CREST Mathematics Olympiad Class 10 Previous Year Papers

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Syllabus:

Section 1: Real Numbers, Polynomials, Pair of Linear Equations in Two Variables, Quadratic Equations, Arithmetic Progressions, Triangles, Coordinate Geometry, Introduction to Trigonometry, Some Applications of Trigonometry, Circles, Constructions, Areas Related to Circles, Surface Areas and Volumes, Statistics, Probability.

Achievers Section: Higher Order Thinking Questions - Syllabus as per Section 1

Sample Paper Previous Year Paper Marking Scheme Free Study Material

Q.1

Q.2

Q.3

Q.4

Q.5

Q.6

Q.7

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Q.9

Q.10

Q.1	Ken and Paul can complete a job in 40 days and 50 days, respectively. They worked on alternative days to complete it. Find the minimum possible time in which they could have completed it.
	a) 44 2/5 days		b) 44 1/2 days
	c) 44 3/5 days		d) 44 4/5 days

Q.2	A tower stands vertically on the ground. From a point on the ground which is 30 m away from the foot of a tower, the angle of elevation of the top of the tower is found to be 45⁰. Find the height of the tower.
	a) 28 m		b) 30 m
	c) 32 m		d) 35 m

Q.3	The houses of a row are numbered consecutively from 1 to 49. If there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find the value of x.
	a) x = 33		b) x = 43
	c) x = 39		d) x = 35

Q.4	In ∆ABC, ∠B = 90⁰. P, Q and R are the midpoints of AB, BC and AC, respectively. Which of the following options can be the vertices of a cyclic quadrilateral?
	a) A, P, Q and R		b) B, P, R and Q
	c) C, Q P and R		d) All of these

Q.5	In the adjoining figure, the bottom of the glass has a hemispherical raised portion. If the glass is filled with orange juice, then find the quantity of juice which a person will get:
	a) 135 π cm3		b) 117 π cm3
	c) 99 π cm3		d) 36 π cm3

Q.6	If the sum of the roots of the equation ax2 + bx + c = 0 is equal to the sum of their squares, then which one of the following is correct?
	a) a2 + b2 = c2		b) a2 + b2 = a + b
	c) 2ac = ab + b2		d) 2c + b = 0

Q.7	Find the values of a and b for which 3x3 - ax2 - 74x + b is a multiple of x2 + 2x - 24.
	a) a = -5, b = 24		b) a = 5, b = 24
	c) a = 13, b = 16		d) a = -13, b = 16

Q.8	In the binomial expansion of (a - b)n, n ≥ 5 the sum of the 5th and 6th terms is zero. Find the value of a/b.
	a) (n - 5)/6		b) (n - 4)/5
	c) 5/(n - 4)		d) 6/(n - 5)

Q.9	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.
	a) √(a2 + b2) / 2√(b2 - a2)		b) 2ab / 2√(b2 - a2)
	c) ab2 / 2√(b2 - a2)		d) 2a2b2 / 2√(b2 - a2)

Q.10	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.
	a) 1:1		b) 1:2
	c) 1:3		d) 3:1

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Students can download the CREST Mathematics Olympiad previous year paper pdf for class 10 from this page. Each question in the paper carries 1 mark. The answer key for all the questions is also provided on the last page.

Students must become familiar with the exam format before taking any competitive exam, such as an Olympiad. CREST Mathematics Olympiad previous year paper will help students to become familiar with the exam pattern.

Once students complete their syllabus, they must start solving the CREST Mathematics Olympiad previous year paper for class 10 to analyze their preparation level. This is the proven way to excel in the CREST Mathematics Olympiad examination.

Additional Preparation Resources

Students can also refer to the following resources to level up their CREST Mathematics Olympiad (CMO) exam preparation for class 10 -

1. CREST Mathematics Worksheets Package for class 10 - It is a package of 5 worksheets. The worksheets are in the same pattern as the previous year paper. Hence, very useful for preparation. Existing users can purchase additional practice worksheets by following these steps: Login at https://www.crestolympiads.com/login -> Dashboard -> Additional Practice -> Buy & new users can visit https://www.crestolympiads.com/registration
2. CREST Mathematics Olympiad book for class 10 - The book covers topic-wise reading material, chapter-wise practice questions with answer key & contains the previous year paper. The book is available in both physical and pdf formats. Proceed now to purchase the Olympiad book. Also, students can view & download the first chapter of the Maths Olympiad book for class 10 for free.

Note: Don’t forget to download the CREST Mathematics Olympiad past year paper pdf for class 10.