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

Question 1

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

A) use math;
B) import math;
C) math::sqrt();
D) return sqrt();

Answer 1

B

Question 2

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

A) sqrt
B) tan
C) asin
D) e

Answer 2

D

Question 3

What equation relates pi to the circumference of a circle?

A) C = 2πr (where r is the radius of the circle)
B) C = πr (where r is the radius of the circle)
C) C = 2πd (where d is the diameter of the circle)
D) C = 2πa (where a is the area of the circle)

Answer 3

A

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?

A) innerAngleB = 360.0 / numSides
B) oneHalfSideS = math.sin(math.radians(halfAngleA))
C) pi = polygonCircumference / 2
D) sideS = oneHalfsideS * 2

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?

A) 2
B) 8
C) 64
D) pi

Question 6

The ____ statement is used to terminate a function.

A) return
B) exit
C) end
D) quit

Question 7

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

A) 1
B) 8
C) 12
D) 16

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?

A) acc
B) for x in range(1, 6):
C) acc = acc + x
D) acc = 0

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?

A) Accumulator variable
B) Range variable
C) Initialization variable
D) Timer variable

Question 10

What is the name of the formula that calculates pi using the following equation?
&It;font_face=symbol> &It;/font>/4 = 1/1 - 1/3 + 1/5 - 1/7 + 1/9 …

A) Archimedes approach
B) Leibniz formula
C) Wallis formula
D) Monte Carlo simulation

Question 11

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

A) must be initialized to zero.
B) is increased by two each iteration.
C) must be initialized to one.
D) is multiplied by two each iteration.

Question 12

The ____ uses probability and random behavior to calculate pi.

A) Archimedes approach
B) Leibniz formula
C) Wallis formula
D) Monte Carlo simulation

Question 13

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

A) math.random()
B) random.random()
C) montecarlo.random()
D) help.random()

Question 14

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

A) ==
B) !=
C) &It;=
D) >=

Question 15

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

A) The condition in line 1 is false, and the condition in line 7 is false.
B) The condition in line 1 is false, and the condition in line 7 is true.
C) The condition in line 1 is true, and the condition in line 7 is false.
D) The condition in line 1 is true, and the condition in line 7 is true.

Question 16

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

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

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).

Question 19

Another name for an if statement is a selection statement.

Question 20

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

Question 21

1. Match each definition with its term.
-True or False

A) Boolean values
B) Selection statement
C) Logical operators
D) Relational expressions

Question 22

1. Match each definition with its term.
-Contains a question and other groups of statements that may or may not be executed, depending on the result of the question.

A) Boolean values
B) Selection statement
C) Logical operators
D) Relational expressions

Question 23

1. Match each definition with its term.
-and, or, and not

A) Boolean values
B) Selection statement
C) Logical operators
D) Relational expressions

Question 24

1. Match each definition with its term.
-Compares two data values.

A) Boolean values
B) Selection statement
C) Logical operators
D) Relational expressions

Question 25

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. Explain, in general terms, how to modify this series of statements in such a way that you would be able to change the number of sides and try the calculation again without needing to retype all of the statements.

Question 26

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. Explain what pattern this code implements and why it is useful.

Question 27

What are some patterns to keep in mind when implementing the Leibniz formula with Python?

Question 28

Explain how a Monte Carlo simulation can be used to calculate the value of pi.

Question 29

Explain the difference between the "=" in line 1 and the "==" in line 2 in the code sample below:
1. >>> apple = 25
2. >>> apple == 25
3. True

Question 30

Explain the term short-circuit evaluation of Boolean expressions. Use an example to illustrate what this means.

Question 31

Why are decisions referred to as "selection" in computer science?

Question 32

Case Study 3:
1. if &It;condition>:
2. if &It;condition>:
3. &It;statements>
4. else:
5. &It;statements>
6. else:
7. if &It;condition>:
8. &It;statements>
9. else:
10. &It;statements>
-Refer to the code in the accompanying Case study 3. Why is this section of code referred to as "nested selection"?

Question 33

Explain how to modify the coordinate system of the drawing window when using the turtle module.