Math-related operations in Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of complex math expression

What is the output of this Python code snippet?

Python

result = (3 + 5) * 2 ** 3 // 4 - 7 % 3
print(result)

A 13

B 15

C 14

D 16

💡 Hint

Remember the order of operations: parentheses, exponents, multiplication/division, addition/subtraction, and modulus.

First, (3 + 5) = 8. Then 2 ** 3 = 8. Multiply 8 * 8 = 64. Integer divide 64 // 4 = 16. Then 7 % 3 = 1. Finally, 16 - 1 = 15. The output is 15, option B.

❓ Predict Output

intermediate

Result of math functions usage

What is the output of this code?

Python

import math
value = math.ceil(math.sqrt(50)) + math.floor(math.log2(16))
print(value)

A 12

B 10

C 11

D 9

💡 Hint

Recall that sqrt(50) is about 7.07, ceil rounds up, log2(16) is exact.

math.sqrt(50) ≈ 7.07, ceil(7.07) = 8. log2(16) = 4, floor(4) = 4. Sum is 8 + 4 = 12. So correct output is 12, option A.

❓ Predict Output

advanced

Output of math with negative and float values

What is the output of this code snippet?

Python

import math
x = -3.7
result = math.ceil(x) + math.floor(x)
print(result)

A -5

B -6

C -8

D -7

💡 Hint

Remember how ceil and floor behave with negative floats.

math.ceil(-3.7) is -3 (smallest integer >= -3.7), math.floor(-3.7) is -4 (largest integer <= -3.7). Sum is -3 + (-4) = -7.

🧠 Conceptual

advanced

Understanding integer division and modulus

Given the code below, what is the value of 'result' after execution?

Python

a = 17
b = 5
result = (a // b) * b + (a % b)
print(result)

A 15

B 16

C 17

D 18

💡 Hint

Think about how integer division and modulus relate to the original number.

Integer division a//b gives how many times b fits into a. Multiplying back and adding remainder (a % b) reconstructs the original number a. So result is 17.

🔧 Debug

expert

Identify the error in math expression

What error does this code raise when executed?

Python

import math
value = math.sqrt(-1)
print(value)

A ValueError

B TypeError

C ZeroDivisionError

D No error, prints a complex number

💡 Hint

Square root of a negative number is not defined in real numbers.

math.sqrt() only works with non-negative real numbers. Passing -1 raises ValueError: math domain error.

Practice

1. Which operator in Python is used to find the remainder of a division?

easy

A. The multiplication operator *

B. The division operator /

C. The exponent operator **

D. The modulus operator %

Solution

1. Step 1: Understand the modulus operator

   The modulus operator % returns the remainder after division of one number by another.

2. Step 2: Compare with other operators

   The division operator / returns the quotient, exponent ** raises to power, and multiplication * multiplies numbers.

3. Final Answer:

   The modulus operator % -> Option D

4. Quick Check:

   Remainder = % operator [OK]

Hint: Remainder uses % operator in math [OK]

Common Mistakes:

• Confusing / with %
• Using * for remainder
• Thinking ** gives remainder

2. Which of the following is the correct operator syntax to calculate 3 to the power of 4 in Python?

easy

A. 3 ^ 4

B. 3 ^^ 4

C. 3 ** 4

D. pow(3, 4)

Solution

1. Step 1: Identify the exponent operator in Python

   Python uses ** to calculate powers, so 3 ** 4 means 3 to the power 4.

2. Step 2: Check other options

   3 ^ 4 is bitwise XOR, pow(3, 4) is a function but not syntax operator, 3 ^^ 4 is invalid syntax.

3. Final Answer:

   3 ** 4 -> Option C

4. Quick Check:

   Power uses ** operator [OK]

Hint: Use ** for powers, not ^ [OK]

Common Mistakes:

• Using ^ instead of **
• Trying ^^ which is invalid
• Confusing pow() function with operator

3. What is the output of this Python code?

result = 10 % 3
print(result)

medium

A. 1

B. 3

C. 0

D. 10

Solution

1. Step 1: Calculate 10 modulo 3

   10 divided by 3 is 3 with remainder 1, so 10 % 3 equals 1.

2. Step 2: Understand print output

   The print statement outputs the value stored in result, which is 1.

3. Final Answer:

   1 -> Option A

4. Quick Check:

   10 % 3 = 1 [OK]

Hint: Modulo gives remainder after division [OK]

Common Mistakes:

• Confusing modulo with division
• Expecting quotient instead of remainder
• Misreading print output

4. Find the error in this code snippet:

value = 5 **
print(value)

medium

A. print() function is used incorrectly

B. Missing second operand for exponent operator

C. Exponent operator should be ^

D. Variable name 'value' is invalid

Solution

1. Step 1: Check the exponent operator usage

   The exponent operator ** needs two numbers, but here only one number (5) is given before it.

2. Step 2: Identify syntax error

   Because the second operand is missing, Python will raise a syntax error before print runs.

3. Final Answer:

   Missing second operand for exponent operator -> Option B

4. Quick Check:

   ** needs two numbers [OK]

Hint: Exponent needs two numbers, not one [OK]

Common Mistakes:

• Using ^ instead of **
• Thinking print() is wrong here
• Assuming variable name causes error

5. You want to calculate the area of a circle with radius 7 using Python. Which code correctly uses math operations to do this?

import math
radius = 7
area = ?
print(area)

hard

A. area = math.pi * (radius ** 2)

B. area = math.pi ** radius

C. area = pi * radius * radius

D. area = math.pi + radius ** 2

Solution

1. Step 1: Recall formula for circle area

   The area of a circle is π times radius squared, or π * r².

2. Step 2: Translate formula to Python code

   Use math.pi for π and radius ** 2 for radius squared, so math.pi * (radius ** 2).

3. Final Answer:

   area = math.pi * (radius ** 2) -> Option A

4. Quick Check:

   Area = π * r² [OK]

Hint: Use ** 2 for square, multiply by math.pi [OK]

Common Mistakes:

• Using addition instead of multiplication
• Using exponent on pi instead of radius
• Forgetting to square radius