Quantitative Skills & Data Analysis

The MCAT is calculator-free, so it rewards estimation and unit reasoning over precise arithmetic. These skills appear in every science section.

Dimensional analysis

Carry units through every calculation; the units of your answer tell you whether the setup is right. If a question asks for a force and your units come out as kg·m/s², you have newtons — you're correct. Mismatched units signal a flipped ratio.

Scientific notation and estimation

• Multiply by adding exponents, divide by subtracting them: $(3\times10^4)(2\times10^{-2}) = 6\times10^{2}$.
• Round aggressively, then adjust. The right answer choice is usually within a factor of 2 of a clean estimate, and distractors are often off by a power of 10.

Ratios, proportions, and percent change

• Many MCAT relationships are proportional: if $F = \frac{kq_1q_2}{r^2}$ and you double $r$, force drops to one-quarter. Reason about how the answer scales rather than plugging numbers.
• Percent change = $\frac{\text{new} - \text{old}}{\text{old}} \times 100\%$. A doubling is a +100% change; halving is −50%.

Logarithms and semi-log plots

• $\text{pH} = -\log[\text{H}^+]$, so each pH unit is a 10× change in concentration. The same log intuition covers pKa, decibels, and the Nernst equation.
• On a semi-log plot, exponential processes (radioactive decay, first-order kinetics, bacterial growth) become straight lines — recognizing this lets you read rate constants off a graph.

Reading graphs under time pressure

Identify the axes and units first, find the trend (linear, saturating, exponential), and locate the specific point the question targets. Most MCAT "calculations" are really careful graph reading plus one proportional step.