TutorVista is known for its well-designed online sessions that make students knowledgeable and confident before their exams. Several proficient academicians are associated with this site and they provide assistance as per the student's learning requirements. Based on the academic standard, students can choose their topics and schedule their sessions anytime from home. Moreover, TutorVista offers personalized attention to students and also covers vast topics in each subject. Math is an important basic subject and students must practice Math rigorously to score well in exams. However, they can take homework help for Math and also can choose unlimited sessions to make their exam preparation constructive and effective in all respects.

By choosing 11th Grade Math tutoring programs of TutorVista, students can not only understand Math concepts, but also learn methods to solve tough Math problems quickly and easily. Online sessions offered by Tutor Vista are complete, comprehensive and quite beneficial for students. The tutor and student talk to each other using voice (VoIP) and share different problems by using an interactive whiteboard. Moreover, students can complete their assessments and other tasks by getting adequate help form virtual tutors. It is proved that one-on-one tutoring sessions are worthwhile as each of these is done under the supervision of proficient subject experts.

- Practice all Math chapters in a repeated manner by taking learning assistance from TutorVista.
- Solve all tough Math problems during your exam preparation.
- Schedule unlimited online sessions to brush up each Math topic in a requisite manner.
- Solve online worksheets and enhance your confidence in each topic.

TutorVista covers all important Math topics included in the class 11 Math syllabus.

- Number System
- Algebra I
- Algebra II
- Pre Calculus
- Calculus
- Statistics
- Geometry
- Trigonometry
- Advanced Trigonometry

Students should practice different Math problems to enhance their subject knowledge. Class 11 is an important stage of learning and all essential topics including algebra, sets and functions, coordinate geometry, statistics and probability are added in the syllabus. Moreover, students are suggested to follow these topics thoroughly to get good scores in exams. Apart from this, sound knowledge in Math makes students eligible to get good jobs in different fields.

### Solved Examples

**Question 1: **Find first term of arithmetic progression whose 7th and 10th terms are 35 and 59 respectively.

** Solution: **

Let 'a' be the first term. Now we have to find the value of 'a' by using given instructions.

Given: 7th term, a$_7$ = 35 and 10th term, a$_{10}$ = 59

We know that the general term of AP is, a$_n$ = a + (n - 1)d

=> a$_7$ = a + 6d = 35

or a + 6d = 35 ...........(i)

and a$_{10}$ = a + 9d = 59

or a + 9d = 59 ..............(ii)

The value of 'a' can be found by subtracting equation (ii) from equation (i)

a + 6d = 35

a + 9d = 59

- - -

-----------------

-3d = -24

-----------------

=> d = 8

Substitute the result of d in equation (i)

a + 6 $\times$ 8 = 35

a + 48 = 35

a = -13

The value of a is -13.

**Question 2: **From 8 men and 5 women, four persons are be selected to form a committee
so that at least 2 women are there on the committee. In how many ways
can it be done.

** Solution: **

The possible number of ways are:

2 women and 2 men = $^5$C$_2$ $\times$ $^8$C$_2$ = 280

3 women and 1 man = $^5$C$_3$ $\times$ $^8$C$_1$ = 80

4 women only = $^5$C$_4$ = 5

So total number of ways = 280 + 80 + 5 = 365

TutorVista offers class 11 solved Math examples for the convenience of students. Students can follow these examples and understand the solutions in a step-by-step manner. They can also practice online Math worksheets under the guidance of virtual tutors.

### Practice Problems

**Question 1: **Sum of first 4 terms of arithmetic progression is 28 and sum of first eight terms is 88. Find sum of first 10 terms. (Answer: S$_{10}$ = 130)

**Question 2: **Use induction to prove that, $\frac{1}{2}$ + $\frac{1}{4}$ +
$\frac{1}{8}$ + ......+ $\frac{1}{2^n}$ = $\frac{2^n - 1}{2^n}$.

Let 'a' be the first term. Now we have to find the value of 'a' by using given instructions.

Given: 7th term, a$_7$ = 35 and 10th term, a$_{10}$ = 59

We know that the general term of AP is, a$_n$ = a + (n - 1)d

=> a$_7$ = a + 6d = 35

or a + 6d = 35 ...........(i)

and a$_{10}$ = a + 9d = 59

or a + 9d = 59 ..............(ii)

The value of 'a' can be found by subtracting equation (ii) from equation (i)

a + 6d = 35

a + 9d = 59

- - -

-----------------

-3d = -24

-----------------

=> d = 8

Substitute the result of d in equation (i)

a + 6 $\times$ 8 = 35

a + 48 = 35

a = -13

The value of a is -13.

The possible number of ways are:

2 women and 2 men = $^5$C$_2$ $\times$ $^8$C$_2$ = 280

3 women and 1 man = $^5$C$_3$ $\times$ $^8$C$_1$ = 80

4 women only = $^5$C$_4$ = 5

So total number of ways = 280 + 80 + 5 = 365

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