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
The areas of two similar triangles are 81 cm2 and 49 cm2, respectively, then what will be the ratio of their corresponding medians?
Q.2
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.3
Simplify the following expression: [(a - b)3 - (a + b)3 ]/2 + a(a2 + 3b2)
Q.4
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.5
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.6
The houses of a row are numbered consecutively from 1 to 49. If there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find the value of x.
Q.7
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.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
The shadow of a pole standing on a horizontal plane is d metre longer when the Sun's altitude is α than when it is β. What is the height of the pole?
Q.10
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.
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
c
Q.2
b
Q.3
d
Q.4
d
Q.5
a
Q.6
d
Q.7
d
Q.8
c
Q.9
c
Q.10
c
Answers to Sample Questions from CREST Olympiads:
Q.1 : c | Q.2 : b | Q.3 : d | Q.4 : d | Q.5 : a | Q.6 : d | Q.7 : d | Q.8 : c | Q.9 : c | Q.10 : c
