Math Olympiad Questions for Class 11

Class 11 is one of the crucial stages of schooling. Giving Maths Olympiad Class 11 gives the students a lift to prepare for their board exams in their next standard. This Math Olympiad questions for class 11 caters to all boards, i.e., CBSE Boards, ICSE Boards, and other International boards. It requires much more dedication to clear up the Maths Olympiad exam.

Students can study from IMO previous year papers for class 11 that contain logical reasoning sections and help the students think out of the box. The students will get to know about the exam question pattern by studying through IMO previous year papers for class 11.

Benefits of Math Olympiad Questions for Class 11

  1. Maths Olympiad challenges the students to boost up their thinking and reasoning ability.
  2. Gives the students an opportunity to compete at the National or International level.
  3. Help the students to solve tricky questions without any hassle.

The students can practice questions from the sample paper and check out their accuracy in solving the problems. Also, you can download the sample questions PDF right through this site. Overall, the student will better understand the subject as these papers are specially designed by subject matter experts.

Syllabus for Math Olympiad Exams

These are the chapters covered in most of the Math Olympiad Exams.

Number Systems

In math, number systems are the means by which numbers are expressed mathematically with the help of a specific set of digits. There are basically four types of number systems.

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Polynomial expressions contain indeterminants and coefficients and can consist of additions, subtractions, multiplications, and other non-negative integer exponentiations of variables.

Example: x2 + y2 = 2.

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Coordinate Geometry

A coordinate system is also known as coordinate geometry; it is used to determine the position of several points or other geometric elements on a given space using a set of numbers.

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Linear Equations in Two Variables

Linear equations in two variables are written in the ax + by + c = 0, where the coefficients a, b, and c would be for variables x and y, respectively.

This equation is ax + b + c = 0, where the coefficients are real numbers a, b, c. Solving an equation means finding the solutions. There can be infinitely many solutions to an equation with two variables.

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Introduction to Euclid’s Geometry

It concerns the possibility of resuming a set of infinitely appealing axioms to obtain many more propositions from them.

Based on axioms and theorems introduced by Greek mathematician Euclid, this can be described as the study of solid figures.

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Lines and Angles

In mathematics, a straight line is defined as a line followed by a point travelling in a constant direction with no curvature. Straight lines connect two points shortest distance.

Lines can be divided into many types, such as horizontal, perpendicular, vertical, and parallel.

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Triangles can be defined as a plane figure which has three straight sides and also three angles made by the intersection of these three sides.

Elements of a triangle include the vertices, sides and the angles of a triangle.

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Quadrilaterals can be defined as four-sided polygons which consist of four angles Within themselves.

Quadrilaterals can be of several types depending upon the specificity of these sides, angles, and diagonally.

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Areas of Parallelograms and Triangles

A triangle is a two-dimensional figure consisting of three lines and corners.

Properties of a Triangle:

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The circle is a location of a point that progresses at a regular distance from a fixed point. These fixed points are called the centre of the circle and this regular distance is called a Radius. If we consider r as the radius of the circle the diameter becomes d=2r.

Diameter is the maximal distance between any of the two points given in a particular circle.

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In geometry, construction refers to drawing angles, shapes, or lines correctly.

The geometrical figures are drawn using a compass and ruler. Compass is used to draw an arc or a circle while rulers are used to draw line segments and calculate the length.

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Heron’s Formula

A Greek mathematician 'Hero' of Alexandria discovered Heron's formula also called (Hero's formula) around 2000 years ago.

If you want to calculate the area of a triangle firstly you need to know the lengths of all three boundaries, then onwards you can calculate the area using the heron's formula.

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Surface Areas and Volumes

Any three-dimensional geometric shape's surface area and volume can be computed. The area or region occupied by the object's surface is its surface area. The quantity of space accessible in an object is referred to as volume.

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Statistics is a discipline of applied mathematics concerned with gathering, organizing, and interpreting data. It's akin to studying the likelihood of occurrences occurring based on data gathering or known quantities of data.

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Probability is a numerical measure of the degree of uncertainty in various situations. It can have a positive value ranging from 0 to 1.

The words 'probably,' 'doubt, "most probably,' 'chances,' and so on all have ambiguous meanings.

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Free Sample Questions for

Question 1

Which of the following is the correct definition of equivalent systems?
A. A number's distance from zero on the number line.
B. An inequality in two variables whose graph is a region of the half plane.
C. A set of two or more equations that use the same variables.
D. Systems that have the same solutions.

Question 2

Write 13^3 = 2197 in logarithmic form.
A. log_13 3 = 2197
B. log_2197 3 = 13
C. log_13 2197 = 3
D. log_2197 13 = 3

Question 3

Which function represents exponential decay?
A. f(x) = 2^x
B. f(x) = 8(0.9)^x
C. f(x) = 6x^2
D. f(x) = 0.9 * x

Question 4

Write 4^2 = x in logarithmic form.
A. log_x4=2
B. log_4x=2
C. log_x2=4
D. log_4 2=x

Question 5

There are 26 slips of equally sized paper in a bag, each with a different letter of the alphabet. Margret will choose 8 of these, one at a time. What is the probability that she will spell the word "light" as she chooses pieces of paper? There can be no spaces between the letters of "light", and the letters before and/or after do not matter.
A. 6.7 xx 10^{-3}
B. 5.1 xx 10^{-7}
C. 6.4 xx 10^{-11}
D. 6.1 xx 10^{-11}

Question 6

Let x represent the real axis and y the imaginary axis in the graph below. Given the complex number 2+4i, represented by C, which of the following represents its conjugate?
A. H
B. D
C. B
D. Its conjugate is not represented by any given value on this graph.

Question 7

Convert (13pi)/36 to degrees.
A. 90
B. 125
C. 65
D. 275

Question 8

Find the domain of f where f (x) = (x^2-16)/(x^2-3x+2.
A. (-oo, 1) U (1, 2) U (2, oo)
B. (oo) U (oo)
C. (-oo, 1) U (2, oo)
D. (-oo, 1) U [1, 2] U (2, oo)

Question 9

Simplify the expression (x-7)/(x^2-x-42).
A. 1/(x+7), \ x!=-6
B. 1/(x+6), \ x!= 7
C. x+7, \ x!= -6, 7
D. x+6, \ x!= -6, 7

Question 10

What is the inverse of f(x) = 3/(x-1) ?
A. f^{-1}(x) = (x+1)/3
B. f^{-1}(x) = (x+3)/x
C. f^{-1}(x) = 3/(x+1)
D. f^{-1}(x) = 4/x