Questions Related to Most Asked Math Questions
Updated on June 11, 2025 | By Learnzy Academy
Q1. What are the surface area and volume formulas for common 3D shapes?
List of surface area and volume formulas for solid figures
| Shape | Surface Area | Volume |
|---|---|---|
| Cube | 6 × a² | a³ |
| Cuboid | 2(lb + bh + hl) | l × b × h |
| Sphere | 4πr² | (4/3)πr³ |
| Hemisphere | Curved: 2πr² Total: 3πr² | (2/3)πr³ |
| Cylinder | Curved: 2πrh Total: 2πr(h + r) | πr²h |
| Cone | Curved: πrl Total: πr(l + r) | (1/3)πr²h |
| Triangular Prism | bh + l(a + b + c) | (1/2) × b × h × l |
| Square Pyramid | b² + 2bl | (1/3) × b² × h |
Notes:
a = side of cube or triangle base
b = breadth or triangle base
l = length or slant height
h = height (vertical)
r = radius
π ≈ 3.1416
Q2. What is the difference between mean, median, and mode?
Mean:
The average of all numbers. Add all the numbers together and then divide by how many numbers there are.
Median:
The middle number when all numbers are arranged in order. If there is an even number of values, the median is the average of the two middle numbers.
Mode:
The number that appears most often in the list. A list can have no mode, one mode, or more than one mode.
Example:
Numbers: 3, 5, 7, 5, 10
Mean = (3 + 5 + 7 + 5 + 10) ÷ 5 = 30 ÷ 5 = 6
Arrange numbers in order: 3, 5, 5, 7, 10
Median = middle number = 5
Mode = number that appears most = 5
Q3. What is the LCM and HCF of two numbers?
LCM (Least Common Multiple) of two numbers is the smallest number that is a multiple of both numbers.
HCF (Highest Common Factor), also called GCD (Greatest Common Divisor), is the largest number that divides both numbers exactly.
How to find them:
- To find LCM, list the multiples of both numbers and pick the smallest common one.
- To find HCF, list the factors of both numbers and pick the biggest common one.
Example with 12 and 18:
Multiples of 12: 12, 24, 36, 48, ...
Multiples of 18: 18, 36, 54, 72, ...
Common multiples: 36, 72, ...
So, LCM = 36
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
Common factors: 1, 2, 3, 6
So, HCF = 6
Q4. How to convert fractions to decimals?
To convert a fraction like a/b to a decimal, divide the top number (a) by the bottom number (b).
Steps:
- Take the top number (numerator).
- Divide it by the bottom number (denominator).
- The answer is the decimal.
Example:
3/4 = 3 ÷ 4 = 0.75
Q5. How to find the area of a triangle?
Area of a triangle = (1/2) × base × height
Steps:
- Find the length of the base.
- Find the height (the straight distance from the base to the opposite corner, at a right angle).
- Multiply base and height.
- Divide the result by 2.
Example:
If base = 8 units and height = 5 units, then
Area = (1/2) × 8 × 5 = 20 square units.
Q6. How to solve a quadratic equation?
A quadratic equation looks like this:
ax² + bx + c = 0
(where a, b, and c are numbers, and a is not zero)
To solve it, use this formula:
x = (-b ± √(b² - 4ac)) ÷ (2a)
Steps:
Find a, b, and c from your equation.
Calculate the discriminant: D = b² - 4ac
Check D:
If D > 0, there are two real answers
If D = 0, there is one real answer
If D < 0, answers are imaginary (complex numbers)
Plug values into the formula to get the answers for x.
Example: Solve 2x² + 3x - 2 = 0
a = 2, b = 3, c = -2
Calculate D = 3² - 4 × 2 × (-2) = 9 + 16 = 25
Since D > 0, two real answers
Find x:
x = (-3 ± √25) ÷ (2 × 2)
x = (-3 ± 5) ÷ 4
So,
x₁ = (-3 + 5) ÷ 4 = 2 ÷ 4 = 0.5
x₂ = (-3 - 5) ÷ 4 = -8 ÷ 4 = -2
Q7. What is the factorial of 100?
100! means multiply all whole numbers from 100 down to 1.
So,
100! = 100 × 99 × 98 × ... × 3 × 2 × 1
For any number n,
n! = n × (n - 1) × (n - 2) × ... × 2 × 1
100! ≈ 9.33262154 × 10^157
This means the number is about 9.33 followed by 157 zeros.
Q8. What is 0 divided by 0?
0 divided by 0 is undefined.
Dividing means finding a number that times the divisor gives the dividend.
For example: 6 divided by 2 means: “What times 2 equals 6?” The answer is 3.
But for 0 divided by 0, we ask: “What times 0 equals 0?”
The answer could be any number because anything times 0 is 0.
Since there is no one right answer, we say 0 divided by 0 is undefined. It means we cannot find a single answer.