Introduction To Graphs

A pie-graph\chart is the used to compare parts of a whole as a circle represents the whole. Each non-intersecting adjacent sector represents of the part of the circle/data.

A line graph displays data which changes continuously over period of time such as speed or distance covered. This graph displays the relationship between two varying quantities.

Under this graph a single line is used to join all the points plotted on the graph paper hence giving more precise depiction of the data to be interpreted.

To find out the co-ordinates of the point X, we draw perpendicular from point X to the x-axis and y-axis simultaneously, and would check at what distance from the origin, they meet both the axis.

The perpendicular drawn from X to x-axis meets at 3units from origin so x co-ordinate of X is 3

Similarly, y co-ordinate is 2

The co-ordinates of the point X are (3,2)

The co-ordinates of points R are (0,3) as the point lies on y-axis so its x co-ordinate is 0 and from the origin it is at distance o f3 units so its y co-ordinates is 3.

The co-ordinates of S are (3,3) and P are (3,0)

The point (3, 4) is at the distance from 3 units from the y axis and 4 units from the x axis.

When the co-ordinates are written the first number indicates distance on x axis or the y co-ordinate and second number indicates distance on y axis or the x co-ordinate from the origin.

Since both the axis are perpendicular to each other they intersect at single point which is termed as origin and its co-ordinates are (0, 0). So (0, 0) is the single point which lies on both the axis.

As the distance from x axis gives y co-ordinate and distance from the y axis gives x co-ordinates, the co-ordinates of the given point are (6,3).

The book is at the distance of 3 units from the y axis so its x co-ordinate is 3 and at the distance of 7 units from the x-axis, so its y co-ordinate is 7. Hence, the required point is (3, 7).

The time taken is denoted on x axis and the number of words types are on y axis. To calculate words types in 30 seconds. We look for the point on the line graph which corresponds 30 on the x axis and from that point on the graph, draw perpendicular on y axis to find the number of words typed. The Answer comes out to be approximately 28 words in 30seconds.

Here length of the side of the square are given on x axis and perimeter is given on y axis.

From the table given in question the points to be plotted on line graph are (1, 4), (2,8) ,(3, 12), (4, 16) and (5, 20)

After checking the graphs given, these points are plotted in the graph number D. Hence the solution is option D

line graph

A line graph displays data which changes continuously over period of time such as speed or distance covered. This graph displays the relationship between two constantly varying quantities.

graph

A graph is the representation of data between two variables where one is independent variable and other is dependent variable. The graph shows how change in quantity of independent variable brings in change in quantity of dependent variable.

a pair (two)

The x coordinate and the y co-ordinate are the two or a pair of point required to plot the point on graph paper. The distance of point from x axis makes y co-ordinate and distance of point from y axis makes x co-ordinate.

y axis

The x co-ordinate is zero means the distance of point from y axis is zero which means it lies on y axis itself at a certain point from the origin.

x axis and y axis, respectively

The horizontal line in a line graph is called as x axis and vertically line is called as y axis which are two mutually perpendicular lines intersecting at Origin (0,0)

the two points required to plot any point on the graph are its two co-ordinates namely x and y. these co-ordinates fixes the exact position of the point on the graph which actually is the distance of the point from the x axis and y axis. This fixing the position of the point is called as plotting of the point on graph.

x co-ordinate

How much distance the point to be plotted is from the y axis is actually the x co-ordinate and similarly, how much distance far away the point is from the x axis is its y co-ordinate or ordinate.

x axis

Y co-ordinate depicts the Distance of the given point from the x axis and if the y co-ordinates are zero that means the distance from x axis is zero i.e; the point is on x axis itself.

2 units

Since the y co-ordinate shows the distance from the x axis hence the point (5,2) means the distance from the x axis is 2 units.

zero (0)

x co-ordinate represents the distance from the y axis is zero therefore the x coordinates of point any point on y axis will be zero.

The y coordinate is the distance of the point from the x axis. In the ordered pair, the second number always denotes the y co-ordinate so; here the y co-ordinate will be 4 units.

Here (4, 7) is an ordered pair of point so 4 denote the x co-ordinate or the distance from the y axis.

The co-ordinates of a point are (5, 4)

X coordinate is written on the first place followed by y co-ordinate in an ordered pair of point,

y co-ordinate

In an ordered pair of point, x coordinate is written on the first place followed by y co-ordinate so the second number denotes the y co-ordinate or the distance of the point from the x axis.

origin

The intersecting point of the two mutually perpendicular x axis and y axis is called as origin with coordinates as (0,0)

True

For fixing a point on the graph sheet we need two coordinates because we draw graph in (x, y) form. One point required for x – axis and one point for y – axis. x – axis goes from left and right and y – axis goes from up and down.

Hence, it is true.

False

A line graph consists of bits of line segments joined consecutively. The graph which have a whole unbroken line called linear graphs.

Hence, it is not true.

False

The distance of any point from x – axis is called its y – coordinate and the distance of a point from y – axis is called its x – coordinate.

Hence, it is not true.

False

Given point is (3, 5)

⇒ Comparing with (x, y) form

⇒ x = 3 and y = 5

⇒ As we know that distance of a point from y – axis is called its x – coordinate

∴ distance of the point from y – axis will 3.

Hence, it is not true.

False

Ordinate also known as y – coordinate of a point. And it is defined as distance from x – axis.

Hence, it is not true.

True

Ordinate is distance from x – axis.

⇒ distance from x – axis = y – coordinate.

∵ distance from x – axis is 3.

∴ ordinate will be 3.

Hence, it is true.

True

Axes intersect when both x and y are zero. Centre of the coordinate system called origin. Coordinates of the origin are (0, 0).

Hence, it is true.

False

The points (3,5) and (5,3) represents different points.

⇒ In Point (3,5):

X – coordinate = 3

Y – coordinate = 5

⇒ In point (5,3)

X – coordinate = 5

Y – coordinate = 3

Hence, it is not true.

True

Points that lies on axis does not lie in any quadrant. If a point lies on y – axis then its x – coordinate will be zero. And if a point lies on x – axis then its y – coordinate will be zero.

Hence, it is not true.

(1→D), (2→F), (3→E), (4→A ), (5→B), (6→C)

1. Given Point is (0,5)

Distance from x – axis = y – coordinate

∴ Distance from x – axis = 5

2. Given Point is (2,3)

Distance from y – axis = x – coordinate

∴ Distance from y – axis = 2

3. Given Point is (4,8)

Distance from x – axis = y – coordinate

∴ Distance from x – axis = 8

Distance from y – axis = x – coordinate

∴ Distance from y – axis = 4

∴ we can say that y – coordinate is double of x – coordinate.

4. Given Point is (3,7)

Here, x – coordinate = 3 and y – coordinate = 7.

⇒ y – coordinate = 2× 3 + 1

⇒ Thus, y – coordinate = 2× (x – coordinate) + 1.

5. Given Point is (0,0)

Centre of the coordinate system is called origin. Coordinates of origin are (0,0)

6. Given Point is (5,0)

Here, x – coordinate = 5 and y – coordinate = 0.

∴ only y – coordinate is zero.

(A→ ii), (B→ iii), (C→ i), (D→ v), (E→ vi), (F→ iv)

In a given coordinate system P(x, y).

⇒ ‘x’ represents abscissa and ‘y’ represents ordinate.

A. Given Point is (7, 0)

Here, abscissa i.e. x – coordinate = 7 and ordinate i.e. y – coordinate = 0.

⇒ Thus, ordinate is zero.

B. Given Point is (11,11)

Here, abscissa i.e. x – coordinate = 11 and ordinate i.e. y – coordinate = 11.

⇒ Thus, ordinate is equal to abscissa.

C. Given Point is (4,8)

Here, abscissa i.e. x – coordinate = 4 and ordinate i.e. y – coordinate = 8.

⇒ Thus, ordinate is double the abscissa.

D. Given Point is (6,2)

Here, abscissa i.e. x – coordinate = 6 and ordinate i.e. y – coordinate = 2.

⇒ Thus, abscissa is triple the ordinate.

E. Given Point is (0,9)

Here, abscissa i.e. x – coordinate = 0 and ordinate i.e. y – coordinate = 9.

⇒ Thus, abscissa is zero.

F. Given Point is (6,3)

Here, abscissa i.e. x – coordinate = 6 and ordinate i.e. y – coordinate = 3.

⇒ Thus, abscissa is double the ordinate.

A) F is the point which indicates the location of the point (2,0)

As the x coordinate is 2 and y-coordinate is 0.

Hence F is the point which indicates the location of the point (2,0).

B) A is the point which indicates the location of the point (0,4)

As the x coordinate is 0

The y- coordinate is 4

Hence F is the point which indicates the location of the point (0,4).

C) B is the point which indicates the location of the point (5,1)

As the x coordinate is 5

The coordinate is 1

Hence F is the point which indicates the location of the point (5,1).

D) B is the point which indicates the location of the point (5,1)

As the x coordinate is 5

The coordinate is 1

Hence F is the point which indicates the location of the point (5,1).

E) E is the point which indicates the location of the point (3,3)

As the x coordinate is 3

The coordinate is 3

Hence F is the point which indicates the location of the point (3,3).

(i) Point A is lying on 0 on x axis and 7.5 on y axis

The coordinates of the point A is (0,7.5)

(ii) Point B is lying on 4 in x axis and 5 in y axis

The coordinates of the point B is (4,5)

(iii) Point C is lying on 7.5 in x axis and 2.5 in y axis

The coordinates of the point C is (7.5,2.5)

(iv) Point D is lying on 11 in x axis and 0 in y axis

The coordinates of the point D is (11,0)

(v) Point E is lying on 14.5 in x axis and 6.5 in y axis

The coordinates of the point E is (14.5,6.5)

(vi) Point F is lying on 18 in x axis and 9.5 in y axis

The coordinates of the point F is (18,9.5)

Draw the x and y axis then plot the given points according to the coordinates.

A) As the x coordinate is lying on A on x axis

The y coordinate is lying on f on y axis

The coordinates of that point be (x,y)(A,f)

Hence the location of lions in the zoo is at the point (A,f)

B) (D,f)→ Monkey

As the coordinate x is D and coordinate y is f i.e., (D,f)

Which is already representing monkeys.

(C,d)→ Elephant

As the coordinate x is C and coordinate y is d i.e., (C,d)

Which is already representing elephants

C) As the x coordinate is lying on 0 on x axis

The y coordinate is lying on e on y axis

The coordinates of that point be (x,y)(0,e)

Hence the location of lions in the zoo is at the point (0,e)

D) As the x coordinate is lying on C on x axis

The y coordinate is lying on c on y axis

The coordinates of that point be (x,y)(C,c)

Hence the location of lions in the zoo is at the point (C,c)

A) 7 which is on the left is the x coordinate the point which is

in the form of (x,y)

B) 5 which is on the left is the x coordinate the point which is

in the form of (x,y)

C) 0 which is on the left is the x coordinate the point which is

in the form of (x,y)

A) 5 which is on the right is the y coordinate the point which is

in the form of (x,y)

B) 0 which is on the right is the y coordinate the point which

is in the form of (x,y)

C) 7 which is on the right is the y coordinate the point which

is in the form (x,y)

The points lie on a straight line.

It is not in a straight line, when joined in the given order a semi arch is formed.

it is not a straight line, when joined in the given order (also AD) a triangle is formed.

Let the x coordinate be x

Y coordinate is 3x (according to the given question)

Forming a table,

Let x = 1(x coordinate)

Y = 3x = 31 = 3 (y coordinate)

Let x = 2(x coordinate)

Y = 3x = 32 = 6 (y coordinate)

Let x = 3(x coordinate)

Y = 3x = 33 = 9 (y coordinate)

Let x = 1(x coordinate)

Y = 3x = 34 = 12 (y coordinate)

Plot the given points on the graph where x axis indicates sides of a square and y axis indicates area of the square.

No, it is not a linear graph because it is not having shape of line. As all the points that make up this graph are not collinear, or in other words, not on the same line

A) Given cost of one notebook = Rs. 10

Cost of 7 notebooks = 710 = Rs. 70

B) Given cost of one notebook = Rs. 10

Number of books for Rs. 50 = = 5

(a) As the distance increase time also increase with equal intervals

(b) The slope part represents that distance increase time also increase and the remaining part represents that distance is

constant for long time.

(c) Distance increase time also increase unequal intervals.

A)

Here, y = 3x + 1

When x = 2,

y = 3(2) + 1 = 6 + 1 = 7

When x = 3,

y = 3(3) + 1 = 9 + 1 = 10

The points in the graph are given as:

A = (0,1)

B = (1,4)

C = (2,7)

D = (3,10)

The line segments:

Here, y = x – 1

When x = 2,

y = 2 – 1 = 1

When x = 4,

y = 4 – 1 = 3

When x = 6,

y = 6 – 1 = 5

The points in the graph are given as

A = (1, 0)

B = (2, 1)

C = (4, 3)

D = (6, 5)

The line segments are

A)

By drawing the lines parallel to the y-axis and the x-axis, we can see at what point they intersect the given graph.

Step 1 :For x = 1, we draw a line parallel to the y-axis at 1 and see where it intersects the graph.

Step 2 :From the point of intersection, we draw another line which is parallel to the x-axis.

Step 3 :The point at which this line intersects the y-axis is the value of y at x = 1.

Similarly, we can find the values of y for each of the given values of x by following the above steps.

B)

Following the steps mentioned above, we can find the values of y for each of the given values of x.

Circumference = 2r

The circumference of a circle depends on the radius of a circle.

So, we plot the circumference on the y-axis as it is the dependent variable and the radius on the x-axis as it is the independent variable.

∴ We get the equation in terms of x and y as

y = 2x

When x = 0,

y = 2 × 0 = 0

When x = 7,

y = 2 × 7 = 2 × × 7 = 44

When x = 14,

y = 2 × 14 = 2 × × 14 = 88

When x = 21,

y = 2 × 21 = 2 × × 21 = 132

The points in the graph are given as

A = (0, 0)

B = (7, 44)

C = (14, 88)

D = (21, 132)

The line segments are

A) When the radius is 42 units, i.e. x = 42,

y = 264 (from the graph)

B) The circumference of the circle will be 220 units when the radius is 35 units (from the graph)

A) The x-axis gives the days of the week on which the temperatures were recorded; whereas the y-axis gives the maximum temperature that was recorded on a particular day.

B) The temperature was higher on most of the days in the first week. If we compare the graphs of the two weeks, we see that the temperature in the first week is more than the temperature in the second week for everyday except Monday and Wednesday.

C) The temperature was same on Wednesday in both the weeks. There is only on point on Wednesday unlike all the other days which have two different points for temperatures in different weeks.

D) The difference in the temperatures was maximum, i.e. 7°C, for both the weeks on Friday.

Difference on Sunday = 35 – 32 = 3°C.

Difference on Monday = 35 – 31 = 4°C.

Difference on Tuesday = 38 – 33 = 5°C.

Difference on Wednesday = 36 – 36 = 0°C.

Difference on Thursday = 37 – 34 = 3°C.

Difference on Friday = 39 – 32 = 7°C.

Difference on Saturday = 37 – 33 = 4°C.

E) The temperature on Thursday for the first week was 37°C and that for the second week was 34°C.

F) The temperature was highest, i.e. 36°C, for the second week on Wednesday.

A) The actual sales was the same as the expected sales in the month of April. This is because the graph has only one point for the month of April which indicates that the value of the y-axis is the same for both the graphs.

B) The difference in actual and expected sales was maximum, i.e. 75, in the month of March.

Difference in January = 100 – 75 = 25

Difference in February = 125 – 100 = 25

Difference in March = 150 – 75 = 75

Difference in April = 125 – 125 = 0

Difference in May = 150 – 100 = 50

Difference in June = 150 – 125 = 25

C) The difference in actual and expected sales was the least, i.e. 0, in the month of April.

D) The sales of cars in Jan = 75

The sales of cars in Feb = 100

The sales of cars in March = 75

∴ The total sales of cars in the three months = 75 + 100 + 75 = 250

E) The last three months are April, May and June.

The sales of cars in April = 125

The sales of cars in May = 100

The sales of cars in June = 150

∴ The total sales of cars in the last 3 months = 125 + 100 + 150

= 375

Average = = = 125.

∴ The average sales of cars in the last three months = 125.

F) The total sales in the first three months = 250

The total sales in the last three months = 375

∴ Ratio = = =

A) The x-axis represents the different subjects while the y-axis represents the marks obtained by Sonia in each subject.

B) In Test I, she scored the highest, i.e. 10 marks, in Maths.

C) She scored the least, i.e. 6 marks, in English and Hindi.

D) She did not score the same marks in any of the subjects in both the tests.

E) She scored 6 marks in English in Test II.

F) The total marks in Test I = 7 + 8 + 10 + 7 + 5 = 37

The total marks in Test II = 6 + 6 + 8 + 9 + 8 = 37

The performance was the same in both the tests.

G) She scored full marks, i.e. 10 marks in Maths in Test I.

The coordinates are starting from the left-most and moving clockwise.

For figure I, the coordinates of its vertices are (1, 1), (2, 3), (4, 2) and (3, 0).

For figure II, the coordinates of its vertices are (0, 5), (2, 4) and (1, 2).

For figure III, the coordinates of its vertices are (1, 5), (2, 6), (3, 6), (4, 5), (4, 4), (2, 4) and (2, 5).

For figure IV, the coordinates of its vertices are (4, 3), (5, 5), (6, 3) and (5, 1).

A) The person started from his home at 10 am, since the distance is 0 km at that time. (Note :Even though the distance at 10 pm is also 0 km, it is after the journey)

B) The first part of the graph stops at the value of 20 on the y-axis after which it first becomes constant and then starts decreasing. Hence, he travelled 20 km in the first hours of his journey.

C) The graph from 3 pm to 5 pm is parallel to the x-axis. This indicates that the person did not travel any distance in those 2 hours. So, the person was at one place from 3 pm to 5 pm.

D) He travels 20 km in the first part of the day and again travels 20 km to come back to his starting point.

∴ Total distance = 20 + 20 = 40 km.

E) The first 8 hours of the journey mean from 10 am to 6 pm. He covered 20 km up to 3 pm.

He was in the same place till 5 pm. So distance covered from 3 pm to 5 pm = 0 km.

The distance at 6 pm is 16 km and at 5 pm is 20 km.

So, distance covered from 5 pm to 6 pm = 20 – 16 = 4 km.

∴ Total distance covered in the first 8 hours = 20 + 4 = 24 km.

F) He covered 16 km of his journey at 2 pm. (Note :Even though the graph shows 16 km at 6 pm, too, the distance covered at 6 pm will be 24 km.)

G)

(a). The total distance travelled from A to B = 20 – 0 = 20 km

Now, we first need to convert 3 pm into 24 hour format.

3 pm = 12 + 3 = 15 pm

The total time taken from A to B = 15 – 10 = 5 hours

∴ Average speed from A to B = = = 4 km/hr.

(b) The total distance travelled from B to C = 0 km (since the distance is constant)

The time taken from B to C = 5 pm – 3 pm = 2 hours.

∴ Average speed from B to C = = = 0 km/hr.

(c) He returned home at 10 pm since the distance becomes 0 again at 10 pm.

The given equation is p = 2q.

Here, p is the dependent variable and q is the independent variable.

So, p will be on the y-axis and q on the x-axis.

When q = 0,

p = 2 (0) = 0

When q = ,

p = 2 = 1

When q = 1,

p = 2 (1) = 2

When q = 2,

p = 2 (2) = 4

The points in the graph are

A = (0, 0)

B = ( , 1)

C = (1, 2)

D = (2, 4)

The line segments are

A) When q = 3,

p = 6 (from the graph)

B) When p = 8,

p = 4 (from the graph)

A) The x-axis shows the days of the week and the y-axis shows the maximum temperature.

∴The graph gives information about the maximum temperature recorded during a particular week.

B) The temperature was the least, i.e. 25°C, on Sunday.

C) The temperature was 31°C on Saturday. (Draw a line from 31, parallel to the x-axis, and find the point at which it coincides with one of the points which are plotted on the graph.)

D) The hottest day is the day with the maximum temperature. The maximum temperature is 34°C, which was recorded on Friday.

∴ Friday was the hottest day.

A) Find the y-coordinate when the x-coordinate is 2.

Here, when x = 2 hours, y = 80 km.

∴ The car travels 80 km in 2 hours.

B) The coordinates of the point R are (5, 200). Since the time is represented by the x-axis, the time taken by the car to reach point R is 5 hours.

C) The x-coordinate when y = 80 is 2. Thus, it takes the car 2 hours to cover 80 km.

D) The coordinates of Q are (3, 120) and those of the starting point are (0, 0). Since the y-axis represents the distance covered, the distance of point Q from the starting point = 120 – 0 = 120 km.

E) The coordinates of point S are (6, 240) and those of the starting point are (0, 0). Since time is denoted on the x-axis, the time when the car reaches S after starting = 6 – 0 = 6 hours.

The points in the graph are

A = (1, 2)

B = (4, 2)

C = (1, 4)

The incomplete rectangle on the graph will look like

The completed rectangle ABCD on the graph is

∴ The coordinates of point D, to complete the rectangle ABCD are D (4, 4).

The points on the graph are

A = (1, 2)

B = (3, 4)

C = (5, 2)

The incomplete rhombus on the graph will look like

The completed rhombus ABCD on the graph is

∴ The coordinates of point D to complete the rhombus ABCD are D (3, 0).

The diagonal AC has the y-coordinate constant, i.e. 2.

∴ The length of AC = difference in x-coordinates = 5 – 1 = 4 units

The diagonal BD has the x-coordinate constant, i.e. 3.

∴ The length of BD = difference in y-coordinates = 4 – 0 = 4 units

∴ The two diagonals of rhombus ABCD are equal in length.

Graph1 : plotting the points

Graph 2 : drawing the lines and finding their intersection

From the second graph , we see that N is the point of intersection of PQ and RS.

Its co-ordinates from the graph can be seen are N(2.1,2.4).

A) From the given graph , we can see that , on Friday vendor A sold 35 ice creams and on the same day , vendor B sold 25 ice creams. So clearly , we can say that vendor A sold more ice creams on Friday.

B) From the given graph , we can see that , on Sunday both the vendors sold 50 ice creams. So clearly , on Sunday the sale of ice creams was same for both the vendors.

C) From the given graph , we can see that , on Sunday the sale of vendor A increase the most as compared to the previous day(Saturday) ie. By 20 sales.

D) From the given graph , we can see that , on Thursday , vendor A sold 20 ice creams and vendor B sold 40. So, the difference between the sales is of 20 ice creams which is clearly the highest. ∴ we can say that, on Thursday , the difference in sales was maximum.

E) From the given graph , we can see that , on Tuesday and Wednesday ,the sale of vendor B was 30.

∴ we can say that, on Tuesday and Wednesday the sales were same for vendor B.

A) From the given graph , we can see that , the temperature at 8am was 7°C.

B) From the given graph , we can see that , at 6am the was temperature 3^oC.

C) From the given graph , we can see that , the fall in temperature was seen after 5am and till 6am.

D) From the given graph , we can see that , the temperature at 7am was 5°C and the temperature at 10am was 8°C , so the change in temperature between 7 am and 10 am is (8-5)°C = 3°C.

E) From the given graph , we can see that , the temperature was constant from 8am to 9am.

A) From the given graph , we can say that , the height at the age of 5 years is 100cm.

B) From the given graph , we can say that , the height of the child at the age of 6 years is 110cm, and the height of the child at the age of 10 years is 130cm.

∴ we can say that the child of age 10 years is taller by 20cm from the child at the age of 6 years.

C) From the given graph , we can say that , between 2 and 4 years the growth in height of the child is of 15cm and between 2 and 4 years the growth in height of the child is of 20cm , so we can say that the 2 consecutive periods between which the child grow more faster were 2-4years and 4-6 years.

A) From the graph we can say that , Sneha made the least progress from the interval 25 minutes to 40 minutes.

We see that initially , she is travelling approximately 0.5km in 10min , 0.25km in 5min , till the first 25 mins. But after 25 mins, her speed decreased as she travelled 0.25km in 15min.

We can say that because of her speed in that interval i.e. = = 1km/hr which the lowest among all.

B) As we know that ,

Average speed = = = = × 60 = 2.18km/hr.

∴ Average speed = 2.18km/hr.

Graph 1 : parallelogram ABCD

Graph 2 : Parallelogram EFGH and JKLM along with ABCD.

The two points A(2,4) and B(4,2) is drawn on the graph paper as shown below:

Let AB is a line segment which is extended from both the ends to meet the axes.

The co-ordinates of the point on y-axis , where the line segment meet will be of the form (0,y) and the co-ordinates of the point on x-axis , where the line segment meet will be of the form (x,0).

Here , in the above figure , we can see that The co-ordinates of the point on y-axis , where the line segment meet is (0,6) and the co-ordinates of the point on x-axis , where the line segment meet is (6,0).

A) From the given graph , we can see that ,from 0 to 20 seconds there is no change in the temperature of the block.

B) From the given graph , we can see that , the change in temperature was from 20 to 50 seconds ie. for (50-20) = 30 seconds.

C) From the given graph , we can see that, after heating for 50 seconds , the temperature became constant at 100°C.

D) From the given graph , we can see that , the temperature after 25 seconds was 20°C.

E) From the given graph , we can see that , the temperature after 50 seconds of heating remains constant at 100°C till infinite time. So we can say that the temperature after 1.5 minutes will be 100°C.

A) The above graph is a line graph.

B) The above graph gives the information about the number of people present at a certain shop at different times.

C) From the given graph , we can see that , the busiest time of day at the shop is 1pm ie. 25 people visited the shop.

D) From the given graph , we can see that , 5 people enter the shop when it opens(at 10am).

E) From the given graph , we can see that , 20 are there in the shop at 1:30 pm.

A) From the graph , we can say that, the man started his journey at 5:30 am and ended at 6pm.

B) From the graph , we can say that, the total duration of journey is hours ie. From 5:30 am to 6pm.

C) From the graph , we can say that, the forward journey was of hours and the return journey was of 4 hours.

∴ The forward journey was of longer duration.

D) From the graph , we can say that, the man did not move for 6 hours(he did not move from 6:30 am to 9:30 am and 10am to 1pm).

E) From the graph , we can say that, the man had the fastest speed from 1pm to 2pm because in that interval he covered 60kms in just 1 hour.

A) The horizontal axis (or the X axis) indicates the time. The vertical axis (or the Y axis) indicates the distance from the town A to B. The dotted line shows the journey of cyclist II.

∴ from the given graph, cyclist II rest at 8.45 AM to 9.00AM for 15 minutes

B) Cyclist II cycling faster after the rest because he covers the distance of 20km (from 10km to 30km) in 1hr (from 9 AM to 10 AM)

C) The two cyclists meet at 9.00AM shows in the graph

D) Cyclist II travelled from the town B to A, he travelled 20Km when he met cyclist I

E) In the given graph, the cyclist I was far from 10KM to town B when cyclist II reached town A

Given that, Ajita goes to school at a uniform speed on her father’s scooter = 30km/h

Time taken to reach her school = 30 min =

Distance between her home and school = speed × time taken to reach

=

= 15 km

∴ Distance = 15 KM

∴ Distance covered by Ajita in 1 min = 1/2 km = 500m

The graph of the above situation is as follows

Let us take years on X axis and gross profit on Y axis.

The line graph is shown below for the annual gross profit of a company for a period of five years.

A) Let us draw a graph as per given chart. Let the age of boys and girls in X axis and their height in Y axis.

Girls in the year 17 and boys in the year 18 achieve their maximum height.

B) Girls grow faster than the boys at puberty shown in the graph.

Let us draw a graph as per given chart. Let the time taken by dhruv walking on a road is in X axis and distance in Y axis.

B) The most progress time periods from 0 to 5 min and from 5 to 10 min were made by Dhruv.

From the given graph, let us observe the following points.

X axis is placed in horizontal and Y axis is in vertical. So,

X = 1, Y = 2.5

X = 2, Y = 5

X = 3, Y = 10

X = 4, Y = 15

∴ Fill the above observed points in the table, it is shown as follows

A) From the given graph, the dropout rate is highest in the year 1990 and lowest in the year 2000.

B) The percentage of students who dropped out of high school first fall below 5% is in the year is 1996

C) In 2007,4.8% of students dropped out of high school. In 2008 0.1% of students stayed in high school.

(a) Let us observe the pattern given and complete the table.

Pattern and toothpicks are related as follows

1→ 4,

2→ 4 + 3 = 7

3→ 7 + 3 = 10

4→ 10 + 3 = 13

5→ 13 + 3 = 16

6→ 16 + 3 = 19

∴ fill the above details in the table. we get,

(b) The graph is plotted as the pattern numbers on the horizontal axis and the number of toothpicks on the vertical axis.

(c) The graph follows y = 3x + 1 pattern.

If x = 7 then y = (3 ×7) + 1 = 22

If x = 8 then y = (3 ×8) + 1 = 25

(d) Yes, X and Y follows the y = 3x + 1 pattern.

(a) Let as plot the graph as per the given table. It is shown as below

This graph follows y = 3x-1 pattern.

(b) The graph follows y = 3x-1 pattern.

If x = 3 then y = (3 ×3)-1 = 5

If x = 8 then y = (3 ×8)-1 = 23

(i)

As per the given statement, point S is plotted and it is on the water. The point S is not in the same place A.

(ii) The points C and D are not in the same place. The coordinates of C is (5,7) and D is (7,5).

(iii) The point (2,7) is in the water and labelled as E.

(iv) The coordinates (7,3) and (5,5) are on the island and exactly 2 km from Point A.

(v) (8.5,3) is the coordinates of the point that is halfway between Points L and P.

(vi) (9,4),(10,4) and (11,5) are the three points on the island with their x-coordinates greater than 8.

(vii) (5,3),(6,2) and (7,2) are the three points on the island with their Y-coordinates less than 4.

A) To observe change in the data over a period of time, we plot a graph and join the points.

B) We can see from the graph that temperature increases from 8°C at 6 am to 21°C at 1 pm (between 12 noon and 2 pm, we can say that temperature is approximately 21°C) and then it decreases to around 9°C at 9 pm(between 8 pm and 10 pm in the graph). It remains constant for an hour (9 pm to 10 pm) and then decreases. We observe that at 12 pm the temperature is 8°C, same as it was at 6 am. Thus, we see that temperature first increases and then decreases from 6 am to 12 pm.

C) On looking carefully at the graph, we see that temperature is around 17°C at 11 am and thus, it is 19°C at 12 noon.

At 8 pm temperature is 10°C.

A) Brands which cost more than Brand D are:

a. Brand F

b. Brand E

B) Bag of Brand D is the heaviest.

C) On looking closely we see that brands which weigh the same are Brand C and Brand E.

D) Brands heavier than brand B are:

i. Brand E

ii. Brand C

iii. Brand D

E) Bag of brand A is the lightest

F) On looking closely we see that brands with the same price are Brand C and Brand A.

A) The two variables represented in the graph are Weight and Height.

B) Point D represents Ostrich because it is tallest among donkey, dog, crocodile.

Point B represents Donkey as after Ostrich it is second tallest among the group.

Point A is for Crocodile as it smallest among all the given animals.

Point C represents Dog.

A) False

From the graph, we can see that the value of car increases with the increase in the age of car. Thus, older car is more valuable. Hence, the given statement is false.

B) True

We observe from the graph that speed increases with the size of the car. Thus, the given statement is true.

C) True

We can see that B is both the larger and older car from the graphs

D) True

We can see that B is both the faster and older car from the graphs

E) False

B which is more valuable than A is also faster than A.

A)

B)

C) No, the points do not lie on the same line.

A)

B)

C)

D) Neither of the graph is linear

A.

B.

Overestimated objects are:

a) EraserZ

b) Palm

c) Geometry box

C.

Underestimated objects are:

a) Math Notebook

D.

When the estimated measurements are more than actual measurements, then it can be said we have Overestimated our data.

When the estimated measurements are less than actual measurements, then it can be said we have Underestimated our data.

We able to determine only one observation accurately, that is, length of a pen.