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
Two vertices of a triangle are (5, -1) and (-2, 3). If the orthocentre of the triangle is the origin, find the third vertex.
Q.2
Solve and find the roots of the equation: 2(x2 - 6) = 3(x - 4)
Q.3
If [(x - a)/(b + c)] + [(x - b)/(c + a)] + [(x - c)/(a + b)] = 3, then find the value of x:
Q.4
What is the value of the expression [(a - b)3 + (b - c)3 + (c - a)3] / [(a - b)(b - c)(c-a)]?
Q.5
f(x) = x4 - 2x3 + 3x2 - ax + b is a polynomial such that when it is divided by (x - 1) and (x + 1), the remainders are 5 and 19, respectively. Determine the remainder when f(x) is divided by (x - 2).
Q.6
Two regular polygons are such that the ratio between their number of sides is 1:2 and the ratio of measures of their interior angles is 3:4. Find the number of sides of each polygon.
Q.7
If sin A = √3/2 and A is an acute angle, then find the value of (tanA - cot A)/(√3 + cosec A).
Q.8
Which term is numerically greatest term in the expansion of (3 + 2x)49, when x = 1/5?
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.
Q.10
30% of the items were sold at a profit of 40% while the remaining were sold at x% loss. If the overall loss is 10%, find the value of x.
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
d
Q.2
d
Q.3
b
Q.4
d
Q.5
b
Q.6
a
Q.7
b
Q.8
c
Q.9
c
Q.10
c
Answers to Sample Questions from CREST Olympiads:
Q.1 : d | Q.2 : d | Q.3 : b | Q.4 : d | Q.5 : b | Q.6 : a | Q.7 : b | Q.8 : c | Q.9 : c | Q.10 : c
