Application of Graphs

Q.

A random survey of the number of children of various age groups playing in park was found as follows:

$\begin{array}{cc}\text{Age (in years)}& \text{Number of children}\\ 1-2& 5\\ 2-3& 3\\ 3-5& 6\\ 5-7& 12\\ 7-10& 9\\ 10-15& 10\\ 15-17& 4\end{array}$

Draw a histogram to represent the data above.

Q.

What is the amount of interest on Rs 20000 for one year?

1. Rs 1500

2. Rs 1000

3. Rs 2000

4. Rs 1200

Q. Question 1(iii)
Draw the graphs for the following tables of values, with suitable scales on the axes.
Interest on deposits for a year.
$\begin{array}{cccccc}Deposit(inRs.)& 1000& 2000& 3000& 4000& 5000\\ SimpleInterest(inRs.)& 80& 160& 240& 320& 400\end{array}$
(i) Does the graph pass through the origin?
(ii) Use the graph to find the interest on Rs 2500 for a year.
(iii) To get an interestofRs280 per year, how much money should be deposited?

Q.

The equation representing the y - axis is

(a) x = 0

(b) y = 0

(c) x = a

(d) y = a

Q.

Use the tables below to draw linear graphs.

(a) The number of days a hill side city received snow in different years.

Year	2003	2004	2005	2006
Days	8	10	5	12

(b) Population (in thousands) of men and women in a village in different years.

Year	2003	2004	2005	2006	2007
Number of men	12	12.5	13	13.2	13.5
Number of women	11.3	11.9	13	13.6	12.8

Q.

A courier-person cycles from a town to a neighboring suburban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph. (a) What is the scale taken for the time axis? (b) How much time did the person take for the travel? (c) How far is the place of the merchant from the town? (d) Did the person stop on his way? Explain. (e) During which period did he ride fastest?

Q. Question 74(i)
The following chart gives the growth in height in terms of percentage of full height of boys and girls with their respective ages.
$\begin{array}{cccccccccccc}Age\left(inYears\right)& 8& 9& 10& 11& 12& 13& 14& 15& 16& 17& 18\\ Boys\left(inpercentage\right)& 72& 75& 78& 81& 84& 88& 92& 95& 98& 99& 100\\ Girls\left(inpercentage\right)& 77& 81& 84& 88& 91& 95& 98& 99& 99.5& 100& 100\end{array}$
Draw the line graph of above data on the same sheet and answer the following questions.
In which year both the boys and the girls achieve their maximum height?

Q. Question 1(ii)
Draw the graphs for the following tables of values, with suitable scales on the axes.
Distance travelled by a car
$\begin{array}{ccccc}Time\left(inhours\right)& 6a.m& 7a.m& 8a.m& 9a.m\\ Distance\left(inkm\right)& 40& 80& 120& 160\end{array}$
(i) How much distance did the car cover during the period 7.30 a.m. to 8 a.m.?
(ii) What was the time when the car had covered a distance of 100 km since its start?

Q. What is jagged line?

Q. A bank gives 10% interest on the deposite by the ladies. Draw a graph showing the relation between the amount deposited and the simple interest earned by the ladies. Find the investment one has to make an interest of ₹70.

Sum Deposited (in ₹)	100	200	300	500	1000
Simple interest (in ₹)	10	20	30	50	100

1. ₹700
2. ₹600
3. ₹500
4. ₹850

Q. If the distance of a point from Y-axis is 2 units and from X-axis is 4 units, then the coordinates of the point is .

1. (2, 4)
2. (4, 2)
3. (1, 2)
4. (2, 1)

Q.

Draw the graphs for the following tables of values, with suitable scales on the axes.

(a) Cost of apples

Number of apples	1	2	3	4	5
Cost (in Rs)	5	10	15	20	25

(b) Distance travelled by a car

Time (in hours)	6 a.m.	7 a.m.	8 a.m.	9 a.m.
Distance (in km)	40	80	120	160

(i) How much distance did the car cover during the period 7.30 a.m. to 8 a.m.?

(ii) What was the time when the car had covered a distance of 100 km since its start?

(c) Interest on deposits for a year:

Deposit (in Rs)	1000	2000	3000	4000	5000
Simple interest (in Rs)	80	160	240	320	400

(i) Does the graph pass through the origin?

(ii) Use the graph to find the interest on Rs 2500 for a year:

(iii) To get an interest of Rs 280 per year, how much money should be deposited?

Q.

The daily pocket expenses of 206 students in a school are given below.

$\begin{array}{ccccccccc}\text{Pocket expense}& 0-5& 5-10& 10-15& 15-20& 20-25& 25-30& 30-35& 35-40\\ \text{(in rupees)}& & & & & & & & \\ \text{Number of students}& 10& 16& 30& 42& 50& 30& 16& 12\\ \text{(Frequency)}& & & & & & & & \end{array}$

Construct a frequency polygon representing the above data. [4 MARKS]

Q. Question 64(c)
The following table gives the growth chart of a child.
$\begin{array}{cccccc}Height\left(incm\right)& 75& 90& 110& 120& 130\\ Age\left(inyears\right)& 2& 4& 6& 8& 10\end{array}$

Draw a line graph for the table and answer the question that follows.
(c) Between which two consecutive periods did the child grow faster?

Q. Question 64(a)
The following table gives the growth chart of a child.
$\begin{array}{cccccc}Height\left(incm\right)& 75& 90& 110& 120& 130\\ Age\left(inyears\right)& 2& 4& 6& 8& 10\end{array}$

Draw a line graph for the table and answer the question that follows.
(a) What is the height at the age of 5 years?

Q.

True or false?

(a) The equation of the x-axis is x = 0.

(b) The line x = 4 is parallel to y-axis

(c) The line y = 8 is perpendicular to x-axis.

(d) The lines x = y and x = − y are perpendicular to each other.

(e) The lines x = 9 and y = 9 are perpendicular to each other.

(f) The graph of y = x² is a straight line.

(g) The line y = 3x + 4 does not intersect x-axis.

(h) In a rectangular coordinate system, the coordinate axes are chosen such that they form a pair of perpendicular lines.

Q.

Draw the temperature-times graph in each of the following cases:
(i) $\begin{array}{ccccccccc}\text{Time (in hours)}:& 7:00& 9:00& 11:00& 13:00& 15:00& 17:00& 19:00& 21:00\\ \text{Temperature in (}{}^{\circ }F):& 100& 101& 104& 102& 100& 99& 100& 98\end{array}$
(ii)$\begin{array}{cccccccc}\text{Time (in hours)}:& 8:00& 10:00& 12:00& 14:00& 16:00& 18:00& 20:00\\ \text{Temperature in (}{}^{\circ }F):& 100& 101& 104& 103& 99& 98& 100\end{array}$

Q.

The graph of y = a is

(a) the x - axis

(b) the y - axis

(c) a line parallel to y - axis

(d) a line parallel to x - axis

Q. The daily pocket expenses of 206 students in a school are given below.

$\begin{array}{ccccccccc}Pocketexpense& 0-5& 5-10& 10-15& 15-20& 20-25& 25-30& 30-35& 35-40\\ \left(inrupees\right)& & & & & & & & \\ Numberofstudents& 10& 16& 30& 42& 50& 30& 16& 12\\ \left(Frequency\right)& & & & & & & & \end{array}$

Construct a frequency polygon representing the above data. [4 MARKS]

Q. John records the growth of a plant as a bar graph. If he were to calculate the height of the plant in the 5th week by finding the average growth rate, how tall would the plant be?

Week

Q.

The following graph shows the temperature of a patient in a hospital, recorded every hour.

(a) What was the patient’s temperature at 1 p.m.?

(b) When was the patient’s temperature 38.5°C?

(c) The patient’s temperature was the same two times during the period given. What were these two times?

(d) What was the temperature at 1.30 p.m? How did you arrive at your answer?

(e) During which periods did the patient’s temperature show an upward trend?

Q. Question 1(v)
The following graph shows the temperature of a patient in a hospital, recorded every hour

During which periods did the patients’ temperature show an upward trend?

Q.

Which of the following does not give a linear graph?

1. y = 9x + 1

2. y = 3

3. y = x²

4. y = x

Q.

Fix up your own coordinate system on a graph paper and locate the following points on the sheet:

(i) P(−3, 5); (ii) Q(0, −8); (iii) R(4, 0); (iv) S(−4, −9)

Q. Question 79(ii)

Consider this input/output table.
$\begin{array}{cccccc}Input& 1& 2& 4& 5& 7\\ Output& 2& 5& 11& 14& 20\end{array}$
Use your graph to predict the outputs for inputs of 3 and 8.

Q.

The below graph shows the relation between the quantity of petrol filled in a car and the cost of petrol.

What will be the cost of 12 litres of Petrol?

1. Rs 500

2. Rs 700

3. Rs 600

4. Rs 400

Q. Question 79(i)

Consider this input/output table.
$\begin{array}{cccccc}Input& 1& 2& 4& 5& 7\\ Output& 2& 5& 11& 14& 20\end{array}$
Graph the values from the table by taking input along horizontal axis from 0 to 8 and output along vertical axis from 0 to 24.

Q. Observe the adjoining graph and answer the following question:

Changes in y when x changes from 0 to 2.

1. 0
2. -4
3. 2
4. 4

Q. Question 66
Draw a parallelogram ABCD on a graph paper with the coordinates given in Table I. Use this table to complete Tables II and III to get the coordinates of E, F, G, H and J, K, L, M.

Table I
$\begin{array}{cc}Point& (x,y)\\ A& (1,1)\\ B& (4,4)\\ C& (8,4)\\ D& (5,1)\end{array}$

Table II
$\begin{array}{cc}Point& (0.5x,0.5y)\\ E& (0.5,0.5)\\ F& \\ G& \\ H& \end{array}$

Table III
$\begin{array}{cc}Point& (2x,1.5y)\\ J& (2,1.5)\\ K& \\ L& \\ M& \end{array}$
Draw parallelograms EFGH and JKLM on the same graph paper. Plot the points (2, 4) and (4, 2) on a graph paper, then draw a line segment joining these two points.

Q.

Mayank deposited Rs. 1400 in a bank at the rate of 10% per annum. Draw a linear graph which shows the relationship between time and the interest earned by Mayank. [4 MARKS]