# 10th Grade Math

The 10th grade math first emphasize on revision of basics that are learned in previous classes on higher levels of the topics and serves also as a base level for some new topics.

The topics that are common from last grades are numbers, exponents, operations, relations and functions, percents, ratios and proportions, direct variation, perimeter & area, volumes and surface areas, geometry, symmetry etc. The new topics include coordinate geometry, one and two variable equation solving, trigonometry, probability, more on statistics, series and sequences etc.

10th grade math is a strong foundation for higher level mathematics as now on more stress will be laid on the application part that has actually begin from previous grade itself. The basics for new concepts are cleared with emphasis on application and how to use of the concept in real life with the help of word problems.

This increases the understanding and knowledge of the student towards the concept that is being followed. With regular practice and timely revision, a student can easily grab all levels of what is taught to him or her at this grade may it be easy, intermediate or difficult.

## Topics

The older topics are all familiar. Let us discuss a little about some of the new ones.
Linear graphs topic covers properties of a line, its slope, various properties of slope, different form of line equations.

Coordinate geometry stresses on plotting ordered pair points on graphs, different quadrants, the method to find the distance of a line etc.

System of linear equation is solving two or three linear equations in two or three variables respectively in order to find the value of all the variables.

It uses various methods for this: graphing, substitution, elimination are some. Higher level word problems are also taken up in order to increase the application knowledge of the learner.

Trigonometry is a complete new topic that is started at this level. This concept is commonly used in many areas. Trigonometric functions like sin, cos, tan etc are discussed with identities related to them and some basic kind of word problems as well as application of trigonometric functions.
Probability is another very important topic not just for higher grades but also in our general life. Its use can easily be seen in daily lifel, the difference isthat we don’t relies we are using probability as we don’t do it in traditional way.

Statistics and data handling is extended further with standard mean, variance, standard deviations etc. along with error handling.
In geometry the concept of areas, perimeter, surface areas and volumes is taken up to a little difficult level than previously done stressing more on the applicative part lengthy and confusing problems.

## Problems

Here are some common problems that are taken up in 10th grade math:

Example 1:  Calculate the height of the pole given that the angle of elevation from the point its top is seen is 45° and the foot of the pole from the point is 10 m.

Solution: We need to find the height of pole. When we try drawing a figure of the same question we find that the height of pole is opposite to the angle of elevation and the distance from point of reference to the foot is the adjacent of the angle of elevation in the right triangle where pole is perpendicular to the horizontal of foot.

So $tan 45$ = $\frac{opposite}{adjacent}$

$\rightarrow$ 1 = $\frac{height\ of\ pole}{horizontal\ distance}$

$\rightarrow$ 1 = $\frac{height}{10}$

$\rightarrow$ Height = 10

Hence, height of the pole = 10 m.

Example 2: The first term of an arithmetic sequence is 5 and the eighth term is 19. Find the 20th term.

Solution:
Let a$_1$ = First term of the sequence = 5

And 8th term = a$_8$ = 19

nth term = a$_n$ = a$_1$ + (n - 1) d

=> a$_8$ = a$_1$ + (8 - 1) d

=> 19 = 5 + 7d

=> 14 = 7d

=> d = 2

Therefore 20th term is,

a$_{20}$ = 5 + (20 - 1) (2)

=> a$_{20}$ = 5 + (19) (2)

=> a$_{20}$ = 5 + 38

=> a$_{20}$ = 43.

Example 3: Find three consecutive integers whose sum is equal to 888.

Solution: Let the three numbers be x, x + 1 and x + 2. Their sum is equal to 888, hence

x + (x + 1) + (x + 2) = 888

Solve for x and find the three numbers

3x + 3 = 888

3x = 888 - 3 = 885

x = $\frac{885}{3}$ = 295

x = 295, x + 1 = 296 and x + 2 = 297.