CREST Mathematics Olympiad Class 10 Sample Paper

The Class 10 Maths Olympiad Sample Paper is a great tool for students to practise advanced concepts, improve accuracy, and get familiar with the Olympiad format.

What's Inside?

• MCQs based on key Class 10 topics
• Sections: Practical Mathematics & Achiever's Section
• Answer key with clear solutions

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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

Sample Questions

Q.1

Q.2

Q.3

Q.4

Q.5

Q.6

Q.7

Q.8

Q.9

Q.10

Q.1	If 1/(a + b), 1/(b + c), and 1/(c + a) are in AP, then which of the following is true?
	a) a2, b2, and c2 are in AP.		b) a2, b2, and c2 are in GP.
	c) b2, a2 and c2 are in HP.		d) b2, a2 and c2 are in AP.

Q.2	If sin A = √3/2 and A is an acute angle, then find the value of (tanA - cot A)/(√3 + cosec A).
	a) -2/5		b) 2/5
	c) 2/(3 + 2√3)		d) -2

Q.3	Find the value of x + y in the solution of the equations x/4 + y/3 = 5/12 and x/2 + y = 1:
	a) 1/2		b) 3/2
	c) 2		d) 5/2

Q.4	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.5	Which term is numerically greatest term in the expansion of (3 + 2x)49, when x = 1/5?
	a) 4th term		b) 5th term
	c) 6th term		d) 7th term

Q.6	Which among the following is a singleton set?
	a) The set A consisting of all prime numbers less than 10.		b) The set B consisting of all squares up to 10.
	c) The set C consisting of all numbers up to 10 that are neither prime nor composite.		d) The set D of all odd numbers up to 10.

Q.7	Two vertices of a triangle are (5, -1) and (-2, 3). If the orthocentre of the triangle is the origin, find the third vertex.
	a) (4, 7)		b) (4, -7)
	c) (-4, 7)		d) (-4, -7)

Q.8	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?
	a) π/2		b) π/3
	c) π/4		d) π/6

Q.9	If α, β are the roots of the equation x2 - 2x + 3 = 0, then find the equation whose roots are 1/α2 and 1/β2.
	a) 9x2 + 2x + 1 = 0		b) x2 + 2x + 1 = 0
	c) 9x2 - 2x + 1 = 0		d) 9x2 + 2x - 1 = 0

Q.10	Find the quadratic equation whose roots are reciprocal of the roots of the equation 3x2 - 20x + 17 = 0.
	a) 17x2 - 20x + 3 = 0		b) 17x2 + 20x + 3 = 0
	c) 17x2 - 20x - 3 = 0		d) 17x2 + 20x - 3 = 0

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