CREST Mathematics Olympiad Class 10 Sample Paper

Q.1

For an acute angle θ, sin θ + cos θ takes the greatest value when θ is:

Q.2

Solve and find the roots of the equation:
2(x² - 6) = 3(x - 4)

Q.3

The shadow of a pole standing on a horizontal plane is d metre longer when the Sun's altitude is α than when it is β. What is the height of the pole?

Q.4

Perpendiculars are drawn from the vertex of the obtuse angles of a rhombus to its sides. The length of each perpendicular is equal to a unit. The distance between their feet is equal to b units. Find the area of the rhombus.

Q.5

If cos x / (1 + cosec x) + cos x / (cosec x - 1) = 2, then which one of the following is one of the values of x?

Q.6

In the binomial expansion of (a - b)ⁿ, n ≥ 5 the sum of the 5^th and 6^th terms is zero. Find the value of a/b.

Q.7

Inside a triangular park, there is a flower bed forming a similar triangle. Around the flower bed runs a uniform path of such a width that the sides of the park are exactly double the corresponding sides of the flower bed. Find the ratio of the area of the path to the flower bed.

Q.8

Find the value of x + y in the solution of the equations x/4 + y/3 = 5/12 and x/2 + y = 1:

Q.9

In the given figure, PQRS is a square of side 7√2 cm. With P and R as centres and PQ as radius, the arcs QAS and QBS are drawn, respectively. Find the area of the shaded region (in cm²).

Q.10

Find the quadratic equation whose roots are reciprocal of the roots of the equation 3x² - 20x + 17 = 0.