University multivariable calculus quiz to download as PDF

This University multivariable calculus quiz has 10 short questions for pupils aged 18-19. Type your answer, check it straight away and read the explanation when you get one wrong.

University multivariable calculus quiz: the 10 questions

\(\frac{\partial}{\partial x}(x^3y)\)?
\(\nabla(x^2+y^2)\) at \((1,1)\)?
\(\int_0^1\int_0^1 xy\,dx\,dy\)?
Area element in polar coordinates?
\(f_{xy}\) vs \(f_{yx}\) for smooth f?
Nature of a critical point with \(D<0\)?
\(|\nabla f|\) is the ... rate of change?
\(\int_0^{2\pi}\int_0^1r\,dr\,d\theta\)?
Tangent plane of \(z=xy\) at \((1,1,1)\): value of \(f_x\)?
Number of first partial derivatives of \(f(x,y,z)\)?

How to use this University multivariable calculus quiz

First, answer every question without a calculator unless the question says so. Then check your answer and read the short explanation. If you get fewer than 7 right, revise the multivariable calculus lesson and try again later. After that, try the multiple choice questions or the multivariable calculus worksheet.

Finally, take this quiz again before a test, because quick retrieval helps you remember. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.