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
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.
Q.2
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.3
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.
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?
Q.5
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.6
The volume of the vessel, in the form of a right circular cylinder, is 448π cm3 and its height is 7 cm. What is the radius of its base?
Q.7
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.8
The arithmetic mean of the squares of the first n natural number is:
Q.9
Simplify the following expression: [(a - b)3 - (a + b)3 ]/2 + a(a2 + 3b2)
Q.10
If 3y + 4x = 1, y = x + 5 and 5y + bx = 3 are concurrent, find the value of 'b'.
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
b
Q.2
b
Q.3
a
Q.4
b
Q.5
b
Q.6
d
Q.7
c
Q.8
c
Q.9
d
Q.10
c
Answers to Sample Questions from CREST Olympiads:
Q.1 : b | Q.2 : b | Q.3 : a | Q.4 : b | Q.5 : b | Q.6 : d | Q.7 : c | Q.8 : c | Q.9 : d | Q.10 : c
