Case study (4 Marks)

Question 14 Marks

Teaching Mathematics through activities is a powerful approach that enhances students' understanding and engagement. Keeping this in mind, Ms. Mukta planned a prime number game for class 5 students. She announces the number 2 in her class and asked the first student to multiply it by a prime number and then pass it to second student. Second student also multiplied it by a prime number and passed it to third student. In this way by multiplying to a prime number, the last student got 173250.
Now. Mukta asked some questions as given below to the students:
(i) What is the least prime number used by students?
(ii) (a) How many students are in the class ?
OR
(b) What is the highest prime number used by students?
(iii) Which prime number has been used maximum times?

Answer

$
173250=2 \times 5^3 \times 3^2 \times 7 \times 11
$
(i) 3
(ii) (a) $173250=2 \times 5^3 \times 3^2 \times 7 \times 11$
Number of students in the class $=3+2+1+1=7$
OR
(ii) (b) $173250=2 \times 5^3 \times 3^2 \times 7 \times 11$
Highest prime number used by students $=11$
(iii) 5

View full question & answer→

Question 24 Marks

Vocational training complements traditional education by providing practical skills and hands-on experience. While education equips individuals with a broad knowledge base, vocational training focuses on job-specific skills, enhancing employability thus making the student self- reliant. Keeping this in view, a teacher made the following table giving the frequency distribution of students/adults undergoing vocational training from the training institute.

Age (in years)	15-19	20-24	25-29	30-34	35-39	40-44	45-49	50-54
Number of participants	62	132	96	37	13	11	10	4

From the above answer the following questions:
(i) What is the lower limit of the modal class of the above data?
(ii) (a) Find the median class of the above data.
OR
(b) Find the number of participants of age less than 50 years who undergo vocational training.
(iii) Give the empirical relationship between mean, median and mode.

Answer

(i) Modalclass is 19.524 .5
Lowelimit $=19.5$
(ii) (a)

Age (in years)	14.5-19.5	19.5-24.5	24.5-29.5	29.5-34.5	34.5-39.5	39.5-44.5	44.5-49.5	49.5-54.5
Number of participa nts	62	132	96	37	13	11	10	4
cf	62	194	290	327	340	351	361	365

$\frac{n}{2}=\frac{365}{2}=182.5$
median class $19.5-24.5$
OR
(ii) (b) $62+132+96+37+13+11+10=361$
(iii) 3median = mode +2 mean

View full question & answer→

Question 34 Marks

A stable owner has four horses. He usually tie these horses with 7 m long rope to pegs at each corner of a square shaped grass field of 20 m length, to graze in his farm. But tying with rope sometimes results in injuries to his horses, so he decided to build fence around the area so that each horse can graze.

Based on the above, answer the following questions:
(i) Find the area of the square shaped grass field.
(ii) (a) Find the area of the total field in which these horses can graze.
OR
(b) If the length of the rope of each horse is increased from 7 m to 10 m , find the area grazed by one horse. (Use $\pi=3.14$ )
(iii) What is area of the field that is left ungrazed, if the length of the rope of each horse is 7 cm ?

Answer

(i) Area of square shaped grass field $=400 m^2$
(ii) (a) area of total field that horses can graze $=4 \times \frac{1}{4} \times \frac{22}{7} \times 7 \times 7$
$=154 m^2$
OR
(ii) (b) area grazed by one horse $=\frac{1}{4} \times 3.14 \times 10 \times 10$
$=78.5 m^2$
(iii) Area of the field left ungrazed = area of square field - area of field in which horses can graze.
$\begin{aligned}
\text { Area of field in which horses can graze } & =4 \times \frac{1}{4} \times \frac{22}{7} \times 7 \times 7 \\
& =154 cm^2
\end{aligned}$Area of the field left ungrazed $=400-0.0154=399.9846 m^2$

View full question & answer→

Maths Case study (4 Marks)

Take a timed test