Cubic Calculus: Turning Points, Inflection and Tangents
Use the first and second derivatives to analyse a cubic graph, locate turning and inflection points, and build the equation of a tangent.
Work through quadratics, the formula, surd equations and inequalities with a method you can trust under pressure, and learn where marks are usually lost.
By the end, you can
choose the right solving method for an equation or inequality and check your answer before moving on.
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Solve Equations and Inequalities with Control
The question before the working
Solving is the most predictable part of Paper 1, and the marks are lost in the same few places every year. 🧮
Almost all of them come from skipping one question: what kind of equation is this? Choose the method before you start writing, and most of the difficulty disappears.
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Next on the Mathematics P1 path · step 2 of 11
Arithmetic and Quadratic Number Patterns
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Use the first and second derivatives to analyse a cubic graph, locate turning and inflection points, and build the equation of a tangent.
Differentiate from first principles when asked, apply the power rule everywhere else, and know what a derivative actually tells you about a graph.
Choose the right financial formula, handle monthly compounding correctly, and work out loan repayments and outstanding balances without guessing.
Read a parabola or exponential graph properly — intercepts, turning point, asymptotes, domain and range — and find an inverse without guessing.
Work with the common ratio, find any term or sum, and know exactly when an infinite series converges and when it does not.
The whole Mathematics P1 path → All High School MicroQuests → Browse all 134 →
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Solve Equations and Inequalities with Control
Free · 14 min · certificate