Math Olympiad Questions for Class 12

It's everyone's dream to qualify for the Olympiad Exams and do so with flying colors. You'll have a better chance of getting a job in the future if you invest in it. Something is alarming about how even the brightest students can get stressed and lose focus. It's also challenging for students with outstanding academic records to do well on such tests.

These incidents happen because you don't practice and prepare well. For this reason, you need to take advantage of Olympiad Sample Question Papers. An Olympiad exam sample paper can be beneficial if you're aspiring to compete. It's a good idea to try some sample questions before attempting the test.

There's no doubt about it. As part of your registration for the Maths Olympiad class 12, you will receive a schedule containing information about preparing for the test.

Taking part in the International Mathematical Olympiad (IMO) can help you better understand classroom concepts. To ensure a bright future for yourself, compete in math competitions.

In these competitions, you'll be tested on your mathematical knowledge. Therefore, you can devise your solutions by thinking for yourself. Your fundamental perceptions of Math need to be taught properly. So you'd be better prepared for math tests and life in general.

Syllabus for Math Olympiad Exams

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

Relations and Functions

The relation refers to a relationship between the different sets of elements of the values with the complete pair of sets. These elements set in their first set are known as Domains. Further, which is related to the whole element set called the Range. Whereas Functions are known as relations are the complete set of the output.

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Inverse Trigonometric Functions

Many trigonometry functions are there that have their inverse. While getting the inverse of a trigonometric function, we will have to look at the co-domain and domain. Some trigonometric functions are sin x, cos x, tan x, etc.

Trigonometric functions

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Matrices and Determinants

The matrix and determinant both are part of maths. The matrix is termed as the numbers that are presented in a square box. There is proper order in a matrix that consists of the number of rows and the number of columns.

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Continuity and Differentiability

The continuity is always referred to as a function that is considered the features of the graphical presentation. At the same time, the differentiability of a function is the functions whose derivatives do exist at the domain of each point.

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Application of Derivatives

The term application of derivatives refers to the term rate of changing in the quantities, increasing and decreasing functions, maxima and minima, and many other terms. The maxima and minima of the functions include the maximum and minimum values of the function that are present in the functions.

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The term integral refers to the critical part of the calculus. It is used to find the central points, volumes, and other things. One is the problem of getting the function when a graph bounds a derivative and area. These problems are related to the definite and indefinite parts of integrals.

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Application of Integrals

The term integration refers to the areas of the two-dimensional regions, including calculating the 3-D volumes of objects. When we find the integral function of x, we get it along with the X-axis area. A problem related to the application of integrals is as follows:

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Differential Equations

The term differential equation refers to an equation that involves the dependent variable, independent variable, and another differential dependent variable coefficient. The differential equation is dy/dx or d2y/d2x.

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Vector Algebra

The term vector refers to the quantity that consists of both direction and magnitude.

Vector AB is a line segment.

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Three Dimensional Geometry

3-D geometry includes many concepts, including the direction cosines of a line, direct ratios of line, straight line, condition of perpendicularity, etc. Generally, the direction cosines of a line consist of making a line with the X and Y axis along with alpha, beta, and gamma.

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The probability words refer to the measurement of the certainty of degree present with the specific event. An experiment is a term that includes the operation with the help of which the set outcomes get produced.

There is a concerned formula that includes the favourable and real events to get the probability of a certain thing. We have to use this formula to get the probability. The event of one number is known as the trail.

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Linear Programming

Linear programming is associated with different sets of problems.

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Free Sample Questions for

Question 1

What is the slope of the tangent line of the function f(x) = 2x^3 - 4x^2 - 3x at x = 2?
A. 2
B. 4
C. 5
D. 7

Question 2

Is h(x)=(x-4)/(x^2-5x+4) continuous or discontinuous at x = 3? Justify using continuity test. If discontinuous, what type?
A. Continuous
B. Infinite discontinuity
C. Jump discontinuity
D. Removable discontinuity

Question 3

Which augmented matrix represents the system of equations 2x=8 and 6=3y+x?
A. [[2,8,,0],[6,3,,1]]
B. [[8,2,,0],[6,3,,1]]
C. [[0,2,,8],[6,3,,1]]
D. [[2,0,,8],[1,3,,6]]

Question 4

What is the maximum number of purely imaginary roots that the polynomial x^3-x^6-x-x^7 can have?
A. 7
B. 1
C. 3
D. 6

Question 5

Evaluate the limit.lim_{x->0^+} f(x) " where " f(x) = {{:(1 \ \ \ \ \ \ \ \ \ \ \ \, x<=0),(-x^2+4x-3, x>0):}
A. 1
B. 0
C. -3
D. does not exist

Question 6

Evaluate: lim_(x->1)-(x^2-1)/(x-1)
A. 0
B. 2
C. -2
D. undefined

Question 7

What x values must be excluded from the domain of f(x)=(-2)/(x+3) ?
A. x = 0
B. x = 3
C. x = -3
D. x = 2

Question 8

What are all the values of x for which the function f defined by f(x)=x^3+3x^2-9x+7 is increasing?
A. -3< x<1
B. -1< x< 1
C. x<-3 and x>1
D. x<-1 and x>3

Question 9

Evaluate int_0^pi-sin(x+pi) \ dx.
A. -1
B. 0
C. 1
D. 2

Question 10

Evaluate. lim_(x->2)(5x+2)
A. 12
B. 20
C. 5
D. 21