Category: Uncategorized

10.6 The diagram shows an outline of part of the Periodic Table. Right-click on the button to open the data booklet in a new tab.   Which statement about elements X, Y and Z is not correct?   A All react with oxygen. B All conduct electricity. C All are metals. D All form coloured compounds.   [1]

  QUESTION 9   This apparatus is used to electrolyse a concentrated solution of sodium chloride. Right-click on the button to open the data booklet in a new tab.   The ionic half-equations for the reactions at the electrodes are negative electrode 2H2O(l) + 2e−

6.2 Use the synoptic code to present the weather data in diagram 2 (4)      

  QUESTION 8   The pie chart shows the relative amounts of some gases in air. Right-click on the button to open the data booklet in a new tab.     8.1 Name of the gas that makes up most of the air. (1)   8.2 What is the approximate percentage of oxygen in air? (1)   Rain water is naturally slightly acidic because carbon dioxide dissolves in it. The word equation for the reaction that occurs is: carbon dioxide + water

Find the absolute maximum of the function \(f(x,y,z)=x^2-2y^2+z^2\) on the ellipsoid \(\frac{x^2}{4}+\frac{y^2}{9}+\frac{z^2}{25}=1\)

Compute the following integral \(\iint_{D} e^{-x^2-y^2}dA\), where \(D\) is the set \(D=\{ (x,y) |\quad 1\leq x^2+y^2 \leq 4, \quad x\geq 0,\quad y\geq 0 \}\)

Compute the directional derivative of \(f(x,y)=x^2+y^2\) at the point \(p=(2,1)\) in the direction of the vector \({\bf v}= \langle 1,1 \rangle\)

Let \(E\) be a solid with volume equal to \(2.\) Let \(S\) be it’s boundary. Compute: \(\iint_{S} {\bf F}\cdot {\bf n} dS\) where \({\bf F}=y{\bf i}+x{\bf j}+3z{\bf k}\) and \({\bf n}\) is oriented outwards.

Calculate \(\frac{\partial(x,y)}{\partial(u,v)}\) if \(u=2x+y\) and \(v=x+\ln(2y)\).

Compute the flux of the vector field \({\bf F}=yz^2{\bf i}+x^2\cos z{\bf j}+xy{\bf k}\) over the paraboloid parametrized by \({\bf r}(u,v)=\langle u,v,1-u^2-v^2 \rangle,\quad u^2+v^2\leq 1\) with downward orientation. [HINT: Try integrating over a different surface]