Media Summary: (a) Verifying the solution of a differential equation (b)(1) A multivariable function and whether its positive or negative (b)(2) Using ... Differentiation. Straightforward application of chain rule and product rule. (a) Finding the equation of a general normal (b) Finding the equation of the normal that leads to the lowest point of intersection (c) ...
Scholarship Calculus 2014 Q5 - Detailed Analysis & Overview
(a) Verifying the solution of a differential equation (b)(1) A multivariable function and whether its positive or negative (b)(2) Using ... Differentiation. Straightforward application of chain rule and product rule. (a) Finding the equation of a general normal (b) Finding the equation of the normal that leads to the lowest point of intersection (c) ... (a) Connecting the roots of a polynomial to a trig proof (b)(i) A 3D linear programming problem (b)(ii) Finding the critical path of a ... (a) Finding an optimal solution to the "tethered goat" (a) A nasty trig identity and polynomial with trigonometric roots (b) The limit of a recursive sequence.
(a) A proof involving complex numbers solved algebraically and geometrically (b) Finding the maximum difference between the ... (a) An interesting problem involving the gamma function (b) Solving a degree 6 polynomial given only one of its roots (c) Using ... (a) Proving a trig identity by using De Moivre's Theorem (b) An arithmetic sequence involving logs and trig (c) A gargantuan trig ... Implicit differentiation. Differentiation. Do not try to integrate! (a) A sneaky algebraic equation (b)(1) Another equation solved using a substitution (b)(2) A linear programming problem with a ... Disguised quadratic. Look carefully before you start.
(a) A beautiful equation involving complex numbers (b)(1) Finding the 3rd derivative of a triple product (b)(2) Solving an equation ... Proof of the geometric series formula. Important to know this. Scholarship Calculus 2020 Q5 (c) NCEA New Zealand
