# Quiz 1#

## Question 1#

An if{.python} statement can have how many elif{.python} parts?

• [ ] 0 \

• [x] Unlimited, i.e., 0 or more \

• [ ] 1 \

## Question 2#

Consider the Boolean expression not (p or not q){.python}. Give the four following values in order, separated only by spaces:

the value of the expression when p{.python} is True{.python}, and q{.python} is True{.python},

the value of the expression when p{.python} is True{.python}, and q{.python} is False{.python},

the value of the expression when p{.python} is False{.python}, and q{.python} is True{.python},

the value of the expression when p{.python} is False{.python}, and q{.python} is False{.python},

Remember, each of the four results you provide should be True{.python} or False{.python} with the proper capitalization.

False False True False{.python}

## Question 3#

A common error for beginning programmers is to confuse the behavior of print{.python} statements and return{.python} statements.

• print{.python} statements can appear anywhere in your program and print a specified value(s) in the console. Note that execution of your pythonthon program continues onward to the following statement. Remember that executing a print{.python} statement inside a function definition does not return a value from the function.

• return{.python} statements appear inside functions. The value associated with the return{.python} statement is substituted for the expression that called the function. Note that executing a return{.python} statement terminates execution of the function definition immediately. Any statements in the function definition following the return{.python} statement are ignored. Execution of your pythonthon code resumes with the execution of the statement after the function call.

As an example to illustrate these points, consider the following piece of code:

def do_stuff():
print "Hello world"
return "Is it over yet?"
print "Goodbye cruel world!"

print do_stuff()


Note that this code calls the function do_stuff{.python} in the last print{.python} statement. The definition of do_stuff{.python} includes two print{.python} statements and one return{.python} statement.

Which of the following is the console output that results from executing this piece of code? While it is trivial to solve this question by cutting and pasting this code into CodeSkulptor, we suggest that you first attempt this problem by attempting to execute this code in your mind.

  Hello world
Is it over yet?
Goodbye cruel world!
Is it over yet?



\

  Hello world



\

  Hello world
Is it over yet?



\

  Hello world
Is it over yet?
Goodbye cruel world!



\

  Hello world
Is it over yet?



## Question 4#

Given a non-negative integer n{.python}, which of the following expressions computes the ten’s digit of n{.python}? For example, if n{.python} is 123, then we want the expression to evaluate to 2.

Think about each expression mathematically, but also try each in CodeSkulptor .

• [x] (n % 100 - n % 10) / 10{.python}\

• [x] ((n - n % 10) % 100) / 10{.python}\

• [ ] (n - n % 10) / 10{.python}\

% has the same precedence as multiplication and division in Python

Integer division may come handy too: 123 % 100 // 10

## Question 5#

The function calls random.randint(0, 10){.python} and random.randrange(0, 10){.python} generate random numbers in different ranges. What number can be generated by one of these functions, but not the other?

(Refer to the CodeSkulptor documentation .)

By the way, we (and most Python programmers) always prefer to use random.randrange(){.python} since it handles numerical ranges in a way that is more consistent with the rest of Python.

10

I recommend that you also get used to the Python documentation: random - functions for integers

## Question 6#

Implement the mathematical function $$f(x) = -5 x^5 69 x^2 - 47$$ as a Python function. Then use Python to compute the function values $$f(0)$$, $$f(1)$$, $$f(2)$$, and $$f(3)$$. Enter the maximum of these four values calculated.

def f(x):
return -5 * x**5 * 69 * x**2 - 47
max(f(0), f(1), f(2), f(3))


-47. (second check: the function is monotonic decreasing for x >= 0)

## Question 7#

When investing money, an important concept to know is compound interest.

The equation $$FV = PV (1 rate)^{periods}$$ relates the following four quantities.

• The present value ( PV ) of your money is how much money you have now.

• The future value ( FV ) of your money is how much money you will have in the future.

• The nominal interest rate per period ( rate ) is how much interest you earn during a particular length of time, before accounting for compounding. This is typically expressed as a percentage.

• The number of periods ( periods ) is how many periods in the future this calculation is for.

Finish the following code, run it, and submit the printed number. Provide at least four digits of precision after the decimal point.

def future_value(present_value, annual_rate, periods_per_year, years):
rate_per_period = annual_rate / periods_per_year
periods = periods_per_year * years

print "$1000 at 2% compounded daily for 3 years yields$", future_value(1000, .02, 365, 3)


future_value(500, .04, 10, 10){.python} should return 745.317442824

1061.8348011259045

def future_value(present_value, annual_rate, periods_per_year, years):
rate_per_period = annual_rate / periods_per_year
periods = periods_per_year * years

return present_value * (1 + rate_per_period) ** periods

print("$500 at 4% compounded every tenth of a year for 10 years yields$", future_value(500, .04, 10, 10))
print("$1000 at 2% compounded daily for 3 years yields$", future_value(1000, .02, 365, 3))


Note that exponentation has a higher precedence than multiplication.

## Question 8#

There are several ways to calculate the area of a regular polygon. Given the number of sides, $$n$$, and the length of each side, $$s$$, the polygon’s area is

$$\frac{n s^2}{ 4 \tan (\frac{\pi}{n})}$$

For example, a regular polygon with 5 sides, each of length 7 inches, has area 84.3033926289 square inches.

Write a function that calculates the area of a regular polygon, given the number of sides and length of each side. Submit the area of a regular polygon with 7 sides each of length 3 inches. Enter a number (and not the units) with at least four digits of precision after the decimal point.

Note that the use of inches as the unit of measurement in these examples is arbitrary. Python only keeps track of the numerical values, not the units.

32.705211996014306

def polygon_area(side_count, side_len):
import math
return side_count * side_len**2 / 4 / math.tan(math.pi/side_count)
print(polygon_area(5, 7))
print(polygon_area(7, 3))


## Question 9#

Running the following program results in the error

SyntaxError: bad input on line 8 ('return').

Which of the following describes the problem?

def max_of_2(a, b):
if a > b:
return a
else:
return b

def max_of_3(a, b, c):
return max_of_2(a, max_of_2(b, c))


Misspelled keyword
Misspelled variable name
Missing parenthesis
Wrong number of arguments in function call
Misspelled function name
Extra parenthesis
Incorrect indentation
Missing colon \

Incorrect indentation \

## Question 10#

The following code has a number of syntactic errors in it. The intended math calculations are correct, so the only errors are syntactic. Fix the syntactic errors.

Once the code has been fully corrected, it should print out two numbers. The first should be 1.09888451159. Submit the second number printed in CodeSkulptor . Provide at least four digits of precision after the decimal point.

define project_to_distance(point_x point_y distance):
dist_to_origin = math.square_root(pointx ** 2 + pointy ** 2)
scale == distance / dist_to_origin
print point_x * scale, point_y * scale

project-to-distance(2, 7, 4)


• 3.84609579056 Python 2 Codeskulptor

• 3.846095790563293 Python 3

def project_to_distance(point_x, point_y, distance):
import math
dist_to_origin = math.sqrt(point_x ** 2 + point_y ** 2)
scale = distance / dist_to_origin
# Python 2
# print point_x * scale, point_y * scale
# Python 3:
print(point_x * scale, point_y * scale)

project_to_distance(2, 7, 4)