Math Expressions Homework

📝 Homework: Multiple Choice

1) What will the following Python code output?

x = 10
y = 3
print(x % y + x // y)

A. 4 B. 5 C. 6 D. 7

2) Which of the following best describes a mathematical expression in programming?

A. A sequence of steps used to solve a problem B. A combination of values, variables, and operators that evaluates to a single value C. A diagram that represents decision-making in code D. A way to store multiple values in a list

3) What is the value of result in the following code?

num1 = 8
num2 = 3
result = num1 * num2 - num1 / num2

A. 21.33 B. 22.0 C. 20.5 D. 21.0

4) What will this code output?

a = 15
b = 4
print(a // b)

A. 3.75 B. 4 C. 3 D. Error

5) Which of the following best represents a % b in Python?

A. Quotient of a divided by b B. Remainder when a is divided by b C. a raised to the power of b D. Absolute value of a - b

6) What is the value of result?

x = 2
y = 5
result = x ** y % 3

A. 2 B. 1 C. 0 D. 32

7) What will this print?

num = 7
print((num + 3) * 2 / 5)

A. 4.0 B. 5.0 C. 3.0 D. 2.0

8) Which expression correctly calculates the distance between points (x1, y1) and (x2, y2)?

A. sqrt((x2 - x1) + (y2 - y1)) B. sqrt((x2 - x1) * (y2 - y1)) C. sqrt((x2 - x1)**2 + (y2 - y1)**2) D. (x2 - x1) + (y2 - y1)

📝 Homework: Free Response

1) Write a function in Python that takes two numbers as inputs and returns the result of:

(x² + y²) ÷ (x + y)

Be sure to handle the case when x + y = 0.

2) Explain how order of operations (PEMDAS) affects the evaluation of:

result = 6 + 4 * 2 % 5

- Show the step-by-step evaluation.
- Write the final answer.

3) Write a Python function called calculate_mod_sum that takes three numbers a, b, and c, and returns the sum of a % b and b % c. Make sure your function handles cases where b or c is zero.

4) Create a Python program that calculates the area of a trapezoid. The formula for the area is:

area = ((base1 + base2) / 2) * height

Ask the user for base1, base2, and height, compute the area, and print the result.

5) Suppose a Fibonacci-like sequence starts with 3 and 5 (instead of 0 and 1). Write a Python function that returns the nth term of this sequence.

6) Explain step-by-step how Python evaluates the following expression using order of operations (PEMDAS):

result = 8 + 12 / 4 * 2 - 5 % 3

Include the intermediate steps and the final value of result.

7) Write a Python function distance_3d that calculates the distance between two points in 3D space: (x1, y1, z1) and (x2, y2, z2). Use the formula:

distance = sqrt((x2 - x1)**2 + (y2 - y1)**2 + (z2 - z1)**2)

Make sure your function accepts six arguments and returns the distance.

8) Consider the expression:

x = 7
y = 2
z = 3
result = x + y * z % 4

Explain step-by-step how Python calculates result and give the final value.