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
What is the value of the expression [(a - b)3 + (b - c)3 + (c - a)3] / [(a - b)(b - c)(c-a)]?
Q.2
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.3
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.
Q.4
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?
Q.5
A certain strain of virus occurs three times every 25 minutes. In how much time will it become 729 times its initial value?
Q.6
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.7
The arithmetic mean of the squares of the first n natural number is:
Q.8
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.9
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.10
The volume of a pyramid whose base is an equilateral triangle is 12 cm3. If the height of the pyramid is 3√3 cm, then find the length of each side of the base:
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
d
Q.2
d
Q.3
c
Q.4
a
Q.5
c
Q.6
b
Q.7
c
Q.8
c
Q.9
c
Q.10
c
Answers to Sample Questions from CREST Olympiads:
Q.1 : d | Q.2 : d | Q.3 : c | Q.4 : a | Q.5 : c | Q.6 : b | Q.7 : c | Q.8 : c | Q.9 : c | Q.10 : c
