Scientific and Mathematical Reasoning Flashcards

A projectile is launched horizontally from a cliff. Ignoring air resistance, which statement about its motion is correct?

Answer: Horizontal and vertical motions are independent of each other

Projectile motion can be resolved into independent horizontal (constant velocity) and vertical (accelerating) components.

If f(x) = 3x² − 12x + 9, for which value of x does f(x) reach its minimum?

Answer: x = 2

For a quadratic ax² + bx + c, the vertex is at x = −b/(2a) = 12/6 = 2.

In an experiment, one group of mice is injected with a potential new drug and another group with a saline solution. Both groups are handled identically. The saline group is called:

Answer: The placebo control group

The saline-injected group is a placebo control, receiving an inert substance to isolate the drug's actual effect.

A line graph shows bacterial population doubling every 20 minutes. After 1 hour starting from 100 bacteria, what is the population?

Answer: 800

Three doublings in 60 minutes: 100 → 200 → 400 → 800.

The atomic number of an element determines its:

Answer: Identity as a specific element based on proton count

The atomic number equals the number of protons, which uniquely identifies each element on the periodic table.

A researcher plots time on the x-axis and distance traveled on the y-axis for two objects. Object A's line has a steeper slope than Object B's. What can be concluded?

Answer: Object A has a greater speed than Object B

On a distance-time graph, slope equals speed; a steeper slope means Object A moves faster.

Which of the following is an example of a hypothesis rather than a theory?

Answer: Cells that receive more sunlight will produce more glucose

A hypothesis is a specific, testable prediction; 'more sunlight → more glucose' is testable and not yet broadly confirmed.