Math Olympiad Questions for Class 10

Throughout elementary, middle, and high schools, Math Olympiad competitions take place. By competing in Math Olympiads, participants develop their math skills and get involved in math.

Genius doesn't come from birth, but brilliance comes from a steep slope of IQ, rationality, and critical thinking. Getting students ready for and participating in the Math Olympiad class 10 can help them achieve this.

Taking part in the Math Olympiad increases your understanding of formulas and makes them fun. Once students become sharp-minded and clever problem solvers, they're well prepared for JEE and other competitive exams.

It's a good idea to use last year's Math olympiad questions for class 10 and IMO class 10 previous year papers to prepare for the exams.

The only resource for class 10 Math Olympiad questions is the Math Olympiad curriculum, so knowing it is the first and most important step to preparing for further training.

Suppose students practice Math Olympiad Worksheets and Math Olympiad sample questions frequently. In that case, they will increase their chances of passing the test quickly.

Syllabus for Math Olympiad Exams

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

Real Numbers

Real numbers are the complete set of rational or irrational numbers. The real numbers are denoted by R.

Every rational & irrational number is a real number. Natural numbers, whole numbers, and integers are other parts of the number system.

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Polynomials

The polynomials are the complete set of rational numbers exponents. They are algebraic expressions. Whereas in the polynomial, the variable exponent is the whole number.

Example of a polynomial:

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Pair of Linear Equations in Two Variables

The linear equations are in the form of ax + by + c = 0. When we see the linear equations, then they are in the form of a straight line. In the above equation, a, b, & c are real numbers, in which a & b are not equal to zero. At the same time, x & y are the two variables. And c is the constant.

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Quadratic Equations

Quadratic polynomials and quadratic equations are related terms. We have to look for the quadratic polynomial to get the quadratic equation. Generally, the quadratic polynomial is a term in which the degree of the polynomial is equal to two. And when we put these quadratic polynomials equal to zero.

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Arithmetic Progressions

The word arithmetic progression is a series of terms in which the numbers are present in the order sequence. And the difference between the consecutive numbers always remains constant. This sequence is also known as Arithmetic progression.

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Triangles

The term triangle refers to a figure that consists of three vertices and three sides. Triangles are of various types. All the types of triangles are different from each other.

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Coordinate Geometry

The term coordinate geometry refers to getting the solution with the help of algebraic methods. The major formula is present for the distance between two points that we have to use. The formula consists of x and y terms.

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Introduction to Trigonometry

Trigonometry refers to the statement that includes the relationship between the sides and right angles. Major trigonometric ratios are sin, cos, cot, tan, cosine, sec, etc.

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Some Applications of Trigonometry

Trigonometry refers to the statement that includes the relationship between the sides and right angles. Major trigonometric ratios are sin, cos, cot, tan, cosine, sec, etc.

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Circles

The circle is a term that has three possibilities, including the non-intersecting point, single common point, or two common points. In the single common point, the line will touch the circle, whereas the line will cut the circle in the two common points.

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Constructions

Construction refers to the concept that is related to shapes and figures. All the construction processes are the figures that we make with the help of different tools.

We have to draw the exact figures to make no mistakes in the angles.

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Areas Related to Circles

The circle is a term that has three possibilities, including the non-intersecting point, single common point, or two common points.

The line will touch the circle in the single common point, whereas the line will cut the circle in the two common points.

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Surface Areas and Volumes

The surface areas are the areas that are only calculated in 3-D shapes. The area where the object will occupy the space within the region. And the space in the object is the volume of the prescribed figure.

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Statistics

The term statistics include various terms, including the mean, median, and mode. The mean is the summation of all the nth terms, and the median is the middle value of all the selected terms. And mode is a term that occurs most of the time in the given series.

We have to take the cumulative frequency to get the solution to some terms.

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Probability

The term probability refers to the measurement of the degree of certainty concerning the event's occurrence. And the operation that produces the set outcomes is considered as the term experiment.

To get the probability there is a set formula that we have to apply and after which we will get our required answer.

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Free Sample Questions for

Question 1

Determine the solutions of x^2 - 14x +49 = 48.
A. - 7 +- 4sqrt3
B. - 7 +- 16sqrt3
C. 7 +- 4sqrt3
D. 7 +- 16sqrt3

Question 2

For the quadratic function in the graph below, which of the following domain restrictions would make it invertible? There may be more than one correct answer. Assume that the horizontal axis represents x values and the vertical axis y values.
A. x<1
B. x < -4
C. x>=5
D. x<0

Question 3

Solve the equation. m^2 - 25=0
A. x = 5
B. x = -5
C. x = +- 5
D. x = +- 12.5

Question 4

If c = 6 and d = 2, evaluate the expression.2c + c(d^2 - 6)
A. 24
B. 0
C. -24
D. 18

Question 5

A student took 60 minutes to answer a combination of 20 multiple choice and extended-response questions. She took 2 minutes to answer each multiple choice and 6 minutes to answer each extended response. How many extended response questions were on the test?
A. 15
B. 5
C. 10
D. None of the above

Question 6

Find the zeros of the function defined by the expression 3x^2 - 14x + 8.
A. x = 2/3, 4
B. x=2,4
C. x = 1,8
D. x = 2, 4/3

Question 7

For a pendulum of length L, its period of oscillation can be modeled by the expression 2 pi sqrt(L/g), where g is the acceleration due to gravity. How would increasing the length of the pendulum by a factor of 2 affect the period of oscillation?
A. It would increase it by a factor of 2.
B. It would increase it by a factor of 4.
C. It would increase it by a factor of sqrt{2}.
D. It would increase it by a factor of 1/sqrt(2).

Question 8

Let f(x) be the function pictured in the graph below. Assume that the domain of the function is x in [0,10]. Also, assume that the scale of the x- and y-axes is one unit. Which of the intervals specified below which would make f(x) invertible? There may be more than one correct answer.
A. (0,6)
B. [2,6] uu (9,10)
C. (6,8)
D. (0,2) uu (6,8)

Question 9

Identify the property used to begin the factoring of the given polynomial.Given: 7p^3r - 5t^3s - 21p^2r -10s^3t^3 Step 1: 7p^3r- 21p^2r - 5t^3s -10s^3t^3
A. Associative Property
B. Commutative Property
C. Distributive Property
D. Substitution Property

Question 10

Solve the system of equations.2x-y+2z=15-x+y+z=33x-y+2z=18
A. (5,3,1)
B. (3,1,5)
C. (-3,5,1)
D. "No Solution"