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MathematicsSeparable Differential Equations: Newton’s Law of Cooling Step by StepHow long does a takeaway coffee stay hot? Learn to solve separable differential equations through Newton's law of cooling, with worked exam examples.Mathematical EconomicsThe Gini Coefficient Formula: Lorenz Curves and Area Between CurvesMeasure inequality with calculus: find the Gini coefficient as the area between the line of equality and a Lorenz curve, step by step.MathematicsImplicit Differentiation Examples: Tangents, Second Derivatives and the MRSHow many pastries is one more coffee worth? Learn implicit differentiation through an indifference curve, then tangents, normals and second derivatives.MathematicsGeometric Series Formula: Savings Plans, Loan Repayments and the Sum to InfinityCompare a fixed-rise and a percentage-rise savings plan, price a loan and a perpetuity, and master the geometric series formula along the way.MathematicsVector Equation of a Line: Do the Drone Paths Cross? Intersection, Skew Lines and AnglesUse r = a + λd to decide whether two drone flight paths cross, pass over each other (skew) or run parallel, and find the angle…MathematicsSine Rule and Cosine Rule Examples: Surveying, Bearings and the Ambiguous CaseSurvey a triangular plot with the sine rule and cosine rule, then tackle bearings, triangle area and the ambiguous case step by step.Mathematical EconomicsSimultaneous Equations Explained: Supply and Demand Equilibrium and the Effect of a TaxSimultaneous equations find where two conditions hold at once. See how they give market equilibrium, the effect of a tax, and line–curve crossings.MathematicsHow to Evaluate Limits: Substitution, 0/0, Conjugates and Limits at InfinityA clear method for evaluating limits, shown on a real cost problem: substitution, factorising 0/0, conjugates and limits at infinity, with 5 practice questions.MathematicsSolving Exponential Equations with Logarithms: Doubling Time, Half-Life and the Rule of 70When will a shop's orders triple? Learn solving exponential equations with logs, from doubling time and half-life to the Rule of 70.MathematicsIntegration by Substitution: Examples, Changing Limits and Real CasesLearn integration by substitution as the chain rule in reverse, with worked examples on drug absorption, app downloads and exam-style integrals.MathematicsRelated Rates Problems: Sliding Ladders, Filling Cones and Falling DemandSolve related rates problems with one reliable recipe: draw, link, differentiate with respect to time, then substitute. Ladder, cone and price examples.MathematicsIntegration by Parts Examples: LIATE, the Tabular Method and the Present Value of a Growing Revenue StreamUse integration by parts to value a growing revenue stream, then master LIATE, repeated parts and the tabular method with exam-style examples.
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