ICSE Maths Class 11 Previous Year Question Papers
ICSE Maths Class 11 Previous Year Question Papers

Previous year question papers can be considered one of the best preparation materials. They not only help you to understand the paper pattern but also furnish you with important topics. Although class 11 exams are conducted by individual schools, they mostly follow the same pattern and syllabus. In this article, we will be discussing the weightage of marks for each class, while talking about exams like class 11 Maths paper for the academic year 2021- 22. We discuss approaches to solve each section of the paper, and at last we will be answering a few FAQs. It is a well-known fact that class 11 exams are not very tough, and that constant hard work will produce good results. ICSE Class 11 Maths is a significant subject for the understudies, as it helps build ideas that are useful in competitive exams. Students can see a steady change in the ICSE Class 11 Maths Syllabus. Consequently, it is essential for them to know the same. The paper consists of 80 marks.

## Details about ICSE class 11 maths paper

The paper is divided into three sections, namely, A,B, and C. The marks weightage for each section is given below:

You have to compulsorily attempt Section A. But for Sections B and C, you have an option to choose any one of them. In the above table, important topics are given as per their weightage and section. Prepare accordingly!  Some of the most important questions from ICSE Maths Class 11 Previous Year Question Papers 2021 are given below:

Question 1. Find the value of ????, when sin(sin−1 3 5 + cos−1 ????) = 1

Answer. We have sin(sin−1 3 5 + cos−1 ????) = 1

⇒ sin−1 3 5 + cos−1 ???? = sin−1 (1) [∵ sin ???? = ???? ⇒ ???? = sin−1 ????]

⇒ sin−1 3 5 + cos−1 ???? = sin−1 (sin ???? 2 ) [∵ sin ???? 2 = 1 ]

⇒ sin−1 3 5 + cos−1 ???? = ???? 2 …

(1) We know that sin−1 ???? + cos−1 ???? = ???? 2 , ???? ???? [−1,1] . . .

(2) Equating equations (1) and (2), we note that the LHSs of both equations are equal. Hence,

sin−1 3 5 + cos−1 ???? = sin−1 ???? + cos−1 ????

⇒ sin−1 3 5 = sin−1 ???? Hence, ???? = 3 5 .

Question 2. . Evaluate: lim????→1 ???? 45−1 ???? 40−1

Answer. We have, lim????→1 ???? 45−1 ???? 40−1 = lim ????→1 {( ???? 45−1 ????−1 ) ÷ ( ???? 40−1 ????−1 )}

= lim ????→1 ( ???? 45−1 ????−1 ) ÷ lim????→1 ( ???? 40−1 ????−1 )

= (45 × 1/ 44) ÷ (40 × 1/ 39)

= 45 40 = 9/8

Hence, lim????→1 ???? 45−1 ???? 40−1 = 9/ 8 .

Question 3. How many terms are there in the AP: 32,36,40,44, … . . ,320?

Answer. Here, ???? = 32, ???? = 36 − 32 = 4 and ???????? = 320

Let ???? be the number of terms.

Now, ???????? = 320 ⇔ ???? + (???? − 1)???? = 320

⇔ 32 + (???? − 1)(4) = 320 [∵ ???? = 32, ???? = 4]

⇔ 32 + 4???? − 4 = 320

⇔ 4???? + 28 = 320

⇔ 4???? = 320 − 28 = 292

⇔ ???? = 292/ 4 = 73

Hence, the given AP contains 73 terms.

Question 4. Find ???? , if (???? + 2)! = 90 × ????!.

Answer. (???? + 2)(???? + 1) × ????! = 90 × ????!

⇒ (???? + 2)(???? + 1) = 90

⇒ ???? 2 + 2???? + ???? + 2 = 90

⇒ ???? 2 + 3???? − 88 = 0

⇒ ???? 2 + 11???? − 8???? − 88 = 0

⇒ ????(???? + 11) − 8(???? + 11) = 0

⇒ (???? + 11)(???? − 8) = 0

⇒ ???? = 8 [∴ ???? ≥ 0]

????????????????????, ???? = 8.

Question 5. Expand (???? 3 + 4????) 4 by the binomial theorem.

Answer. We have, (???? 3 + 4????) 4

Using the binomial theorem, we get (???? 3 + 4????) 4 = ????0 4 (???? 3 ) 4 + ????1 4 (???? 3 ) 3 (4????) + ????2 4 (???? 3 ) 2 (4????) 2 + ????3 4 (???? 3 ) 1 (4????) 3 + ????4 4 (4????) 4

= 1 ∙ ???? 12 + 4 ∙ ???? 9 ∙ (4????) + 6 ∙ ???? 6 ∙ 16 ∙ ???? 2 + 4 ∙ ???? 3 ∙ 64 ∙ ???? 3 + 1 ∙ 256 ∙ ???? 4 = ???? 12 + 36 ∙ ???? 9 ∙ ???? + 96 ∙ ???? 6 ∙ ???? 2 + 256 ∙ ???? 3 ∙ ???? 3 + 256 ∙ ???? 4

Hence, (???? 3 + 4????) 4

= ???? 12 + 36???? 9???? + 96???? 6???? 2 + 256???? 3???? 3 + 256???? 4

## How to solve class 11 ICSE maths paper?

Maths is a subject that is based on many formulas and concepts. In short, it’s a technical subject. So, it will be quite beneficial if you follow the below mentioned points diligently.

• Before starting your preparations check ICSE Maths Class 11 Previous Year Question Papers 2021 to get some insights on the type of questions that are asked frequently.
• Practice numericals daily. Try to have conceptual clarity, as it will help you to solve each section of the paper easily.
• Make short notes of all the important formulas like those in “Statistics”; you can revise these notes at the last moment.
• Always solve questions in the same order as in the question paper. Don’t answer in an unordered manner, as this will leave a bad impression on the examiner.
• Analyze all questions properly before answering them. Don’t solve them in a hurry.
• Use time productively while solving the Physics paper. For that you have to have a good speed. Otherwise, under the challenging factor of less time you cannot tackle even the most straightforward and simple issues.
• Notably, marks are given stepwise for each solution. Hence, it will be in your best interests if you solve the entire question with each step in order to fetch full marks for that question.
• Don’t get stuck on a particular question if you find it difficult to solve it. Move on and leave some space for it so that you can solve it later.
• Never leave any question unanswered. Marks are given on each step, so be smart and work accordingly.
• Don’t panic, solve each question properly without haste.

## Frequently Asked Questions of Class 11 ICSE Maths

### Question 1. Is class 11th Maths difficult?

Answer. No, it’s not tough. You just have to clear your concepts and learn formulas by heart. Practice daily, and all the best.

### Question 2. How to prepare for the maths exam?

Answer. Complete one chapter daily. Focus on those questions that are frequently asked in the exams. Take weekly tests to know your weak points.

### Question 3. Is it necessary to study from NCERT books?

Answer. Not really but NCERT books are very helpful in clearing doubts. You can refer to them for having more clarity of concepts.

### Question 4. What are Cartesian equations?

Answer. A cartesian equation for a curve is an equation in terms of x and y only. It is an important topic and is asked very fluently in class 11 maths papers.