Imperial Chemical Engineering: ESAT requirements

One question per module

Imperial Chemical Engineering asks for Mathematics 1, Mathematics 2 and Chemistry. 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. 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 $k$ $>4$

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 $0.96\,\mathrm{g}$