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
If 1/(a + b), 1/(b + c), and 1/(c + a) are in AP, then which of the following is true?
Q.2
A square is drawn by joining midpoints of the sides of a square. Another square is drawn inside the second square in the same way and the process is continued indefinitely. If, the side of the first square is 16 cm, then what is the sum of the areas of all the squares?
Q.3
Write the general term in the expansion of (x2 -y)6:
Q.4
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.5
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.6
A tower stands vertically on the ground. From a point on the ground which is 30 m away from the foot of a tower, the angle of elevation of the top of the tower is found to be 45⁰. Find the height of the tower.
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
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
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.10
Two regular polygons are such that the ratio between their number of sides is 1:2 and the ratio of measures of their interior angles is 3:4. Find the number of sides of each polygon.
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
a
Q.2
b
Q.3
b
Q.4
a
Q.5
c
Q.6
b
Q.7
d
Q.8
a
Q.9
c
Q.10
a
Answers to Sample Questions from CREST Olympiads:
Q.1 : a | Q.2 : b | Q.3 : b | Q.4 : a | Q.5 : c | Q.6 : b | Q.7 : d | Q.8 : a | Q.9 : c | Q.10 : a
