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Level 3 Calculus, Scholarship Calculus - Coggle Diagram
Level 3 Calculus
Scholarship Calculus
Algebra/Complex numbers
Sum and product of roots
Prove trig identities with complex numbers
De Moires' theorem on one side, binomial on the other side.
Equate real and imaginary parts
Get familiar with 1/x. They're way too common in the questions
Locus
|z-i| is a circle shifted up by 1
|z-1| is a circle shifted right by 1
Rationalisation
Integration
Definitie integrals
Asking to evaluate the integral
Just evaluate
Asking to find the areas
Identify intersections and split the integral
Differential equations
The exponential formula: dy/dx=ky
Newton's law of cooling
Substitution
IBP
Only used if desperate
Trig sub
Draw the triangle it substitutes
Identites and uses
Trig products
Double angle
Evaluate power trig integrals
Areas and volumes
Symmetrical graphs can be simplified
Watch out for intersections
Differential equations
Include constant k in rates e.g dP/dt=kP
Get good with fraction integration into ln functions
Trigonometry and geometry
Proof identities
LHS working to match RHS
RHS working to match LHS
Differentiation
Conics
Sequences & series
Permutations and combinations