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 value of x + y in the solution of the equations x/4 + y/3 = 5/12 and x/2 + y = 1:
Q.2
If sin A = √3/2 and A is an acute angle, then find the value of (tanA - cot A)/(√3 + cosec A).
Q.3
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.4
Find the quadratic equation whose roots are reciprocal of the roots of the equation 3x2 - 20x + 17 = 0.
Q.5
If 3y + 4x = 1, y = x + 5 and 5y + bx = 3 are concurrent, find the value of 'b'.
Q.6
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.7
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.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
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.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
b
Q.2
b
Q.3
d
Q.4
a
Q.5
c
Q.6
b
Q.7
a
Q.8
c
Q.9
a
Q.10
a
Answers to Sample Questions from CREST Olympiads:
Q.1 : b | Q.2 : b | Q.3 : d | Q.4 : a | Q.5 : c | Q.6 : b | Q.7 : a | Q.8 : c | Q.9 : a | Q.10 : a
