Question 1

In order to use the sqrt() function, you must use which of the following Python statements?

Accepted Answer

The sqrt() function is part of the math module in Python, so you need to import the math module using "import math" to access it.

Question 2

Which of the following is a constant in the math module?

Accepted Answer

The constant 'e' represents the base of the natural logarithm and is a mathematical constant in the math module.

Question 3

What equation relates pi to the circumference of a circle?

Accepted Answer

The circumference of a circle is given by the formula C = 2πr, where r is the radius.

Question 4

Case Study 1:
>>> import math
>>> numSides = 8
>>> innerAngleB = 360.0 / numSides
>>> halfAngleA = innerAngleB / 2
>>> oneHalfSideS = math.sin(math.radians(halfAngleA))
>>> sideS = oneHalfSideS * 2
>>> polygonCircumference = numSides * sideS
>>> pi = polygonCircumference / 2
>>> pi
3.0614674589207183
-Refer to the session in the accompanying case study 1. Which line uses the math module?

Accepted Answer

The math module is used to perform mathematical operations. In this case, the math.sin() function is used to calculate the sine of the half angle.

Question 5

Case Study 1:
>>> import math
>>> numSides = 8
>>> innerAngleB = 360.0 / numSides
>>> halfAngleA = innerAngleB / 2
>>> oneHalfSideS = math.sin(math.radians(halfAngleA))
>>> sideS = oneHalfSideS * 2
>>> polygonCircumference = numSides * sideS
>>> pi = polygonCircumference / 2
>>> pi
3.0614674589207183
-Refer to the session in the accompanying case study 1. How many sides does the polygon in this approximation have?

Accepted Answer

The variable `numSides` is set to 8, indicating the polygon has 8 sides.

Question 6

The ____ statement is used to terminate a function.

Accepted Answer

The return statement is used to terminate a function and return a value to the caller.

Question 7

How many times will the following print statement be executed?
>>> for sides in range(8, 100, 8):
Print(sides, archimedes(sides))

Accepted Answer

The range function range(8, 100, 8) generates numbers starting from 8 up to but not including 100, with a step of 8. This results in the sequence: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, which has 12 numbers. Thus, the print statement will be executed 12 times.

Question 8

Case Study 2:
>>> acc = 0
>>> for x in range(1, 6):
acc = acc + x
>>> acc
15
-Refer to the session in the accompanying case study 2. Which of the following is the initialization statement?

Accepted Answer

The initialization statement is "acc = 0" because it sets the initial value of the accumulator variable 'acc' before the loop starts.

Question 9

Case Study 2:
>>> acc = 0
>>> for x in range(1, 6):
acc = acc + x
>>> acc
15
-Refer to the session in the accompanying case study 2. What type of variable is acc?

Accepted Answer

The variable 'acc' is an accumulator variable because it is used to accumulate the sum of numbers in the loop.

Question 10

What is the name of the formula that calculates pi using the following equation?
π/4 = 1/1 - 1/3 + 1/5 - 1/7 + 1/9 …

Accepted Answer

The answer of What is the name of the formula...

Question 11

When calculating pi using the Wallis formula, the accumulator variable:

Accepted Answer

The Wallis formula for calculating pi involves multiplying fractions, so the accumulator variable must be initialized to one to correctly accumulate the product of fractions.

Question 12

The ____ uses probability and random behavior to calculate pi.

Accepted Answer

The Monte Carlo simulation uses random sampling and probability to estimate mathematical values, including pi.

Question 13

To create a random number in Python, use the ____ function.

Accepted Answer

The random.random() function is used to generate a random number in Python.

Question 14

The relational operator that means "not equal" is represented with which operator in Python?

Accepted Answer

The != operator in Python represents the "not equal" condition.

Question 15

Case Study 3: 1. if : 2. if : 3. 4. else: 5. 6. else: 7. if : 8. 9. else: 10. -Refer to the code in the accompanying case study. Under what circumstances are the statements on line 10 executed?

Accepted Answer

The statements on line 10 are executed when the first condition (line 1) is false, leading to the execution of the else block starting at line 6. Within this else block, if the condition in line 7 is also false, the else block at line 9 is executed, which contains the statements on line 10.

Question 16

The parameters passed to the print function are, by default, separated by a space when printed.

Accepted Answer

By default, the print function in Python uses a space as the separator between multiple arguments.

Question 17

The code in the accompanying case study 2 (see below) is used to calculate a running product.
>>> acc = 0
>>> for x in range(1, 6):
acc = acc + x
>>> acc
15

Accepted Answer

The code uses a running sum. It is using an accumulator.

Question 18

When using the Wallis function, the larger the value of the parameter passed into the function, the less accurate the result. Therefore, wallis(100) will be more accurate than wallis(10000).

Accepted Answer

The larger the value, the more accurate the result.

Question 19

Another name for an if statement is a selection statement.

Accepted Answer

An if statement is often referred to as a selection statement because it selects which block of code to execute based on a condition.

Question 20

To create a drawing window, use the Screen constructor contained in the turtle module.

Accepted Answer

The turtle module in Python provides a Screen constructor to create a drawing window for turtle graphics.

Quiz 2: Pthon: Estimating PI: Math and Random Methods, Selection and Boolean Expressions, the Print Function

In order to use the sqrt() function, you must use which of the following Python statements?

Which of the following is a constant in the math module?

What equation relates pi to the circumference of a circle?

The ____ statement is used to terminate a function.

How many times will the following print statement be executed? >>> for sides in range(8, 100, 8) : Print(sides, archimedes(sides) )

Case Study 2: >>> acc = 0 >>> for x in range(1, 6) : acc = acc + x >>> acc 15 -Refer to the session in the accompanying case study 2. Which of the following is the initialization statement?

Case Study 2: >>> acc = 0 >>> for x in range(1, 6) : acc = acc + x >>> acc 15 -Refer to the session in the accompanying case study 2. What type of variable is acc?

What is the name of the formula that calculates pi using the following equation? π/4 = 1/1 - 1/3 + 1/5 - 1/7 + 1/9 …