The 11th grade math emphasize on the learning of basics of the topics that are required now on higher levels and serves as a base level for these new concepts.

11th grade math is a strong foundation for higher level mathematics as now stress is laid on the application part completely along with more complex topics that starts from here.

The basics for new concepts are cleared with lots and lots of emphasis on their application part and on how to make use of the concept in real life. This will increase the knowledge and application behavior of the student towards the concept that is taken up. With constant practice and revision on timely basis, a student can easily understand all the levels of whatever is being taught to him or her which may be easy, intermediate or difficult levels.

## Topics

Grade 11th math is divided in two types: Mathematics I and Mathematics II.

The common topics included in both Mathematics I and II are: sequences and series, permutations & combinations, binomial theorem, principal of mathematical induction, straight lines, sets, relations and functions, trigonometric functions, linear and quadratic inequalities, limits & continuity and probability.

The topics that differ in mathematics-I are: conic sections, introduction to three dimensional geometry, complex numbers & quadratic equations.

The topics that differ in mathematics II are: stocks, shares and debentures, statistics, average and partition values.

The difference in topics is due to the use of them in the type of studies a student has opted for. We all know that 11th grade is the time when a student decides on whether to move ahead with science subjects, or commerce subjects or arts etc. Basically the time of deciding subjects on the basis of choice of career comes in this grade. Mathematics is a common subject to all the sections of choices made.

The difference lies in the matter of study. Likewise a commerce student does not need to study vectors as such neither does a engineering student needs to study about shares and debentures. So the matter is divided differently where we see some of the topics are still common which all have to study. The engineering math students need to study mathematics I while the commerce based students require learning of mathematics II. This idea made it easier for students for wasting time and logical energy on the topics that are not concerned to their field at all.

## Problems

Here is a problem that is taken up in 11th grade math which is common in both mathematics I and II:

**Example 1:**Given a statement: sum of ‘n’ natural numbers is equal to n(n + 1)/2.

Solution: Let us check for n = 1.

When $n$ = 1, $\frac{n(n + 1)}{2}$ = $\frac{1(1 + 1)}{2}$ = 1

We can see it is true for base case.

Assuming that for some $k \leq n$, the statement is true.

$\rightarrow$ 1 + 2 + …. + k = $\frac{k (k + 1)}{2}$ ….(i)

Now check for k + 1 terms.

That is to prove that: 1 + 2 + … + k + (k + 1) = $\frac{(k + 1)(k + 2)}{2}$

Consider

1 + 2 + 3 + … + k + (k + 1)

= $\frac{k (k + 1)}{2}$ + (k + 1) [from (i)]

= (k + 1) [$\frac{k}{2}$ + 1]

= $\frac{(k + 1)(k + 2)}{2}$

Hence the statement holds true for $k + 1$.

Thus by the rule of mathematical induction we can say that the sum of first ‘n’ natural numbers is $\frac{n(n + 1)}{2}$.

Total number of ways = 4 + 3 + 7 = 14.

Number of possible ways (orange color marbles) = 3

Probability = $\frac{3}{14}$

Let us apply foils law to write the complex numbers into standard form.

Given: (6 + 2i) (-4 - 10i)

Applying foils law we get, ((6 x -4) + (6 x -10i) + (2i x -4) + (2i x -10i))

= (-24 - 60i - 8i - 20 i$^2$)

= (-24 - 68i - 20 (-1)) = (-24 - 68i + 20) = -4 - 68i.

Which is the required form.

**Example 2:**There are 4 white, 3 orange, and 7 brown color marbles in a box, if one marble is picked at random, what is the probability of getting a orange color marble?**Solution:**Total number of ways = 4 + 3 + 7 = 14.

Number of possible ways (orange color marbles) = 3

Probability = $\frac{3}{14}$

**Example 3:**Write the following complex numbers into standard form: (6 + 2i) (-4 - 10i)**Solution:**Let us apply foils law to write the complex numbers into standard form.

Given: (6 + 2i) (-4 - 10i)

Applying foils law we get, ((6 x -4) + (6 x -10i) + (2i x -4) + (2i x -10i))

= (-24 - 60i - 8i - 20 i$^2$)

= (-24 - 68i - 20 (-1)) = (-24 - 68i + 20) = -4 - 68i.

Which is the required form.