Strictly Based on Latest Syllabus Issued by CBSE for 2017 · PDF fileof 2, 3, 5. Decimal...

Strictly Based on Latest Syllabus Issued by CBSE for 2017 Examination

OSWAAL CBSE

MATHEMATICS

SAMPLEQUESTIONPAPERSCLASS 10

TERM 1 SEPTEMBER 2016 EXAMINATION

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OUR DISTRIBUTORS

CONTENTS

z Syllabus v - vii

z On Tips Notes 9 - 22

z Sample Question Papers

� Sample Question Paper - 1 (Solved) 23 - 26





z Self Assessment

� Sample Question Paper - 6 40 - 43





z Solutions






qq

(iii)

Latest Syllabus for Academic year - 2016-17MATHEMATICS

CLASS X

First Term Marks : 90

UNITS MARKS

I. NUMBER SYSTEMS 11

II. ALGEBRA 23

III. GEOMETRY 17

IV. TRIGONOMETRY 22

V. STATISTICS 17

TOTAL 90

UNIT I : NUMBER SYSTEMS

1. REAL NUMBER (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 irrationality

of 2, 3, 5. Decimal representation of rational numbers in terms of terminating/non-

terminating recurring decimals.

UNIT II : ALGEBRA

1. POLYNOMIALS (7) Periods Zerosofapolynomial.Relationshipbetweenzerosandcoefficientsofquadraticpolynomials.

Statementandsimpleproblemsondivisionalgorithmforpolynomialswithrealcoefficients.

2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES (15) Periods

Pairoflinearequationsintwoveriablesandgraphicalmethodoftheirsolution,consistency/

inconsistency.

Algebraic conditions fornumberof solutions,Solutionofapairof linearequations in two

variables algebraically-by substitution, by elimination and by cross multiplication method.

Simplesituationalproblems.Simpleproblemsonequationsreducibletolinearequations.

(v)

UNIT III : GEOMETRY

1. TRIANGLES (15) Periods Definitions,examples,counplerexamplesofsimilartriangles. 1. (Prove) if a line is drawn parallel to one side of a triangle to intersect the other two sides

in distinct points, the other two sides are divided in the same ratio. 2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel

tto the third side. 3. (Motivate) Ifintwotriangles,thecorrespondinganglesareequal,theircorresponding

sides are proportional and the triangles are similar. 4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding

anglesareequalandthetwotrianglesaresimilar. 5. (Motivate) Ifoneangleofatriangleisequaltooneangleofanothertriangleandthe

sides including these angles are proportional, the two triangles are similar. 6. (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle

to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other.

7. (Prove)Theratiooftheareasoftwosimilartrianglesisequaltotheratioofthesquareson their corresponding sides.

8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of thesquaresontheothertwosides.

9. (Prove)Inatriangle,ifthesquareononesideisequaltosumofthesquaresontheothertwosides,theanglesoppositetothefirstsideisarightangle.

UNIT IV : TRIGONOMETRY

1. INTRODUCTION TO TRIGONOMETRY (10) Periods Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well

defined);motivatetheratioswhicheveraredefinedat0°and90°.Values(withproofs)ofthetrigonometricratiosof30°,45°and60°.Relationshipsbetweentherations.

2. TRIGONOMETRIC IDENTITIES (15) Periods Proof and applications of the identity sin2A + cos2A = 1, Only simple identities to be given.

Trigonometric ratios of complementary angles.

UNIT V : STATISTICS

1. STATISTICS (18) Periods Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative

frequencygraph.

PRESCRIBED BOOKS : (18) Periods 1. Mathematics - Textbook for class X - NCERT Publication. 2. Guidelines for Mathematics Laboratory in Schools, class X - CBSE Publication. 3. A handbook for Designing Mathematics Laboratory in Schools - NCERT Publication. 4. Laboratory Manual - Mathematics, secondary stage - NCERT publication. 5. Mathematics exemplar problems for class X, NCERT publication.

(vi)

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(vii)

Writing Notes

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ON TIPS NOTESNote-making is a skill that we use in many walks of life: at school, at university and in the world of work. However, accurate note-making requires a thorough understanding of concepts. We, at Oswaal, have tried to encapsulate all the chapters from the given syllabus into the following ON TIPS NOTES. These notes will not only facilitate better understanding of concepts, but will also ensure that the each and every concept is taken up and every chapter is covered in totality. So, go ahead and use these to your advantage… go get the OSWAAL ADVANTAGE!!

CHAPTER 1 : Real Numbers

Fundamentals :

� A non-negative integer ‘p’ is said to be divided by an integer ‘q’ if there exists an integer ‘d’ such that: p = qd.

� ± 1 divides every non-zero integer. � 0 does not divide any integer.

Euclid’s Division Lemma : Let a and b be any two positive integers, then there exists unique integers q and r such that: a = bq + r, 0 £ r < b

Euclid’s Division Algorithm : Let a and b be any two positive integers such that a > b and ‘q’ and ‘r’ as quotient and remainder

Take a as dividend and b as divisor \ a = bq + r, 0 £ r < b then every common divisor of a and b is a common divisor of b and r.

� Finding HCF of two positive integers using Euclid’s Division Algorithm : Step 1 : Apply Euclid’s lemma to a and b : a = bq1 + r1. Step 2 : If r1 = 0, then HCF = b. Step 3 : If r1 ¹ 0, then again apply Euclid’s lemma : b = q1r1 + r2

Step 4 : If r2 = 0, then HCF = r1 . Step 5 : If r2 ¹ 0 , then again apply Euclid’s lemma till remainder rn = 0, then the divisor is HCF.

Fundamental Theorem of Arithmetic: Every composite number can be expressed as a product of primes, and this factorisation is unique

except for the order in which the prime factors occur. Important Theorems : 1. Let p be a prime number and a be a positive integer. If p divides a2, then p divides a.

2. Consider two positive integers a and b, then LCM × HCF = a × b.

3. Let x be a rational number whose decimal expansion terminates.

Then we can express x in the form ,pq

where p and q are co-prime and the prime Factorisation of q is

of the form 2n5m, where n, m are non-negative integers.

Oswaal CBSE CCE Sample QuestionPapers For Class 10 Term I (April to

September 2016) Mathematics

Publisher : Oswaal Books ISBN : 9789351279389 Author : Panel Of Experts

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