ESAT Physics & Chemistry Shortcuts: Fast 90-Second Ratios

The Science Pacing Challenge#

ESAT science questions are specifically designed so numbers cancel out cleanly. If your working involves dividing multi-digit decimals, you are taking the long route.

Examiners test proportional relationships: what happens when radius doubles, or voltage triples across a fixed resistance?

Physics Shortcut 1: Potential Divider Ratio Grid#

In series resistor circuits across supply $V_{\text{in}}$, avoid finding current $I$ first. Treat the resistors as an integer ratio:

• If $R_1 = 30\,\Omega$ and $R_2 = 60\,\Omega$, the ratio is $1:2$ (3 total parts).
• Across $18\text{ V}$, each part is $6\text{ V}$.
• Hence $V_1 = 6\text{ V}$ and $V_2 = 12\text{ V}$.

Sensor components:

• LDR: Light increases $\implies$ Resistance falls $\implies$ Share of voltage falls.
• NTC Thermistor: Temperature increases $\implies$ Resistance falls $\implies$ Share of voltage falls.

Physics Shortcut 2: Proportional Scaling Laws#

Use proportional notation ($\propto$) instead of substituting full numbers:

• Kinetic Energy: $E_k = \frac{p^2}{2m}$. If momentum increases by $50\%$ ($p \to 1.5p$), then $E_k \propto p^2 \implies E_k^{\prime} = (1.5)^2 E_k = 2.25 E_k$ ($+125\%$, not $+50\%$).
• Power in Resistors: $P = \frac{V^2}{R}$. Tripling voltage across fixed $R$ increases power by $3^2 = 9\times$.

Physics Shortcut 3: Scientific Notation & Powers of 10#

Separate the mantissa from the exponent ($10^k$):

1. Add/subtract exponents first.
2. Round and estimate the single-digit mantissa.
3. Compare the power of 10 to the answer choices—often only one option has the matching exponent.

Chemistry Shortcut 1: 24.0 dm³ Molar Gas Volume#

At RTP ($20^\circ\text{C}$, $1\text{ atm}$), 1 mole of any ideal gas occupies $24.0\text{ dm}^3$:

• $12.0\text{ dm}^3 = 0.5\text{ mol}$
• $6.0\text{ dm}^3 = 0.25\text{ mol}$
• $4.8\text{ dm}^3 = 0.20\text{ mol}$
• $2.4\text{ dm}^3 = 0.10\text{ mol}$

Recognizing these fractions solves gas volume stoichiometry in under 20 seconds.

Chemistry Shortcut 2: Stoichiometric Ratio Pruning#

The most common trap is omitting mole ratios (e.g. comparing $\text{HCl}$ to $\text{H}_2\text{SO}_4$, or forgetting diatomic $\text{O}_2$):

Burning $0.2\text{ mol}$ of propane requires $0.2 \times 5 = 1.0\text{ mol}$ of $\text{O}_2$ ($24.0\text{ dm}^3$). Identifying the 1:5 ratio eliminates options that assume a 1:1 ratio before calculating.

Dimensional Analysis: Rule Out Distractors Fast#

Before computing, check units across the answer choices:

• Finding velocity requires $\text{m s}^{-1}$. An option with $\sqrt{gh}$ has units $\sqrt{(\text{m s}^{-2})(\text{m})} = \text{m s}^{-1}$ (valid).
• An option with $gh$ has units $\text{m}^2 \text{s}^{-2}$ (invalid—energy per unit mass, not velocity).
• Pruning dimensionally invalid options turns a 5-option question into a 2-option decision.