors with the sign students drop, and Gaussian elimination to reduced row echelon form.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Math explained</category></item><item><title>Vectors: magnitude, direction, the dot product and the cross product, worked on one pair, and which question wants which</title><link>https://ysrstudies.com/blog/math/vectors-dot-and-cross-product/</link><guid isPermaLink="true">https://ysrstudies.com/blog/math/vectors-dot-and-cross-product/</guid><description>Vectors worked on one pair: magnitude, the dot product and the angle, the cross product and the area, the sign error in the middle component, which to use.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Math explained</category></item><item><title>Domain and range, inverse functions and transformations: how to read a function&#x27;s shape from its equation, worked on one function</title><link>https://ysrstudies.com/blog/math/domain-and-range/</link><guid isPermaLink="true">https://ysrstudies.com/blog/math/domain-and-range/</guid><description>Domain and range read from the equation, the inverse found with its domain restricted, and the transformations that built the graph, all on one function.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Math explained</category></item><item><title>Dividing polynomials: long division, synthetic division, the remainder and factor theorems, and one cubic factored all the way</title><link>https://ysrstudies.com/blog/math/polynomial-division/</link><guid isPermaLink="true">https://ysrstudies.com/blog/math/polynomial-division/</guid><description>Synthetic division and long division on one cubic, the remainder and factor theorems, the sign in the box students get wrong, and the cubic factored.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Math explained</category></item><item><title>Asymptotes and rational functions: vertical, horizontal and oblique asymptotes, holes, and how to read the whole graph from the algebra</title><link>https://ysrstudies.com/blog/math/asymptotes-and-rational-functions/</link><guid isPermaLink="true">https://ysrstudies.com/blog/math/asymptotes-and-rational-functions/</guid><description>Asymptotes from the algebra: factor, cancel for holes, read vertical asymptotes from what remains, compare degrees for the horizontal. One function worked.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Math explained</category></item><item><title>Logarithm rules: the three laws, where each comes from, and how to solve an exponential equation and a logarithmic equation without a false root</title><link>https://ysrstudies.com/blog/math/logarithm-rules/</link><guid isPermaLink="true">https://ysrstudies.com/blog/math/logarithm-rules/</guid><description>The three log rules derived from the exponent laws, the change of base, and two equations worked, one exponential and one logarithmic, with the false root.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Math explained</category></item><item><title>Riemann sums to the Fundamental Theorem of Calculus: why the area under a curve is an antiderivative, with one integral done both ways</title><link>https://ysrstudies.com/blog/math/riemann-sums-and-the-fundamental-theorem-of-calculus/</link><guid isPermaLink="true">https://ysrstudies.com/blog/math/riemann-sums-and-the-fundamental-theorem-of-calculus/</guid><description>Riemann sums and the Fundamental Theorem on one integral: left, right and midpoint sums, then F(b) − F(a), and why they agree. The evaluation fault named.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Math explained</category></item><item><title>The unit circle: how to build it in two minutes instead of memorising it, and how radians become degrees</title><link>https://ysrstudies.com/blog/math/unit-circle/</link><guid isPermaLink="true">https://ysrstudies.com/blog/math/unit-circle/</guid><description>The unit circle built from two triangles and four signs, not memorised: exact sin, cos and tan of the special angles, radians to degrees, one angle worked.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Math explained</category></item><item><title>The best AI for math is the one that checks your line against a verified answer, not the one that writes the solution: what to ask of it, and one derivative worked</title><link>https://ysrstudies.com/blog/ai-for-studying/best-ai-for-math/</link><guid isPermaLink="true">https://ysrstudies.com/blog/ai-for-studying/best-ai-for-math/</guid><description>The best AI for math checks your line against a verified answer instead of writing the solution for you. 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isPermaLink="true">https://ysrstudies.com/blog/exams/ap-biology/</guid><description>How to study for AP Biology: the units in our words, the exam&#x27;s shape, vocabulary against mechanism, the data and FRQ habits, and an eight-week plan.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Exams</category></item><item><title>AP exam season: how to plan backwards from the exam fortnight when you are writing several exams, with the practice-test method staggered across them</title><link>https://ysrstudies.com/blog/exams/ap-exam-schedule/</link><guid isPermaLink="true">https://ysrstudies.com/blog/exams/ap-exam-schedule/</guid><description>AP exam season: how to plan backwards from the exam fortnight when you write several exams, with the practice-test method staggered across them.</description><pubDate>Sat, 07 Nov 2026 00:00:00 +0000</pubDate><category>Exams</category></item><item><title>The PSAT: what it is for, where the official practice test is, how to study for 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