# CLASS X FORMULAE MATHS

Size: px
Start display at page:

Transcription

1 Real numbers: Euclid s division lemma Given positive integers a and b, there exist whole numbers q and r satisfying a = bq + r, 0 r < b. Euclid s division algorithm: This is based on Euclid s division lemma. According to this, the HCF of any two positive integers a and b, with a > b, is obtained as follows: Step 1: Apply the division lemma to find q and r where a = bq + r, 0 r < b. Step 2: If r = 0, then HCF is b. If r 0, apply Euclid s lemma to b and r. Step 3: Continue the process till the remainder is zero. The divisor at this stage will be HCF (a, b). Also, HCF (a, b) = HCF (b, r). The fundamental theorem of arithmetic Every composite number can be expressed (factorised) as a product of primes, and this factorization is unique, apart from the order in which the prime factors occur. Let x = p/q be a rational number, such that prime factorisation of q is of the form 2 n 5 m, where m,n are nonnegative integers. Then x has a decimal expansion which is terminating. Let x = p/q be a rational number, such that prime factorization of q is not of the form 2 n 5 m, where m, n are non-negative integers. Then x has a decimal expansion which is non-terminating repeating. Polynomial: A quadratic polynomial in x with real coefficients is of the form ax 2 + bx + c, where a, b, c are real numbers with a 0. The zeroes of a polynomial p(x) are precisely the x-coordinates of the points, where the graph of y = p(x) intersects the x -axis. A quadratic polynomial can have at most 2 zeroes and a cubic polynomial can have at most 3 zeroes. If α and β are the zeroes of the quadratic polynomial ax 2 + bx + c, then

2 Sum of zeroes (α +β) = b a Product of zeroes (αβ) = c a If α, β, γ are the zeroes of the cubic polynomial ax 3 + bx 2 + cx + d = 0, then Sum of zeroes taken one at time (α +β + γ) = b a Sum of zeroes taken two at time (αβ+ βγ+ γα) = c a Product of zeroes (αβγ) = d a Pair of linear equations in two variables: If the lines intersect at a point, then that point gives the unique solution of the two equations. In this case, the pair of equations is consistent. If the lines coincide, then there are infinitely many solutions each point on the line being a solution. In this case, the pair of equations is dependent (consistent). If the lines are parallel, then the pair of equations has no solution. In this case, the pair of equations is inconsistent. Simultaneous pair of Linear equation a x + b y + c = 0 a x + b y + c = 0 Condition a a b b Graphical representation Intersecting lines; The intersecting point coordinate is the only solution Algebraic interpretation One unique solution only a x + b y + c = 0 a x + b y + c = 0 a a = b b = c c Coincident lines; The any coordinate on the line is the solution. Infinite solutions

3 a x + b y + c = 0 a x + b y + c = 0 a a = b b c c Parallel Lines No solution Cross multiplication method: a x + b y + c = 0 a x + b y + c = 0 x y 1 = = b c b c a c a c a b a b Value of x can be obtained by using first and last expression. Value of y can be obtained by using second and last expression. Quadratic equation: The roots of quadratic equation ax 2 + bx + c = 0, a 0 are given by ± " provided D 0. Discriminant of the quadratic equation ax 2 + bx + c = 0, a 0 is given by D = b 2-4 ac b 2-4ac > 0 then we will get two real solutions to the quadratic equation. b 2-4ac = 0 then we will get two equal real solutions to the quadratic equation. b 2-4ac > 0 then we will no real solution to the quadratic equation. A quadratic equation can also be solved by method of completing square. (a +b) 2 = a 2 + b 2 + 2ab (a -b) 2 = a 2 + b 2 2ab Arithmetic Progression: If a, b, c are in AP, then 2b = a + c nth term of an arithmetic progression: T n = a + (n 1)d

4 Number of terms of an arithmetic progression: n = la d + 1 Where n = number of terms, a= the first term, l = last term, d= common difference Additional notes on AP To solve most of the problems related to AP, the terms can be conveniently taken as: 3 terms: (a d), a, (a +d) 4 terms: (a 3d), (a d), (a + d), (a +3d) 5 terms: (a 2d), (a d), a, (a + d), (a +2d) The nth term of an A.P is the difference of the sum to the first n terms and the sum to first (n-1) terms of it: T n = S n - S n -1 If each term of an AP is increased, decreased, multiplied or divided by the same non-zero constant, the resulting sequence also will be in AP. In an AP, sum of terms equidistant from beginning and end will be constant. A.P which contain finite term is called finite A.P and which contains infinite terms is called infinite term. Triangles: ABC ~ PQR " " = " " = " " = By A.A. test or S.A.S test or by S.S.S. test C.P.S.T. Areas of ~ s are proportional to squares of their corresponding sides. A 1 = A 2 = "#\$ = "#\$ A median divides a into 2 s with equal area. An area of s meeting at common vertex and base through the same straight line is proportional to their bases. If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then the triangles on both sides of the perpendicular are similar to the whole triangle and also to each other. Coordinate geometry : Distance formula Distance = x x + y y. (The same formula is to be used to find the length of line segment, sides of a triangle, square, rectangle, parallelogram etc.) Section formula

5 Point (x, y) =, If point P(x, y) divides AB in k:1, then the coordinates of point P will be (kx 2 /k+1, ky 2 +y 1 /k+1) Mid-point =, Centroid of a triangle =, To prove co-linearity of the given three points A,B, and C, You have to find length of AB, BC, AC then use the condition AB + BC = AC. Area of triangle Area of triangle: 1/2[x 1 (y 2 y 3 ) + x 2 (y 3 y 1 ) + x 3 (y 1 y 2 )] = 0 Area cannot be negative so, we shall ignore negative sign if it s occurring in the problem. If the area of the triangle is zero, then vertices of the triangle are collinear. To find the area of quadrilateral we shall divide it into two triangles by joining two opposite vertices, find their areas and add them. Introduction to trigonometry: Wherever Square appears think of using the identities (i) Sin 2 θ + Cos 2 θ = 1 (ii) Sec 2 θ Tan 2 θ = 1 (iii) Cosec 2 θ Cot 2 θ = 1 Try to convert all the values of the given problem in terms of Sin θ and Cos θ Cosec θ may be written as 1/Sin θ Sec θ may be written as 1/Cos θ Cot θ may be written as 1/Tan θ Tan θ may be written as Sin θ / Cos θ Wherever fractional parts appears then think of taking their LCM Think of using (a + b) 2, (a b) 2, (a + b) 3, (a b) 3 formulae etc.

6 Rationalise the denominator [If a + b, (or) a b format is given in the denominator] You may separate the denominator "# "# "# For Ex: as "# "# + "# "# = 1 + Cot θ Sin (90 θ) = Cos θ : Cos (90 θ) = Sin θ Sec (90 θ) = Cosec θ : Cosec (90 θ) = Sec θ Tan (90 θ) = Cot θ : Cot (90 θ) = Tan θ Circles: The tangent to a circle is perpendicular to the radius through the point of contact. The lengths of the two tangents from an external point to a circle are equal. Area related to circle: Area of a Circle = π r 2 Perimeter of a Circle = 2πr Area of sector = θ/360 (πr 2 ) Length of an arc = θ/360 (2πr) Area of ring = π (R 2 r 2 ) Area of segment = Area of the corresponding sector Area of the corresponding triangle = ( " sinθ) "# Where, θ is the central angle in degrees. Distance moved by a wheel in one revolution = Circumference of the wheel. Angle described by minute hand in 60 minutes = Angle described by minute hand in 1minute = "# Number of revolutions = " = 60 "#\$% "#\$%&'( "#\$% "#\$%&'(#()\$( " "# "##\$ Surface areas and volume: Cylinder Volume of a cylinder = πr 2 h Curved surface area = 2πrh Total surface area = 2πrh + 2πr 2 = 2πr (h + r) Volume of hollow cylinder = πr 2 h πr 2 h = π(r 2 r 2 )h TSA of hollow cylinder = Outer CSA + Inner CSA + 2 Area of ring = 2πRh + 2 πrh + 2[πR 2 πr 2 ] Cone Volume of a Cone = πr2 h CSA of a Cone = πrl (Here l refers to Slant Height ) [where l = h + r ] TSA of a Cone = πrl + πr 2 = πr (l + r)

7 Frustum Volume of a frustum = πh [R2 + r 2 + Rr] CSA of a frustum = πl[r +r] (Here l refers to Slant height ) [where l = h + (R r) ] TSA of a frustum = πl(r +r)+ πr 2 + πr 2 = Sphere Surface area of a Sphere = 4 πr 2 (In case of Sphere, CSA = TSA i.e. they are same) Volume of hemisphere = πr3 [Take half the volume of a sphere] CSA of hemisphere = 2πr 2 [Take half the SA of a sphere] TSA of hemisphere = 2πr 2 + πr 2 = 3πr 2 Volume of a sphere = πr3 Volume of spherical shell = Outer volume Inner volume = π (R3 r 3 ) While solving the problems based on combination of solids it would be better if you take common. T.S.A of combined solid = C.S.A of solid 1 + C.S.A of solid 2 + C.S.A of solid 3 If a solid is melted and, recast into number of other small solids, then Volume of the larger solid = No of small solids x Volume of the smaller solid For Ex: A cylinder is melted and cast into smaller spheres. Find the number of spheres Volume of Cylinder = No of sphere Volume of sphere If an ice cream cone with hemispherical top is given then you have to take (a) Total Volume = Volume of Cone + Volume of Hemisphere (b) Surface area = CSA of Cone + CSA of hemisphere Statistics: Mean The mean for grouped data can be found by: (i) The direct method: X = "#" " (ii) The assumed mean method: X = a +, where d " = x a (iii) The step deviation method: X = a + h, where u " = Mode The mode for the grouped data can be found by using the formula: Mode = l + h l = lower limit of the modal class. f = frequency of the modal class. f =frequency of the preceding class of the modal class. f = frequency of the succeeding class of the modal class. h = size of the class interval.

8 Median The median for the grouped data can be found by using the formula: Median = l + " h l = lower limit of the median class. n = number of observations. cf = cumulative frequency of class interval preceding the median class. f = frequency of median class. h = class size. Empirical Formula: Mode = 3 median 2 mean. Probability: Probability of an event: P (event) = "#\$%& " "#\$%"&'( "#\$%&' "#\$% "#\$%& " "#\$%&' In a deck of playing cards, there are four types of cards: (Spades in Black colour) having A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, K, and Q total 13 cards (Clubs in Black colour) having A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, K, and Q total 13 cards (Hearts in Red colour) having A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, K, and Q total 13 cards (Diamond in Red colour) having A, 2, 3, 4, 5, 6, 7,8, 9, 10, J, K, and Q total 13 cards 52 cards Jack, King and Queen are known as Face Cards, as these cards are having some pictures on it. Always remember Ace is not a face card as it doesn t carry any face on it.

### MATHEMATICS FORMULAE AND CONCEPTS. for CLASS X CHAPTER WISE IMPORTANT FORMULAS & CONCEPTS, Prepared by

MATHEMATICS FORMULAE AND CONCEPTS for CLASS X 017 18 CHAPTER WISE IMPORTANT FORMULAS & CONCEPTS, Prepared by M. S. KUMARSWAMY, TGT(MATHS) M. Sc. Gold Medallist (Elect.), B. Ed. Kendriya Vidyalaya GaCHiBOWli

### MATHEMATICS ( CANDIDATES WITH PRACTICALS/INTERNAL ASSESSMENT ) ( CANDIDATES WITHOUT PRACTICALS/INTERNAL ASSESSMENT )

Total No. of Printed Pages 6 X/5/M 0 5 MATHEMATICS ( CANDIDATES WITH PRACTICALS/INTERNAL ASSESSMENT ) Full Marks : 80 Pass Marks : 4 ( CANDIDATES WITHOUT PRACTICALS/INTERNAL ASSESSMENT ) Full Marks : 00

### CBSE QUESTION PAPER CLASS-X MATHS

CBSE QUESTION PAPER CLASS-X MATHS SECTION - A Question 1:If sin α = 1 2, then the value of 4 cos3 α 3 cos α is (a)0 (b)1 (c) 1 (d)2 Question 2: If cos 2θ = sin(θ 12 ), where2θ and (θ 12 ) are both acute

### UNIT I : NUMBER SYSTEMS

CLASS X First Term Marks : 80 UNITS MARKS I. NUMBER SYSTEMS 10 II. ALGEBRA 20 III. GEOMETRY 15 IV TRIGONOMETRY 20 V STATISTICS 15 TOTAL 80 UNIT I : NUMBER SYSTEMS 1. REAL NUMBERS (15) Periods Euclid's

### COURSE STRUCTURE CLASS -X

COURSE STRUCTURE CLASS -X Units Unit Name Marks I NUMBER SYSTEMS 06 II ALGEBRA 20 III COORDINATE GEOMETRY 06 IV GEOMETRY 15 V TRIGONOMETRY 12 VI MENSURATION 10 VII STATISTICS & PROBABILTY 11 Total 80 UNIT

### Blue print Chapters 1mark 2marks 3marks 4marks total

PRE-BOARD SAMPLE PAPER 2018-19 CLASS-X BLUEPRINT Blue print Chapters 1mark 2marks 3marks 4marks total real numbers 1 1 5 Polynomials 1 1 4 Linear equations 1 1 6 quadratic equation 1 1 6 A.P. 1 4 Triangles

### MATHEMATICS. IMPORTANT FORMULAE AND CONCEPTS for. Summative Assessment -II. Revision CLASS X Prepared by

MATHEMATICS IMPORTANT FORMULAE AND CONCEPTS for Summative Assessment -II Revision CLASS X 06 7 Prepared by M. S. KUMARSWAMY, TGT(MATHS) M. Sc. Gold Medallist (Elect.), B. Ed. Kendriya Vidyalaya GaCHiBOWli

### Class X Mathematics Sample Question Paper Time allowed: 3 Hours Max. Marks: 80. Section-A

Class X Mathematics Sample Question Paper 08-9 Time allowed: Hours Max. Marks: 80 General Instructions:. All the questions are compulsory.. The questions paper consists of 0 questions divided into sections

### Question 1 ( 1.0 marks) places of decimals? Solution: Now, on dividing by 2, we obtain =

Question 1 ( 1.0 marks) The decimal expansion of the rational number places of decimals? will terminate after how many The given expression i.e., can be rewritten as Now, on dividing 0.043 by 2, we obtain

### X- MATHS IMPORTANT FORMULAS SELF EVALUVATION 1. SETS AND FUNCTIONS. 1. Commutative property i ii. 2. Associative property i ii

X- MATHS IMPORTANT FORMULAS SELF EVALUVATION 1. SETS AND FUNCTIONS 1. Commutative property i ii 2. Associative property i ii 3. Distributive property i ii 4. De Morgan s laws i ii i ii 5. Cardinality of

### KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD-32. SECTION A Questions 1 to 6 carry 1 mark each.

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD-32 SAMPLE PAPER TEST 05 (2018-19) (SAMPLE ANSWERS) SUBJECT: MATHEMATICS MAX. MARKS : 80 CLASS : X DURATION : 3 HRS SECTION A Questions 1 to 6 carry 1 mark

### Class X Mathematics Sample Question Paper Time allowed: 3 Hours Max. Marks: 80. Section-A

Class X Mathematics Sample Question Paper 08-9 Time allowed: Hours Max. Marks: 80 General Instructions:. All the questions are compulsory.. The questions paper consists of 0 questions divided into sections

### MATHS X STD. Try, try and try again you will succeed atlast. P.THIRU KUMARESA KANI M.A., M.Sc.,B.Ed., (Maths)

MATHS X STD Try, try and try again you will succeed atlast P.THIRU KUMARESA KANI M.A., M.Sc.,B.Ed., (Maths) Govt.Girls High School,Konganapuram Salem (Dt.) Cell No. 9003450850 Email : kanisivasankari@gmail.com

### CBSE Class X Mathematics Board Paper 2019 All India Set 3 Time: 3 hours Total Marks: 80

CBSE Class X Mathematics Board Paper 2019 All India Set 3 Time: 3 hours Total Marks: 80 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 30 questions divided

### DESIGN OF THE QUESTION PAPER Mathematics Class X NCERT. Time : 3 Hours Maximum Marks : 80

DESIGN OF THE QUESTION PAPER Mathematics Class X Weightage and the distribution of marks over different dimensions of the question shall be as follows: (A) Weightage to Content/ Subject Units : S.No. Content

### PRE BOARD EXAMINATION CODE : E SESSION CLASS : X MAXIMUM MARKS: 80 SECTION A

PRE BOARD EXAMINATION CODE : E SESSION 017-018 CLASS : X MAXIMUM MARKS: 80 SUBJECT : MATHEMATICS TIME : HOURS General Instructions: (i) All questions are compulsory. (ii) The question paper consists of

### MATHEMATICS ( CANDIDATES WITH PRACTICALS/INTERNAL ASSESSMENT ) ( CANDIDATES WITHOUT PRACTICALS/INTERNAL ASSESSMENT )

Total No. of Printed Pages 6 X/3/M 0 3 MATHEMATICS ( CANDIDATES WITH PRACTICALS/INTERNAL ASSESSMENT ) Full Marks : 80 Pass Marks : 4 ( CANDIDATES WITHOUT PRACTICALS/INTERNAL ASSESSMENT ) Full Marks : 00

### CBSE CLASS-10 MARCH 2018

CBSE CLASS-10 MARCH 2018 MATHEMATICS Time : 2.30 hrs QUESTION & ANSWER Marks : 80 General Instructions : i. All questions are compulsory ii. This question paper consists of 30 questions divided into four

### 1. SETS AND FUNCTIONS

. SETS AND FUNCTIONS. For two sets A and B, A, B A if and only if B A A B A! B A + B z. If A B, then A + B is B A\ B A B\ A. For any two sets Pand Q, P + Q is " x : x! P or x! Q, " x : x! P and x b Q,

### *P59022A0228* International GCSE Mathematics Formulae sheet Higher Tier DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA

Arithmetic series Sum to n terms, S n = n 2 The quadratic equation International GCSE Mathematics Formulae sheet Higher Tier [2a + (n 1)d] Area The solutions of ax 2 + bx + c = 0 where a ¹ 0 are given

### TERMWISE SYLLABUS SESSION CLASS-X SUBJECT : MATHEMATICS Course Structure

TERMWISE SYLLABUS SESSION--19 CLASS-X SUBJECT : MATHEMATICS Course Structure Units Unit Name Marks I NUMBER SYSTEMS 06 II ALGEBRA 20 III COORDINATE GEOMETRY 06 IV GEOMETRY 15 V TRIGONOMETRY 12 VI MENSURATION

### X- MATHS IMPORTANT FORMULAS SELF EVALUVATION

X- MATHS IMPORTANT FORMULAS SELF EVALUVATION 1. SETS AND FUNCTIONS 1. Commutative property i ii 2. Associative property i ii 3. Distributive property i ii 4. De Morgan s laws i ii i ii 5. Cardinality of

OSWAAL BOOKS LEARNING MADE SIMPLE FOR CBSE MARCH 2019 EXAM SOLVED PAPER 2018 MATHEMATICS CLASS 10 Published by : OSWAAL BOOKS 1/11, Sahitya Kunj, M.G. Road, Agra - 282002, UP (India) Ph.: 0562 2857671,

### 1 / 23

CBSE-XII-07 EXAMINATION CBSE-X-009 EXAMINATION MATHEMATICS Series: HRL Paper & Solution Code: 0/ Time: Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question paper

### CBSE Board Class X Mathematics

CBSE Board Class X Mathematics Time: 3 hrs Total Marks: 80 General Instructions: 1. All questions are compulsory.. The question paper consists of 30 questions divided into four sections A, B, C, and D.

### CBSE CLASS-10 MARCH 2018

CBSE CLASS-10 MARCH 2018 MATHEMATICS Time : 2.30 hrs QUESTION Marks : 80 General Instructions : i. All questions are compulsory ii. This question paper consists of 30 questions divided into four sections

### TOPIC-1. Unit -I : Number System. Chapter - 1 : Real Numbers. Euclid s Division Lemma and Fundamental Theorem of Arithmetic.

Unit -I : Number System Chapter - : Real Numbers TOPIC- Euclid s Division Lemma and Fundamental Theorem of rithmetic lgorithm : n algorithm is a series of well defined steps which gives a procedure for

### MATHEMATICS. Time allowed : 3 hours Maximum Marks : 100 QUESTION PAPER CODE 30/1/1 SECTION - A

MATHEMATICS Time allowed : 3 hours Maximum Marks : 100 GENERAL INSTRUCTIONS : 1. All questions are compulsory 2. The question paper consists of 30 questions divided into four sections - A, B, C and D.

### KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD-32. SECTION A Questions 1 to 6 carry 1 mark each.

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD-32 SAMPLE PAPER TEST 10 (2018-19) (SAMPLE ANSWERS) SUBJECT: MATHEMATICS MAX. MARKS : 80 CLASS : X DURATION : 3 HRS General Instruction: (i) All questions

### SAMPLE QUESTION PAPER Class-X ( ) Mathematics. Time allowed: 3 Hours Max. Marks: 80

SAMPLE QUESTION PAPER Class-X (017 18) Mathematics Time allowed: 3 Hours Max. Marks: 80 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 30 questions divided

### Contents Real Numbers Polynomials 2 0 Pair of Linear Equations in Two Variables 3 8 Quadratic Equations 7 0

Foreword Preface Contents 1. Real Numbers 1 1.1 Introduction 1 1. Euclid s Division Lemma 1.3 The Fundamental Theorem of Arithmetic 7 1.4 Revisiting Irrational Numbers 11 1.5 Revisiting Rational Numbers

### KENDRIYA VIDYALAYA SANGATHAN CHANDIGARH REGION MATHEMATICS

KENDRIYA VIDYALAYA SANGATHAN CHANDIGARH REGION MATHEMATICS 1. REAL NUMBERS : 06 MARKS 2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES 3. QUADRATIC EQUATIONS 12 MARKS 4. ARTHMETIC PROGRESSION 5. COORDINATE

### CBSE Class IX Syllabus. Mathematics Class 9 Syllabus

Mathematics Class 9 Syllabus Course Structure First Term Units Unit Marks I Number System 17 II Algebra 25 III Geometry 37 IV Co-ordinate Geometry 6 V Mensuration 5 Total 90 Second Term Units Unit Marks

### Secondary School Certificate Examination Syllabus MATHEMATICS. Class X examination in 2011 and onwards. SSC Part-II (Class X)

Secondary School Certificate Examination Syllabus MATHEMATICS Class X examination in 2011 and onwards SSC Part-II (Class X) 15. Algebraic Manipulation: 15.1.1 Find highest common factor (H.C.F) and least

### CBSE Sample Question Paper 1 ( )

CBSE Sample Question Paper (07-8 Time: Hours Maximum Marks: 80 General Instructions: (i All questions are compulsory. (ii The question paper consists of 0 questions divided into four sections A, B, C and

### MATHEMATICS (IX-X) (Code No. 041)

MATHEMATICS (IX-X) (Code No. 041) The Syllabus in the subject of Mathematics has undergone changes from time to time in accordance with growth of the subject and emerging needs of the society. The present

### RAMANUJAN MATHEMATICS CLUB,

A. B Q R C A=, BQ= AC=11 BC=... In the adjacent figure, If A= cm, BQ= cm and AC=11 cm, then BC=...cm. 1 ) 1 ) ) 1 8. ; Match the following. a) r h ) b) ) c) ) d) 1 r r r h 1 a, b, c, d ) 1 d, c, b, a )

### DESIGN OF THE QUESTION PAPER Mathematics Class X

SET-I DESIGN OF THE QUESTION PAPER Mathematics Class X Time : 3 Hours Maximum Marks : 80 Weightage and the distribution of marks over different dimensions of the question shall be as follows: (A) Weightage

### S.S.L.C. - MATHS BOOK BACK ONE MARK STUDY MATERIAL

1 S.S.L.C. - MATHS BOOK BACK ONE MARK STUDY MATERIAL DEAR STUDENTS, I have rearranged MATHS-one mark book questions in the order based on value of the answer so that, you can understand easily Totally

### SAMPLE QUESTION PAPER 09 Class-X ( ) Mathematics

SAMPLE QUESTION PAPER 09 Class-X (2017 18) Mathematics Time allowed: 3 Hours Max. Marks: 80 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 30 questions divided

### KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD-32. SECTION A Questions 1 to 6 carry 1 mark each.

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD-32 SAMPLE PAPER TEST 03 (2018-19) (ANSWERS) SUBJECT: MATHEMATICS MAX. MARKS : 80 CLASS : X DURATION : 3 HRS General Instruction: (i) All questions are compulsory.

### KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32 SAMPLE PAPER 05 (2018-19) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit

### Kendriya Vidyalaya Sangathan Class -X Subject- Mathematics Time - M.M - 80

Kendriya Vidyalaya Sangathan Class -X Subject- Mathematics Time - M.M - 80 General Instruction :-. All Questions are compulsory, however internal choices are given in some questions.. This question paper

### KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 04 (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit

### KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 03 (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit

### KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE G È.G È.G È.. Æ fioê, d È 2018 S. S. L. C. EXAMINATION, JUNE, 2018

CCE RR REVISED & UN-REVISED O %lo ÆË v ÃO y Æ fio» flms ÿ,» fl Ê«fiÀ M, ÊMV fl 560 00 KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE 560 00 G È.G È.G È.. Æ fioê, d È 08 S. S. L.

### MODEL QUESTION PAPERS WITH ANSWERS SET 1

MTHEMTICS MODEL QUESTION PPERS WITH NSWERS SET 1 Finish Line & Beyond CLSS X Time llowed: 3 Hrs Max. Marks : 80 General Instructions: (1) ll questions are compulsory. (2) The question paper consists of

### Mathematics, Algebra, and Geometry

Mathematics, Algebra, and Geometry by Satya http://www.thesatya.com/ Contents 1 Algebra 1 1.1 Logarithms............................................ 1. Complex numbers........................................

### KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32. SECTION A Questions 1 to 6 carry 1 mark each.

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32 SAMPLE PAPER TEST 09 (2018-19) (SAMPLE ANSWERS) SUBJECT: MATHEMATICS MAX. MARKS : 80 CLASS : X DURATION : 3 HRS General Instruction: (i) All questions

### Mathematics Class 9 Syllabus. Course Structure. I Number System 17 II Algebra 25 III Geometry 37 IV Co-ordinate Geometry 6 V Mensuration 5 Total 90

Mathematics Class 9 Syllabus Course Structure First Term Units Unit Marks I Number System 17 II Algebra 25 III Geometry 37 IV Co-ordinate Geometry 6 V Mensuration 5 Total 90 Second Term Units Unit Marks

### Since x + we get x² + 2x = 4, or simplifying it, x² = 4. Therefore, x² + = 4 2 = 2. Ans. (C)

SAT II - Math Level 2 Test #01 Solution 1. x + = 2, then x² + = Since x + = 2, by squaring both side of the equation, (A) - (B) 0 (C) 2 (D) 4 (E) -2 we get x² + 2x 1 + 1 = 4, or simplifying it, x² + 2

### 1 / 23

CBSE-XII-07 EXAMINATION CBSE-X-00 EXAMINATION MATHEMATICS Series: LRH/ Paper & Solution Code: 30// Time: 3 Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question

### MATHEMATICS SYLLABUS SECONDARY 4th YEAR

European Schools Office of the Secretary-General Pedagogical Development Unit Ref.:010-D-591-en- Orig.: EN MATHEMATICS SYLLABUS SECONDARY 4th YEAR 6 period/week course APPROVED BY THE JOINT TEACHING COMMITTEE

### SAMPLE QUESTION PAPER Class-X ( ) Mathematics. Time allowed: 3 Hours Max. Marks: 80

SAMPLE QUESTION PAPER Class-X (017 18) Mathematics Time allowed: 3 Hours Max. Marks: 80 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 30 questions divided

### 81-E If set A = { 2, 3, 4, 5 } and set B = { 4, 5 }, then which of the following is a null set? (A) A B (B) B A (C) A U B (D) A I B.

81-E 2 General Instructions : i) The question-cum-answer booklet contains two Parts, Part A & Part B. ii) iii) iv) Part A consists of 60 questions and Part B consists of 16 questions. Space has been provided

### KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 3 SAMPLE PAPER 06 (018-19) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I ( marks) SA II (3 marks) LA (4 marks) Total Unit

### Time: 3 Hrs. M.M. 90

Class: X Subject: Mathematics Topic: SA1 No. of Questions: 34 Time: 3 Hrs. M.M. 90 General Instructions: 1. All questions are compulsory. 2. The questions paper consists of 34 questions divided into four

### REVISED vide circular No.63 on

Circular no. 63 COURSE STRUCTURE (FIRST TERM) CLASS -IX First Term Marks: 90 REVISED vide circular No.63 on 22.09.2015 UNIT I: NUMBER SYSTEMS 1. REAL NUMBERS (18 Periods) 1. Review of representation of

### MATHEMATICS (IX-X) (Code No. 041)

MATHEMATICS (IX-X) (Code No. 041) The Syllabus in the subject of Mathematics has undergone changes from time to time in accordance with growth of the subject and emerging needs of the society. The present

### CBSE Class X Mathematics Sample Paper 04

CBSE Class X Mathematics Sample Paper 04 Time Allowed: 3 Hours Max Marks: 80 General Instructions: i All questions are compulsory ii The question paper consists of 30 questions divided into four sections

### Paper: 03 Class-X-Math: Summative Assessment - I

1 P a g e Paper: 03 Class-X-Math: Summative Assessment - I Total marks of the paper: 90 Total time of the paper: 3.5 hrs Questions: 1] Triangle ABC is similar to triangle DEF and their areas are 64 cm

### KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32 SAMPLE PAPER 02 (2018-19) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit

### 2. In an AP. if the common difference (d) = -4, and the seventh term (a7) is 4, then find the first term.

CBSE Board Class X Set 3 Mathematics Board Question Paper 2018 Time: 3 hrs. Marks: 80 Note: Please check that this question paper contains 11 printed pages. Code number given on the right hand side of

### Latest Syllabus - NMO

Latest Syllabus - NMO CLASS 1 Numerals and Number Name (2 digit numbers) Addition, Subtraction Knowledge of currency notes. Knowledge of clock. Knowledge of basic units of Length,. Knowledge of basic figures

### CCE RR. ( / English Version ) ( / New Syllabus ) ( / Regular Repeater )

CCE RR 1 81-E : 81-E Code No. : 81-E CCE RR Subject : MATHEMATICS ( / English Version ) ( / New Syllabus ) ( / Regular Repeater ) General Instructions : i) The Question-cum-Answer Booklet consists of objective

### SAMPLE QUESTION PAPER MATHEMATICS

SAMPLE QUESTION PAPER 07-8 MATHEMATICS Time allowed : 3 hrs Maximum marks : 80 General Instructions : All questions are compulsory. The question paper consists of 30 questions divided into four sections

### CONTENTS. iii v viii FOREWORD PREFACE STUDENTS EVALUATION IN MATHEMATICS AT SECONDARY STAGE

CONTENTS FOREWORD PREFACE STUDENTS EVALUATION IN MATHEMATICS AT SECONDARY STAGE iii v viii CHAPTER Real Numbers CHAPTER Polynomials 8 CHAPTER 3 Pair of Linear Equations in Two Variables 6 CHAPTER 4 Quadratic

### COURSE STRUCTURE CLASS IX Maths

COURSE STRUCTURE CLASS IX Maths Units Unit Name Marks I NUMBER SYSTEMS 08 II ALGEBRA 17 III COORDINATE GEOMETRY 04 IV GEOMETRY 28 V MENSURATION 13 VI STATISTICS & PROBABILITY 10 Total 80 UNIT I: NUMBER

### The Grade Descriptors below are used to assess work and student progress in Mathematics from Year 7 to

Jersey College for Girls Assessment criteria for KS3 and KS4 Mathematics In Mathematics, students are required to become familiar, confident and competent with a range of content and procedures described

### Learning Objectives These show clearly the purpose and extent of coverage for each topic.

Preface This book is prepared for students embarking on the study of Additional Mathematics. Topical Approach Examinable topics for Upper Secondary Mathematics are discussed in detail so students can focus

### KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 08 (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit

### KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 01 (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit

### SAMPLE QUESTION PAPER 11 Class-X ( ) Mathematics

SAMPLE QUESTION PAPER 11 Class-X (2017 18) Mathematics GENERAL INSTRUCTIONS (i) All questions are compulsory. (ii) The question paper consists of 30 questions divided into four sections A, B,C and D. (iii)

### ADVANCED MATHS TEST - I PRELIMS

Model Papers Code : 1101 Advanced Math Test I & II ADVANCED MATHS TEST - I PRELIMS Max. Marks : 75 Duration : 75 Mins. General Instructions : 1. Please find the Answer Sheets (OMR) with in the envelop

### 1 / 23

CBSE-XII-017 EXAMINATION CBSE-X-008 EXAMINATION MATHEMATICS Series: RLH/ Paper & Solution Code: 30//1 Time: 3 Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question

### Core A-level mathematics reproduced from the QCA s Subject criteria for Mathematics document

Core A-level mathematics reproduced from the QCA s Subject criteria for Mathematics document Background knowledge: (a) The arithmetic of integers (including HCFs and LCMs), of fractions, and of real numbers.

### Mathematics CLASS : X. Time: 3hrs Max. Marks: 90. 2) If a, 2 are three consecutive terms of an A.P., then the value of a.

1 SAMPLE PAPER 4 (SAII) MR AMIT. KV NANGALBHUR Mathematics CLASS : X Time: 3hrs Max. Marks: 90 General Instruction:- 1. All questions are Compulsory. The question paper consists of 34 questions divided

### KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32 SAMPLE PAPER 03 (2018-19) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit

### [Class-X] MATHEMATICS SESSION:

[Class-X] MTHEMTICS SESSION:017-18 Time allowed: 3 hrs. Maximum Marks : 80 General Instructions : (i) ll questions are compulsory. (ii) This question paper consists of 30 questions divided into four sections,

### Paper: 02 Class-X-Math: Summative Assessment - I

1 P a g e Paper: 02 Class-X-Math: Summative Assessment - I Total marks of the paper: 90 Total time of the paper: 3.5 hrs Questions: 1] The relation connecting the measures of central tendencies is [Marks:1]

### CHAPTER 1 REAL NUMBERS KEY POINTS

CHAPTER 1 REAL NUMBERS 1. Euclid s division lemma : KEY POINTS For given positive integers a and b there exist unique whole numbers q and r satisfying the relation a = bq + r, 0 r < b. 2. Euclid s division

### MATHEMATICS (IX-X) (CODE NO. 041) Session

MATHEMATICS (IX-X) (CODE NO. 041) Session 2018-19 The Syllabus in the subject of Mathematics has undergone changes from time to time in accordance with growth of the subject and emerging needs of the society.

### KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 07 (017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I ( marks) SA II (3 marks) LA (4 marks) Total Unit Total

### Candidate Name Centre Number Candidate Number MATHEMATICS UNIT 2: CALCULATOR-ALLOWED HIGHER TIER SPECIMEN PAPER SUMMER 2017

GCSE MATHEMATICS Specimen Assessment Materials 61 Candidate Name Centre Number Candidate Number 0 GCSE MATHEMATICS UNIT 2: CALCULATOR-ALLOWED HIGHER TIER SPECIMEN PAPER SUMMER 2017 1 HOUR 45 MINUTES ADDITIONAL

### CBSE MATHEMATICS (SET-2)_2019

CBSE 09 MATHEMATICS (SET-) (Solutions). OC AB (AB is tangent to the smaller circle) In OBC a b CB CB a b CB a b AB CB (Perpendicular from the centre bisects the chord) AB a b. In PQS PQ 4 (By Pythagoras

### Ramagya Institute. Grade 10 Physics

Grade 10 Physics S.No. Current Electricity 1. Effects of Current 1.1 Electric current, potential difference and electric current 1.2 Ohm s Law; Resistance, Resistivity, Factors on which the resistance

### Mathematics 1 Lecture Notes Chapter 1 Algebra Review

Mathematics 1 Lecture Notes Chapter 1 Algebra Review c Trinity College 1 A note to the students from the lecturer: This course will be moving rather quickly, and it will be in your own best interests to

PRE-HALFYEARLY ASSESSMENT- [P-H-A MATHS SYLLABUS] ANSWER KEY & SOLUTIONS General Instructions:. The question paper comprises of four sections, A, B, C & D.. All questions are compulsory. 3. Section A Q

### COURSE STRUCTURE CLASS -IX

environment, observance of small family norms, removal of social barriers, elimination of gender biases; mathematical softwares. its beautiful structures and patterns, etc. COURSE STRUCTURE CLASS -IX Units

### GRADE - 10 MATH WORKPLAN

GRADE - 10 MATH WORKPLAN 2018-19 DATES TOPIC DETAILS 5 th to 9 th Real numbers 1. Learn Divisibility of Integers (Euclid s Division Algorithm - Technique to compute HCF of two positive integers.) 2. Multiplication

### CBSE QUESTION PAPER CLASS-X MATHS

CBSE QUESTION PAPER CLASS-X MATHS SECTION - A Question 1: In figure, AB = 5 3 cm, DC = 4cm, BD = 3cm, then tan θ is (a) (b) (c) (d) 1 3 2 3 4 3 5 3 Question 2: In figure, what values of x will make DE

### Marking Scheme. Mathematics Class X ( ) Section A

Marking Scheme Mathematics Class X (017-18) Section A S.No. Answer Marks 1. Non terminating repeating decimal expansion.. k ±4 3. a 11 5 4. (0, 5) 5. 9 : 49 6. 5 Section B 7. LCM (p, q) a 3 b 3 HCF (p,

### Mathematics. Sample Question Paper. Class 10th. (Detailed Solutions) Sample Question Paper 13

Sample uestion aper Sample uestion aper (etailed Solutions) Mathematics lass 0th 5. We have, k and 5 k as three consecutive terms of an. 8 Their common difference will be same. 5 i.e. k k k k 5 k 8 k 8

### MINIMUM LEVEL LEARNING MATERIAL

MATHEMATICS MINIMUM LEVEL LEARNING MATERIAL for CLASS X 018 19 Prepared by M. S. KUMARSWAMY, TGT(MATHS) M. Sc. Gold Medallist (Elect.), B. Ed. Kendriya Vidyalaya gachibowli DEDICATED TO MY FATHER LATE

### Class X Delhi Math Set-3 Section A

Class X Delhi Math Set-3 Section A 1. The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30. The distance of the car from the base of the tower (in m.) is:

### 10 th MATHS SPECIAL TEST I. Geometry, Graph and One Mark (Unit: 2,3,5,6,7) , then the 13th term of the A.P is A) = 3 2 C) 0 D) 1

Time: Hour ] 0 th MATHS SPECIAL TEST I Geometry, Graph and One Mark (Unit:,3,5,6,7) [ Marks: 50 I. Answer all the questions: ( 30 x = 30). If a, b, c, l, m are in A.P. then the value of a b + 6c l + m