Mathematics
Mathematics lessons from algebra to calculus, with worked examples for AP Calculus, Cambridge 9709 and IB Analysis and Approaches.
MathematicsThe Harmonic Form R cos(x − α): Combining a sin x + b cos x, with Tides and Maximum ValuesLearn the harmonic form R cos(x − α): combine a sin x + b cos x, find maximum and minimum values, and solve equations, with a…MathematicsSolving Trigonometric Equations: All Solutions in an Interval, with a Daylight-Hours ModelSolving trigonometric equations: find all solutions in an interval using the CAST diagram, quadratics in sin x and cos x, and a daylight-hours model.MathematicsBinomial Expansion Explained: Pascal’s Triangle, nCr and Approximations like 1.02¹⁰Binomial expansion explained: use Pascal's triangle and nCr to expand (a + b)^n, find a single term, and approximate values like 1.02¹⁰ with worked examples.MathematicsFactor Theorem and Remainder Theorem: Polynomial Division Step by Step, with a Box-Volume CaseLearn the factor theorem and remainder theorem: find remainders, factorise cubics with synthetic division, and solve a box-volume design case step by step.MathematicsComposite and Inverse Functions: How to Find f(g(x)) and f⁻¹(x), with Currency and Tax ExamplesLearn composite and inverse functions step by step: find f(g(x)) and f⁻¹(x), restrict domains, and solve a currency and tax case with worked examples.Mathematical EconomicsL’Hôpital’s Rule Explained: 0/0 and ∞/∞ Limits, Repeated Use and When It FailsLearn L'Hôpital's rule for 0/0 and ∞/∞ limits: when it applies, repeated use, when it fails, plus a present-value case and exam-style practice questions.MathematicsCompleting the Square: Vertex Form, Maximum Revenue and Circle EquationsWhat ticket price brings in the most money? Completing the square answers it in four lines, then solves quadratics and circle equations too.MathematicsMaclaurin Series: Approximating eˣ, sin x and ln(1 + x), with a Continuous Compounding CaseHow much does continuous compounding really add? Use a Maclaurin series to find out to the cent, with error bounds, worked examples and exam practice.Mathematical EconomicsNewton–Raphson Method: Finding an Investment’s IRR Step by StepSolar panels cost $8,000 and save $2,000 a year. What return do they earn? Use the Newton–Raphson method to find the IRR in three quick steps.MathematicsVolume of Revolution: Disc and Washer Methods, Worked Through a Wine GlassWhere should the 175 ml line go on a wine glass? Learn the disc and washer methods for volume of revolution with worked examples and exam…
This topic has a full chapter in Mathematics Made Simple, with 1,565 fully worked practice questions in the bundle.Mathematics Made Simple Complete Bundle — Textbook + 1,565 Practice Questions
Get it for $16