ICSE Class 10 Maths Competency Focused Practice Questions Solution-Long Answer Questions-1 (Graph based)

Maths Competency Focused Practice Questions Solution

Long Answer Questions-1 (Graph based)- 5 marks

Question 106
Plot the points A(2, 2) and B(6, -2) in the graph and answer the following :

(a) Reflect points A in origin to point D and write the co-ordinates of point D.

(b) Reflect points A in line y = -2 to point C and write the co-ordinates of point C.

(d) Write the geometrical name of the closed figure ABCD.

(e) Write the co-ordinates of the point of intersection of the diagonals of ABCD.

Answer:

The graph is shown below:

maths-competency-focused=practice-questions-solution

From graph,

(a) Co-ordinates of D = (-2, -2).

(b) Co-ordinates of C = (2, -6).

∴ It is invariant under reflection in x = 0.

Co-ordinates of P = (0, -4).

(d) ABCD is a square.

(e) H is the point of intersection of diagonals of ABCD.

Co-ordinates of H = (2, -2).

Question 107
Plot points A(0, 3), B(4, 0), C(6, 2) and D(5, 0). Reflect the points as given below and write their coordinates:

(a) Reflect A on x-axis to A’.

(b) Reflect B on y-axis to B’.

(d) D remain invariant when reflected on the line whose equation is …………… .

(e) Join the points A, B, C, D, C’, B, A’, B’ and A to form a closed figure. Name the closed figure BCDC’.

Answer:

The graph is shown below:

(a) Coordinates of A’ = (0, -3).

(b) Coordinates of B’ = (-4, 0).

(d) D lies on x-axis.

∴ It is invariant in the line x-axis or y = 0.

D remain invariant when reflected on the line whose equation is y = 0.

(e) BCDC’ is a concave quadrilateral.

Question 108
The following data represents the daily wages in rupees of a certain number of employees of a company:

Daily wages (in ₹)	No. of Employees
30 – 40	8
40 – 50	14
50 – 60	12
60 – 70	17
70 – 80	20
80 – 90	26
90 – 100	13
100 – 110	10

Use a graph to answer the following questions:

(a) Represent the above distribution by an ogive.

(b) Find the following on the graph drawn:

(i) median wage.

(ii) percentage of employees who earn more than ₹ 84 per day.

(iii) number of employees who earn ₹56 and below.

Answer:

(a) Cumulative frequency distribution table:

Daily wages (in ₹)	No. of Employees (f)	Cumulative frequency (cum f)
30 – 40	8	8
40 – 50	14	22
50 – 60	12	34
60 – 70	17	51
70 – 80	20	71
80 – 90	26	97
90 – 100	13	110
100 – 110	10	120

Here, n = 120 (even)

Median = n/2 = 120/2 = 60 th term

Steps of construction :

Plotting the points (40, 8), (50, 22), (60, 34), (70, 51), (80, 71), (90, 97), (100, 110) and (110, 120) and making a cumulative frequency graph, we get:

(b) (i) Median wage = 60 th term = ₹74.

(ii) No. of employees earning more than ₹ 84 per day = 120 – 81 = 39.

Percentage of employees earning more than ₹84

\[=\frac{No.\;of\;employees\;earning\;more\;than\;₹84\;}{Total\;employees}\times100\%\\=\frac{39}{120}\times100\;\%\\=\frac{65}2=32.5\%\]

Hence, Percentage of employees earning more than ₹84 = 32.5%

(iii) From graph,

I = 30.

Hence, No. of employees earning less than or equal to ₹ 56 per day = 30.

Question 109
Study the graph and answer the questions that follow: