OCR Further Additional Pure 2017 Specimen — Question 3 5 marks

Exam BoardOCR
ModuleFurther Additional Pure (Further Additional Pure)
Year2017
SessionSpecimen
Marks5
TopicImplicit equations and differentiation
TypeShow dy/dx equals given expression
DifficultyStandard +0.8 This is a Further Maths partial differentiation question requiring four derivatives and algebraic manipulation to verify an identity. While mechanically straightforward (differentiate twice with respect to each variable), it demands careful bookkeeping and the insight that terms will cancel systematically. The 5-mark allocation and Further Maths context place it moderately above average difficulty.
Spec8.05d Partial differentiation: first and second order, mixed derivatives

Given \(z = x\sin y + y\cos x\), show that \(\frac{\partial^2 z}{\partial x^2} + \frac{\partial^2 z}{\partial y^2} + z = 0\). [5]

Given $z = x\sin y + y\cos x$, show that $\frac{\partial^2 z}{\partial x^2} + \frac{\partial^2 z}{\partial y^2} + z = 0$. [5]

\hfill \mbox{\textit{OCR Further Additional Pure 2017 Q3 [5]}}