The night before the ESAT

Tonight, in 45 minutes

1. ID. Your booking name must match your original, unexpired photo ID. Save the confirmation offline.
2. Route. Plan to arrive 30 minutes early.
3. Recall. Go through the sheet below from memory. Star at most three shaky items.
4. Stop. Set alarms, lay out clothes, go to bed.

Calculator, paper, watch, food and drink stay outside the room. The centre gives you an erasable notebook and pen.

Formula recall

Mathematics 1, plus only your own modules.

Mathematics 1

• $x$ $=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$; the discriminant $b^2-4ac$ sets the number of roots.
• Scale factor $k$: length $k$, area $k^2$, volume $k^3$. Percentage change: multiply by $1\pm r/100$.
• Exact $\sin$, $\cos$, $\tan$ at $0^\circ,30^\circ,45^\circ,60^\circ,90^\circ$.
• Probability: multiply along a branch, add branches. Without replacement, the next denominator drops.

Mathematics 2

• $S_n$ $=\frac n2[2a+(n-1)d]$; $S_\infty$ $=\frac a{1-r}$ only when $|r|$ $<1$.
• $s$ $=R\theta$, sector area $\frac12R^2\theta$ in radians; $c^2$ $=a^2+b^2-2ab\cos C$.
• $\log(xy)$ $=\log x+\log y$, $\log(x^k)$ $=k\log x$.
• $\frac d{dx}x^n$ $=nx^{n-1}$; $\int x^n\,dx$ $=\frac{x^{n+1}}{n+1}+C$ for $n$ $\ne-1$.

Physics

• $R$ $=V/I,\ P$ $=IV$ $=I^2R$; $V_s/V_p$ $=n_s/n_p$ and ideal $V_pI_p$ $=V_sI_s$.
• $v^2-u^2$ $=2as,\ F$ $=ma,\ p$ $=mv,\ E_k$ $=\frac12mv^2,\ E_p$ $=mgh$.
• $E$ $=mc\Delta T,\ \rho$ $=m/V,\ p$ $=h\rho g,\ v$ $=f\lambda$. Half-life means repeated halving.

Chemistry and Biology

• $n$ $=m/M_r$; at rtp $V$ $=24n\,\mathrm{dm^3}$; $c$ $=n/V$ with $V$ in $\mathrm{dm^3}$.
• $\Delta H$ $\approx\sum E_{\mathrm{broken}}$${}-\sum E_{\mathrm{formed}}$; one pH unit is a factor of 10 in $[\mathrm H^+]$.
• Genetics: list alleles and gametes; independent events multiply.

Worked example

Tomorrow

Eat normally and arrive 30 minutes early. More than 15 minutes late and you may be turned away. Test the pen before the timer starts.

Each module is 40 minutes. Check the clock at 13, 26 and 38 minutes, and fill every blank before time runs out. If something goes wrong, raise your hand straight away.