Scientific and Mathematical Reasoning Flashcards

A scientist is testing the effect of a new nutrient supplement on plant growth. She prepares three identical pots with the same soil and seeds. Pot A receives no supplement. Pot B receives the recommended dose of the supplement. Pot C receives double the recommended dose. All pots are kept in the same location with identical light and water exposure. Which of the following is the primary purpose of Pot A in this experiment?

Answer: To serve as a control group to provide a baseline for comparison.

Pot A is the control group. By receiving no supplement, it provides a baseline measurement of normal plant growth under the given conditions. The growth of plants in Pot B and Pot C can then be compared against this baseline to determine the supplement's actual effect.

A car's fuel efficiency is 8 litres per 100 kilometres. The fuel tank has a capacity of 50 litres. If the driver starts with a full tank and drives 450 kilometres, how many litres of fuel will be remaining in the tank?

Answer: 14 litres

First, calculate the total fuel consumed: (450 km / 100 km) * 8 litres = 4.5 * 8 = 36 litres. Then, subtract the consumed fuel from the full tank capacity: 50 litres - 36 litres = 14 litres remaining.

The following table shows the results of a survey asking 200 people about their preferred mode of transport in two different cities. | Transport Mode | City X (Respondents) | City Y (Respondents) | |---|---|---| | Car | 60 | 35 | | Public Transit | 25 | 45 | | Bicycle | 15 | 20 | What percentage of the total respondents from City Y preferred Public Transit?

Answer: 45%

First, find the total number of respondents from City Y: 35 (Car) + 45 (Public Transit) + 20 (Bicycle) = 100 respondents. Next, calculate the percentage who preferred Public Transit: (45 / 100) * 100% = 45%.

A sequence of patterns is created using dots. Pattern 1 has 3 dots, Pattern 2 has 5 dots, and Pattern 3 has 7 dots. If this trend continues, which formula can be used to determine the number of dots (d) in any given pattern number (n)?

Answer: d = 2n + 1

The number of dots increases by 2 for each new pattern, indicating a linear relationship with a slope of 2. We can test the formula d = 2n + 1. For n=1, d = 2(1) + 1 = 3. For n=2, d = 2(2) + 1 = 5. For n=3, d = 2(3) + 1 = 7. The formula correctly describes the sequence.

A gear system consists of two connected cogs. Cog A has 12 teeth and Cog B has 36 teeth. For every complete revolution of Cog B, how many revolutions does Cog A make?

Answer: 3

The relationship is based on the ratio of the number of teeth. The ratio of teeth from Cog B to Cog A is 36:12, which simplifies to 3:1. This means that for every one revolution of the larger cog (B), the smaller cog (A) must complete three revolutions.

A medical researcher states: 'Our study found a positive correlation between daily coffee consumption and reported levels of alertness. Therefore, drinking coffee causes an increase in alertness.' Which of the following statements represents the most significant logical flaw in the researcher's conclusion?

Answer: Correlation does not necessarily imply causation; other factors could be involved.

The fundamental error is equating correlation with causation. While two variables may move together (correlation), it doesn't prove that one causes the other. For example, people who drink coffee might also sleep less, and the lack of sleep could be the true cause of their alertness levels, or another third factor could influence both.