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.
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
If p1 and p2 are two odd prime numbers such that p1 > p2, then p12 - p22 is:
Q.2
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.3
Find the quadratic equation whose roots are reciprocal of the roots of the equation 3x2 - 20x + 17 = 0.
Q.4
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?
Q.5
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?
Q.6
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.7
In the given figure, AB || DE and the area of the parallelogram ABFD is 24 cm2. Find the areas of triangles AFB, AGB, and AEB.
Q.8
W borrowed a certain sum of money from X at the rate of 10% per annum under simple interest and lent one-fourth of the amount to Y at 8% per annum under simple interest and the remaining amount to Z at 15% per annum under simple interest. If at the end of 15 years, W made a profit of $5850 in the deal, then find the sum that W had lent to Z.
Q.9
Simplify the following expression: [(a - b)3 - (a + b)3 ]/2 + a(a2 + 3b2)
Q.10
What is the value of the expression [(a - b)3 + (b - c)3 + (c - a)3] / [(a - b)(b - c)(c-a)]?
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
a
Q.2
c
Q.3
a
Q.4
c
Q.5
b
Q.6
d
Q.7
b
Q.8
c
Q.9
d
Q.10
d
Answers to Sample Questions from CREST Olympiads:
Q.1 : a | Q.2 : c | Q.3 : a | Q.4 : c | Q.5 : b | Q.6 : d | Q.7 : b | Q.8 : c | Q.9 : d | Q.10 : d
