## CREST Mathematics Olympiad Sample Papers

The CREST Mathematics Olympiad (CMO) is an international competitive exam held online for students in Classes KG-10. For students of Classes KG-2, there will be only one level. There will be 2 levels for students of Classes 3-10. The exam is an objective-type test that the students need to complete in 60 minutes. For students of Classes KG and 1, the exam will be parent/teacher assisted. The time of the exam will be 45 minutes for KG students.

For students of Classes KG-10 set to appear for the Mathematics CREST Olympiad (CMO) examination, nothing could be more apt than solving Maths Olympiad sample papers.

## CREST Mathematics Olympiad Class 10th Sample Questions

1. 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

2. 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)

3. 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

4. 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

5. 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

Note:
Math Olympiad Questions practice through sample papers is beneficial for the preparation as these help in many ways. Aspirants get to know the marks distribution for the questions, reduces time to attempt each question, help students get rid of the fear of the unknown, an important tool to boost the preparation in the last few weeks or months and more

Students from 3500+ schools across the globe participate in the International Mathematics Olympiad examination of CREST. The competitors are increasing every year to a large number making the exam more competitive and becoming quite challenging for the students to secure Top-rank.

Competing in the International Math Olympiad of CREST gives a great exposure to students of Classes KG-10 from an early age. It helps students to sharpen Mathematical skills, improves problem-solving skills, encourages imagination, analytical skills and more.

Students who did well in the Math Olympiad took sample papers to practice seriously and solved the questions many times to ensure that they meet the accuracy and at the same time increase the speed of solving the question. Practice Olympiad past papers rigorously to assess your performance and then perform better in the actual examination. Furthermore, you can practice from CREST Workbooks too.

CREST conducts Online Olympiad exams in Mathematics, Science, English, Reasoning, Cyber and Spell Bee (Winter and Summer). The standard of the questions asked in these exams encourages students to think, tests different skills in each exam subject and aims to level up the skills in the students through solving the questions asked in the exams.

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