تعلّم
سؤال واحد، بإجابة مباشرة، ومن تحته الطريقة محلولة.
الإجابة باختصار
ستة عشر موضوعاً من تدريسنا للصفوف 1–10 وامتحاني GCSE وSAT، كلٌّ مكتوب كسؤال واحد بإجابة مباشرة وطريقة محلولة. إنها الشروح نفسها التي يقدّمها معلّمونا في الحصص، مكتوبةً.
- كيف تُتعلَّم جداول الضربالرياضياتابدأ بجداول 2 و5 و10، واستعمل قاعدة التبديل لتقليل العمل إلى النصف، وابنِ الحقائق الصعبة من حقائق قريبة، ثم درِّب على الحقائق العشر التي تبقى بطيئة وحدها.
- كيف تُجرى القسمة المطوّلةالرياضياتاقسم، اضرب، اطرح، أنزِل — دورة من أربع خطوات تتكرر مرة عن كل رقم من أرقام المقسوم. مثال محلول بالكامل على 4728 ÷ 12، مع التعامل مع الباقي في صوره الثلاث.
- كيف تحوّل بين الكسور والأعداد العشرية والنِّسب المئويةالرياضياتاقسم البسط على المقام لتحصل على عدد عشري، واضرب في 100 للنسبة المئوية، واعكس الاتجاهين للعودة إلى ما بدأت منه. تحويلات محلولة لـ 3/8 و0.375 و37.5% و9/20.
- كيف تحلّ معادلات الجبر الأساسيةالرياضياتافتح الأقواس، واجمع الحروف في جهة والأعداد في الجهة الأخرى، ثم اقسم ليبقى الحرف وحده. حل كامل للمعادلة 3(2x + 1) = x + 18، مع التحقق بالتعويض الذي يثبت صحته.
- كيف تحلّ المعادلات الآنيةالرياضياتكبِّر المعادلتين حتى يتطابق معاملا أحد الحرفين، واجمع أو اطرح لحذفه، ثم عوّض بالناتج لإيجاد الحرف الآخر. حل كامل للمعادلتين 3x + 2y = 19 و4x − 5y = 10.
- كيف تحلّ المعادلات التربيعيةرياضيات GCSEرتّب المعادلة على الصورة ax² + bx + c = 0، ثم حلّلها إلى قوسين، أو استعمل القانون العام. مثالان محلولان: x² + 5x = 24 و3x² + 5x − 1 = 0، مع دور المميّز.
- كيف تستعمل نظرية فيثاغورسالرياضياتاجمع مربعي الضلعين لإيجاد الوتر، واطرح لإيجاد ضلع أقصر، ثم خذ الجذر التربيعي. أمثلة محلولة على مثلث 5-12-13 ووتر طوله 10 سم، مع اختبار النظرية العكسية.
- كيف تستعمل SOHCAHTOAرياضيات GCSEسمِّ المقابل والمجاور والوتر انطلاقًا من الزاوية، وعلِّم الضلعين المهمّين، ثم اختر النسبة التي تجمعهما. مثالان محلولان: إيجاد ضلع وإيجاد زاوية مجهولة.
- ما الاحتمال وكيف يُحسب؟الرياضياتالاحتمال يمتد من 0 إلى 1. عُدّ النواتج المواتية على مجموع النواتج، واستعمل 1 − P(A) للعكس، واضرب مع «و»، واجمع مع «أو»، وعدِّل الكسر عند السحب دون إرجاع.
- ما البناء الضوئي؟العلومتستعمل النباتات طاقة الضوء لبناء الغلوكوز من ثاني أكسيد الكربون والماء، فتُطلق الأكسجين. المعادلة بالكلمات وبالرموز، والمرحلتان، والعوامل التي تحدّ من المعدل.
- ما أجزاء الخلية وما وظيفة كل جزء؟العلومالنواة والميتوكوندريا والرايبوسومات والغشاء — وظيفة كل عُضيّ، والفرق بين الخلايا بدائية النواة وحقيقية النواة، وما تزيده الخلية النباتية على الحيوانية.
- كيف تقرأ الجدول الدوريالعلومسبع دورات وثماني عشرة مجموعة، مرتّبة بالعدد الذري. ماذا يخبرك كل مربع فيها، ولماذا تشترك عناصر المجموعة الواحدة في كيميائها، وأين تقع الفلزات واللافلزات.
- ما قوانين نيوتن الثلاثة للحركة؟العلوميحفظ الجسم سرعته المتجهة ما لم تؤثر فيه قوة محصّلة؛ وتلك القوة تساوي الكتلة في التسارع؛ والقوى تأتي أزواجًا متساوية متعاكسة تؤثر في جسمين مختلفين لا في جسم واحد.
- كيف تبني هيكل المقالاللغة الإنجليزيةاكتب الأطروحة أولًا، ورتّب الأسباب قبل الكتابة، وابنِ كل فقرة عرض على فكرة واحدة بدليل وتفسير وربط بالأطروحة، ثم اختم بمعاودة تناولها لا بمجرد تكرارها.
- كيف تحسّن الفهم القرائياللغة الإنجليزيةاستطلع النص، واقرأ على مقاطع قصيرة وأعد سرد كل مقطع بكلماتك، ولاحظ اللحظة التي يتوقف عندها الفهم، وأجب عن الأسئلة بالعودة إلى السطر الذي يثبت الإجابة.
- ماذا يتضمن قسم الرياضيات في Digital SAT؟تحضير SATوحدتان مدة كل منهما 35 دقيقة، و44 سؤالًا، والآلة الحاسبة مسموحة طوال القسم. الجبر والرياضيات المتقدمة 35% لكل منهما، وحل المسائل والهندسة 15% لكل منهما.
- شرح القيمة المكانيةالرياضياتالرقم 4 في 4000 والرقم 4 في 40 هما الرقم نفسه بقيمة أكبر بألف مرة. كيف تعمل الخانات، والمفاهيم الخاطئة التي تستمر حتى الصف الثامن.
- الجمع بالخانات مع الحملالرياضياتالحمل ليس حيلة، بل هو ما يحدث حين تبلغ الخانة عشرة أو أكثر. مثال محلول على 487 + 356، وأين يوضع الرقم المحمول، وكيف تتحقق.
- الطرح بالخانات مع الاستلافالرياضياتالاستلاف مبادلة معكوسة — عشرة واحدة تُفكَّك إلى عشرة آحاد. مثال محلول على 604 − 287، وكيف تتعامل مع الأصفار، والأخطاء الأغلى ثمنًا.
- متتاليات الأعدادالرياضياتمتتاليات الأعداد هي الأزواج التي تكوّن مجموعًا فورًا. لماذا تحدد متتاليات 10 و20 جودة طرق الخانات، وكيف تُبنى الاستدعاء الحقيقي.
- كيف تقرّب الأعدادالرياضياتالتقريب إلى أقرب 10 و100 وإلى منازل عشرية. أي رقم يحسم، ولماذا يُقرَّب 5 إلى الأعلى، ومزلق التقريب المتسلسل الذي يحوّل 2.449 إلى 2.5.
- التقدير والتحقق من الإجاباتالرياضياتكيف تقدّر قبل الحساب وتتحقق بعده، وكيف تكتشف الإجابات المستحيلة. أرخص مصدر لدرجات إضافية في أي امتحان رياضيات.
- Long MultiplicationالرياضياتLong 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 NumeralsالرياضياتI, 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 NumbersالرياضياتWhy 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)الرياضياتBrackets, 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 FactorsالرياضياتWhat 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 LCMالرياضياتHighest 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 FractionsالرياضياتMultiplying 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 FractionsالرياضياتWhy 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 FractionsالرياضياتMultiply 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 FractionsالرياضياتKeep, 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 ValueالرياضياتDecimals 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 ProportionالرياضياتHow 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 DecreaseالرياضياتMultipliers 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 InterestالرياضياتSimple interest is calculated on the original amount; compound interest on the growing balance. The formulas, the difference, and depreciation.
- Indices and PowersالرياضياتAdd 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 FormالرياضياتHow to write numbers as A × 10ⁿ where A is between 1 and 10, convert back, and multiply or divide without a calculator.
- SurdsالرياضياتA 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 BracketsالرياضياتMultiply 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 QuadraticsالرياضياتFind 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 FormulaeالرياضياتDo 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 InequalitiesالرياضياتSolve 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 TermالرياضياتFind 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)الرياضياتWhat 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 GraphicallyالرياضياتThe 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 AreaالرياضياتPerimeter 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 CircleالرياضياتWhich 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 SolidsالرياضياتVolume 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 PointsالرياضياتAngles 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 PolygonsالرياضياتInterior 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 TheoremsالرياضياتThe 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 TransformationsالرياضياتThe 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 GridsالرياضياتAlong 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 FactorsالرياضياتSimilar shapes have equal angles and proportional sides. Why area scales by k² and volume by k³ — the rule that catches out most students.
- BearingsالرياضياتAlways 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°.
- VectorsالرياضياتA 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 RulesالرياضياتSOHCAHTOA 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 TimeالرياضياتSpeed equals distance over time, and rearranging it. Unit conversion, average speed over two legs, and reading distance-time graphs.
- Mean, Median, Mode and RangeالرياضياتHow 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 PictogramsالرياضياتHow 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 CorrelationالرياضياتReading correlation from a scatter graph, drawing a line of best fit, and why interpolation is reliable while extrapolation is not.
- Cumulative FrequencyالرياضياتPlot at the upper bound, read the median at half the total, and find the interquartile range. How cumulative frequency leads into box plots.
- HistogramsالرياضياتFrequency 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 SetsالرياضياتFill the overlap first, then work outward. Union, intersection, complement and the notation examiners use, plus probability from a Venn diagram.
- Probability Tree DiagramsالرياضياتMultiply 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 TimetablesالرياضياتReading clocks, converting between 12-hour and 24-hour time, and working out journey durations without slipping into decimal minutes.
- Money ProblemsالرياضياتWorking 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?رياضيات 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 Boundariesرياضيات 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 Paperرياضيات 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 Sheetرياضيات 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 Worksرياضيات 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 Questionsرياضيات 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 Sectionتحضير 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 Adaptsتحضير 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 Scoredتحضير 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 Questionsتحضير 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 Analysisتحضير SATRatios, rates, percentages, unit conversion and interpreting tables and graphs. The SAT content area most connected to everyday quantitative reasoning.
- SAT Advanced Mathتحضير SATQuadratic equations, exponential growth, polynomial and radical expressions, and function notation. The hardest content area and where top scores are decided.
- SAT Grammar Rulesتحضير SATStandard English Conventions tests a limited set of rules — clause joining, agreement, modifiers, punctuation. The full list and how to study it.
- SAT Time Managementتحضير 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 MatterالعلومParticle arrangement explains every property of solids, liquids and gases. Melting, boiling, evaporation and why temperature holds steady during a change of state.
- The Water CycleالعلومHow 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 WebsالعلومArrows 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 SystemالعلومMouth to intestine, what each organ does, which enzymes break down which food group, and why the small intestine is so long.
- RespirationالعلومRespiration releases energy from glucose in every living cell. The equations, the difference from breathing, and what happens without enough oxygen.
- Atoms, Elements and CompoundsالعلومProtons, neutrons and electrons; how elements differ from compounds; and why a mixture can be separated but a compound cannot.
- Chemical Reactions and Balancing EquationsالعلومAtoms 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 BasesالعلومThe pH scale, what makes something acidic or alkaline, the neutralisation reaction, and how to name the salt a reaction produces.
- Forces and FrictionالعلومWhat balanced and unbalanced forces do, why friction is not always unhelpful, and how terminal velocity follows from forces coming into balance.
- Energy Transfer and ConservationالعلومEnergy is stored and transferred, never used up. The stores, the transfer pathways, conduction, convection and radiation, and what efficiency measures.
- Electric CircuitsالعلومCurrent, voltage and resistance, how they behave differently in series and parallel, and how to use V = IR without confusing the three quantities.
- Magnetism and ElectromagnetsالعلومLike 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 ReflectionالعلومThe law of reflection, why a straw looks bent in water, and the common misconception that eyes emit light rather than receive it.
- Sound WavesالعلومSound is a longitudinal wave made of compressions and rarefactions. What changes pitch, what changes volume, and why sound cannot cross a vacuum.
- The Solar SystemالعلومThe eight planets in order, why we have day and night, what causes the seasons, and the difference between rotation and orbit.
- Genetics and InheritanceالعلومGenes, alleles, dominant and recessive traits, and how to use a Punnett square to predict inheritance ratios.
- Evolution and Natural SelectionالعلومVariation, competition, survival and inheritance — the mechanism in four steps, plus why organisms do not adapt during their own lifetime.
- Ecosystems and BiodiversityالعلومThe vocabulary from organism to ecosystem, what affects population size, and why losing one species can destabilise an entire community.
- Parts of Speechاللغة الإنجليزيةThe 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 Rulesاللغة الإنجليزيةWhen each mark is correct, why the comma splice is the most common error in English, and how apostrophes actually work.
- Active and Passive Voiceاللغة الإنجليزيةActive 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 Languageاللغة الإنجليزيةThe main devices, how to tell a simile from a metaphor, and how to write about effect rather than just naming the technique.
- Persuasive Writingاللغة الإنجليزيةHow 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 Textاللغة الإنجليزيةSeparating main ideas from supporting detail, writing in your own words, and why a summary is not a shortened copy of the original.
- Creative Writing Openingsاللغة الإنجليزيةStart in the middle of something, show rather than explain, and avoid the three openings examiners see most often.
- Formal Letter Writingاللغة الإنجليزيةThe conventional layout, why Yours sincerely and Yours faithfully are not interchangeable, and how to keep the register consistent.
- Reading a Historical SourceالتاريخWho 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 HistoryالتاريخHow to categorise causes, weigh their relative importance, and write an argument rather than a list of factors.
- Map Skills and Grid ReferencesالجغرافياAlong the corridor and up the stairs — four and six-figure grid references, scale, distance and what contour lines show about the land.
- Rivers and ErosionالجغرافياThe four erosion processes, four transport processes, and how waterfalls, meanders and oxbow lakes form along a river's course.
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