Scholarship Calculus 93202
Complex numbers, differentiation, integration and differential equations, with strategy prompts, worked steps and s/o marking.
350 problems · 10 free to try now
Free problems
- Complex numbers: de Moivre's theorem and rootsBridge
- Complex numbers: loci on the Argand diagramBridge
- Complex roots of real polynomialsBridge
- De Moivre's theorem: multiple-angle identities and cubic equationsBridge
- Complex numbers: powers of cis θ and integrationBridge
- Roots of unity and exact trigonometric valuesBridge
- Cubic equations: roots in arithmetic progressionBridge
- Exponential equations reducible to quadratics; parameter analysisBridge
- Tangency and number of solutions of transcendental equationsBridge
- Inverse functions and numerical solution (Newton's method)Bridge
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Complex numbers · 6
- Complex numbers: de Moivre's theorem and rootsBridge
- Complex numbers: loci on the Argand diagramBridge
- Complex roots of real polynomialsBridge
- De Moivre's theorem: multiple-angle identities and cubic equationsBridge
- Complex numbers: powers of cis θ and integrationBridge
- Roots of unity and exact trigonometric valuesBridge
Equations, logs and inequalities · 7
- Cubic equations: roots in arithmetic progressionBridge
- Exponential equations reducible to quadratics; parameter analysisBridge
- Tangency and number of solutions of transcendental equationsBridge
- Trigonometric equations: quadratic form and R-sin formBridge
- Systems of three equations: parameters and geometric interpretationBridge
- Simultaneous equations in contextBridge
- Parametric systems: unique, infinite and no solutionsBridge
Functions and inverse functions · 2
- Inverse functions and numerical solution (Newton's method)Bridge
- Reciprocal functions: features from the parent graphBridge
Trigonometry · 3
- Trigonometric identities: double-angle formulae and exact valuesBridge
- Multiple-angle identities and equationsBridge
- Sum-to-product identities in equationsBridge
Conics and coordinate geometry · 5
- Ellipse: parametric tangents and optimisationBridge
- Parabola: focal chords and tangentsBridge
- Hyperbola: key features and minimum distanceBridge
- Circles and tangent linesBridge
- Conics as loci: focus–directrix definitionBridge
Limits, FTC and continuity · 4
- Discontinuities: removable vs infinite; asymptotic behaviourBridge
- Continuity and differentiability of piecewise functionsBridge
- Limits: standard results and first principlesBridge
- Limits at infinity involving surdsBridge
Differentiation techniques · 3
- Implicit differentiation: horizontal and vertical tangentsBridge
- Parametric curves: gradients and self-intersectionBridge
- Normals to curves and minimising chord lengthBridge
Optimisation and rates · 7
- Related rates: volume and surface of liquid in a coneBridge
- Optimisation under a curve; points of inflectionBridge
- Optimisation in context: minimising total areaBridge
- Curve analysis: stationary points, inflection and tangentsBridge
- Using calculus to compare numbersBridge
- Related rates with trigonometric modelsBridge
- Kinematics: displacement vs distanceBridge
Integration techniques · 8
- Integration by substitution: definite integralsBridge
- Area between curvesBridge
- Area with a parameter; bisecting a regionBridge
- Integrals of the form f′(x)/f(x)Bridge
- Numerical integration: trapezium vs Simpson's ruleBridge
- Odd powers of sine: substitution and patternsBridge
- Antiderivatives with initial conditions; proving positivityBridge
- Definite integrals with an unknown limitBridge
Differential equations · 5
- Newton's law of coolingBridge
- Separable DEs with a restricted domainBridge
- Growth with constant removal: forming and interpreting a DEBridge
- Mixing problemsBridge
- Torricelli's law: draining tanksBridge