Solve Equations and Inequalities with Control
Work through quadratics, the formula, surd equations and inequalities with a method you can trust under pressure, and learn where marks are usually lost.
Read a hyperbola from its equation — both asymptotes, the shape, the axes of symmetry and its domain and range — and sketch it with confidence.
By the end, you can
find the asymptotes of a hyperbola, describe its shape and state its domain and range.
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The Hyperbola and Its Asymptotes
The graph with a hole in it
A hyperbola is the graph of a fraction with x in the denominator, and it behaves differently from every other function in Grade 12: it comes in two separate pieces, and there are values it can never take. 🪝
Those forbidden values are the asymptotes, and they are where almost all the marks in this topic sit.
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The Hyperbola and Its Asymptotes
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Work through quadratics, the formula, surd equations and inequalities with a method you can trust under pressure, and learn where marks are usually lost.
Tell arithmetic patterns from quadratic ones using differences, build the general term for each, and read sigma notation without panic.
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.
The whole Mathematics P1 path → All High School MicroQuests → Browse all 134 →
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The Hyperbola and Its Asymptotes
R19 · 13 min · certificate