AZSCI Math & Computational Thinking 1 — Questions and Answers
Question 1: A biologist is studying the population growth of a specific bacteria that doubles every 20 minutes. If the initial population is 500 bacteria, which mathematical expression correctly models the population (P) after 't' hours?
- P = 500 * 2^t
- P = 500 * 2^(t/20)
- P = 500 * 2^(3t) (Correct answer)
- P = 500 * (2t)
Correct answer: P = 500 * 2^(3t)
There are 60 minutes in an hour, so in 't' hours, there are 60t minutes. The population doubles every 20 minutes, so the number of doubling periods is (60t / 20) = 3t. The formula for exponential growth is Initial Population * (growth factor)^(number of periods). Therefore, the correct model is P = 500 * 2^(3t).
Question 2: A student measures the length of a copper wire at different temperatures and plots the data on a graph with temperature on the x-axis and length on the y-axis. A line of best fit is drawn that is linear and has a positive slope. What does the slope of this line represent?
- The initial length of the wire at 0°C
- The rate at which the wire's length changes per degree Celsius (Correct answer)
- The final temperature of the wire
- The total change in the wire's length
Correct answer: The rate at which the wire's length changes per degree Celsius
In a linear relationship (y = mx + b), the slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x). In this case, it's the change in length for each unit change in temperature.
Question 3: An environmental scientist uses a computer model to predict the spread of a pollutant in a river. Which of the following is a primary limitation of using such a computational model?
- The model can process large amounts of data faster than a human.
- The model can simulate scenarios that are too dangerous to test in reality.
- The model's accuracy is dependent on the assumptions and data used to build it. (Correct answer)
- The model can visualize complex data in an easy-to-understand format.
Correct answer: The model's accuracy is dependent on the assumptions and data used to build it.
While models are powerful, they are simplifications of complex real-world systems. Their predictions are only as good as the underlying assumptions, equations, and input data. Incomplete or inaccurate data will lead to inaccurate predictions.
Question 4: A physics class finds that the force applied to a cart and its acceleration are directly proportional. If a force of 10 N results in an acceleration of 2 m/s², what force is required to produce an acceleration of 5 m/s² on the same cart?
- 15 N
- 20 N
- 25 N (Correct answer)
- 50 N
Correct answer: 25 N
According to Newton's second law (F=ma), force and acceleration are directly proportional if mass is constant. First, find the mass: m = F/a = 10 N / 2 m/s² = 5 kg. Then, calculate the new force: F = ma = 5 kg * 5 m/s² = 25 N. Alternatively, using proportions: (F1/a1) = (F2/a2), so (10/2) = (F2/5), which gives F2 = 25 N.
Question 5: A student collects the following data for the volume of a gas at constant pressure: Temperature (K): 200, 300, 400, 500; Volume (L): 4, 6, 8, 10. Which mathematical statement best describes the relationship between temperature (T) and volume (V)?
- V = T + 196
- V = 0.02 * T (Correct answer)
- V = T / 50
- V = 2 * T
Correct answer: V = 0.02 * T
This demonstrates Charles's Law, where volume is directly proportional to the absolute temperature (V/T = constant). Checking the ratios: 4/200 = 0.02; 6/300 = 0.02; 8/400 = 0.02; 10/500 = 0.02. Therefore, the constant of proportionality is 0.02, and the relationship is V = 0.02 * T.
Question 6: When analyzing a large dataset of star brightness over time, an astronomer uses a computer algorithm to filter out 'noise' from atmospheric interference. This use of computational thinking is an example of:
- Decomposition
- Pattern recognition
- Abstraction (Correct answer)
- Algorithm design
Correct answer: Abstraction
Abstraction involves focusing on the important information while ignoring irrelevant detail. In this case, the algorithm abstracts the true star brightness data by removing the 'noise' or irrelevant details caused by the atmosphere, simplifying the complex dataset to what is most important.
Question 7: A chemist calculates the density of a substance by dividing its mass (15.50 g) by its volume (5.2 cm³). Using the rules for significant figures, how should the density be reported?
- 3 g/cm³
- 3.0 g/cm³ (Correct answer)
- 2.98 g/cm³
- 2.9808 g/cm³
Correct answer: 3.0 g/cm³
When multiplying or dividing measurements, the result should have the same number of significant figures as the measurement with the fewest significant figures. The mass (15.50 g) has four significant figures, while the volume (5.2 cm³) has two. Therefore, the answer must be rounded to two significant figures. 15.50 / 5.2 = 2.9807..., which rounds to 3.0.
AZSCI Math & Computational Thinking 1
A biologist is studying the population growth of a specific bacteria that doubles every 20 minutes.
If the initial population is 500 bacteria, which mathematical expression correctly models the population (P) after 't' hours?