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Dieciséis temas de nuestra enseñanza de 1º a 10º curso, GCSE y SAT, cada uno escrito como una sola pregunta con respuesta directa y método resuelto. Son las explicaciones que nuestros profesores dan en clase, puestas por escrito.
- Cómo aprender las tablas de multiplicarMatemáticasEmpiece por las tablas del 2, el 5 y el 10, use la regla del intercambio para reducir el trabajo a la mitad y practique solo los diez que siguen lentos.
- Cómo hacer una división largaMatemáticasDividir, multiplicar, restar y bajar: un ciclo de cuatro pasos que se repite una vez por cifra. Ejemplo completo de 4728 ÷ 12 y qué hacer con el resto.
- Cómo convertir entre fracciones, decimales y porcentajesMatemáticasDivida el numerador entre el denominador para el decimal, multiplique por 100 para el porcentaje e invierta los dos pasos para volver. Conversiones resueltas.
- Cómo resolver ecuaciones básicas de álgebraMatemáticasQuite los paréntesis, reúna las letras a un lado y los números al otro, y divida. Solución completa de 3(2x + 1) = x + 18 con la comprobación que la prueba.
- Cómo resolver sistemas de ecuacionesMatemáticasEscale las ecuaciones hasta que coincidan los coeficientes de una letra, sume o reste para quitarla y sustituya. Solución de 3x + 2y = 19 y 4x − 5y = 10.
- Cómo resolver ecuaciones cuadráticasMatemáticas GCSEReordene a ax² + bx + c = 0, factorice en dos paréntesis o use la fórmula cuadrática. Ejemplos de x² + 5x = 24 y 3x² + 5x − 1 = 0, los dos comprobados.
- Cómo usar el teorema de PitágorasMatemáticasSume los cuadrados para hallar la hipotenusa y reste para hallar un cateto. Ejemplos con un triángulo 5-12-13 y una hipotenusa de 10, más el recíproco.
- Cómo usar SOHCAHTOAMatemáticas GCSEEtiquete opuesto, adyacente e hipotenusa, marque los dos lados que importan y elija la razón que usa los dos. Ejemplos para hallar un lado y un ángulo.
- ¿Qué es la probabilidad y cómo se calcula?MatemáticasLa probabilidad va de 0 a 1. Cuente los casos favorables entre el total, use 1 − P(A) para lo contrario, multiplique para la "y" y sume para la "o" excluyente.
- ¿Qué es la fotosíntesis?CienciasLas plantas usan la energía de la luz para formar glucosa a partir de dióxido de carbono y agua, y liberan oxígeno. La ecuación, las etapas y los límites.
- ¿Cuáles son las partes de una célula y qué hace cada una?CienciasNúcleo, mitocondrias, ribosomas y membrana: qué hace cada orgánulo, en qué se diferencian las procariotas y las eucariotas, y qué añade la célula vegetal.
- Cómo leer la tabla periódicaCienciasSiete periodos, dieciocho grupos, ordenados por número atómico. Qué dice cada casilla, por qué un grupo comparte química y dónde están los metales y los no metales.
- ¿Cuáles son las tres leyes del movimiento de Newton?CienciasUn cuerpo conserva su velocidad mientras no actúe una fuerza resultante; esa fuerza es masa por aceleración; y las fuerzas van en pares iguales y opuestos.
- Cómo estructurar un ensayoInglésEscriba primero la tesis, ordene las razones, construya cada párrafo sobre una idea con pruebas y explicación, y cierre retomando el argumento planteado.
- Cómo mejorar la comprensión lectoraInglésExplore el texto antes, léalo por tramos cortos y cuente cada uno, note dónde se detiene la comprensión y responda volviendo a la línea que lo demuestra.
- ¿Qué hay en la sección de Math del Digital SAT?Preparación SATDos módulos de 35 minutos, 44 preguntas y calculadora en todo momento. Algebra y Advanced Math pesan un 35% cada uno; los otros dos dominios, un 15% cada uno.
- Place Value ExplainedMatemáticasThe 4 in 4,000 and the 4 in 40 are the same digit worth a thousand times more. How columns work, and the misconceptions that survive into Grade 8.
- Column Addition with CarryingMatemáticasCarrying is not a trick — it is what happens when a column holds ten or more. A worked example of 487 + 356, where the carried digit goes, and how to check.
- Column Subtraction with BorrowingMatemáticasBorrowing is exchange run backwards — one ten broken into ten ones. A worked example of 604 − 287, how to handle zeros, and the errors that cost most marks.
- Number BondsMatemáticasNumber bonds are the pairs that make a total instantly. Why bonds to 10 and 20 decide how well column methods work, and how to build genuine recall.
- How to Round NumbersMatemáticasRounding to the nearest 10, 100 and to decimal places. Which digit decides, why 5 rounds up, and the chained-rounding trap that turns 2.449 into 2.5.
- Estimation and Checking AnswersMatemáticasHow to estimate before calculating, check afterwards, and spot answers that cannot be right. The single cheapest source of extra marks in any maths exam.
- Long MultiplicationMatemáticasLong multiplication of 342 × 27, why the second row gets a zero, where carried digits go, and how to check. The method that makes multi-digit multiplication routine.
- Roman NumeralsMatemáticasI, V, X, L, C, D, M and the subtraction rule that makes IX nine and XI eleven. How to read and write Roman numerals, and why they show what place value gave us.
- Negative NumbersMatemáticasWhy subtracting a negative adds, how the number line settles every argument, and the sign errors that cost marks in algebra for years afterwards.
- Order of Operations (BIDMAS)MatemáticasBrackets, indices, division and multiplication, addition and subtraction. Why the last four are two pairs read left to right, not four ranked steps.
- Prime Numbers and FactorsMatemáticasWhat makes a number prime, why 1 is not, how to build a factor tree, and how prime factorisation makes HCF and LCM straightforward instead of guesswork.
- HCF and LCMMatemáticasHighest common factor and lowest common multiple using prime factorisation and Venn diagrams, plus how to decide which one a word problem is asking for.
- Equivalent FractionsMatemáticasMultiplying or dividing top and bottom by the same number changes how a fraction looks, not what it is worth. Simplifying, comparing and the errors in between.
- Adding and Subtracting FractionsMatemáticasWhy denominators must match before you add, how to find the lowest common denominator, and how to handle mixed numbers without losing the whole-number part.
- Multiplying FractionsMatemáticasMultiply the tops, multiply the bottoms — no common denominator needed. Why 'of' means multiply, how cancelling first saves work, and why the answer gets smaller.
- Dividing FractionsMatemáticasKeep, change, flip — and the reason it works. Why dividing by a fraction usually makes the answer bigger, with worked examples and the errors to avoid.
- Decimal Place ValueMatemáticasDecimals continue the same place value columns to the right of the point. Why 0.5 is bigger than 0.25, and how to compare decimals reliably.
- Ratio and ProportionMatemáticasHow to share an amount in a given ratio, when to use the unitary method, and the difference between a part-to-part ratio and a fraction of the whole.
- Percentage Increase and DecreaseMatemáticasMultipliers make percentage change one step instead of two. How to increase, decrease, find a percentage change, and undo one with a reverse percentage.
- Simple and Compound InterestMatemáticasSimple interest is calculated on the original amount; compound interest on the growing balance. The formulas, the difference, and depreciation.
- Indices and PowersMatemáticasAdd indices to multiply, subtract to divide, multiply to raise a power to a power. Why anything to the power zero is 1 and what a negative index means.
- Standard FormMatemáticasHow to write numbers as A × 10ⁿ where A is between 1 and 10, convert back, and multiply or divide without a calculator.
- SurdsMatemáticasA surd is a root that cannot be written exactly as a fraction. How to simplify using square factors, add like surds, and rationalise a denominator.
- Expanding BracketsMatemáticasMultiply every term inside by the term outside. Single brackets, double brackets, the negative-outside trap, and how to expand three brackets without losing terms.
- Factorising QuadraticsMatemáticasFind two numbers that multiply to c and add to b. How to factorise when a is not 1, the difference of two squares, and what to do when it will not factorise.
- Rearranging FormulaeMatemáticasDo the same thing to both sides, in reverse order of operations. How to change the subject when the letter appears twice or sits inside a root.
- Solving InequalitiesMatemáticasSolve inequalities like equations, with one exception — multiplying or dividing by a negative flips the sign. Number line notation and integer solutions.
- Sequences and the nth TermMatemáticasFind the nth term of a linear sequence from its common difference, handle quadratic sequences with second differences, and recognise the standard special sequences.
- Straight Line Graphs (y = mx + c)MatemáticasWhat m and c actually mean, how to find a gradient from two points, and how to sketch a line in seconds without a table of values.
- Solving Simultaneous Equations GraphicallyMatemáticasThe solution to a pair of simultaneous equations is the point where their graphs intersect. How to plot, read off, and what parallel or identical lines mean.
- Perimeter and AreaMatemáticasPerimeter is the distance around, area is the space inside. Formulas for rectangles, triangles, parallelograms and trapeziums, plus compound shapes and units.
- Area and Circumference of a CircleMatemáticasWhich formula uses the radius and which uses the diameter, how to tell area from circumference, and how to handle answers left in terms of π.
- Volume of SolidsMatemáticasVolume of a prism is cross-section times length. The formulas for cylinders, pyramids, cones and spheres, plus surface area and unit conversion traps.
- Angles on Lines and at PointsMatemáticasAngles on a straight line add to 180°, at a point to 360°. Vertically opposite, corresponding, alternate and co-interior angles, and how to reason with them.
- Angles in PolygonsMatemáticasInterior angles sum to (n − 2) × 180, exterior angles always total 360. How to find each angle in a regular polygon and work backwards from an angle to n.
- Circle TheoremsMatemáticasThe angle at the centre is twice the angle at the circumference, angles in a semicircle are 90°, and the rest — with the wording examiners expect.
- Symmetry and TransformationsMatemáticasThe four transformations, what must be stated to describe each fully, and why a missing centre or scale factor loses the mark even when the drawing is right.
- Coordinates and GridsMatemáticasAlong the corridor then up the stairs — reading and plotting coordinates in all four quadrants, plus midpoint and distance between two points.
- Similar Shapes and Scale FactorsMatemáticasSimilar shapes have equal angles and proportional sides. Why area scales by k² and volume by k³ — the rule that catches out most students.
- BearingsMatemáticasAlways measured clockwise from north and always written with three figures. How to find a back bearing and why 045° is not the same as 45°.
- VectorsMatemáticasA vector has magnitude and direction. Column vector notation, adding and subtracting, scalar multiples, and how parallel vectors prove points lie on a line.
- The Sine and Cosine RulesMatemáticasSOHCAHTOA only works in right-angled triangles. Which rule to use for any triangle, how to choose between them, and the area formula.
- Speed, Distance and TimeMatemáticasSpeed equals distance over time, and rearranging it. Unit conversion, average speed over two legs, and reading distance-time graphs.
- Mean, Median, Mode and RangeMatemáticasHow to calculate each average, why outliers ruin the mean, and how to choose the right one. Includes finding the mean from a frequency table.
- Bar Charts and PictogramsMatemáticasHow to read a scale correctly, why the key on a pictogram decides every answer, and the labelling that earns marks when drawing a chart.
- Scatter Graphs and CorrelationMatemáticasReading correlation from a scatter graph, drawing a line of best fit, and why interpolation is reliable while extrapolation is not.
- Cumulative FrequencyMatemáticasPlot at the upper bound, read the median at half the total, and find the interquartile range. How cumulative frequency leads into box plots.
- HistogramsMatemáticasFrequency density is frequency divided by class width, and area represents frequency. Why histograms differ from bar charts and how to read one backwards.
- Venn Diagrams and SetsMatemáticasFill the overlap first, then work outward. Union, intersection, complement and the notation examiners use, plus probability from a Venn diagram.
- Probability Tree DiagramsMatemáticasMultiply along the branches and add between outcomes. How to handle with and without replacement, and why each set of branches must total 1.
- Telling the Time and Reading TimetablesMatemáticasReading clocks, converting between 12-hour and 24-hour time, and working out journey durations without slipping into decimal minutes.
- Money ProblemsMatemáticasWorking with currency means keeping units consistent and always writing two decimal places. Calculating change, comparing value and multi-step budgeting.
- GCSE Maths: Foundation or Higher?Matemáticas GCSEFoundation caps at grade 5, Higher starts at grade 4. What each tier covers, who each suits, and why the safe choice is not always the lower one.
- GCSE Maths Grade BoundariesMatemáticas GCSEBoundaries are set after the exam, not before, so a harder paper needs fewer marks. What that means for revision targets and for reading last year's figures.
- The GCSE Maths Non-Calculator PaperMatemáticas GCSEOne of the three GCSE maths papers is sat without a calculator. Which skills it actually tests, and how to prepare for arithmetic you cannot delegate.
- The GCSE Maths Formula SheetMatemáticas GCSESome formulae are printed in the exam and some must be memorised. Which is which, and why knowing the difference changes how you revise.
- A GCSE Maths Revision Plan That WorksMatemáticas GCSEWhy past papers beat re-reading notes, how to log errors so they stop repeating, and a realistic weekly structure for the final months.
- GCSE Maths Problem-Solving QuestionsMatemáticas GCSEMulti-step worded questions carry the most marks and the least guidance. How to extract the maths, work from both ends, and earn method marks.
- The Digital SAT Reading and Writing SectionPreparación SATShort passages with one question each, across four content domains. What the section tests, how it is timed, and where students lose the most points.
- How the Digital SAT AdaptsPreparación SATThe test adapts between modules, not between questions. What that means for pacing, for guessing, and for why the first module matters most.
- How the SAT Is ScoredPreparación SATTwo sections of 200–800 combine to a total out of 1600. What percentiles mean, why raw marks are converted, and how to read a score report.
- SAT Algebra QuestionsPreparación SATLinear equations, inequalities and systems make up the largest share of SAT Math. The question shapes that recur and how to translate words into equations.
- SAT Problem Solving and Data AnalysisPreparación SATRatios, rates, percentages, unit conversion and interpreting tables and graphs. The SAT content area most connected to everyday quantitative reasoning.
- SAT Advanced MathPreparación SATQuadratic equations, exponential growth, polynomial and radical expressions, and function notation. The hardest content area and where top scores are decided.
- SAT Grammar RulesPreparación SATStandard English Conventions tests a limited set of rules — clause joining, agreement, modifiers, punctuation. The full list and how to study it.
- SAT Time ManagementPreparación SATHow to pace each module, when to flag and move on, and why finishing every question matters more than perfecting any single one.
- States of MatterCienciasParticle arrangement explains every property of solids, liquids and gases. Melting, boiling, evaporation and why temperature holds steady during a change of state.
- The Water CycleCienciasHow water moves between ocean, air and land. The stages, what drives them, and why the cycle has no beginning or end.
- Food Chains and Food WebsCienciasArrows show the direction energy flows, not who eats whom. Producers, consumers, decomposers, and why food chains are rarely more than five links long.
- The Human Digestive SystemCienciasMouth to intestine, what each organ does, which enzymes break down which food group, and why the small intestine is so long.
- RespirationCienciasRespiration releases energy from glucose in every living cell. The equations, the difference from breathing, and what happens without enough oxygen.
- Atoms, Elements and CompoundsCienciasProtons, neutrons and electrons; how elements differ from compounds; and why a mixture can be separated but a compound cannot.
- Chemical Reactions and Balancing EquationsCienciasAtoms are never created or destroyed, so both sides must match. How to balance step by step, and why you may change coefficients but never formulae.
- Acids and BasesCienciasThe pH scale, what makes something acidic or alkaline, the neutralisation reaction, and how to name the salt a reaction produces.
- Forces and FrictionCienciasWhat balanced and unbalanced forces do, why friction is not always unhelpful, and how terminal velocity follows from forces coming into balance.
- Energy Transfer and ConservationCienciasEnergy is stored and transferred, never used up. The stores, the transfer pathways, conduction, convection and radiation, and what efficiency measures.
- Electric CircuitsCienciasCurrent, voltage and resistance, how they behave differently in series and parallel, and how to use V = IR without confusing the three quantities.
- Magnetism and ElectromagnetsCienciasLike poles repel, field lines run north to south, and a current makes a magnetic field. How to make an electromagnet stronger and why that matters.
- Light and ReflectionCienciasThe law of reflection, why a straw looks bent in water, and the common misconception that eyes emit light rather than receive it.
- Sound WavesCienciasSound is a longitudinal wave made of compressions and rarefactions. What changes pitch, what changes volume, and why sound cannot cross a vacuum.
- The Solar SystemCienciasThe eight planets in order, why we have day and night, what causes the seasons, and the difference between rotation and orbit.
- Genetics and InheritanceCienciasGenes, alleles, dominant and recessive traits, and how to use a Punnett square to predict inheritance ratios.
- Evolution and Natural SelectionCienciasVariation, competition, survival and inheritance — the mechanism in four steps, plus why organisms do not adapt during their own lifetime.
- Ecosystems and BiodiversityCienciasThe vocabulary from organism to ecosystem, what affects population size, and why losing one species can destabilise an entire community.
- Parts of SpeechInglésThe eight word classes, how to identify them by the job a word does rather than by the word itself, and why the same word can change class.
- Punctuation RulesInglésWhen each mark is correct, why the comma splice is the most common error in English, and how apostrophes actually work.
- Active and Passive VoiceInglésActive voice puts the doer first; passive puts the receiver first. How to identify each, convert between them, and when the passive is the better choice.
- Figurative LanguageInglésThe main devices, how to tell a simile from a metaphor, and how to write about effect rather than just naming the technique.
- Persuasive WritingInglésHow to build an argument that changes a reader's mind — audience, structure, rhetorical technique, and why addressing the opposing view makes you stronger.
- Summarising a TextInglésSeparating main ideas from supporting detail, writing in your own words, and why a summary is not a shortened copy of the original.
- Creative Writing OpeningsInglésStart in the middle of something, show rather than explain, and avoid the three openings examiners see most often.
- Formal Letter WritingInglésThe conventional layout, why Yours sincerely and Yours faithfully are not interchangeable, and how to keep the register consistent.
- Reading a Historical SourceHistoriaWho wrote it, when, and why — how to evaluate a source without dismissing it as biased, and why bias makes a source more useful, not less.
- Causes and Consequences in HistoryHistoriaHow to categorise causes, weigh their relative importance, and write an argument rather than a list of factors.
- Map Skills and Grid ReferencesGeografíaAlong the corridor and up the stairs — four and six-figure grid references, scale, distance and what contour lines show about the land.
- Rivers and ErosionGeografíaThe four erosion processes, four transport processes, and how waterfalls, meanders and oxbow lakes form along a river's course.
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