Tenth Grade Math

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Tenth Grade Math comprises of various important theories like algebra, geometry & trigonometry, understanding number system, probability or data organization and measurements. In case of algebra we discuss concepts like rationalization, factorization, solving linear and quadratic equations, sketching graphs and understand the characteristics of different equations etc. Questions based on algebra can be solved by using general mathematical formulas.

In probability and data management we would study about problems regarding arrangement of statistical data, arithmetic and geometric means, discrete & continuous frequency distribution techniques etc. Measurements include theorems like Pythagoras theorem, construction of angle bisectors, perpendiculars bisectors, medians and measures of various angles using compass. In trigonometric math we study about the trigonometric functions like sine, cosine, tangent etc. and their uses in solving the problems related to heights and distances. Let us take some examples of 10th grade math.

Example 1: Factorize the quadratic equation 4 x² + 9 x + 5 = 0?

Solution: Method that we can use here for factorizing the quadratic polynomial is mid – term splitting. We do it as follows:

4 x² + 9 x + 5 = 0

4 x² + 4 x + 5 x + 5 = 0

4 x (x + 1) + 5 (x + 1) = 0

Or x = -1, -5 /4

Example 2: If the triangle ABC is a right angled triangle with side of the longest side equal to 5 units and that of base equal to 4 units then find base?

Solution: Here we make use of Pythagoras theorem:

5² = 4² + x²

Or x = 3 units.

Next we discuss about the concept of Latent heat of vaporization which can be defined as the amount of warmth that is freed or absorbed by any system or a substance when it alters its state without altering the temperature. For instance, melting of ice.

In icse 2013 solved papers these concepts have been detailed. In the next session we will discuss about Circle Area.