MCAT Chemical and Physical Foundations of Biological Systems Flashcards: Interpret Patterns Data Tables Figures Graphs

What this deck covers

This deck focuses on Interpret Patterns Data Tables Figures Graphs, giving you a quick way to review the definitions, rules, and examples that matter most for MCAT Chemical and Physical Foundations of Biological Systems.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What does a horizontal line on a $y$-versus-$x$ graph indicate about $y$ as $x$ changes?

Answer: $y$ is constant; slope $m = 0$. A horizontal line shows y remains unchanged as x varies, resulting in zero slope.

Flashcard 2: What does the slope of a position-versus-time graph represent physically?

Answer: Velocity, $v = \frac{\Delta x}{\Delta t}$. The slope represents the rate of change of position with respect to time, defining velocity.

Flashcard 3: What does the slope of a velocity-versus-time graph represent physically?

Answer: Acceleration, $a = \frac{\Delta v}{\Delta t}$. The slope indicates the rate of change of velocity over time, which is acceleration.

Flashcard 4: What does the area under a velocity-versus-time curve represent physically?

Answer: Displacement, $\Delta x = \int v\,dt$. The area under the curve is the integral of velocity over time, yielding displacement.

Flashcard 5: What does the area under an acceleration-versus-time curve represent physically?

Answer: Change in velocity, $\Delta v = \int a\,dt$. The area under the curve integrates acceleration over time to give the change in velocity.

Flashcard 6: What is the correct slope formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ on a graph?

Answer: $m = \frac{y_2-y_1}{x_2-x_1}$. Slope is the ratio of the change in y to the change in x between two points.

Flashcard 7: What does a vertical line on an $x$-$y$ plot indicate about $x$ as $y$ changes?

Answer: $x$ is constant; slope is undefined. A vertical line indicates x is fixed while y changes, making the slope undefined.

Flashcard 8: What does a log-log plot with slope $n$ imply about the relationship between $y$ and $x$?

Answer: Power law: $y \propto x^n$. A linear log-log plot with slope n shows y is proportional to x raised to the power n.

Flashcard 9: What does a semilog plot of $\ln(y)$ versus $x$ being linear imply about $y(x)$?

Answer: Exponential: $y = Ae^{kx}$. Linearity in $\ln(y)$ vs x indicates y follows an exponential function of x.

Flashcard 10: What does a semilog plot of $y$ versus $\ln(x)$ being linear imply about $y(x)$?

Answer: Logarithmic: $y = a\ln(x)+b$. Linearity in y vs $\ln(x)$ suggests y depends logarithmically on x.

Flashcard 11: Identify the relationship if doubling $x$ causes $y$ to quadruple in a data table.

Answer: Quadratic: $y \propto x^2$. Quadrupling y when x doubles implies y is proportional to the square of x.

Flashcard 12: Identify the relationship if doubling $x$ causes $y$ to double in a data table.

Answer: Direct proportionality: $y \propto x$. Doubling y when x doubles demonstrates direct proportionality between them.

Flashcard 13: Identify the relationship if doubling $x$ causes $y$ to halve in a data table.

Answer: Inverse proportionality: $y \propto \frac{1}{x}$. Halving y when x doubles indicates inverse proportionality.

Flashcard 14: What is the correct interpretation when two lines on a graph are parallel?

Answer: Equal slopes; constant difference in $y$. Parallel lines have identical slopes, maintaining a constant vertical difference.

Flashcard 15: What is the correct interpretation when two curves intersect at one point on a $y$-versus-$x$ plot?

Answer: They have equal $y$ at that $x$ value. Intersection at a point means both curves share the same y-value for that x.

Flashcard 16: Identify the correct conclusion if error bars for two means overlap substantially.

Answer: No clear evidence of a difference from the plot alone. Overlapping error bars suggest no statistically significant difference is evident.

Flashcard 17: What does a steep slope on a linear plot indicate about sensitivity of $y$ to changes in $x$?

Answer: Large $\frac{\Delta y}{\Delta x}$; high sensitivity. A steep slope shows y changes significantly with small variations in x.

Flashcard 18: What is the correct way to compute percent change from $A$ to $B$ in a table?

Answer: $\%\Delta = \frac{B-A}{A}\times 100\%$. Percent change is the relative difference from initial value A to B, expressed as a percentage.

Flashcard 19: What is the correct definition of a ratio from two table entries $y_1$ and $y_2$?

Answer: Ratio $= \frac{y_2}{y_1}$. The ratio quantifies the relative magnitude of y2 compared to y1.

Flashcard 20: Identify the median of the ordered dataset $[2,3,9,10,11]$ as read from a table.

Answer: Median $= 9$. In an ordered dataset with odd count, the median is the middle value.

Flashcard 21: Identify the mean of the dataset $[2,3,9,10,11]$ as read from a table.

Answer: Mean $= 7$. The mean is calculated as the sum of all values divided by the number of values.

Flashcard 22: What does it suggest if a scatter plot shows points tightly clustered around a line?

Answer: Strong correlation; high goodness of fit. Tight clustering around a line indicates strong linear relationship and good model fit.

Flashcard 23: What does it suggest if a scatter plot shows a clear trend but with increasing spread at larger $x$?

Answer: Heteroscedasticity; variance increases with $x$. Increasing spread with x indicates non-constant variance in the data.

Flashcard 24: Identify the dependent variable in a standard plot where the horizontal axis is labeled $x$.

Answer: The $y$-axis variable (vertical axis). The dependent variable is plotted on the y-axis, responding to the independent variable on x.