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Class 10 Maths Chapter 1 Assignments

Class 10 Maths Chapter 1 Real Numbers Assignments and Worksheets with solutions and answers updated for academic session 2023-24. All the chapter is divided into 4 assignments taking easy, average, and difficult questions. These set of questions provide a complete revision for the preparation of CBSE and State board exams 2023-24.

CBSE NCERT Class 10 Maths Chapter 1 Real Numbers Assignments

• Class 10 Maths Chapter 1 Real Numbers Assignments 1
• Class 10 Maths Chapter 1 Real Numbers Assignments 1 Solutions
• Class 10 Maths Chapter 1 Real Numbers Assignments 2
• Class 10 Maths Chapter 1 Real Numbers Assignments 2 Solutions
• Class 10 Maths Chapter 1 Real Numbers Assignments 3
• Class 10 Maths Chapter 1 Real Numbers Assignments 3 Solutions
• Class 10 Maths Chapter 1 Real Numbers Assignments 4
• Class 10 Maths Chapter 1 Real Numbers Assignments 4 Solutions
• Class 10 Maths Chapter 1 Real Numbers Solution Page

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There are 4 assignments and worksheets. Assignments contains MCQ, Fill in the Blanks, and True false questions. We have covered every topic in the chapter 1 of class 10 Maths. Answers and solutions of each assignment is also given free to use. Students can download these assignments and solve themselves. After solving they can check the answers given on website.

There are some easy questions based on understanding only. Some questions contains tricky methods and 17 percent questions are little bit difficult one. Students need to put effort to explore these questions. These assignments are guarantee to get good marks in exams. The questions based on Case Study will also be included in later chapters.

Download links are given for each assignments. Download and print it and solve it. Match the answers and solutions given on website to know the accuracy. Assignments are deign level wise, so do the first assignment first and the fourth assignment in the last.

Please suggest us, if any, about these assignments, so that we can improve the quality of the contents. We are preparing assignments for all the chapters. Gradually it will be uploaded before the final exams. Students are advised to solve these assignments to prepare the chapter and get confidence in topics.

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Assignments are helpful in the revision of chapter as well as preparation for exams.

How many assignment should do to prepare the chapter?

At least 3 or 4 assignments which cover the entire chapter will be sufficient to know the chapter well.

How do solve the assignment?

Do yourself each assignment. If a part of assignment is not cleared or creating confusion, discuss with your classmate or teachers and solve it again.

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CBSE Class 10 Maths Exam 2024: The Central Board of Secondary Education (CBSE) Class 10 board exams are almost over. The last examination will be on March 13, 2024. On March 11, 2024, the CBSE 10th Mathematics exam was conducted for 041 and 241 subject codes. The examination was scheduled from 10:30 a.m. to 1:30 p.m. A few students felt the paper was a bit tricky but solvable if given more time. Well, that’s just a view of a handful of students; a larger group might have a different opinion.

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• Chapter 1: Real Numbers

NCERT Solutions for Class 10 Maths Chapter 1- Real Numbers

NCERT Solutions Class 10 Maths Chapter 1 Real Numbers are provided here. These solutions are prepared by our expert faculty to help students in their board exam preparations. They solve and provide the NCERT Solutions for Maths to aid the students in solving the problems easily. They also focus on preparing the solutions in such a way that it is easy to understand for the students. A detailed and step-wise explanation is given for each question given in the exercises of NCERT books.

Download Exclusively Curated Chapter Notes for Class 10 Maths Chapter – 1 Real Numbers

Download most important questions for class 10 maths chapter – 1 real numbers.

Answers to the questions present in Real Numbers are given in the first chapter of Maths Solutions of NCERT Class 10. Here, students are introduced to several important concepts that will be useful for those who wish to pursue mathematics as a subject in their Class 11. Based on these solutions of Class 10 NCERT , students can prepare for their upcoming board exam. These solutions are helpful as they are in accordance with the CBSE Syllabus for 2023-24.

• Chapter 1 Real Numbers
• Chapter 2 Polynomials
• Chapter 3 Pair of Linear Equations in Two Variables
• Chapter 4 Quadratic Equations
• Chapter 5 Arithmetic Progressions
• Chapter 6 Triangles
• Chapter 7 Coordinate Geometry
• Chapter 8 Introduction to Trigonometry
• Chapter 9 Some Applications of Trigonometry
• Chapter 10 Circles
• Chapter 11 Constructions
• Chapter 12 Areas Related to Circles
• Chapter 13 Surface Areas and Volumes
• Chapter 14 Statistics
• Chapter 15 Probability
• Exercise 1.1 Chapter 1 Real Numbers
• Exercise 1.2 Chapter 1 Real Numbers
• Exercise 1.3 Chapter 1 Real Numbers
• Exercise 1.4 Chapter 1 Real Numbers

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Access Answers to NCERT Class 10 Maths Chapter 1 – Real Numbers

Exercise 1.1 page: 7.

1. Use Euclid’s division algorithm to find the HCF of:

i. 135 and 225

ii. 196 and 38220

iii. 867 and 255

As you can see from the question, 225 is greater than 135. Therefore, by Euclid’s division algorithm, we have,

225 = 135 × 1 + 90

Now, remainder 90 ≠ 0, thus again using division lemma for 90, we get,

135 = 90 × 1 + 45

Again, 45 ≠ 0, repeating the above step for 45, we get,

90 = 45 × 2 + 0

The remainder is now zero, so our method stops here. Since, in the last step, the divisor is 45, therefore, HCF (225,135) = HCF (135, 90) = HCF (90, 45) = 45.

Hence, the HCF of 225 and 135 is 45.

In this given question, 38220>196, therefore the by applying Euclid’s division algorithm and taking 38220 as divisor, we get,

38220 = 196 × 195 + 0

We have already got the remainder as 0 here. Therefore, HCF(196, 38220) = 196.

Hence, the HCF of 196 and 38220 is 196.

As we know, 867 is greater than 255. Let us apply now Euclid’s division algorithm on 867, to get,

867 = 255 × 3 + 102

Remainder 102 ≠ 0, therefore taking 255 as divisor and applying the division lemma method, we get,

255 = 102 × 2 + 51

Again, 51 ≠ 0. Now 102 is the new divisor, so repeating the same step we get,

102 = 51 × 2 + 0

The remainder is now zero, so our procedure stops here. Since, in the last step, the divisor is 51, therefore, HCF (867,255) = HCF(255,102) = HCF(102,51) = 51.

Hence, the HCF of 867 and 255 is 51.

2. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

Let a be any positive integer and b = 6. Then, by Euclid’s algorithm, a = 6q + r, for some integer q ≥ 0, and r = 0, 1, 2, 3, 4, 5, because 0≤r<6.

Now substituting the value of r, we get,

If r = 0, then a = 6q

Similarly, for r= 1, 2, 3, 4 and 5, the value of a is 6q+1, 6q+2, 6q+3, 6q+4 and 6q+5, respectively.

If a = 6q, 6q+2, 6q+4, then a is an even number and divisible by 2. A positive integer can be either even or odd Therefore, any positive odd integer is of the form of 6q+1, 6q+3 and 6q+5, where q is some integer.

3. An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Number of army contingent members = 616

Number of army band members = 32

If the two groups have to march in the same column, we have to find out the highest common factor between the two groups. HCF(616, 32), gives the maximum number of columns in which they can march.

By using Euclid’s algorithm to find their HCF, we get,

Since, 616>32, therefore,

616 = 32 × 19 + 8

Since, 8 ≠ 0, therefore, taking 32 as new divisor, we have,

32 = 8 × 4 + 0

Now we have got remainder as 0, therefore, HCF (616, 32) = 8.

Hence, the maximum number of columns in which they can march is 8.

4. Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

Let x be any positive integer and y = 3.

By Euclid’s division algorithm, then,

x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.

Therefore, x = 3q, 3q+1 and 3q+2

Now as per the question given, by squaring both the sides, we get,

x 2 = (3q) 2 = 9q 2 = 3 × 3q 2

Let 3q 2 = m

Therefore, x 2 = 3m ……………………..(1)

x 2 = (3q + 1) 2 = (3q) 2 +1 2 +2×3q×1 = 9q 2 + 1 +6q = 3(3q 2 +2q) +1

Substitute, 3q 2 +2q = m, to get,

x 2 = 3m + 1 ……………………………. (2)

x 2 = (3q + 2) 2 = (3q) 2 +2 2 +2×3q×2 = 9q 2 + 4 + 12q = 3 (3q 2 + 4q + 1)+1

Again, substitute, 3q 2 +4q+1 = m, to get,

x 2 = 3m + 1…………………………… (3)

Hence, from equation 1, 2 and 3, we can say that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

5. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.

x = 3q+r, where q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.

Therefore, putting the value of r, we get,

Now, by taking the cube of all the three above expressions, we get,

Case (i): When r = 0, then,

x 2 = (3q) 3 = 27q 3 = 9(3q 3 )= 9m; where m = 3q 3

Case (ii): When r = 1, then,

x 3 = (3q+1) 3 = (3q) 3 +1 3 +3×3q×1(3q+1) = 27q 3 +1+27q 2 +9q

Taking 9 as common factor, we get,

x 3 = 9(3q 3 +3q 2 +q)+1

Putting = m, we get,

Putting (3q 3 +3q 2+ q) = m, we get ,

Case (iii): When r = 2, then,

x 3 = (3q+2) 3 = (3q) 3 +2 3 +3×3q×2(3q+2) = 27q 3 +54q 2 +36q+8

x 3 =9(3q 3 +6q 2 +4q)+8

Putting (3q 3 +6q 2 +4q) = m, we get ,

Therefore, from all the three cases explained above, it is proved that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.

Exercise 1.2 Page: 11

1. Express each number as a product of its prime factors:

By taking the LCM of 140, we will get the product of its prime factor.

Therefore, 140 = 2 × 2 × 5 × 7 × 1 = 2 2 ×5×7

By Taking the LCM of 156, we will get the product of its prime factor.

Hence, 156 = 2 × 2 × 13 × 3 × 1 = 2 2 × 13 × 3

By taking the LCM of 3825, we will get the product of its prime factor.

Hence, 3825 = 3 × 3 × 5 × 5 × 17 × 1 = 3 2 ×5 2 ×17

By Taking the LCM of 5005, we will get the product of its prime factor.

Hence, 5005 = 5 × 7 × 11 × 13 × 1 = 5 × 7 × 11 × 13

By taking the LCM of 7429, we will get the product of its prime factor.

Hence, 7429 = 17 × 19 × 23 × 1 = 17 × 19 × 23

2. Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.

(i) 26 and 91

(ii) 510 and 92

(iii) 336 and 54

Expressing 26 and 91 as product of its prime factors, we get,

26 = 2 × 13 × 1

91 = 7 × 13 × 1

Therefore, LCM (26, 91) = 2 × 7 × 13 × 1 = 182

And HCF (26, 91) = 13

Verification

Now, product of 26 and 91 = 26 × 91 = 2366

And product of LCM and HCF = 182 × 13 = 2366

Hence, LCM × HCF = product of the 26 and 91.

Expressing 510 and 92 as product of its prime factors, we get,

510 = 2 × 3 × 17 × 5 × 1

92 = 2 × 2 × 23 × 1

Therefore, LCM(510, 92) = 2 × 2 × 3 × 5 × 17 × 23 = 23460

And HCF (510, 92) = 2

Now, product of 510 and 92 = 510 × 92 = 46920

And Product of LCM and HCF = 23460 × 2 = 46920

Hence, LCM × HCF = product of the 510 and 92.

Expressing 336 and 54 as product of its prime factors, we get,

336 = 2 × 2 × 2 × 2 × 7 × 3 × 1

54 = 2 × 3 × 3 × 3 × 1

Therefore, LCM(336, 54) = = 3024

And HCF(336, 54) = 2×3 = 6

Now, product of 336 and 54 = 336 × 54 = 18,144

And product of LCM and HCF = 3024 × 6 = 18,144

Hence, LCM × HCF = product of the 336 and 54.

3. Find the LCM and HCF of the following integers by applying the prime factorisation method.

(i) 12, 15 and 21

(ii) 17, 23 and 29

(iii) 8, 9 and 25

Writing the product of prime factors for all the three numbers, we get,

HCF(12,15,21) = 3

LCM(12,15,21) = 2 × 2 × 3 × 5 × 7 = 420

HCF(17,23,29) = 1

LCM(17,23,29) = 17 × 23 × 29 = 11339

HCF(8,9,25)=1

LCM(8,9,25) = 2×2×2×3×3×5×5 = 1800

4. Given that HCF (306, 657) = 9, find LCM (306, 657).

Solution: As we know that,

HCF×LCM=Product of the two given numbers

9 × LCM = 306 × 657

LCM = (306×657)/9 = 22338

Hence, LCM(306,657) = 22338

5. Check whether 6 n can end with the digit 0 for any natural number n.

Solution: If the number 6 n ends with the digit zero (0), then it should be divisible by 5, as we know any number with unit place as 0 or 5 is divisible by 5.

Prime factorization of 6 n = (2×3) n

Therefore, the prime factorization of 6 n doesn’t contain prime number 5.

Hence, it is clear that for any natural number n, 6 n is not divisible by 5, and thus it proves that 6 n cannot end with the digit 0 for any natural number n.

6. Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

Solution: By the definition of composite number, we know, if a number is composite, then it means it has factors other than 1 and itself. Therefore, for the given expression;

7 × 11 × 13 + 13

Taking 13 as common factor, we get,

=13(7×11×1+1) = 13(77+1) = 13×78 = 13×3×2×13

Hence, 7 × 11 × 13 + 13 is a composite number.

Now let’s take the other number,

7 × 6 × 5 × 4 × 3 × 2 × 1 + 5

Taking 5 as a common factor, we get,

=5(7×6×4×3×2×1+1) = 5(1008+1) = 5×1009

Hence, 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 is a composite number.

7. There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

Solution: Since, Both Sonia and Ravi move in the same direction and at the same time, the method to find the time when they will be meeting again at the starting point is LCM of 18 and 12.

Therefore, LCM(18,12) = 2×3×3×2×1=36

Hence, Sonia and Ravi will meet again at the starting point after 36 minutes.

Exercise 1.3 Page: 14

1. Prove that √ 5 is irrational.

Solutions: Let us assume, that √ 5 is rational number.

i.e.  √ 5 = x/y (where, x and y are co-primes)

Squaring both the sides, we get,

(y √ 5) 2 = x 2

⇒5y 2 = x 2 ……………………………….. (1)

Thus, x 2 is divisible by 5, so x is also divisible by 5.

Let us say, x = 5k, for some value of k and substituting the value of x in equation (1), we get,

5y 2 = (5k) 2

⇒y 2 = 5k 2

is divisible by 5 it means y is divisible by 5.

Clearly, x and y are not co-primes. Thus, our assumption about  √ 5 is rational is incorrect.

Hence,  √ 5 is an irrational number.

2. Prove that 3 + 2√5 + is irrational.

Solutions: Let us assume 3 + 2 √ 5 is rational.

Then we can find co-prime x and y (y ≠ 0) such that 3 + 2√5 = x/y

Rearranging, we get,

Since, x and y are integers, thus,

Therefore, √ 5 is also a rational number. But this contradicts the fact that √ 5 is irrational.

So, we conclude that 3 + 2 √ 5 is irrational.

3. Prove that the following are irrationals:

(iii) 6 + √ 2

Let us assume 1/√2 is rational.

Then we can find co-prime x and y (y ≠ 0) such that 1/√2 = x/y

Since, x and y are integers, thus, √2 is a rational number, which contradicts the fact that √2 is irrational.

Hence, we can conclude that 1/√2 is irrational.

Let us assume 7√5 is a rational number.

Then we can find co-prime a and b (b ≠ 0) such that 7√5 = x/y

Since, x and y are integers, thus, √5 is a rational number, which contradicts the fact that √5 is irrational.

Hence, we can conclude that 7√5 is irrational.

Let us assume 6 +√2 is a rational number.

Then we can find co-primes x and y (y ≠ 0) such that 6 +√2 = x/y⋅

√2 = (x/y) – 6

Since, x and y are integers, thus (x/y) – 6 is a rational number and therefore, √2 is rational. This contradicts the fact that √2 is an irrational number.

Hence, we can conclude that 6 +√2 is irrational.

Exercise 1.4 Page: 17

1. Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:

(i) 13/3125 (ii) 17/8 (iii) 64/455 (iv) 15/1600 (v) 29/343 (vi) 23/(2 3 5 2 ) (vii) 129/(2 2 5 7 7 5 ) (viii) 6/15 (ix) 35/50 (x) 77/210

Note: If the denominator has only factors of 2 and 5 or in the form of 2 m ×5 n then it has terminating decimal expansion.

If the denominator has factors other than 2 and 5 then it has a non-terminating decimal expansion.

(i) 13/3125

Factorizing the denominator, we get,

3125 = 5 × 5 × 5 × 5 × 5 = 5 5

Since, the denominator has only 5 as its factor, 13/3125 has a terminating decimal expansion.

8 = 2×2×2 = 2 3

Since, the denominator has only 2 as its factor, 17/8 has a terminating decimal expansion.

(iii) 64/455

455 = 5×7×13

Since, the denominator is not in the form of 2 m × 5 n , thus 64/455 has a non-terminating decimal expansion.

(iv) 15/ 1600

1600 = 2 6 ×5 2

Since, the denominator is in the form of 2 m × 5 n , thus 15/1600 has a terminating decimal expansion.

343 = 7×7×7 = 7 3 Since, the denominator is not in the form of 2 m × 5 n thus 29/343 has a non-terminating decimal expansion.

(vi)23/(2 3 5 2 )

Clearly, the denominator is in the form of 2 m × 5 n .

Hence, 23/ (2 3 5 2 ) has a terminating decimal expansion.

(vii) 129/(2 2 5 7 7 5 )

As you can see, the denominator is not in the form of 2 m × 5 n .

Hence, 129/ (2 2 5 7 7 5 ) has a non-terminating decimal expansion.

(viii) 6/15

Since, the denominator has only 5 as its factor, thus, 6/15 has a terminating decimal expansion.

35/50 = 7/10

Factorising the denominator, we get,

Since, the denominator is in the form of 2 m × 5 n thus, 35/50 has a terminating decimal expansion.

77/210 = (7× 11)/ (30 × 7) = 11/30

30 = 2 × 3 × 5

As you can see, the denominator is not in the form of 2 m × 5 n .Hence, 77/210 has a non-terminating decimal expansion.

2. Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.

13/3125 = 0.00416

17/8 = 2.125

(iii) 64/455 has a non terminating decimal expansion

(iv)15/ 1600

15/1600 = 0.009375

(v) 29/ 343 has a non terminating decimal expansion

(vi)23/ (2 3 5 2 ) = 23/(8×25)= 23/200

23/ (2 3 5 2 ) = 0.115

(vii) 129/ (2 2 5 7 7 5 ) has a non terminating decimal expansion

(viii) 6/15 = 2/5

(ix) 35/50 = 7/10

35/50 = 0.7

(x) 77/210 has a non-terminating decimal expansion.

3. The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form, p q what can you say about the prime factors of q?

(i) 43.123456789

(ii) 0.120120012000120000. . .

Since it has a terminating decimal expansion, it is a rational number in the form of p/q and q has factors of 2 and 5 only.

Since, it has non-terminating and non- repeating decimal expansion, it is an irrational number.

Since it has non-terminating but repeating decimal expansion, it is a rational number in the form of p/q and q has factors other than 2 and 5.

NCERT Solutions for Class 10 Maths Chapter 1 – Real Numbers

Real Number is one of the important topics in Maths, and it has a weightage of 6 marks in Class 10 (Unit – Number Systems) Maths board exams. The average number of questions asked in this chapter is usually 3. Three questions were asked from this chapter in the previous year board examination (2018).

• One out of three questions in part A (1 mark).
• One out of three questions in part B (2 marks).
• One out of three questions in part C (3 marks).

This chapter talks about

• Euclid’s Division Algorithm
• The Fundamental Theorem of Arithmetic
• Revisiting Rational & Irrational Numbers
• Decimal Expansions

List of Exercises in Class 10 Maths Chapter 1: Exercise 1.1 Solutions 5 Questions ( 4 long, 1 short) Exercise 1.2 Solutions 7 Questions ( 4 long, 3 short) Exercise 1.3 Solutions 3 Questions ( 3 short) Exercise 1.4 Solutions 3 Questions ( 3 short)

Real Numbers is introduced in Class 9, and this is discussed in further detail in Class 10. NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers provides the answers to the questions present in this chapter. The chapter discusses real numbers and their applications. The divisibility of integers using Euclid’s division algorithm says that any positive integer a can be divided by another positive integer b such that the remainder will be smaller than b. On the other hand, The Fundamental Theorem of Arithmetic works on the multiplication of positive integers.

The chapter starts with the introduction of real numbers in section 1.1, followed by two very important topics in sections 1.2 and 1.3

• Euclid’s Division Algorithm – It includes 5 questions based on Theorem 1.1 – Euclid’s Division Lemma.
• The Fundamental Theorem of Arithmetic – Explore the applications of this topic which talks about the multiplication of positive integers, through solutions of the 7 problems in Exercise 1.2.

Next, it discusses the following topics, which were introduced in Class 9.

• Revisiting Rational & Irrational Numbers – In this, the solutions for 3 problems in Exercise 1.3 are given, which also use the topic in the last Exercise 1.2.
• Decimal Expansions – It explores when the decimal expansion of a rational number is terminating and when it is recurring. It includes a total of 3 problems with sub-parts in Exercise 1.4

Key Features of NCERT Solutions for Class 10 Maths Chapter 1- Real Numbers

• These NCERT Solutions help you solve and revise the updated CBSE syllabus of Class 10 for 2023-24.
• After going through the stepwise solutions given by our subject expert teachers, you will be able to score more marks.
• It follows NCERT guidelines which help in preparing the students competently.
• It contains all the important questions from the examination point of view.

Disclaimer –

Dropped Topics – 

1.2 Euclid’s division lemma 1.5 Revisiting rational numbers and their decimal Expansions

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CBSE Class 10 Mathematics paper was easy but lengthy with questions from NCERT

The cbse class 10 mathematics board exam, held on march 11, 2024, was considered reasonably easy though a little lengthy. the paper was of easy to moderate level in difficulty with ncert questions..

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The CBSE board exam 2024 began for both Classes 10 and 12 on February 15 and the Class 10 Mathematics paper was held on March 11. Students said that the Math paper was of easy to moderate level in difficulty.

The paper was a little lengthy but not so much that students couldn't complete it. Several students noted that the long answer questions or case studies were a little tough.

Questions were given from the NCERT and Exemplar questions. Those who had prepared well found the paper moderately easy.

Ansh from Cambridge School says most of the questions were from the NCERT: "Around 30%-40% of the questions were based on the sample papers and PYQs only."

"It was an easy paper and wasnt too lenthy. The case study section was a little tricky," he adds.

Koustav from Bal Bharti found the Math Basic paper quite easy but lengthy. "The long-answer section was little tricky," he says.

"The paper was very easy. I completed with 30 minutes left. The section with the case studies was the trickiest," he adds.

Yadhvi from Bal Bharti Public School, who appeared for the Mathematics Standard paper, says she had a great exam.

"The paper was lengthy. One 5-marker question from Triangles chapter was very difficult. But the rest of the paper was very easy," she says.

Amit from Lord Mahavira School, who appeared for the Standard paper, says the Math paper was lengthy but easy.

"There were many NCERT Exemplar-based questions in the paper. There was nothing unexpected. Section D was a little tough," he says.

Sayona from Bal Bharti Public School found the Math Standard paper quite touch. "The MCQs were very lengthy. The 2- and 3-mark questions were lengthy as well. I found the sample paper easier than the paper itself."

WHAT TEACHERS HAVE TO SAY

The Class 10 Mathematics paper received positive feedback from both students and teachers, aligning well with CBSE sample papers. The timely completion by students and the ease of the case study-based questions suggest a well-balanced and accessible paper,” says Harmeet Kaur, HOD Mathematics at Silverline Prestige School, Ghaziabad

“The provision of appropriate choices in the paper further contributed to student satisfaction, reflecting a successful examination,” Kaur adds.

“The CBSE Class 10 Mathematics paper maintained an easy to moderate difficulty level, effectively testing students' application and problem-solving skills,” says Jayant Kumar, TGT Mathematics, Seth Anandram Jaipuria School, Lucknow.

“Students who had a good grasp of core concepts found the paper manageable, although some areas were noted to be tricky,” he says.

“Overall, the exam was aligned with the sample paper format and marking scheme, offering a mix of easy and engaging questions,” he adds.

"The CBSE Class 10 Math paper (Standard) was moderate and encompassed all the necessary skills outlined in the syllabus. Questions were based on the NCERT textbooks, ensuring familiarity for students. Notably, there were no unexpected or unfamiliar questions that could unsettle examinees," says Anjani Rai, Coordinator, VidyaGyan School, Bulandshahr (UP).

"Most questions followed a clear format, allowing students who had diligently practiced from NCERT and similar resources to attempt and answer them confidently. Students encountered difficulty with a case study question from the Real Number chapter, describing it as tricky,' she says.

"Compared to the previous year's paper, this one was considered a little difficult, with focus on conceptual understanding rather than numeracy skills," she adds.

"In one case study, in a question from areas related to circles, some misprint in numbers were observed. The geometry questions were directly sourced from the NCERT book. It is expected that sincere students would have completed the paper well within the allotted time," Rai says.

"The paper maintained a balanced mix of question types, consistent with the sample question papers provided by CBSE," she adds.

Regarding the CBSE Class 10 Basic Mathematics paper, Rai says it was well-balanced with easy and straightforward questions.

"None of the questions were excessively time-consuming, maintaining a fair distribution of question types as per CBSE's sample question papers. Overall, the paper was well-structured and aligned with the expectations of students preparing for the Basic Mathematics examination," Rai adds.

“The CBSE Mathematics paper (Standard and Basic) can be considered moderate. The questions were as per the CBSE pattern. The syllabus was entirely covered in Standard as well as Basic Mathematics," says Mamta Chauhan, HOD Mathematics, Billabong High International School, Malad.

"In both Mathematics (Standard and Basic) some questions in Section B,C and D can be considered anticipated. Some MCQs in section A were tricky, though easy. There weren’t lengthy calculations. Some MCQs were too easy," Chauhan says.

"Overall Section B was easy to solve. Section C contained regularly practiced questions, Trigonometry proof was moderate. The difficulty level of questions in Section D was moderate," she adds.

"Overall Section E was easy to solve. While in Mathematics (Basic), Section A had MCQs can be considered as easy to average, Section B had Overall Section B was easy to solve. Sections C and D were moderately difficult while Section E was easy to solve," Chauhan says.

“The CBSE Class 10 Math question paper was easier than the CBSE Class 10 sample question paper. The paper was not lengthy at all, Most students felt Section-E was not difficult but time-consuming,” says Ajit Pratap Singh, PGT Maths, KIIT World School, Gurugram.

“The questions on the exam ranged in difficulty from easy and done within 3 hours. Case study-based questions required students to use some extra effort and time but they were easy,” he adds.

“The CBSE class 10 Basic Math paper struck a moderate balance. It featured logical questions that required a comprehensive understanding of the chapters. One question was from an exercise that had been removed from the NCERT,” says Ajay Pal Singh, Principal of Bhai Parmanand Vidya Mandir.

“Section A presented an easy level. Section B was comparatively simpler, whereas Sections C and D posed an above-average challenge, demanding careful reading of the questions. Despite being sourced from NCERT, the questions proved to be of a challenging difficulty level,” Singh says.

“Section E attained a moderate difficulty level. The exam's design, aimed at assessing students' competency, was challenging. Overall, it encompassed various types and topics of Mathematics,” he adds.

"The overall difficulty of the question paper was moderate, offering a fair evaluation for all students. This allowed above-average students to showcase their skills while remaining accessible to those with a solid grasp of the concepts," says Benasir PA, TGT Mathematics, JAIN International Residential School, Bengaluru.

"It's commendable that the paper maintained consistency within question sets, ensuring fairness and preventing discrepancies in difficulty levels. However, Set 3 questions were slightly more challenging compared to Sets 1 and 2. Care should be taken to ensure that any increase in difficulty is reasonable and doesn't unfairly disadvantage students," the teacher says.

"The distribution of weightage between textbook-based questions and multiple-choice questions (MCQs) in the basic question paper seemed uneven. While it's important to include textbook-aligned questions to assess understanding, MCQs should be designed with basic-level students in mind, ensuring clarity and accessibility," the teacher adds.

"The mathematics paper for the Class 10 board examination was moderate, with most of the questions found to be from the syllabus. However, the paper had an inclusion of both theoretical and application-based problems," states BYJU'S instructors.

"Overall, the mathematics paper was found to be in line with expectations," they add.

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3

Using the CBSE Class 10 Maths Answer key 2024, Students can check their responses and predict their Scores. Access the Class 10 Mathematics Answer key 2024 of Set 1,2,3 on this page.

Table of Contents

As per the Schedule, The Central Board of Secondary Education (CBSE) has conducted the CBSE Class 10 Maths Exam 2024 for basic and standard levels today, March 11. The CBSE Both tests began at 10:30 a.m. and ended at 1:30 p.m. After the exam, we are going to provide the Class 10 Maths Answer Key along with a detailed explanation. The CBSE Class 10 Mathematics Answer Key 2024 is created by highly skilled specialists, and all of the answers are correct and error-free. Stay connected and refresh the page to receive the latest Class 10 math exam questions and answers as soon as possible.

Class 10 Maths Answer Key 2024

The CBSE Class 10 Maths exam Exam is now over at 01:30 P.M. After reaching home from the center, Students rush to find the CBSE Class 10 Maths Answer key 2024 on the Internet.  Using the Class 10 Maths Answer Key 2024, students may compare their answers to all of the questions on the exam and forecast their grades. Our professionals are prepared to supply maths Class 10 Answer Key 2024 to students, so they do not need to visit other websites. Students should bookmark this page and visit it frequently since we publish Class 10 Maths answer key 2024 for all sets before anyone else.

CBSE Class 10 Maths Answer Key 2024

The CBSE Board will hold the Math Exam for the basic and standard levels for a total of 80 points each, with 20 marks for internal assessment. The exam will last three hours, and candidates will have an additional 15 minutes to peruse the question paper. The exam writing time will begin at 10:30 a.m. Check out the highlights of the CBSE Class 10 Maths Exam in the table below:

Class 10 Maths Answer Key 2024 of All Standard and Basic

If you are looking for the Class 10th Maths Answer Key 2024, you can stop the search here. Following the CBSE Class 10 Maths Exam, we will offer the detailed, 100% authentic CBSE Class 10 Maths Answer key 2024 for all sets as soon as possible. Our in-house experts are continually reviewing the Maths solution keys for all sets in depth. Stay connected to us.

Class 10 Maths Answer Key 2024 Set 1

SECTION A This section comprises Multiple Choice Questions (MCQs) of 1 mark each. 20×1=20

1. The next (4th) term of the A.P. √18, √50, √98, is: (A) √128 Answer:  (B) √140 (D) √200

Answer: Answer:  2. If 3 = 2 sin A, 3 = 2 cos A, then the value of x2 + y2 is: (A) 36 (B) 9 (C) 6 (D) 18

Answer: (A) 36

3. If 4 sec θ – 5 = 0, then the value of cot θ is: (A) 3/4 (C) 5/3 (B) 4 /5 (D) 4/ 3

Answer: (D) 4/ 3

4. Which out of the following type of straight lines will be represented by the system of equations 3x + 4y = 5 and 6x + 8y = 7 ? (A) Parallel (B) Intersecting (C) Coincident (D) Perpendicular to each other

Answer: (A) Parallel

5. The ratio of the sum and product of the roots of the quadratic equation 5×2-6x+21 = 0 is : (A) 5:21 (C) 21:5 (B) 2:7 (D) 7:2

Answer: (B) 2:7

6. For the data 2, 9, x + 6, 2x + 3, 5, 10, 5; if the mean is 7, then the value of x is: (A) 9 (B) 6 (C) 5 (D) 3

Answer: (D) 3

7. One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number which is a multiple of 7 is: (A) 1/7 (C) 1 /5 (B) 1/ 8 (D) 7/ 40

Answer: (B) 1/ 8

8. The perimeter of the sector of a circle of radius 21 cm which subtends an angle of 60° at the centre of circle, is: (A) 22 cm (B) 43 cm (C) 64 cm (D) 462 cm

Answer: (C) 64 cm

9. The length of an arc of a circle with radius 12 cm is 10 cm. The angle subtended by the arc at the centre of the circle, is : (A) 120° (B) 6° (C) 75° (D) 150°

Answer: (D) 150°

10. The greatest number which divides 281 and 1249, leaving remainder 5 and 7 respectively, is : (A) 23 (B) 276 (C) 138 (D) 69

Answer: (C) 138

11. The number of terms in the A.P. 3, 6, 9, 12, …, 111 is: (A) 36 (C) 37 (B) 40 (D) 30

Answer: (C) 37

12. A chord of a circle of radius 10 cm subtends a right angle at its centre. The length of the chord (in cm) is :

(A) 5√2 (B) 10/2 (C) 5 √2 (D) 5

Answer: (B) 10/2

13. The LCM of three numbers 28, 44, 132 is: (A) 258 (B) 231 (C) 462 (D) 924

Answer: (D) 924

14. If the product of two co-prime numbers is 553, then their HCF is : (A) 1 (C) 7 (B) 553 (D) 79

Answer: (A) 1 15. If a and ẞ are the zeroes of the polynomial p(x) = kx² – 30x + 45k and α + β = αβ, then the value of k is : (A) -2/3 (C) 3/2 (B) -3/2 (D) 2/3

Answer: (D) 2/3

16. In the given figure, RJ and RL are two tangents to the circle. If RJL = 42°, then the measure of ✓ JOL is:

Answer: (B) 84°

17. In the given figure, in A ABC, DE || BC. If AD = 2.4 cm, DB = 4 cm and AE = 2 cm, then the length of AC is :

Answer: (C) 16/3 cm

18. If a vertical pole of length 7.5 m casts a shadow 5 m long on the ground and at the same time, a tower casts a shadow 24 m long, then the height of the tower is: (A) 20 m (B) 40 m (C) 60 m (D) 36 m

Answer: (D) 36 m

19. Assertion (A): ABCD is a trapezium with DC || AB. E and F are points on AD and BC respectively, such that EF || AB. Then AE / ED =BF/FC Reason (R): Any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally.

Answer: (A) 20. Assertion (A): Degree of a zero polynomial is not defined. Reason (R):Degree of a non-zero constant polynomial is 0.

Answer: (B)

CBSE Class 10 Maths Standard Answer Key 2024 for QP Code: 30/4/1

1. If ax + by = a²-b² and bx + ay = 0, then the value of x + y is:

Answer: (C) a-b

2. The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x, then the value of x is:

Answer: (B) 13

3. If a polynomial p(x) is given by p(x) = x²- 5x + 6, then the value of p(1) + p(4) is: Answer: (B) 4

4. If the discriminant of the quadratic equation 3x² – 2x + c = 0 is 16, then the value of c is: Answer: (C) -1

5. If an arc subtends an angle of 90° at the centre of a circle, then the ratio of its length to the circumference of the circle is : Answer:   (B) 1:4

6. The area of the sector of a circle of radius 12 cm is 60 cm². The central angle of this sector is : Answer: (D) 150°

7. If the difference of mode and median of a data is 24, then the difference of its median and mean is: Answer: (A) 12

8. Two dice are tossed simultaneously. The probability of getting odd numbers on both the dice is: Answer:   (D) 9/36

8. Two dice are tossed simultaneously. The probability of getting odd numbers on both the dice is : Answer: (D) 9/36

9. The ratio of total surface area of a solid hemisphere to the square of its radius is: Answer:   (C) 3π : 1

10. If sine = 1, then the value of [(1/2)*(sin(0/2))] is: Answer:  (A) 1/2/2 11. Two lines are given to be parallel. The equation of one of these lines is 5x – 3y = 2. The equation of the second line can be : Answer:  (D) 15x9y = 5 12. Three numbers in A.P. have the sum 30. What is its middle term? Answer:  (B) 10 13. In A ABC, DE || BC (as shown in the figure). If AD = 4 cm, AB = 9 cm and AC = 13.5 cm, then the length of EC is: Answer:  (B) 7.5 cm 14. At some time of the day, the length of the shadow of a tower is equal to its height. Then, the Sun’s altitude at that time is : Answer:  (B) 45° 15. In the given figure, AB and AC are tangents to the circle. If ∠ABC = 42°, then the measure of BAC is: Answer:  (A) 96° 16. The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2, 3), B(6, 7) and C(8, 3) is:

Answer: (B) (0, -1) 17. For an event E, if P(E) + P(E) = q, then the value of q² – 4 is: Answer:  (A) -3

18. In the given figure, QR is a common tangent to the two given circles touching externally at A. The tangent at A meets QR at P. If AP = 4.2 cm, then the length of QR is : Answer:  (C) 8.4 cm 19. Assertion : Mid-point of a line segment divides the line segment in the ratio 1: 1. Reason (R): The ratio in which the point (-3, k) divides the line segment joining the points (-5, 4) and (-2, 3) is 1: 2.

Answer:  (C) Assertion (A) is true, but Reason (R) is false. 20. Assertion (A): If the circumference of a circle is 176 cm, then its radius is 28 cm. Reason (R): Circumference = 2 x radius of a circle. Answer:  (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

CBSE Class 10 Maths Answer Key 2024 Set 2

1. If a and ẞ are the zeroes of the polynomial p(x) = kx²- 30x + 45k and α + β = aẞ, then the value of k is: (A) – 2/3 (B) 3 /2 (C) -3/2 (D) 2 /3

2. A chord of a circle of radius 10 cm subtends a right angle at its center. The length of the chord (in cm) is :

3. The next (4th) term of the A.P. √7, √28, √63, is: (A) √70 (B) √84 (C) √97 (D) √112

4. If the product of two co-prime numbers is 553, then their HCF is : (A) 1 (B) 553 (C) 7 (d) 79

5. If x = a cos 0 and y = b sin 0, then the value of b²x² + a2y² is: (A) a²b² (B) ab (9) a4b4 (D) a² + b²

6. If the quadratic equation ax2 + bx + c = 0 has real and equal roots, then the value of c is:

(A) b /2a (B) -b /2a – (C) b²/ 4a (D) -b²/ 4a

7. In the given figure, in A ABC, DE || BC. If AD = 2.4 cm, DB = 4 cm and AE = 2 cm, then the length of AC is :

(A) 10/3 cm (C) 16/3 cm (B) 3/10cm (D) 1.2 cm

8. The length of an arc of a circle with radius 12 cm is 10 cm. The angle subtended by the arc at the centre of the circle, is : (A) 120° (C) 75° (B) 6° (D) 150°

9. If 4 sec 0-5 = 0, then the value of cot 0 is:

(A) 3/4 (B) 4/5 (C) 5/3 (D) 4/3

10. The perimeter of the sector of a circle of radius 21 cm which subtends an angle of 60° at the center of circle, is: (A) 22 cm (B) 43 cm (C) 64 cm (D) 462 cm

11. In the given figure, RJ and RL are two tangents to the circle. If RJL = 42°, then the measure of ✓ JOL is:

12. If the prime factorisation of 2520 is 23 x 3a × b x 7, then the value of a + 2b is: (A) 12 (C) 9 (B) 10 (D) 7

13. Which out of the following type of straight lines will be represented by the system of equations 3x + 4y = 5 and 6x + 8y = 7 ? (A) Parallel (B) Intersecting (C) Coincident (D) Perpendicular to each other

14. One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number which is a multiple of 7 is:

(A) 1/7 (C) 1/5 (B) 1/8 (D) 7/40

15. The LCM of three numbers 28, 44, 132 is: (A) 258 (C) 462 (B) 231 (D) 924

16. The number of terms in the A.P. 3, 6, 9, 12, …, 111 is: (A) 36 (C) 37 (B) 40 (D) 30

17. The ratio of the length of a pole and its shadow on the ground is 1 : √3. The angle of elevation of the Sun is : (A) 90° (B) 60° (C) 45° (D) 30°

18. If the mean and mode of a data are 24 and 12 respectively, then its median is: (A) 25 (2) 20 (B) 18 (D) 22

CBSE Class 10 Maths Paper Analysis 2024

In the CBSE Class 10 Math Paper Analysis 2024. We evaluate the question paper based on the number of incorrect questions, the amount of questions that are not on the syllabus, and the difficulty level of the question paper. We provided a section-by-section analysis of the Class 10 Mathematics Paper based on feedback from students and professionals in this part.

CBSE Class 10 Maths Exam 2024 -Student’s Reviews

We talked to the students who appeared in Today’s Exam, Several students have expressed varying opinions about the difficulty level of the CBSE Class 10 Maths exam.

• While some found the paper doable and within their expectations, others were challenged by specific questions, particularly those involving sophisticated computations and application-based challenges.
• Many students rated the exam as Easy, but they hoped for more clarity in some of the problems. Overall, students are optimistic that their preparation efforts will produce satisfactory outcomes.

Maths Answer Key & Marking Scheme

The CBSE Class 10 Maths Answer Key 2024 and marking scheme might assist pupils in forecasting their exam scores. Check out the Class 10 Maths Paper Marking Scheme tabulated below.

• The theory paper of class 10 basic and standard level exams is held for a total of 80 points each.
• The CBSE 10th maths question paper will consist of five sections: A, B, C, D, and E.
• Section A contains 20 multiple-choice questions (MCQs) worth one mark each.
• Section B consists of five short answer-I (SA-I) questions worth two points each.
• Section C includes six short answer-II (SA-II) questions for three points each.
• Section D consists of four long answer (LA) questions worth five marks each.
• Section E comprises three units of assessment of four marks each: source-based, case-based, passage-based, or integrated, with sub-parts worth one, one, and two marks each.

Class 10 Maths Board Paper 2024 PDF Download

CBSE Class 10 Math Papers 2024 will be available here. Candidates can predict their results by obtaining the Class 10 SST Question Papers and reading the Class 10 Maths Answer Key 2024.

Class 10 Standard Maths Answer key with Solutions (Last Year)

This section comprises multiple choice questions (MCQ) of 1 mark each.

4. In the given figure, DE || BC. The value of x is

Answer: (c) 6.5 cm

9. Water in a river which is 3 m deep and 40 m wide is flowing at the rate of 2 km/h. How much water will fall into the sea in 2 minutes?

14. The 11th term from the end of the A.P.: 10, 7, 4, 62 is:

17. Which of the following numbers cannot be the probability of happening of an event?

19 Find the sum of first 30 terms of AP: -30, 24, -18,/..

Solution:  a= -30, d= 6

= 15 [-60 + 29 (6)]

= 15 [-60+174]

 If an AP is Sn = n(4n+1), then find the AP

Solution: S1 = T1 = 5

S2= T1 + T2= 18

S2-S1 = T2= 13

AP= 5, 13, 21, 29, …

21. A solid metallic sphere of radius 10.5 cm is melted and recast into a number of smaller cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so formed. 

Solution:  r1 = 10.5 cm (sphere) and r2 (cone)= 3.5 cm, h2= 3cm

4/3πr³ = n x 1/3πr2² h

4r³ = nr2² h

4 x (105/10)³= n x 35/10 x 35/10 x 3

Number of cones formed= 126

22. (a) Find the value of m for which the quadratic equation 

(m-1) x² + 2(m-1)x + 1 = 0

Solution:  D= 0

4 (m-1)² – 4(m-1) = 0

4 (m-1) [m-1-1]= 0

(m-1) (m-2)= 0

(b) Solve the following quadratic equation for x: √3x² + 10x + 7√3= 0

Solution:  √3x² + 3x + 7x + 7√3= 0

√3x (x+ √3) + 7 (x + √3)= 0

(x+ √3) [√3x + 7]= 0

x= √3 || x= -7/√3

23. Find the mode of the following frequency distribution: 

Solution:  l= 40, f1= 17, f2= 4, fo= 12

Mode= l + f1-fo / 2f1 – fo- f2

= 40 + 17-12 / 34-12-4 x 10

= 40 + 5/18 x 10

= 40 + 25/9

= 40 + 2.78

Q.5: The product of Rehan’s age (in years) 5 years ago and his age 7 years from now, is one more than twice his present age. Find his present age. 

(x-5) (x+7) = 2x + 1

x² + 2x -35 = 2x+1

x² – 36 = 0

Present Age- 6 years

Q.6 Two concentric circles are of radii 4 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Q.7: For what value of x, is the median of the following frequency distribution 34:5? 

Q.8: Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Construct tangents to the circle from these two points P and Q.

Q.9: (a) The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, then find the height of the building.

tan 60° = 50/b

b= 50/ tan 60°

b= 50√3 / 3

tan 30° = h/(50√3/3)

h= 50√3/3 x 1/√3

= 50/3 m= 16.67 metres

Q.9:(b) From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45° respectively. If the bridge is at a height of 3 m from the banks,  then find the width of the river.

Q.10: Following is the daily expenditure on lunch by 30 employees of a company, Find the mean daily expenditure of the employees.

Q.11: From a solid cylinder of the height of 30 cm and radius of 7 cm, a conical cavity of height of 24 cm and same radius is hollowed out. Find the total surface area of the remaining solid. 

Solution:  H= 30 cm

Total Surface Area of Cylinder = Curved Surface Area of Cylinder + Curved Surface Area of Cone + πr²

TSA = 2 πrh +  πrl + πr²

= πr (2h+ l+ r)

= 22/7 x 7 (60+25 + 7)

TSA= 2024 cm 

Q.12: In figure 1, a traingle ABC with angle B = 90 degrees is shown. Taking AB as diameter, a circle has been drawn intersecting AC at point P. Prove that the tangent drawn at point P bisects BC. 

Case Study:1

Q.13: In Mathematics, relations can be expressed in various ways. The matchstick patterns are based on linear relations. Different strategies can be used to calculate the number of matchsticks used in different figures. 

One such pattern is shown below. Observe the pattern and answer the following questions using Arithmetic Progression::

(a)  Write the AP for the number of triangles used in the figures. Also, write the nth term of this AP. Which figure has 61 matchsticks? 

Solution-  AP = 4, 6, 8, 10

Tn = 4 + 2(n-1)

Tn= = 4 + 2n – 2

(b) Which figures has 61 matchstickes?

Solution:  12, 19, 26, …

a + (n-1) d= 61

12 + 7(n-1) = 61

7(n-1) = 49

8th figure has 61 matchsticks

Q.14 Gadisagar lake is located in the jaisalmer district of Rajasthan. It was built by king of jaisalmer ad rebuilt by Gadsi Singh in 14th Century. The lake has many chattris. One of them is shown below: 

Observe the picture. From a point A h m above from water level, the angle of elevation of top of chattari (point B) is 45 degrees and angle of depression of its reflection in water(Point C) is 60 degrees. If the height of chhattri above the water level is 10m, then

a) Draw a well-labelled figure based on the above information;

b) Find the height of the point A above the water level. 

(Use √3 = 1.73)

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Where can I get the CBSE Class 10 Maths Answer key 2024 Standard?

The CBSE Class 10 Maths Answer key 2024 for board Standard and Basic Level will be shared on this page.

What is the total Marks of the CBSE Class 10 Maths Paper?

The CBSE Class 10 Maths Theory page Paper is of 80 Marks. remaining 20 marks is allocated for the Internal assessment.

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11 Real World Math Activities That Engage Students

Bridging the gap between abstract math concepts and real life experiences can make the subject accessible and relevant for kids.

During a unit on slope, José Vilson’s students just weren’t getting it, and their frustration was growing. The former middle school math teacher began brainstorming creative ways to illustrate the concept. “I kept thinking, ‘My students already understand how this works—they just don’t know that they know,’” Vilson writes in a recent article for Teacher2Teacher . “How can I activate knowledge they don’t believe they have?”

Then he thought about a hill a couple of blocks from school that his students “walk up every day to get to the subway.” He tacked up paper and began sketching stick figures on the hill. “One was at the top of the hill, one was halfway up, one was near the bottom skating on flat ground, and one was on a cliff,” writes Vilson, now the executive director of EduColor. “Which of these figures will go faster and why?” he asked his students. “That got my kids laughing because, of course, my stick figures weren’t going to hang in the MoMA.” Still, his sketch got them thinking and talking, and it provided a simple stepping stone that “gave that math relevance and belonging in their own lives,” Vilson concludes. 

“It’s not unusual for students to walk into our classrooms thinking that math belongs to people who are smarter, who are older, or who aren’t in their immediate circle,” Vilson writes. “But every time I teach math in a way that’s accessible and real for my students, I’m teaching them: ‘The math is yours.’”

To build on Vilson’s idea, we posted on our social channels asking teachers to share their favorite strategies for connecting math to students’ experiences and lives outside of school. We received hundreds of responses from math educators across grade levels. Here are 11 teacher-tested ideas that get students seeing and interacting with the math that surrounds them each day.

Hunt for clues

Coordinate systems can feel abstract to some students—but using coordinates to navigate a familiar space can solidify the concept in a relevant and fun way. “Before starting a unit on coordinates, I make gridded maps of the school—I make them look old using tea staining —and send my students off on a treasure hunt using the grid references to locate clues,” says Kolbe Burgoyne, an educator in Australia. “It’s meaningful, it’s fun, and definitely gets them engaged.”

Budget a trip

Students enjoy planning and budgeting for imaginary trips, teachers tell us, offering ample opportunities to practice adding, subtracting, and multiplying large numbers. In Miranda Henry’s resource classroom, for example, students are assigned a budget for a fictional spring break trip; then they find flights, hotels, food, and whatever else they’ll need, while staying within budget.

Math teacher Alicia Wimberley has her Texas students plan and budget a hypothetical trip to the Grand Canyon. “They love the real world context of it and start to see the relevance of the digits after the decimal—including how the .00 at the end of a price was relevant when adding.” One of Wimberley’s students, she writes, mixed up his decimals and nearly planned a $25,000 trip, but found his mistake and dialed back his expenses to under $3,000.

Tap into pizza love

Educators in our audience are big fans of “pizza math”—that is, any kind of math problem that involves pizza. “Pizza math was always a favorite when teaching area of a circle,” notes Shane Capps. If a store is selling a 10-inch pizza, for example, and we know that’s referring to its diameter, what is its total area? “Pizza math is a great tool for addition, subtraction, multiplication, word problems, fractions, and geometry,” another educator writes on our Instagram. There are endless pizza-based word problems online. Here’s a simple one to start, from Jump2Math : “The medium pizza had six slices. Mom and Dad each ate one slice. How much pizza is left?”

Break out the measuring cups

Lindsey Allan has her third-grade students break into pairs, find a recipe they like online, and use multiplication to calculate how much of each ingredient they’d need in order to feed the whole class. The class then votes on a favorite recipe, and they write up a shopping list—“which involves more math, because we have to decide, ‘OK, if we need this much butter for the doubled recipe, will we need three or four sticks, and then how much will be left over?’” Allan writes. “And then it turns out students were also doing division without even realizing!” 

Sometimes, a cooking mistake teaches students about proportions the hard way. “Nobody wants a sad chocolate chip cookie where you doubled the dough but not the chocolate chips,” adds teacher Holly Satter.

Heading outdoors is good for kids’ bodies , of course, but it can also be a rich mathematical experience. In second grade, kids can head out to measure perimeters, teacher Jenna McCann suggests—perhaps of the flower boxes in the school garden. If outdoors isn’t an option, there’s plenty of math to be found by walking around inside school—like measuring the perimeter of the tables in the cafeteria or the diameters of circles taped off on the gym floor.

In Maricris Lamigo’s eighth-grade geometry class, “I let [students] roam around the school and take photos of things where congruent triangles were applied,” says Lamigo. “I have students find distances in our indoor courtyard between two stickers that I place on the floor using the Pythagorean theorem,” adds Christopher Morrone, another eighth-grade teacher. In trigonometry, Cathee Cullison sends students outside “with tape measures and homemade clinometers to find heights, lengths, and areas using learned formulas for right and non-right triangles.” Students can make their own clinometers , devices that measure angles of elevation, using protractors and a few other household items.

Plan for adult life

To keep her math lessons both rigorous and engaging, Pamela Kranz runs a monthlong project-based learning activity where her middle school students choose an occupation and receive a salary based on government data. Then they have to budget their earnings to “pay rent, figure out transportation, buy groceries,” and navigate any number of unexpected financial dilemmas, such as medical expenses or car repairs. While learning about personal finance, they develop their mathematical understanding of fractions, decimals, and percents, Kranz writes.

Dig into sports stats

To help students learn how to draw conclusions from data and boost their comfort with decimals and percentages, fourth-grade teacher Kyle Pisselmyer has his students compare the win-loss ratio of the local sports team to that of Pisselmyer’s hometown team. While students can struggle to grasp the relevance of decimals—or to care about how 0.3 differs from 0.305—the details snap into place when they look at baseball players’ stats, educator Maggierose Bennion says.

March Madness is a great source of real world data for students to analyze in math class, says sixth-grade math teacher Jeff Norris. Last March, Norris decorated his classroom like a basketball court, then had his students do basic statistical analysis—like calculating mean, median, and mode—using March Madness data, including individual game scores and the total win rate of each team. “We also did some data collection through our own basketball stations to make it personally relevant,” Norris says; students lined up in teams to shoot paper balls into a basket in a set amount of time, recorded their scores in a worksheet, and then examined the scoring data of the entire class to answer questions about mean, median, mode, range, and outliers.

Go on a (pretend) shopping spree

“My students love any activities that include SHOPPING!” says Jessie, a sixth-grade teacher who creates shopping-related problems using fake (or sometimes real) store ads and receipts. Her students practice solving percentage problems, and the exercise includes opportunities to work with fractions and decimals.

To get students more engaged with the work, math educator Rachel Aleo-Cha zeroes in on objects she knows students are excited about. “I make questions that incorporate items like AirPods, Nike shoes, makeup, etc.,” Aleo-Cha says. She also has students calculate sales tax and prompts them to figure out “what a 50% off plus 20% off discount is—it’s not 70% off.”

Capture math on the fly

Math is everywhere, and whipping out a smartphone when opportunities arise can lead to excellent content for math class. At the foot of Mount Elbert in Colorado, for example, math teacher Ryan Walker recorded a short word problem for his fourth- and fifth-grade students. In the video, he revealed that it was 4:42 a.m., and it would probably take him 249 minutes to reach the summit. What time would he reach the summit, he asked his students—and, assuming it took two-thirds as long to descend, what time would he get back down?

Everyday examples can be especially relatable. At the gas station, “I record a video that tells the size of my gas tank, shows the current price of gas per gallon, and shows how empty my gas tank is,” says Walker. “Students then use a variety of skills (estimation, division, multiplying fractions, multiplying decimals, etc.) to make their estimate on how much money it will cost to fill my tank.”

Connect to social issues

It can be a powerful exercise to connect math to compelling social issues that students care about. In a unit on ratios and proportions, middle school teacher Jennifer Schmerler starts by having students design the “most unfair and unjust city”—where resources and public services like fire departments are distributed extremely unevenly. Using tables and graphs that reflect the distribution of the city’s population and the distribution of its resources, students then design a more equitable city.

Play entrepreneur

Each year, educator Karen Hanson has her fourth- and fifth-grade students brainstorm a list of potential business ideas and survey the school about which venture is most popular. Then the math begins: “We graph the survey results and explore all sorts of questions,” Hanson writes, like whether student preferences vary with age. Winning ideas in the past included selling T-shirts and wallets made of duct tape.

Next, students develop a resource list for the business, research prices, and tally everything up. They calculate a fair price point for the good they’re selling and the sales quantity needed to turn a profit. As a wrap-up, they generate financial statements examining how their profits stack up against the sales figures they had projected.

HELP OTHER TEACHERS OUT!

We’d love this article to be an evolving document of lesson ideas that make math relevant to kids. So, teachers, please tell us about your go-to activities that connect math to kids’ real world experiences.

CBSE NCERT Solutions

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Class 10 Mathematics Statistics Assignments

We have provided below free printable Class 10 Mathematics Statistics Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 10 Mathematics Statistics . These Assignments for Grade 10 Mathematics Statistics cover all important topics which can come in your standard 10 tests and examinations. Free printable Assignments for CBSE Class 10 Mathematics Statistics , school and class assignments, and practice test papers have been designed by our highly experienced class 10 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Statistics Class 10 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Statistics Class 10. Students can click on the links below and download all Pdf Assignments for Mathematics Statistics class 10 for free. All latest Kendriya Vidyalaya Class 10 Mathematics Statistics Assignments with Answers and test papers are given below.

Mathematics Statistics Class 10 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 10 Mathematics Statistics . Students and teachers can download and save all free Mathematics Statistics assignments in Pdf for grade 10th. Our expert faculty have covered Class 10 important questions and answers for Mathematics Statistics as per the latest syllabus for the current academic year. All test papers and question banks for Class 10 Mathematics Statistics and CBSE Assignments for Mathematics Statistics Class 10 will be really helpful for standard 10th students to prepare for the class tests and school examinations. Class 10th students can easily free download in Pdf all printable practice worksheets given below.

Topicwise Assignments for Class 10 Mathematics Statistics Download in Pdf

Advantages of Class 10 Mathematics Statistics Assignments

• As we have the best and largest collection of Mathematics Statistics assignments for Grade 10, you will be able to easily get full list of solved important questions which can come in your examinations.
• Students will be able to go through all important and critical topics given in your CBSE Mathematics Statistics textbooks for Class 10 .
• All Mathematics Statistics assignments for Class 10 have been designed with answers. Students should solve them yourself and then compare with the solutions provided by us.
• Class 10 Students studying in per CBSE, NCERT and KVS schools will be able to free download all Mathematics Statistics chapter wise worksheets and assignments for free in Pdf
• Class 10 Mathematics Statistics question bank will help to improve subject understanding which will help to get better rank in exams

Frequently Asked Questions by Class 10 Mathematics Statistics students

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We provide here Standard 10 Mathematics Statistics chapter-wise assignments which can be easily downloaded in Pdf format for free.

You can click on the links above and get assignments for Mathematics Statistics in Grade 10, all topic-wise question banks with solutions have been provided here. You can click on the links to download in Pdf.

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We have provided the best collection of question bank and practice tests for Class 10 for all subjects. You can download them all and use them offline without the internet.

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