10th Maths Guide pdf

10th Maths Guide PDF Download 2022 to 2023- Book Solutions for Class X (Samcheer Kalvi)

10th Maths Guide PDF Download 2022-2023 NCERT Solutions for Class X (Samcheer Kalvi) Free Download Samcheer Kalvi

10th Maths Guide – NCERT Solutions for Class 10 Maths Book Class 10 PDF Free Download, SYLLABUS & Course Structure Class 10th Guide- Samcheer kalvi PDF Download Now by below given link.

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10th Maths Guide pdf download free for 2022 of Class – Xth. You can download full free pdf of 10th Maths Guide and Question Bank (KV) of Session 2021-2002.

THEORY & SYLLABUS – 10th Maths Guide PDF Download


1. REAL NUMBERS (15) Periods
Euclid’s division lemma, Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of results – irrationality of
2, 3, 5 decimal expansions of rational numbers in terms of terminating/non-terminating recurring decimals.


1. POLYNOMIALS (7) Periods
Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients.

Pair of linear equations in two variables and their graphical solution. Geometric representation of different possibilities of solutions/inconsistency.
Algebraic conditions for number of solutions. Solution of pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication. Simple situational problems must be included. Simple problems on equations reducible to linear equations may be included.

Standard form of a quadratic equation ax2 + bx + c = 0, (a „j 0). Solution of the quadratic equations (only real roots) by factorization and by using quadratic formula. Relationship between discriminant and nature of roots. Problems related to day to day activities to be incorporated. Situational problems based on quadratic equations related to day to day activities to be incorporated.

4. ARITHMETIC PROGRESSIONS Periods Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms and their application in solving daily life problems.


1. LINES (In two-dimensions) (14) Periods
Review the concepts of coordinate geometry done earlier including graphs of linear equations. Distance between two points and section formula (internal). Area of a triangle.



  1. INTRODUCTION TO TRIGONOMETRY (10) Periods Trigonometric ratios of an acute angle of a right-angled Proof of their existence (well defined); motivate the ratios, whichever are defined at 00 & 900. Values (with proofs) of the trigonometric ratios of 300, 450 & 600. Relationships between the ratios.
  1. TRIGONOMETRIC IDENTITIES (15) Periods Proof and applications of the identity sin2A + cos2A = Only simple identities to be given. Trigonometric ratios of complementary angles.
  1. HEIGHTS AND DISTANCES (8) Periods Simple and believable problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 300, 450 & 600



  1. STATISTICS (18) Periods

Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.

  1. PROBABILITY (10) Periods

Classical definition of probability. Connection with probability as given in Class IX. Simple problems on single events, not using set notation.


  • Pen Paper Test and Multiple Assessment (5+5) 10 Marks
  • Portfolio 05 Marks
  • Lab Practical (Lab activities to be done from the prescribed books) 05 Marks


Name of Chapter


Real Numbers




Pair of Linear





Co – ordinate



Introduction to trigonometry


Area related to circles





1. If m = pq3 and n = p3q,then HCF (m, n) =
a) pq b) pq3 c) p3q3 d) p2q3

2. HCF of co-primes a and b is
a) ab b) 1 c) a d) b

3. The LCM of smallest composite number and the smallest prime number is
a) 2 b) 1 c) 4 d) 3

4. Which of the following rational numbers have terminating decimal?
i) 16 125
ii) 5 18
iii) 2 21

iv) 7 250

a) i and ii b) ii and iii c) i and iii d) i and iv

5. After how many places the decimal expansion of 13 23 × 52
a) 3 b) 2 c) 4 d) 1

6. The LCM and HCF of two rational numbers are equal, then the numbers must be
a) prime b) co-prime c) composite d) equal

7. Two positive numbers have their HCF as 12 and their product as 6336.The number of pairs possible for the numbers, is….
a) 2 b) 3 c) 4 d) 5

8. If the LCM of a and 18 is 36 and the HCF of a and 18 is 2, then a = …
a) 2 b) 3 c) 4 d) 1

9. The least number that is divisible by all the numbers between 1 and 10 (both inclusive) is
a) 2520 b) 2450 c) 2420 d) 2250

10. The smallest number which gives remainders 8 and 12 when divided by 28 and 32 respectively is..
a) 180 b) 240 c) 204 d) 210

11. The smallest 4 digit number divisible by 24,15 and 36 is
a) 1000 b) 1208 c) 1800 d)1080

12. The largest number which exactly divides 280 and 1245 leaving remainders 4 and 3respectively is…
a) 36 b) 54 c) 138 d) 72

13. The ratio of LCM and HCF of the least composite and the least prime numbers is
a) 1:2 b) 2:1 c) 1:1 d) 1:3

14. If sum of two numbers is 1215 and their HCF is 81, then the possible number of pairsof such numbers are
a) 2 b) 3 c) 4 d) 5

15. The sum of the exponents of the prime factors in the prime factorisation of 196,is
a) 1 b) 2 c) 4 d) 6

16. The LCM of two numbers is 1200,Which of the following cannot be their HCF?
a) 600 b) 500 c) 400 d) 200

17. 3.2��7� is
a) an integer b) a rational number c) a natural number d) an irrational number

Answers- 10th Maths Guide: –

1 (a) 2 (b) 3 (c) 4 (d) 5 (a) 6 (d) 7 (a)
8 (c) 9 (a) 10 (c) 11 (d) 12 (c) 13 (b) 14 (c)
15 (c) 16 (b) 17 (b)        
10th Maths Guide pdf download free


1. Three sets of English, Hindi and Mathematics books have to be stacked in such a way that all the books are stored topic-wise and the height of each stack is same. The number of English books is 96,the number of Hindi books is 240 and the number of Mathematics books is 336. Assuming that the books are of the same thickness. Using this data answer the following questions

i. The maximum number of books in each stack is
a) 12 b) 24 c) 48 d) 36

ii. Number of stacks of English books is
a) 2 b) 7 c) 5 d) 12

iii. Number of stacks of Mathematics books is
a) 2 b) 7 c) 5 d) 12

iv. Number of stacks of Hindi books is
a) 2 b) 7 c) 5 d) 12

v. Which Mathematical concept was used in finding the maximum number of books in each stack?
a) LCM b) HCF c) Neither HCF nor LCM d) Fundamental theorem of Arithmetic

2. 105 goats,140 donkeys and 175 cows have to be taken across a river. There is only one boat which will have to make many trips in order to do so. The lazy boatman has his own conditions for transporting them. He insists that he will take the same number of animals in every trip and they have to be of same kind. He will naturally like to take the largest possible number each time.

i. How many animals have been taken in each trip?
a) 12 b) 35 c) 70 d) 24

ii. How many trips to be done so that all animals crossed the river?
a) 12 b) 35 c) 70 d) 24

iii. When the animals were doubled,how many animals could be taken in each trip?
a) 12 b) 35 c) 70 d) 24

iv. The LCM of all animals is
a) 2400 b) 2300 c) 2100 d) 2000

3. To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections –Section A and Section B of grade X. There are 32 students in section A and 36 students in section B

i. What is the minimum number of books you will acquire for the class library, so that they can bedistributed equally among students of Section A or Section B?
a) 144 b) 128 c) 288 d) 272

ii. If the product of two positive integers is equal to the product of their HCF and LCM is true, thenthe HCF(32,36)is..
a) 2 b) 4 c) 6 d) 8

iii. 36 can be expressed as a product of its primes as
a) 22 x 32 b) 21 x 33 c) 23 x 31 d) 20 x 30

iv. 7 x 11 x 13 x 15 + 15 is a
a) Prime number b) composite number c) neither prime or composite d) None of the above

v. If p and q are positive integers such that p = ab2 and q = a2b,where a and b are prime numbers, then the LCM (p, q) is…
a) ab b) a2b2 c) a3b2 d) a3b3

4. A seminar is being conducted by an Educational Organisation,where the participants will be educators of different subjects. The number of participants in Hindi,English and Mathematics are 60, 84 and 108 respectively.
i. In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number participants that can accommodated in each room are
a) 14 b) 12 c) 16 d) 18

ii. What is the minimum number of rooms required during the event?
a) 11 b) 31 c) 41 d) 21

iii. The LCM of HCF and LCM of 60, 84 and 108 is
a) 3780 b) 3680 c) 4780 d) 4680

iv. The product of HCF and LCM 60,84 and 108 is…
a) 55360 b) 35360 c) 45500 d) 45360

v. 108 can be expressed as a product of its primes as
a) 22 x 32 b) 23 x 33 c) 22 x 32 d) 22 x 33

1 (i) (c) 1 (ii) (a) 1 (iii) (b) 1 (iv) (c) 1 (v) (b) 2 (i) (b) 2 (ii) (a)
2 (iii) (c) 2 (iv) (c) 3 (i) (c) 3 (ii) (b) 3 (iii) (a) 3 (iv) (b) 3 (v) (b)
4 (i) (b) 4 (ii) (d) 4 (iii) (a) 4 (iv) (d) 4 (v) (d)   10th Maths Guide

NCERT Solutions for Class 10 Maths Book Class 10

10th Maths Guide – NCERT Solutions for Class 10 Maths Book

10th Maths Guide

NCERT Solutions for Class 10 Maths Book Class 10th Maths Guide

10th Maths Guide PDF Full Download

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