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
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.
Q.2
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.3
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.4
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.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
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
For an acute angle θ, sin θ + cos θ takes the greatest value when θ is:
Q.8
Find the value of x + y in the solution of the equations x/4 + y/3 = 5/12 and x/2 + y = 1:
Q.9
A bag contains 63 cards (numbered 1, 2, 3, ….., 63). Two cards are picked at random from the bag (one after another and without replacement). What is the probability that the sum of the numbers of both the cards drawn is even?
Q.10
The average mark obtained by the students in a class is 43. If the average marks obtained by 25 boys are 40 and the average marks obtained by the girl students are 48, then what is the number of girl students in the class?
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
b
Q.2
a
Q.3
b
Q.4
b
Q.5
b
Q.6
d
Q.7
b
Q.8
b
Q.9
d
Q.10
a
Answers to Sample Questions from CREST Olympiads:
Q.1 : b | Q.2 : a | Q.3 : b | Q.4 : b | Q.5 : b | Q.6 : d | Q.7 : b | Q.8 : b | Q.9 : d | Q.10 : a
