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

For the absolute value function shown below, where is the function decreasing? Assume 1 unit intervals for both axes.
A. The function is never decreasing.
B. For all values of x.
C. x>0
D. x<0

Question 2

Based on the graph of f(x) =x^2, what is the average rate of change from x=-2 to x=3?
A. -3/2
B. 1
C. 5
D. -5

Question 3

If (f@g)(x) = 10x - 2, which of the following are possible function rules for f(x) and g(x) ? Choose all correct answers.
A. f(x) = 10x + 10, \ \ g(x) = x - 12
B. f(x) = 2x-4, \ \ g(x) = 5x+1
C. f(x) = 8x-9, \ \ g(x) = 5/4 x - 11/4
D. f(x) = 1/2x - 3 \ \ g(x) = 20x + 2

Question 4

Find the mean, median, and mode for the data set {15, 12, 10, 18, 5}.
A. mean 10, median 12, mode 15
B. mean 11, median 12, mode 12
C. mean 12, median 12, mode none
D. mean 12, median 12, mode 12

Question 5

When graphing a quadratic function, it does not extend to all values of x.
A. True
B. False

Question 6

Find the a, b, and c for this quadratic equation. -6x^2-12=0
A. a=-6, b =0, and c=-12
B. a=6, b = 0, and c= 12
C. a=0, b= 12, and c =-6
D. a= -12, b=-6, and c= 0

Question 7

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

Question 8

The ordered pair, (2, -1), is a solution of 2x + y < 5.
A. True
B. False

Question 9

What is the domain of the function f(x)=3log_2 x ?
A. [0,oo)
B. (0,oo)
C. (3,oo)
D. [2,oo)

Question 10

What is the surface area of cylinder with radius of 2 cm and height 8 cm?
A. 125.6 \ "cm"^2
B. 120 \ "cm"^2
C. 225.6 \ "cm"^2
D. 225 \ "cm"^2