CREST Mathematics Olympiad (CMO) Class 10 Sample Paper

CLASS

10
SAMPLE PAPER

CREST Mathematics Olympiad (CMO)

Syllabus for CMO is available at https://www.crestolympiads.com/cmo-syllabus

Pattern And Marking Scheme
Class Topic/Section No. of Marks per Questions Total Marks
Questions
Practical Mathematics 25 1 25
Achiever’s Section 10
st th
1 to 4 2 20
Grand Total 35 - 45
Practical Mathematics 40 1 40
5th to 10th Achiever’s Section 10 2 20
Grand Total 50 - 60

1. If √a > √b > √c > √d, where a, b, c and d are consecutive natural numbers, then which
of the following is true?

(a) √a – √b > √c – √d (b) √c – √d > √a –√b
(c) √c – √d = √a – √b (d) None of the above

2. Places A and B are 100 km apart on a highway. One car starts from A and another from
B at the same time. If the car travels in the same direction, then they meet in 5 hours. If
they travel towards each other, then they meet in 1 hour. Find the speeds of both the
cars:

(a) 60 km/h, 40 km/h (b) 30 km/h, 45 km/h
(c) 45 km/h, 60 km/h (d) 75 km/h, 90 km/h

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3. A small terrace at a football ground comprises of 15 steps, each of which is 50 m long
and built of solid concrete. Each step has a rise of 1/4 m and a tread of 1/2 m. Calculate
the total volume of concrete required to build the terrace:

(a) 650 m3 (b) 750 m3
(c) 795 m3 (d) 845 m3

4. The co-ordinates of the mid-points of the sides of a triangle are (4, 2), (3, 3) and (2, 2).
What will be the co-ordinates of the centroid of the triangle?

(a) (3, 7/3) (b) (-3, -7/3)
(c) (3, -7/3) (d) (-3, 7/3)

5. The decorative block shown in the figure given below is made of two solids, a cube and
a hemisphere. The base of the block is a cube with the edge 5 cm and the hemisphere
fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block:

(a) 150 cm2 (b) 160.86 cm2
(c) 162.86 cm2 (d) 163.86 cm2

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6. There are 35 cards numbered from 1 to 35. A card is selected at random. What is the
probability that the drawing card will be a:
(i) multiple of 3 or 5.
(ii) prime number
(iii) multiple of 7, respectively?

(a) 15/35, 9/35, 1/5 (b) 19/35, 12/35, 12/35
(c) 16/35, 11/35, 1/7 (d) 21/35, 10/35, 9/35

7. A TV tower stands vertically on a bank of a canal. From the point on the other bank,
directly opposite the tower, the angle of elevation of the top of the tower is 60⁰. From
another point 20 m away from this point on line joining this point to the foot of the tower,
the angle of elevation of the top of the tower is 30⁰. Find the height of the tower:

(a) 10√3 m (b) 10 m
(c) 15 m (d) 24 m

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8. An archery target has three regions formed by three concentric circles as shown in the
figure given below. If the diameters of the circles are in the ratio 1: 2: 3, then find the
ratio of the areas of three regions:

(a) 1: 2: 4 (b) 1: 3: 4
(c) 1: 3: 5 (d) 2: 3: 4

Achiever’s Section
9. Let ABC be a right-angled triangle in which AB = 3 cm, BC = 4 cm and angle B = 90⁰.
BD is the perpendicular from B on AC. The circle through B, C and D is drawn. The
steps of constructions of a pair of tangents from A to this circle is given below. Which of
the following steps is incorrect?

Step I: Draw triangle ABC and perpendicular BD from B on AC.
Step II: Draw a circle with BC as a diameter. This circle will pass through D.
Step III: Let O be the mid-point of BC. Join AO.
Step IV: draw a circle with AO as diameter. This circle cuts the circle drawn in step II at
B and P. Join AO, AP and AB are desired tangents drawn from A to the circle
passing through B, C and D.

(a) Only step I (b) Only step II
(c) Only step III (d) Only step IV

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10. If the four sides of a quadrilateral ABCD are tangential to a circle, then which of the
following is true?

(a) AC + AD = BD + CD
(b) AB + CD = BC + AD
(c) AB + CD = AC + BD
(d) AC + AD = BC + AB

Answers
1. (b), 2. (a), 3. (b), 4. (a), 5. (d), 6. (c), 7. (a), 8. (c), 9. (d), 10. (b)

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