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
Find the values of a and b for which 3x3 - ax2 - 74x + b is a multiple of x2 + 2x - 24.
Q.2
The areas of two similar triangles are 81 cm2 and 49 cm2, respectively, then what will be the ratio of their corresponding medians?
Q.3
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
Q.4
In the given figure, PQRS is a square of side 7√2 cm. With P and R as centres and PQ as radius, the arcs QAS and QBS are drawn, respectively. Find the area of the shaded region (in cm2).
Q.5
The angles of elevation of the top of a tower from two points at distances m and n metres are complementary. If the two points and the base of the tower are on the same straight line, then what will be the height of the tower?
Q.6
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.7
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.8
If tan A = 1/2 and tan B = 1/3, then which of the following is true?
Q.9
W borrowed a certain sum of money from X at the rate of 10% per annum under simple interest and lent one-fourth of the amount to Y at 8% per annum under simple interest and the remaining amount to Z at 15% per annum under simple interest. If at the end of 15 years, W made a profit of $5850 in the deal, then find the sum that W had lent to Z.
Q.10
In the adjoining figure, the bottom of the glass has a hemispherical raised portion. If the glass is filled with orange juice, then find the quantity of juice which a person will get:
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
a
Q.2
c
Q.3
a
Q.4
d
Q.5
a
Q.6
b
Q.7
b
Q.8
a
Q.9
c
Q.10
b
Answers to Sample Questions from CREST Olympiads:
Q.1 : a | Q.2 : c | Q.3 : a | Q.4 : d | Q.5 : a | Q.6 : b | Q.7 : b | Q.8 : a | Q.9 : c | Q.10 : b
