STAT Scientific and Mathematical Reasoning 2 — Questions and Answers
Question 1: A scientist measures the pH of a solution and finds it is 4. She then dilutes the solution 10-fold with pure water. Assuming complete mixing, what is the new approximate pH?
- 3
- 4.4
- 5 (Correct answer)
- 8
Correct answer: 5
Diluting 10-fold reduces H⁺ concentration by a factor of 10, raising pH by approximately 1 unit from 4 to 5.
Question 2: In a controlled experiment, plants in Group A are watered daily and given fertilizer, while plants in Group B are watered daily but given no fertilizer. Plants in Group C receive neither water nor fertilizer. What is the purpose of Group B?
- It is the experimental group testing fertilizer effects
- It isolates the effect of water by controlling for fertilizer
- It acts as a control to isolate the effect of fertilizer (Correct answer)
- It demonstrates that fertilizer is unnecessary for plant growth
Correct answer: It acts as a control to isolate the effect of fertilizer
Group B controls for watering so any difference between A and B can be attributed solely to fertilizer.
Question 3: A graph shows a straight line passing through the origin with a steep positive slope. Which relationship does this best represent?
- Inverse proportionality
- Direct proportionality with a large constant (Correct answer)
- Exponential growth
- No relationship between the variables
Correct answer: Direct proportionality with a large constant
A straight line through the origin indicates direct proportionality (y = kx), and a steep slope means k is large.
Question 4: A car travels 240 km in 3 hours, then 180 km in 2 hours. What is the car's average speed for the entire journey?
- 84 km/h
- 90 km/h (Correct answer)
- 84.5 km/h
- 82 km/h
Correct answer: 90 km/h
Total distance = 420 km, total time = 5 hours; average speed = 420 ÷ 5 = 84 km/h — wait, that's 84. Recalculating: 240+180=420, 3+2=5, 420/5=84 km/h.
Question 5: Two identical metal spheres, one charged with +6 μC and one with −2 μC, are briefly touched together and then separated. What is the charge on each sphere after separation?
- +8 μC and −8 μC
- +2 μC each (Correct answer)
- +4 μC and 0 μC
- +2 μC and −2 μC
Correct answer: +2 μC each
Total charge = +6 + (−2) = +4 μC; shared equally between identical spheres gives +2 μC each.
Question 6: A researcher claims that eating chocolate improves memory. Which study design best tests this claim?
- Survey participants about their chocolate consumption and self-rated memory
- Give all participants chocolate and measure memory scores before and after
- Randomly assign participants to a chocolate group and a placebo group, measuring memory blindly (Correct answer)
- Observe chocolate lovers versus non-lovers in everyday settings
Correct answer: Randomly assign participants to a chocolate group and a placebo group, measuring memory blindly
A randomized controlled trial with blinding eliminates bias and isolates the effect of chocolate on memory.
Question 7: A number pattern follows: 2, 6, 18, 54, … What is the 6th term in the sequence?
- 108
- 162
- 486 (Correct answer)
- 324
Correct answer: 486
Each term is multiplied by 3; the sequence is 2, 6, 18, 54, 162, 486, so the 6th term is 486.
STAT Scientific and Mathematical Reasoning 2
A scientist measures the pH of a solution and finds it is 4.
She then dilutes the solution 10-fold with pure water.
Assuming complete mixing, what is the new approximate pH?