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
Which term is numerically greatest term in the expansion of (3 + 2x)49, when x = 1/5?
Q.2
Inside a triangular park, there is a flower bed forming a similar triangle. Around the flower bed runs a uniform path of such a width that the sides of the park are exactly double the corresponding sides of the flower bed. Find the ratio of the area of the path to the flower bed.
Q.3
If [(x - a)/(b + c)] + [(x - b)/(c + a)] + [(x - c)/(a + b)] = 3, then find the value of x:
Q.4
If 3y + 4x = 1, y = x + 5 and 5y + bx = 3 are concurrent, find the value of 'b'.
Q.5
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.6
If p1 and p2 are two odd prime numbers such that p1 > p2, then p12 - p22 is:
Q.7
Ken and Paul can complete a job in 40 days and 50 days, respectively. They worked on alternative days to complete it. Find the minimum possible time in which they could have completed it.
Q.8
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.9
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.10
The following steps are involved in finding a number, if the positive number is less than its square by 30. Arrange them in sequential order:
(A) x2 - x - 30 = 0 (B) x = 6 (C) x2 - x = 30 (D) (x + 5) (x - 6) = 0
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
c
Q.2
d
Q.3
b
Q.4
c
Q.5
d
Q.6
a
Q.7
a
Q.8
a
Q.9
b
Q.10
a
Answers to Sample Questions from CREST Olympiads:
Q.1 : c | Q.2 : d | Q.3 : b | Q.4 : c | Q.5 : d | Q.6 : a | Q.7 : a | Q.8 : a | Q.9 : b | Q.10 : a
