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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.
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
- b) 13915
- c) 11
- b) 23
- a) composite number
- 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.
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= 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 d) 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,- 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) (^) √ , √
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,- c) -2, 3, 1 d) -3, -1, 2 e) -2, -3, - 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 ¼ 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.
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 =
x-1/4y =
solving these two
x=96 and y= 24
1. He answered 96 questions correctly. 2. He attempted 24 questions by guessing. 3. Marks = 80- ¼ 0f 40 = 4. x – ¼ 0f (120-x) = 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.
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 =
2. A person travels a distance of 50km. The amount he has to pay is a) Rs. b) Rs. c) Rs. d) Rs.
Refer situation 2
3. What will a person have to pay for travelling a distance of 30km? a) Rs. b) Rs. c) Rs. d) Rs. 4. The graph of lines representing the conditions are: (situation 2)
ANSWERS:
1. B
2. C
3. B
4. (iii)
ANSWERS:
- a) 2(x + 5)km
- c) 25km/ hour
- a) 20km/ hour
- 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) x^2 + 30 x − 200 = 0 b) x^2 + 20 x − 400 = 0 c) x^2 + 30 x − 400 = 0 d) x^2 − 20 x − 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
- b) distance=(speed)/ time
- c) x^2 + 30 x – 400= 0
- b) 10 km/hour
- 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.
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) - c) 18 d) -
ANSWER:
- b
- c
- b
- a
- a
CASE STUDY 3:
Your elder brother wants to buy a car and plans to take loan from a bank for his car. He repays his total loan of Rs 1,18,000 by paying every month starting with the first instalment of Rs 1000. If he increases the instalment by Rs 100 every month , answer the following:
1. The amount paid by him in 30th^ installment is a) 3900 b) 3500 c) 3700 d) 3600 2. The amount paid by him in the 30 installments is a) 37000 b) 73500 c) 75300 d) 75000 3. What amount does he still have to pay offer 30th^ installment? a) 45500 b) 49000 c) 44500 d) 54000 4. If total installments are 40 then amount paid in the last installment?
