UCL Electronic and Electrical Engineering: ESAT requirements

One question per module

UCL Electronic and Electrical Engineering asks for Mathematics 1, Biology, Chemistry, Physics and Mathematics 2. Try one original question from each.

1. Mathematics 1

   A map has a scale of $1:25\,000$. A lake has an area of $12\,\mathrm{cm^2}$ on the map. What is the actual area of the lake?
   A $0.3\,\mathrm{km^2}$B $0.75\,\mathrm{km^2}$C $3\,\mathrm{km^2}$D $7.5\,\mathrm{km^2}$E $75\,\mathrm{km^2}$

2. Biology

   The graph shows how the rate of reaction catalysed by two enzymes, $A$ and $B$, changes with temperature. Which of the following statements are correct? 1 $\;$At $45\,^\circ\mathrm{C}$, the reaction catalysed by enzyme $A$ is faster than the reaction catalysed by enzyme $B$. 2 $\;$Enzyme $B$ has a low rate at $30\,^\circ\mathrm{C}$ because its active site has been denatured. 3 $\;$The fall in rate of enzyme $B$ above $70\,^\circ\mathrm{C}$ is caused by a change in the shape of its active site.

   01020304050607080904812temperature / °Crate / arbitrary unitsenzyme $A$enzyme $B$

   A 1 onlyB 2 onlyC 1 and 3 onlyD 2 and 3 onlyE 1, 2 and 3

3. Chemistry

   Magnesium reacts with excess dilute hydrochloric acid in the apparatus shown: $\mathrm{Mg+2HCl\rightarrow MgCl_2+H_2}$. At the end, the gas syringe contains $96\,\mathrm{cm^3}$ of hydrogen. One mole of gas occupies $24\,\mathrm{dm^3}$ under the conditions used, and $A_r(\mathrm{Mg})$ $=24$. What mass of magnesium reacted?
   A $0.0040\,\mathrm{g}$B $0.048\,\mathrm{g}$C $0.096\,\mathrm{g}$D $0.192\,\mathrm{g}$E $0.96\,\mathrm{g}$

4. Physics

   A trolley of mass $2.0\,\mathrm{kg}$ moving at $3.0\,\mathrm{m\,s^{-1}}$ collides with a stationary trolley of mass $1.0\,\mathrm{kg}$. The two trolleys stick together. How much kinetic energy is transferred to other stores in the collision?
   A $0\,\mathrm{J}$B $3.0\,\mathrm{J}$C $6.0\,\mathrm{J}$D $7.5\,\mathrm{J}$E $9.0\,\mathrm{J}$

5. Mathematics 2

   For which values of $k$ does the equation $kx^2+4x+k$ $=3$ have no real solutions?
   A $-1$ $<k$ $<4$B $k$ $<-4$ or $k$ $>1$C $-4$ $<k$ $<1$D $k$ $>4$ onlyE $k$ $<-1$ or $k$ $>4$