Mathematics Olympiad Sample Papers for Class 12

Math Olympiad Sample Paper for Class 12

Welcome to the Math Olympiad Sample Paper for Class 12! This paper is designed to help students practice and strengthen their math skills through engaging questions, activities, and creative exercises. The focus is on algebra, geometry, trigonometry, calculus, arithmetic, and logical reasoning.

Algebra

Questions:

Solve for x: x^2 - 6x + 9 = 0
If a + b = 12 and a - b = 6, find a and b.
Expand: (x - 3)^2
Find the value of: 5a^2 - 2b, if a = 3, b = 4

Geometry

Draw a triangle with sides 9 cm, 12 cm, and 15 cm.
What is the sum of the angles in a decagon?
Define a parallelogram and list its properties.

Trigonometry

Find the value of sin 45° + cos 45°.
If tan θ = √3, what is the value of θ?
State the sine rule.

Calculus

Find the derivative of x^2 + 3x + 2.
Integrate: ∫(2x) dx
What is the area under the curve y = x from x = 0 to x = 2?

Arithmetic

Find the HCF of 60 and 90.
Calculate: 425 × 22
What is 2200 ÷ 44?

Word Problems

A train travels 360 km in 6 hours. What is its average speed?

Sample Questions

Solve: 2x^2 - 8 = 0
What is the area of a triangle with base 15 cm and height 10 cm?
Draw a circle and mark its chord.
Write the next term in the sequence: 10, 20, 40, 80, ___?

Practice Activity

Activity:

List all prime numbers between 100 and 150.
Draw a parallelogram and color it.

Fun Activity

Create a calculus puzzle for your friends and solve it together.