28 Jan 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 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 business exercise

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1 MATHEMATICS (IX-X) (CODE NO. 041) Session 2022-23 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 revised syllabus has been designed in accordance with National Curriculum Framework 2005 and as per guidelines given in the Focus Group on Teaching of Mathematics which is to meet the emerging needs of all categories of students. For motivating the teacher to relate the topics to real life problems and other subject areas, greater emphasis has been laid on applications of various concepts. The curriculum at Secondary stage primarily aims at enhancing the capacity of students to employ Mathematics in solving day-to-day life problems and studying the subject as a separate discipline. It is expected that students should acquire the ability to solve problems using algebraic methods and apply the knowledge of simple trigonometry to solve problems of height and distances. Carrying out experiments with numbers and forms of geometry, framing hypothesis and verifying these with further observations form inherent part of Mathematics learning at this stage. The proposed curriculum includes the study of number system, algebra, geometry, trigonometry, mensuration, statistics, graphs and coordinate geometry, etc. The teaching of Mathematics should be imparted through activities which may involve the use of concrete materials, models, patterns, charts, pictures, posters, games, puzzles and experiments. Objectives The broad objectives of teaching of Mathematics at secondary stage are to help the learners to:  consolidate the Mathematical knowledge and skills acquired at the upper primary stage;? acquire knowledge and understanding, particularly by way of motivation and visualization, of basic concepts, terms, principles and symbols and underlying processes and skills;? develop mastery of basic algebraic skills;? develop drawing skills;? feel the flow of reason while proving a result or solving a problem;? apply the knowledge and skills acquired to solve problems and wherever possible, by more than one method;? to develop ability to think, analyze and articulate logically;? to develop awareness of the need for national integration, protection of environment, observance of small family norms, removal of social barriers, elimination of gender biases;? to develop necessary skills to work with modern technological devices and mathematical software’s.? to develop interest in mathematics as a problem-solving tool in various fields for its beautiful structures and patterns, etc.? to develop reverence and respect towards great Mathematicians for their contributions to the field of Mathematics;? to develop interest in the subject by participating in related competitions;? to acquaint students with different aspects of Mathematics used in daily life;? to develop an interest in students to study Mathematics as a discipline.?
2 COURSE STRUCTURE CLASS ?IX Units Unit Name Marks I NUMBER SYSTEMS 10 II ALGEBRA 20 III COORDINATE GEOMETRY 04 IV GEOMETRY 27 V MENSURATION 13 VI STATISTICS & PROBABILITY 06 Total 80 UNIT I: NUMBER SYSTEMS 1. REAL NUMBERS (18) Periods 1. Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers. 2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as, and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number. 3. Definition of nth root of a real number. 4. Rationalization (with precise meaning) of real numbers of the type and (and their combinations) where x and y are natural number and a and b are integers. 5. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.) UNIT II: ALGEBRA 1. POLYNOMIALS (26) Periods Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of ax2 + bx + c, a ?? 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. Recall of algebraic expressions and identities. Verification of identities: + and their use in factorization of polynomials.
3 2. LINEAR EQUATIONS IN TWO VARIABLES (16) Periods Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax + by + c=0.Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line. UNIT III: COORDINATE GEOMETRY COORDINATE GEOMETRY (7) Periods The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations. UNIT IV: GEOMETRY 1. INTRODUCTION TO EUCLID’S GEOMETRY (7) Periods History – Geometry in India and Euclid’s geometry. Euclid’s method of formalizing observed phenomenon into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates of Euclid. Showing the relationship between axiom and theorem, for example: (Axiom) 1. Given two distinct points, there exists one and only one line through them. (Theorem) 2. (Prove) Two distinct lines cannot have more than one point in common. 2. LINES AND ANGLES (15) Periods 1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180O and the converse. 2. (Prove) If two lines intersect, vertically opposite angles are equal. 3. (Motivate) Lines which are parallel to a given line are parallel. 3. TRIANGLES (22) Periods 1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence). 2. (Prove) Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence).
4 3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence). 4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (RHS Congruence) 5. (Prove) The angles opposite to equal sides of a triangle are equal. 6. (Motivate) The sides opposite to equal angles of a triangle are equal. 4. QUADRILATERALS (13) Periods 1. (Prove) The diagonal divides a parallelogram into two congruent triangles. 2. (Motivate) In a parallelogram opposite sides are equal, and conversely. 3. (Motivate) In a parallelogram opposite angles are equal, and conversely. 4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal. 5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely. 6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and in half of it and (motivate) its converse. 5. CIRCLES (17) Periods 1.(Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse. 2.(Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord. 3. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely. 4.(Prove) The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle. 5.(Motivate) Angles in the same segment of a circle are equal. 6.(Motivate) If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle. 7.(Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180? and its converse. UNIT V: MENSURATION 1. AREAS (5) Periods Area of a triangle using Heron’s formula (without proof) 2. SURFACE AREAS AND VOLUMES (17) Periods Surface areas and volumes of spheres (including hemispheres) and right circular cones.
5 UNIT VI: STATISTICS & PROBABILITY STATISTICS (15) Periods Bar graphs, histograms (with varying base lengths), and frequency polygons. MATHEMATICS QUESTION PAPER DESIGN CLASS ? IX (2022-23) Time: 3 Hrs. Max. Marks: 80 S. No. Typology of Questions Total Marks % Weightage (approx.) 1 Remembering: Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers. Understanding: Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas 43 54 2 Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way. 19 24 3 Analysing : Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations Evaluating: Present and defend opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria. Creating: Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions 18 22 Total 80 100 INTERNAL ASSESSMENT 20 MARKS 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
6 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 I: NUMBER SYSTEMS 1. REAL NUMBER (15) Periods Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of UNIT II: ALGEBRA 1. POLYNOMIALS (8) Periods Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. 2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES (15) Periods Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination. Simple situational problems. 3. QUADRATIC EQUATIONS (15) Periods Standard form of a quadratic equation ax2 + bx + c = 0, (a ?? 0). Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day to day activities to be incorporated.
7 4. ARITHMETIC PROGRESSIONS (10) Periods Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. and their application in solving daily life problems. UNIT III: COORDINATE GEOMETRY Coordinate Geometry (15) Periods Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). UNIT IV: GEOMETRY 1. TRIANGLES (15) Periods Definitions, examples, counter examples of similar triangles. 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 to the third side. 3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar. 4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar. 5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar. 2. CIRCLES (10) Periods Tangent to a circle at, point of contact 1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact. 2. (Prove) The lengths of tangents drawn from an external point to a circle are equal.
8 UNIT V: TRIGONOMETRY 1. INTRODUCTION TO TRIGONOMETRY (10) Periods Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios whichever are defined at 0o and 90o. Values of the trigonometric ratios of 300, 450 and 600. Relationships between the ratios. 2. TRIGONOMETRIC IDENTITIES (15) Periods Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given. 3. HEIGHTS AND DISTANCES: Angle of elevation, Angle of Depression. (10)Periods Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30?, 45?, and 60?. UNIT VI: MENSURATION 1. AREAS RELATED TO CIRCLES (12) Periods Area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60?, 90? and 120? only. 2. SURFACE AREAS AND VOLUMES (12) Periods Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones. UNIT VII: STATISTICS AND PROBABILITY 1. STATISTICS (18) Periods Mean, median and mode of grouped data (bimodal situation to be avoided). 2. PROBABILITY (10) Periods Classical definition of probability. Simple problems on finding the probability of an event.
9 MATHEMATICS-Standard QUESTION PAPER DESIGN CLASS ? X (2022-23) Time: 3 Hours Max. Marks: 80 S. No. Typology of Questions Total Marks % Weightage (approx.) 1 Remembering: Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers. Understanding: Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas 43 54 2 Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way. 19 24 3 Analysing : Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations Evaluating: Present and defend opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria. Creating: Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions 18 22 Total 80 100 INTERNAL ASSESSMENT 20 MARKS 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
10 MATHEMATICS-Basic QUESTION PAPER DESIGN CLASS ? X (2022-23) Time: 3Hours Max. Marks: 80 S. No. Typology of Questions Total Marks % Weightage (approx.) 1 Remembering: Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers. Understanding: Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas 60 75 2 Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way. 12 15 3 Analysing : Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations Evaluating: Present and defend opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria. Creating: Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions 8 10 Total 80 100 PRESCRIBED BOOKS: 1. Mathematics – Textbook for class IX – NCERT Publication 2. Mathematics – Textbook for class X – NCERT Publication 3. Guidelines for Mathematics Laboratory in Schools, class IX – CBSE Publication 4. Guidelines for Mathematics Laboratory in Schools, class X – CBSE Publication 5. Laboratory Manual – Mathematics, secondary stage – NCERT Publication 6. Mathematics exemplar problems for class IX, NCERT publication. 7. Mathematics exemplar problems for class X, NCERT publication. INTERNAL ASSESSMENT 20 MARKS 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
REAL NUMBERS- CASE STUDY CASE STUDY 1. 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. 1. What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B? a) 144 b) 128 c) 288 d) 272 2. If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32 , 36) is a) 2 b) 4 c) 6 d) 8
3. 36 can be expressed as a product of its primes as a) b) c) d) 4. 7 is a a) Prime number b) Composite number c) Neither prime nor composite d) None of the above 5. If p and q are positive integers such that p = a and q= b, where a , b are prime numbers, then the LCM (p, q) is a) ab b) c) d) 1. c) 288 2. b) 4 3. a) 4. b) composite number 5. b) CASE STUDY 2: 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.
1. 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 2. What is the minimum number of rooms required during the event? a) 11 b) 31 c) 41 d) 21 3. The LCM of 60, 84 and 108 is a) 3780 b) 3680 c) 4780 d) 4680 4. The product of HCF and LCM of 60,84 and 108 is a) 55360 b) 35360 c) 45500 d) 45360 5. 108 can be expressed as a product of its primes as a) b) c) d) 1. b) 12 2. d) 21 3. a) 4. d)45360 5. d)
CASE STUDY 3: A Mathematics Exhibition is being conducted in your School and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience. Observe the following factor tree and answer the following: 1. What will be the value of x? a) 15005 b) 13915 c) 56920 d) 17429 2. What will be the value of y? a) 23 b) 22 c) 11 d) 19 3. What will be the value of z? a) 22 b) 23 c) 17 d) 19 x 5 2783 z y 253 11
4. According to Fundamental Theorem of Arithmetic 13915 is a a) Composite number b) Prime number c) Neither prime nor composite d) Even number 5. The prime factorisation of 13915 is a) b) c) d) ANSWERS 1. b) 13915 2. c) 11 3. b) 23 4. a) composite number 5. c) POLYNOMIALS- CASE STUDY CASE STUDY 1: The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.
1. In the standard form of quadratic polynomial, , a, b and c are a) All are real numbers. b) All are rational numbers. c) ?a? is a non zero real number and b and c are any real numbers. d) All are integers. 2. If the roots of the quadratic polynomial are equal, where the discriminant D = ? 4ac, then a) D > 0 b) D < 0 c) D d) D = 0 3. If are the zeroes of the qudratic polynomial 2 then k is a) 4 b) c) d) 2 4. The graph of x2+1=0 a) Intersects x?axis at two distinct points. b) Touches x?axis at a point. c) Neither touches nor intersects x?axis. d) Either touches or intersects x? axis. 5. If the sum of the roots is ?p and product of the roots is – , then the quadratic polynomial is a) k ( )
b) k ( ) c) k ( ) d) k ( ) ANSWERS 1. c) ?a? is a non zero real number and b and c are any real numbers. 2. d) D=0 3. b) 4. c) Neither touches nor intersects x?axis. 5. c) k ( ) CASE STUDY 2: An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial. 1. The shape of the poses shown is a) Spiral b) Ellipse c) Linear d) Parabola 2. The graph of parabola opens downwards, if _______
a) a 0 b) a = 0 c) a 0 3. In the graph, how many zeroes are there for the polynomial? a) 0 b) 1 c) 2 d) 3 4. The two zeroes in the above shown graph are a) 2, 4 b) -2, 4 c) -8, 4 d) 2,-8 5. The zeroes of the quadratic polynomial ?? ?? are a) ?? , ?? b) ?? , ?? c) ?? , – ?? d) – ?? , ?? ANSWERS 1. Parabola 2. c) a < 0 3. c) 2 4. b) -2, 4 5. b) ?? , ??
CASE STUDY 3: Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial. 1. The shape of the path traced shown is a) Spiral b) Ellipse c) Linear d) Parabola 2. The graph of parabola opens upwards, if _______ a) a = 0 b) a 0 d) a 0 3. Observe the following graph and answer
In the above graph, how many zeroes are there for the polynomial? a) 0 b) 1 c) 2 d) 3 4. The three zeroes in the above shown graph are b) 2, 3,-1 c) -2, 3, 1 d) -3, -1, 2 e) -2, -3, -1 5. What will be the expression of the polynomial? a) b) c) d) ANSWERS 1. d) parabola 2. c) a > 0 3. d) 3 4. c) -3, -1, 2 5. a) LINEAR EQUATIONS INTWO VARIABLES CASE STUDY-1: A test consists of ?True? or ?False? questions. One mark is awarded for every correct answer while ? mark is deducted for every wrong answer. A student knew answers to some of the questions. Rest of the questions he attempted by guessing. He answered 120 questions and got 90 marks.
Type of Question Marks given for correct answer Marks deducted for wrong answer True/False 1 0.25 1. If answer to all questions he attempted by guessing were wrong, then how many questions did he answer correctly? 2. How many questions did he guess? 3. If answer to all questions he attempted by guessing were wrong and answered 80 correctly, then how many marks he got? 4. If answer to all questions he attempted by guessing were wrong, then how many questions answered correctly to score 95 marks? Answers: Let the no of questions whose answer is known to the student x and questions attempted by cheating be y x + y =120 x-1/4y =90 solving these two x=96 and y= 24 1. He answered 96 questions correctly. 2. He attempted 24 questions by guessing. 3. Marks = 80- ? 0f 40 =70 4. x ? ? 0f (120-x) =95 5x=500, x = 100 CASE STUDY-2: Amit is planning to buy a house and the layout is given below. The design and the measurement has been made such that areas of two bedrooms and kitchen together is 95 sq.m.
Based on the above information, answer the following questions: 1. Form the pair of linear equations in two variables from this situation. 2. Find the length of the outer boundary of the layout. 3. Find the area of each bedroom and kitchen in the layout. 4. Find the area of living room in the layout. 5. Find the cost of laying tiles in kitchen at the rate of Rs. 50 per sq.m ANSWER: 1. Area of two bedrooms= 10x sq.m Area of kitchen = 5y sq.m 10x + 5y = 95 2x + y =19 Also, x + 2+ y = 15 x + y = 13 2. Length of outer boundary= 12 + 15 + 12 + 15= 54m 3. On solving two equation part(i) x= 6m and y =7m area of bedroom = 5 x 6= 30m area of kitchen = 5 x 7= 35m 4. Area of living room = (15×7)-30 = 105-30 = 75 sq.m 5. Total cost of laying tiles in the kitchen = Rs 50 x35 = Rs 1750
Case study-3 : It is common that Governments revise travel fares from time to time based on various factors such as inflation ( a general increase in prices and fall in the purchasing value of money) on different types of vehicles like auto, Rickshaws, taxis, Radio cab etc. The auto charges in a city comprise of a fixed charge together with the charge for the distance covered. Study the following situations Name of the city Distance travelled (Km) Amount paid (Rs.) City A 10 75 15 110 City B 8 91 14 145 Situation 1: In city A, for a journey of 10 km, the charge paid is Rs 75 and for a journey of 15 km, the charge paid is Rs 110. Situation 2: In a city B, for a journey of 8km, the charge paid is Rs91 and for a journey of 14km, the charge paid is Rs 145. Refer situation 1 1. If the fixed charges of auto rickshaw be Rs x and the running charges be Rs y km/hr, the pair of linear equations representing the situation is a) x + 10y =110, x + 15y = 75 b) x + 10y =75, x + 15y = 110 c) 10x + y =110, 15x + y = 75 d) 10x + y = 75, 15 x + y =110
2. A person travels a distance of 50km. The amount he has to pay is a) Rs.155 b) Rs.255 c) Rs.355 d) Rs.455 Refer situation 2 3. What will a person have to pay for travelling a distance of 30km? a) Rs.185 b) Rs.289 c) Rs.275 d) Rs.305 4. The graph of lines representing the conditions are: (situation 2) ANSWERS: 1. B 2. C 3. B 4. (iii)
QUADRATIC EQUATIONS CASE STUDY 1: Raj and Ajay are very close friends. Both the families decide to go to Ranikhet by their own cars. Raj?s car travels at a speed of x km/h while Ajay?s car travels 5 km/h faster than Raj?s car. Raj took 4 hours more than Ajay to complete the journey of 400 km. 1. What will be the distance covered by Ajay?s car in two hours? a) 2(x +5)km b) (x ? 5)km c) 2( x + 10)km d) (2x + 5)km 2. Which of the following quadratic equation describe the speed of Raj?s car? a) x2 – 5 x – 500 = 0 b) x2 + 4x – 400 = 0 c) x2 + 5x – 500 = 0 d) x2 – 4x + 400 = 0 3. What is the speed of Raj?s car? a) 20 km/hour b) 15 km/hour c) 25 km/hour d) 10 km/hour 4. How much time took Ajay to travel 400 km? a) 20 hour b) 40 hour c) 25 hour d) 16 hour
ANSWERS: 1. a) 2(x + 5)km 2. c) 25km/ hour 3. a) 20km/ hour 4. d) 16 hour CASE STUDY 2: The speed of a motor boat is 20 km/hr. For covering the distance of 15 km the boat took 1 hour more for upstream than downstream. 1. Let speed of the stream be x km/hr. then speed of the motorboat in upstream will be a) 20 km/hr b) (20 + x) km/hr c) (20 – x) km/hr d) 2 km/hr 2. What is the relation between speed ,distance and time? a) speed = (distance )/time b) distance = (speed )/time c) time = speed x distance d) speed = distance x time 3. Which is the correct quadratic equation for the speed of the current ? a) x2+ 30x ?? 200 = 0 b) x2+ 20x ?? 400 = 0 c) x 2+ 30x ?? 400 = 0 d) x2?? 20x ?? 400 = 0 4. What is the speed of current ? a) 20 km/hour b) 10 km/hour
c) 15 km/hour d) 25 km/hour 5. How much time boat took in downstream? a) 90 minute b) 15 minute c) 30 minute d) 45 minute ANSWERS: 1. c) (20 ? x)km/hr 2. b) distance=(speed)/ time 3. c) x 2+ 30x ? 400= 0 4. b) 10 km/hour 5. c) 45 minute ARITHMETIC PROGRESSION CASE STUDY 1: India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year.
Based on the above information, answer the following questions: 1. Find the production during first year. 2. Find the production during 8th year. 3. Find the production during first 3 years. 4. In which year, the production is Rs 29,200. 5. Find the difference of the production during 7th year and 4th year. ANSWER: 1. Rs 5000 2. Production during 8th year is (a+7d)= 5000 + 2(2200) =20400 3. Production during first 3 year= 5000 + 7200 + 9400=21600 4. N=12 5. Difference= 18200-11600=6600 CASE STUDY 2: Your friend Veer wants to participate in a 200m race. He can currently run that distance in 51 seconds and with each day of practice it takes him 2 seconds less.He wants to do in 31 seconds . 1. Which of the following terms are in AP for the given situation a) 51,53,55?. b) 51, 49, 47?.
c) -51, -53, -55?. d) 51, 55, 59? 2. What is the minimum number of days he needs to practice till his goal is achieved a) 10 b) 12 c) 11 d) 9 3. Which of the following term is not in the AP of the above given situation a) 41 b) 30 c) 37 d) 39 4. If nth term of an AP is given by an = 2n + 3 then common difference of an AP is a) 2 b) 3 c) 5 d) 1 5. The value of x, for which 2x, x+ 10, 3x + 2 are three consecutive terms of an AP a) 6 b) -6 c) 18 d) -18 ANSWER: 1. b 2. c 3. b 4. a 5. a
CASE STUDY 3: Your el