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 arithmetic mean of the squares of the first n natural number is:
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
Find the value of x + y in the solution of the equations x/4 + y/3 = 5/12 and x/2 + y = 1:
Q.4
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.5
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.6
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.7
In the given figure, AB || DE and the area of the parallelogram ABFD is 24 cm2. Find the areas of triangles AFB, AGB, and AEB.
Q.8
Which term is numerically greatest term in the expansion of (3 + 2x)49, when x = 1/5?
Q.9
Write the general term in the expansion of (x2 -y)6:
Q.10
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.
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
c
Q.2
b
Q.3
b
Q.4
c
Q.5
a
Q.6
a
Q.7
b
Q.8
c
Q.9
b
Q.10
b
Answers to Sample Questions from CREST Olympiads:
Q.1 : c | Q.2 : b | Q.3 : b | Q.4 : c | Q.5 : a | Q.6 : a | Q.7 : b | Q.8 : c | Q.9 : b | Q.10 : b
