SOF - IMO Level 2 Sample Papers for Class 10

Q.1

A piece of equipment cost a certain factory 600,000. If it depreciates in value, 15% the first year, 13.5 % the next year, 12% the third year, and so on, what will be its value at the end of 10 years, all percentages applying to the original cost?

Q.2

If 4x = sec θ and 4/x = tanθ then find 8(x² - 1/x²).

Q.3

The arc AB of the circle with centre at O and radius 10 cm has length 16 cm. What is the area of the sector bounded by the radii OA, OB and the arc AB?

Q.4

Two circles C1 and C2 touch each other internally at P. Two lines PCA and PDB meet the circles C1 in C, D and C2 in A, B respectively. If ∠BDC = 120°, then find the value of ∠ABP.

Q.5

For what value of k, the equation x² + 2(k - 4) x + 2k = 0 has equal roots?

Q.6

Find the sum and the product of the roots of the quadratic equation x² + 20x + 3 = 0.

Q.7

Find the quadratic equation whose roots are 3 and -1.

Q.8

What will come in place of the question mark (?) in the following number series?
1727, 1333, 997, ?, 507

Q.9

In a right-angled triangle, the product of two sides is equal to half of the square of the third side i.e. hypotenuse. One of the acute angle must be?

Q.10

A tower subtends an angle of 30° at a  point on the same level as the foot of the tower. At a second point h m above the first, the depression of the foot of tower is 60°. What is the horizontal distance of the tower from the point?