STAT Scientific and Mathematical Reasoning 4 — Questions and Answers
Question 1: A projectile is launched horizontally from a cliff. Ignoring air resistance, which statement about its motion is correct?
- Horizontal velocity decreases due to gravity
- Vertical velocity remains constant throughout flight
- Horizontal and vertical motions are independent of each other (Correct answer)
- The projectile follows a straight-line path
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.
Question 2: If f(x) = 3x² − 12x + 9, for which value of x does f(x) reach its minimum?
- x = −2
- x = 2 (Correct answer)
- x = 3
- x = 4
Correct answer: x = 2
For a quadratic ax² + bx + c, the vertex is at x = −b/(2a) = 12/6 = 2.
Question 3: 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:
- The experimental group
- The independent variable
- The placebo control group (Correct answer)
- The dependent variable
Correct answer: The placebo control group
The saline-injected group is a placebo control, receiving an inert substance to isolate the drug's actual effect.
Question 4: A line graph shows bacterial population doubling every 20 minutes. After 1 hour starting from 100 bacteria, what is the population?
- 600
- 800 (Correct answer)
- 1,600
- 3,200
Correct answer: 800
Three doublings in 60 minutes: 100 → 200 → 400 → 800.
Question 5: The atomic number of an element determines its:
- Mass in grams
- Number of neutrons in the nucleus
- Identity as a specific element based on proton count (Correct answer)
- Isotope type
Correct 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.
Question 6: 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?
- Object A traveled a longer total distance
- Object A has a greater speed than Object B (Correct answer)
- Object B started moving before Object A
- Object B will eventually overtake Object A
Correct 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.
Question 7: Which of the following is an example of a hypothesis rather than a theory?
- Germ theory explains that microorganisms cause disease
- Cells that receive more sunlight will produce more glucose (Correct answer)
- Evolution explains the diversity of life through natural selection
- The law of conservation of energy applies to all physical systems
Correct 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.
STAT Scientific and Mathematical Reasoning 4
A projectile is launched horizontally from a cliff.
Ignoring air resistance, which statement about its motion is correct?