The 9th grade math starts with higher levels of the topics covered in lower standards and a lower level for some new topics as well.
The common topics from previous grades and extended level are numbers, exponents, relations and functions, operations,  ratios and proportions, direct variation, percents, perimeter & area, volumes and surface areas, symmetry etc.
The new topics include coordinate geometry, one and two variable equation solving, probability, statistics, linear functions, sequences, etc.

9th grade math forms a strong foundation for higher level mathematics as more stress is given on application part starting from this grade onwards. Apart for clearing the basics for new concepts, emphasis is laid on the application and real time use of the knowledge of the concept to make it clear, knowledge of using the concept in real problems with the help of word problems.
This will enhance the understanding of the student towards the concept being followed. With regular practice and timely revision a student can attain expertise in all levels may it be easy, intermediate or difficult, of 9th grade math.
 

Topics

The older topics are all known. Let us discuss a little about some of the new ones.
Coordinate geometry is the concept of making ordered pairs of points and plotting them on graphs, quadrants and the method to find the distance of a line are discussed
In linear graphs topic, properties of a line, its slope, different form of line equations, and various properties of slope of a line as well are taken up.

System of linear equation is solving two linear equations in two variables in order to find the value of the variables. It uses three main methods for this: graphing, substitution, elimination. In addition word problems are also discussed for increasing the application knowledge of the student.

Single-variable inequalities are a new topic where instead of equation we solve inequalities to obtain some relation. Graphing inequalities is also included.
Probability is another topic which means chance of occurrence. This is very important topic not just for higher grades but also for general life. It is taken up in daily use as well, the difference is just that we don’t use the word probability so frequent but do calculate it often.

Statistics and data handling is an extended yet new version of data handling done in previous grades. Here student learn about mean, mode, median, range, quartiles etc.

In geometry the concept of areas, perimeter, surface areas and volumes is taken up to a little difficult level than 8th grade stressing more on the applicative part with tricky or lengthy problems been taken up.

Problems

Here are some common problems that are taken up in 9th grade math:

Example 1: Solve for x & y:  2x+ 7y = 4, x + 3y = 6

Solution:

Let us solve given system of equations using substitution method:

x + 3y = 6 => x = 6 - 3y

Substitute it in the other equation we get,

2(6 - 3y) + 7y = 4 

=> 12 - 6y + 7y = 4 

=> y = -8
x = 6 - 3y = 6 - 3(-8) = 30

Hence x = 30 and y = -8.

Example 2: Find the probability of drawing a queen of black from a deck of cards.

Solution:

A deck of cards is the collection of 52 cards containing 26 black cards.
So P (drawing a queen of black) = $\frac{drawing\  a\  black\  queen}{Total\  number\  of\  black\     cards}$

= $\frac{1}{26}$

Example 3: Find a number such that the sum of the ($\frac{1}{6}$)$^{th}$ part and ($\frac{1}{3}$)$^{rd}$ part is 50.

Solution: Let the number be m.

According to given statement:

$\frac{m}{6}$ + $\frac{m}{3}$ = 50

$\frac{m + 2m}{6}$ = 50

$\frac{3m}{6}$ = 50

$\frac{m}{2}$ = 50

m = 50 x 2 = 100

m = 100