Description
1 Part 1: Math quiz-generator / equation-solver – 40 points
You would like to help in your community center teach elementary and high school students math. To reach as many kids
as possible, you decided to write some software that can automate some tasks for you. As starting point, you decided to
make an automatic quiz generator and grader for elementary school pupils and a quadratic equation solver for highschool
pupils – but unlike the solver you did in your Lab 2, this quadratic equation solver needs to handle all possible cases
including those when the given quadratic equation has complex numbers for solutions. In case of elementary school pupils,
your understanding is that they already know well addition and multiplication but that they struggle with exponentiation
and its inverse.
For this part, I provided you with starter code in file called a2_part1_xxxxxx.py. Begin by replacing xxxxxx in file
name with your student number. Then open the file. Your solution (code) for this part must go into that file in clearly
indicated spaces. You are not allowed to delete or comment-out any parts of the provided code except for the keywords
pass.
For this part you need to submit two files: a2_part1_xxxxxx.py and a2_part1_xxxxxx.txt
a2_part1_xxxxxx.py needs to contain your program for Part 1 as explained above and a2_part1_xxxxxx.txt needs
to contain the proof that you tested your two core functions from this part, namely elementary_school_quiz and
high_school_quiz
1.1 The Core Functions
Your solution in a2_part1_xxxxxx.py must have two functions called: elementary_school_quiz and high_school_quiz.
You should design and test these functions first before moving onto the main part of the program. Here are specifications
for the two functions:
elementary_school_quiz: This function has two parameters, namely an integer flag that takes only values 0 or 1 and
an integer n that takes only values 1 or 2. If flag is 0, elementary_school_quiz helps practice the inverse of
exponentiation i.e. logarithm. But if flag is 1, elementary_school_quiz helps practice exponentiation. In both
cases only questins with base 2 will be asked. The function, elementary_school_quiz then generates n math
problems that a pupil must answer in turn. For each question, it generates one random number between 0 and 10
inclusively (check out python’s random module to see if there’s a useful function in there) and asks the pupil for the
answer to the math problem with the random number. Specifically, if flag is 0 and random number generated is,
for example, 5 the question asked should be: “2 to what is 32 i.e. what is the result of log2
(32)?”. (The reason 32
is picked is because 2
5 = 32. See section 3 for more examples. If flag is 1 and random number generated is, for
example, 6 the question asked should be: “What is the result of 2
6
?”
elementary_school_quiz then prompts the pupil for the answer, and checks if her answer is correct. At the end of
n questions, elementary_school_quiz returns the number of questions answered correctly.
high_school_quiz: This function has three parameters representing three real numbers for the coefficients of the quadratic
equation ax2 +bx+c = 0. The function displays/prints the equation frist and then prints its solutions. The function
must display correct and meaningful solutions given any three real numbers for coefficients a, b and c. See examples
2
in Section 3 to understand what that means. Please consider the examples to be a part of the function/program
specifications that must be followed.
Do not use Python’s complex numbers class to solve this problem.
1.2 The User Interaction i.e. the main part of the program
Now that you have the two functions that perform the core functionality, you want to make it more user friendly for the
pupils (after all, alas, the pupil may not know how to write code and call functions in Python shell). In the main part of
your program, write your code in specified places. You code must follow the behaviour indicated in the example runs in
Section 3.
For example, for elementary school pupils, called Mia, you will first ask her whether she would like to practice
exponentiation or its inverse. Then ask her how many practice questions she’d like (if she says 0, then your code should
not ask her to solve any math questions). Using her responses, call the elementary_school_quiz function with the
appropriate values. When it returns the number of correct answers, display a message to the pupil:
• If she go all questions correctly display on screen: Congratulations Mia! You’ll probably get an A tomorrow.
Good bye Mia!
• If she got half of them correctly display on screen: You did ok Mia, but I know you can do better. Good
bye Mia!
• If she did all incorrectly, display on screen: I think you need some more practice Mia. Good bye Mia!
For high school pupils, in the main part of your program in the specified places, you need to write some code that asks
the pupil for the coefficients a, b and c. Then you need to make the call to high_school_quiz to display the solutions.
After that your program should ask the pupil if they would like another quadratic equation solved. If the pupil says
anything but yes the program terminates by printing a good bye message as in the examples. Otherwise, as long as pupil
answers yes (and any form of typing yes should be acceptable, including with lots of white space before and after, and
with capital letters and lower case letter etc), she should be asked for the coefficients again and the resulting new quadratic
equation should be solved. Since you have not seen while loops yet, I provided the code for that in a2_part1_xxxxxx.py.
The rest of the specifications for your program in Part 1 can be inferred from examples in Section 3. You will notice
that the program is required to display greetings surrounded with stars. You may write a separate function for that.
2 Part 2: A Library of Functions
For this part of the assignment, you are required to write and test four functions (as you did in Assignment 1). You
need to save all functions in part2_xxxxxx.py where you replace xxxxxx by your student number. You need to test your
functions (like you did in Assignment 1) and copy/paste your tests in part2_xxxxxx.txt. Thus, for this part you need
to submit two files: a2_part2_xxxxxx.py and a2_part2_xxxxxx.txt
2.1 min_enclosing_rectangle(radius, x, y) – 5 points
Computing a smallest (axis-aligned) rectangle that encloses a set of objects in the plane is a very common computational
problem arising in graphics and thus game development too. Write a function, called min_enclosing_rectangle, that has
3 input parameters. The first is a number representing a radius of a circle and the next two are two numbers representing
the x- and y-coordinates of its center. Consider the smallest axis-aligned rectangle that contains that circle. The function
should return the x- and y-coordinates of the bottom-left corner of that rectangle. If radius is a negative number,
min_enclosing_rectangle should return None.
>>> min_enclosing_rectangle(1,1,1)
(0, 0)
>>> min_enclosing_rectangle(4.5, 10, 2)
(5.5, -2.5)
>>> min_enclosing_rectangle(-1, 10, 2)
>>> min_enclosing_rectangle(500, 1000, 2000)
(500, 1500)
2.2 vote_percentage (results) – 5 points
Write a function called vote_percentage that takes a string as input. The function has one input parameter, called
results. Your function should count the number of substrings ’yes’ in the string results and the number of substrings ’no’
3
in the string results, and it should return the percentage of ’yes’ (among all ’yes’ and ’no’). (You may assume that string
results has at least one yes or no and that the only words present are yes, no and/or abstained).
Hint: you may use count method from Python’s str module/library.
>>> vote_percentage(‘yes yes yes yes yes abstained abstained yes yes yes yes’)
1.0
>>> vote_percentage(‘yes,yes, no, yes, no, yes, abstained, yes, yes,no’)
0.6666666666666666
>>> vote_percentage(‘abstained no abstained yes no yes no yes yes yes no’)
0.5555555555555556
>>> vote_percentage(‘no yes no no no, yes yes yes no’)
0.4444444444444444
2.3 vote() – 5 points
If there is a vote at a meeting, there are several possible outcomes based on the number of yes and no votes (abstains
are not counted). If all the votes are yes, then the proposal passes “unanimously”, if at least 2/3 of the votes are yes,
then the proposal passes with “super majority”, if at least 1/2 of the votes are yes, then the proposal passes by “simple
majority”, and otherwise it fails. Write a function called vote that asks a user to enter all yes-s and no-s and abstained-s
and then press enter. The function then prints the outcome of the vote. You solution must involve making a call to
function vote_percentage (You may assume that the user will enter at least one yes or no and that the only words present
are yes, no and/or abstained)
>>> vote()
Enter the yes, no, abstained votes one by one and then press enter:
yes yes yes yes yes abstained abstained yes yes yes yes
proposal passes unanimously
>>> vote()
Enter the yes, no, abstained votes one by one and then press enter:
yes,yes, no, yes, no, yes, abstained, yes, yes,no
proposal passes with super majority
>>> vote()
Enter the yes, no, abstained votes one by one and then press enter:
abstained no abstained yes no yes no yes yes yes no
proposal passes with simple majority
>>> vote()
Enter the yes, no, abstain votes one by one and then press enter:
no yes no no no, yes yes yes no
proposal fails
2.4 l2lo(w) – 5 points
Write a function called l2lo(w) that takes a non-negative number w as input and returns a pair of numbers (l,o) such
that w = l + o/16 and l is an integer and o is a non-negative number smaller than 16. Note that the solution l and o
are unique.
>>> l2lo(7.5)
(7, 8.0)
>>>
>>> l2lo(9.25)
(9, 4.0)
>>>
3 Testing your code in Part 1
Here is how you should test your two functions from Part 1 in Python shell.
>>> elementary_school_quiz(0,2)
Question 1:
2 to what is 256 i.e. what is the result of log_2 (256)? 7
Question 2:
2 to what is 8 i.e. what is the result of log_2 (8)? 3
1
>>> elementary_school_quiz(0,1)
Question 1:
4
2 to what is 64 i.e. what is the result of log_2 (64)? 5
0
>>> elementary_school_quiz(0,1)
Question 1:
2 to what is 16 i.e. what is the result of log_2 (16)? 4
1
>>> elementary_school_quiz(1,1)
Question 1:
What is the result of 2^10? 512
0
>>> elementary_school_quiz(1,1)
Question 1:
What is the result of 2^1? 2
1
>>> elementary_school_quiz(1,2)
Question 1:
What is the result of 2^9? 512
Question 2:
What is the result of 2^8? 256
2
>>>
>>> high_school_quiz(1,3,1)
The quadratic equation 1·x^2 + 3·x + 1 = 0
has the following real roots:
-0.3819660112501051 and -2.618033988749895
>>>
>>>
>>> high_school_quiz(3,2,15)
The quadratic equation 3·x^2 + 2·x + 15 = 0
has the following two complex roots:
-0.3333333333333333 + i 2.2110831935702664
and
-0.3333333333333333 – i 2.2110831935702664
>>>
>>>
>>> high_school_quiz(3,2,-15)
The quadratic equation 3·x^2 + 2·x + -15 = 0
has the following real roots:
1.9274433277084226 and -2.5941099943750894
>>>
>>>
>>> high_school_quiz(1,2,1)
The quadratic equation 1·x^2 + 2·x + 1 = 0
has only one solution, a real root:
-1.0
>>>
>>>
>>> high_school_quiz(0,2,4)
The linear equation 2·x + 4 = 0
has the following root/solution: -2.0
>>>
>>>
>>> high_school_quiz(0,0,0)
The quadratic equation 0·x + 0 = 0
is satisfied for all numbers x
>>>
>>>
>>> high_school_quiz(0,0,10)
The quadratic equation 0·x + 10 = 0
is satisfied for no number x
Here is what pressing Run on your program (Part 1) should look like:
*******************************************
* *
* __Welcome to my math quiz-generator__ *
* *
*******************************************
What is your name? Vida
Hi Vida. Are you in? Enter
1 for elementary school
2 for high school or
3 or other character(s) for none of the above?
5
1
****************************************************************************
* *
* __Vida, welcome to my quiz-generator for elementary school students.__ *
* *
****************************************************************************
Vida what would you like to practice? Enter
0 for inverse of exponentiation
1 for exponentiation
0
How many practice questions would you like to do? Enter 0, 1, or 2: 2
Vida, here is your 2 questions:
Question 1:
2 to what is 2 i.e. what is the result of log_2 (2)? 1
Question 2:
2 to what is 16 i.e. what is the result of log_2 (16)? 4
Congratulations Vida! You’ll probably get an A tomorrow.
Good bye Vida!
Another example run:
*******************************************
* *
* __Welcome to my math quiz-generator__ *
* *
*******************************************
What is your name? Vida Dujmovic
Hi Vida Dujmovic. Are you in? Enter
1 for elementary school
2 for high school or
3 or other character(s) for none of the above?
Ah
Vida Dujmovic you are not a target audience for this software.
Good bye Vida Dujmovic!
Another example run:
>>>
*******************************************
* *
* __Welcome to my math quiz-generator__ *
* *
*******************************************
What is your name? Arya Stark
Hi Arya Stark. Are you in? Enter
1 for elementary school
2 for high school or
3 or other character(s) for none of the above?
2
************************************************************************
* *
* __quadratic equation, a·x^2 + b·x + c= 0, solver for Arya Stark__ *
* *
************************************************************************
Arya Stark, would you like a quadratic equation solved? YeS
Good choice!
Enter a number the coefficient a: 1
Enter a number the coefficient b: 2
Enter a number the coefficient c: 3
The quadratic equation 1.0·x^2 + 2.0·x + 3.0 = 0
has the following two complex roots:
-1.0 + i 1.4142135623730951
and
-1.0 – i 1.4142135623730951
6
Arya Stark, would you like a quadratic equation solved? yeS
Good choice!
Enter a number the coefficient a: -1
Enter a number the coefficient b: 10
Enter a number the coefficient c: 36
The quadratic equation -1.0·x^2 + 10.0·x + 36.0 = 0
has the following real roots:
-2.810249675906654 and 12.810249675906654
Arya Stark, would you like a quadratic equation solved? YES
Good choice!
Enter a number the coefficient a: 0
Enter a number the coefficient b: 2.5
Enter a number the coefficient c: 3.246
The linear equation 2.5·x + 3.246 = 0
has the following root/solution: -1.2984
Arya Stark, would you like a quadratic equation solved? yes
Good choice!
Enter a number the coefficient a: 0
Enter a number the coefficient b: 0
Enter a number the coefficient c: 2.5
The quadratic equation 0.0·x + 2.5 = 0
is satisfied for no number x
Arya Stark, would you like a quadratic equation solved? yes
Good choice!
Enter a number the coefficient a: 0
Enter a number the coefficient b: 0
Enter a number the coefficient c: 0
The quadratic equation 0.0·x + 0.0 = 0
is satisfied for all numbers x
Arya Stark, would you like a quadratic equation solved? NO
Good bye Arya Stark!
Another example run:
*******************************************
* *
* __Welcome to my math quiz-generator__ *
* *
*******************************************
What is your name? Ji-Ah
Hi Ji-Ah. Are you in? Enter
1 for elementary school
2 for high school or
3 or other character(s) for none of the above?
1
******************************************************************************
* *
* __ Ji-Ah, welcome to my quiz-generator for elementary school students.__ *
* *
******************************************************************************
Ji-Ah what would you like to practice? Enter
0 for inverse of exponentiation
1 for exponentiation
5
Invalid chose. Only 0 or 1 is accepted.
Good bye Ji-Ah!
Another example run:
*******************************************
* *
* __Welcome to my math quiz-generator__ *
* *
*******************************************
What is your name? Hippolyta
Hi Hippolyta. Are you in? Enter
1 for elementary school
2 for high school or
7
3 or other character(s) for none of the above?
1
*********************************************************************************
* *
* __Hippolyta, welcome to my quiz-generator for elementary school students.__ *
* *
*********************************************************************************
Hippolyta what would you like to practice? Enter
0 for inverse of exponentiation
1 for exponentiation
0
How many practice questions would you like to do? Enter 0, 1, or 2: 0
Zero questions. OK. Good bye
Good bye Hippolyta!
Another example run:
*******************************************
* *
* __Welcome to my math quiz-generator__ *
* *
*******************************************
What is your name? Leti
Hi Leti. Are you in? Enter
1 for elementary school
2 for high school or
3 or other character(s) for none of the above?
1
****************************************************************************
* *
* __Leti, welcome to my quiz-generator for elementary school students.__ *
* *
****************************************************************************
Leti what would you like to practice? Enter
0 for inverse of exponentiation
1 for exponentiation
1
How many practice questions would you like to do? Enter 0, 1, or 2: 5
Only 0,1, or 2 are valid choices for the number of questions.
Good bye Leti!
8
