Scientific and Mathematical Reasoning Flashcards

A data set of exam scores has a mean of 70 and a standard deviation of 10. If a student scores 90, how many standard deviations above the mean is this score?

Answer: 2

z = (90 − 70) ÷ 10 = 2, so the score is exactly 2 standard deviations above the mean.

When a solid is heated at constant pressure, which energy change primarily occurs at its melting point?

Answer: Potential energy of particles increases while temperature stays constant

At the melting point, energy input overcomes intermolecular forces (increases potential energy) without raising temperature.

A rectangle has a length that is three times its width. If the area is 75 cm², what is the width?

Answer: 5 cm

Let width = w; then 3w × w = 75, so 3w² = 75, w² = 25, w = 5 cm.

A scientist observes that taller plants produce more seeds. She concludes that height causes increased seed production. What is the main flaw in this reasoning?

Answer: Correlation does not imply causation — a third factor may explain both

An observed correlation between two variables cannot establish causality without ruling out confounding factors.

Light travels from water (refractive index 1.33) into air (refractive index 1.00). Compared to its speed in water, the speed of light in air is:

Answer: Faster

Refractive index = c/v; a lower refractive index means higher speed, so light travels faster in air than in water.

A bag contains 4 red and 6 blue marbles. Two marbles are drawn without replacement. What is the probability that both are red?

Answer: 2/15

P(both red) = (4/10) × (3/9) = 12/90 = 2/15.

A bar chart shows five cities' average annual rainfall. City C's bar is twice the height of City A's bar. Which conclusion is valid?

Answer: City C receives twice the rainfall of City A

Bar height directly represents the measured value, so twice the bar height means twice the average annual rainfall.