DAV Class 8 Maths Chapter 13 Practice Worksheet
Introduction to Graphs Practice Worksheet
Section - I
A. Tick (✓) the correct option.
1.
The point at which the x-axis and y-axis intersect on the Cartesian Plane is
\(
\begin{aligned}
(a) \, & \, \text{ abscissa } \\
(b) \, & \, \text{ origin } \\
(c) \, & \, \text{ ordinate } \\
(d) \, & \, x\text{-coordinate} \\
\end{aligned}
\)
Answer \( \color{orange} (b) \ \color{red} \text{origin} \)
2.
If a point lies on the x-axis, its coordinates are
\(
\begin{aligned}
(a) \, & \, (x, 0) \\
(b) \, & \, (0, 0) \\
(c) \, & \, (x, y) \\
(d) \, & \, (0, y) \\
\end{aligned}
\)
Answer \( \color{orange} (a) \ \color{red} (x, 0) \)
3.
The distance of a point A (5, 4) from x-axis is
\(
\begin{aligned}
(a) \, & \, 3 \text{ units} \\
(b) \, & \, 4 \text{ units} \\
(c) \, & \, 5 \text{ units} \\
(d) \, & \, 1 \text{ unit} \\
\end{aligned}
\)
Answer \( \color{orange} (b) \ \color{red} 4\, \text{units} \)
4.
The distance of a point from y-axis is called
\(
\begin{aligned}
(a) \, & \, \text{ ordinate } \\
(b) \, & \, y\text{ -coordinate } \\
(c) \, & \, \text{ abscissa } \\
(d) \, & \, \text{origin} \\
\end{aligned}
\)
Answer \( \color{orange} (c) \ \color{red} \text{abscissa} \)
5.
The coordinates of the origin is
\(
\begin{aligned}
(a) \, & \, (x, 0) \\
(b) \, & \, (0, 0) \\
(c) \, & \, (x, y) \\
(d) \, & \, (0, y) \\
\end{aligned}
\)
Answer \( \color{orange} (b) \ \color{red} (0, 0) \)
6.
The distance of the point C (7,4) from x-axis is
\(
\begin{aligned}
(a) \, & \, 11 \text{ units} \\
(b) \, & \, 4 \text{ units} \\
(c) \, & \, 3 \text{ units} \\
(d) \, & \, 1 \text{ unit} \\
\end{aligned}
\)
Answer \( \color{orange} (b) \ \color{red} 4\, \text{units} \)
7.
The point Q (0,2) lies on
\(
\begin{aligned}
(a) \, & \, x\text{-axis} \\
(b) \, & \, y\text{-axis} \\
(c) \, & \, \text{origin} \\
(d) \, & \, \text{abscissa } \\
\end{aligned}
\)
Answer \( \color{orange} (b) \ \color{red} y\text{-axis} \)
8.
The point P (0,0) lies at
\(
\begin{aligned}
(a) \, & \, y\text{-axis} \\
(b) \, & \, \text{origin} \\
(c) \, & \, \text{axis} \\
(d) \, & \, \text{ordinate} \\
\end{aligned}
\)
Answer \( \color{orange} (b) \ \color{red} \text{origin} \)
9.
The distance of a point from x-axis is called
\(
\begin{aligned}
(a) \, & \, \text{ordinate} \\
(b) \, & \, y\text{-coordinate} \\
(c) \, & \, \text{abscissa} \\
(d) \, & \, \text{origin} \\
\end{aligned}
\)
Answer \( \color{orange} (a) \ \color{red} \text{ordinate} \)
10.
The distance between the points A (0,5) and B (0,7) is
\(
\begin{aligned}
(a) \, & \, 2 \text{ units} \\
(b) \, & \, 5 \text{ units} \\
(c) \, & \, 7 \text{ units} \\
(d) \, & \, 12 \text{ unit} \\
\end{aligned}
\)
Answer \( \color{orange} (a) \ \color{red} 2\, \text{units} \)
11.
The point (2, 2) is
\(
\begin{aligned}
(a) \, & \, \text{near to x-axis} \\
(b) \, & \, \text{near to y-axis} \\
(c) \, & \, \text{near to origin} \\
(d) \, & \, \text{equidistant from x-axis and y-axis} \\
\end{aligned}
\)
Answer \( \color{orange} (d) \ \color{red} \text{equidistant from x-axis and y-axis} \)
12.
The ordinate of the point lying on x-axis is
\(
\begin{aligned}
(a) \, & \, 1 \\
(b) \, & \, 0 \\
(c) \, & \, 2 \\
(d) \, & \, 3 \\
\end{aligned}
\)
Answer \( \color{orange} (b) \ \color{red} 0 \)
13.
A graph that displays data that changes continuously over periods of time is called
\(
\begin{aligned}
(a) \, & \, \text{ Bar graph} \\
(b) \, & \, \text{ Pie chart} \\
(c) \, & \, \text{ Histogram} \\
(d) \, & \, \text{ Linear Graph} \\
\end{aligned}
\)
Answer \( \color{orange} (d) \ \color{red} \text{Linear Graph} \)
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
14.
Assertion (A): The perpendicular distance of the point C (3, 4) from the x-axis is 4.
Reason (R): The perpendicular distance of a point from y-axis is called its x-coordinate.
Answer \( \color{orange} (a) \) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
15.
Assertion (A): Points (1,1), (2,4), (4,16) will lie on the graph representing the relation of side versus area of a square.
Reason (R): The relation of the Side (S) versus Area (A) of a square is represented by the equation \( A = \text{Side} \times \text{Side} \).
Answer \( \color{orange} (a) \) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
Section - II
16. Plot the points on the Cartesian plane: M (2, 1), N (5, 3), O (6, 4), P (8, 0)
Answer
Scale
x-axis: 1 unit = 1 unit
y-axis: 1 unit = 1 unit
17. State True or False. Justify:
(i) A point whose \( x \)-coordinate is zero will lie on the \( y \)-axis.
Answer True
A point with \( x = 0 \) lies on the \( y \)-axis because the coordinates will be \( (0,y) \).
(ii) The coordinates of the origin are (1, 0).
Answer False
The coordinates of the origin are \( (0,0) \).
18. Plot the points P (1, 1), Q (3, 4), R (6, 2) on the graph. Connect the points in that order to get a closed figure PQR. What type of figure do you get?
Answer
Scale
x-axis: 1 unit = 1 unit
y-axis: 1 unit = 1 unit
The closed figure formed is triangle PQR or \( \triangle PQR\).
19. Plot the points A (3, 3), B (6, 6), C (4, 4). Join these points in pairs. Do they lie on the line passing through the origin?
Answer
Scale
x-axis: 1 unit = 1 unit
y-axis: 1 unit = 1 unit
Yes, the points lie on the line passing through the origin.
20. Coordinates of three points A, B, and C are (4, 5), (6, 7), and (4, 0) respectively. Find the:
(i) value of (Abscissa of B – Ordinate of A).
Answer
\[ \begin{align*} & B(6,7) \\ & A(4,5) \\ \\ \text{Abscissa of B} & = 6 \\ \text{Ordinate of A} &= 5 \\ \\ \text{Abscissa of B} & - \text{Ordinate of A} \\ &= 6-5 \\ & = \color{red} 1 \\ \end{align*} \]
(ii) Distance between the points A and C.
Answer
\( \begin{align*} & A(4,5) \\ & C(4,0) \\ Distance &= \color{red} 5\, units \end{align*} \)
Section - III
21.
The number of pairs of shoes sold from an outlet of a company in a particular week are given below:
Draw a graph for the above data.
Day
1 2 3 4 5 6 7
No. of pairs of shoes sold
24 20 18 16 23 11 21
Answer
Scale:
x-axis: 1 unit = 1 day
y-axis: 1 unit = 2 pairs of shoes
22.
A man travels by a bike. Draw a linear graph showing the relationship between speed and distance covered for different speeds.
Speed (km/hr)
10 20 30 40 50
Distance (km)
60 120 180 240 300
Answer
Scale:
x-axis: 1 unit = 10 km/hr
y-axis: 1 unit = 60 km
23.
A car is going on a long journey starting at 5:00 hour. The speed of the car at different hours is given below:
Draw a speed-time graph for the above data.
Time (in hr)
5:00 7:00 9:00 11:00 13:00 15:00 17:00
Speed (in km/hr)
30 50 60 75 70 55 65
Answer
Scale:
x-axis: 1 unit = 2 hours
y-axis: 1 unit = 10 km/hr
24.
Mohan can drive a car continuously at a speed of 80 km/hr. Draw a time-distance graph for this situation. Also find:
(i) The time taken by Mohan to cover 240 km.
(ii) The distance covered by Mohan in \(4 \frac{1}{2}\) hours.
Answer
| Hours | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Distance (km) | 80 | 160 | 240 | 320 | 400 | 480 |
Scale:
x-axis: 1 unit = 1 hour
y-axis: 1 unit = 80 km
(i) To cover 240 km:
\(
\begin{align*}
\\
\text{Time} &= \frac{\text{Distance}}{\text{Speed}} \\ \\
& = \frac{240}{80} \\ \\
\color{red}Time &= \color{red} 3\, \text{hours}\\ \\
\end{align*}
\)
(ii) Distance in \( \displaystyle 4 \frac{1}{2}\) hours:
\(
\begin{align*}
\\
\text{Distance} &= \text{Speed} \times \text{Time} \\
&= 80 \times 4.5 \\
\color{red} \text{Distance} &= \color{red} 360\, \text{km}
\end{align*}
\)
25.
The quantity of petrol filled in a bike and the cost of petrol are given below:
Draw a graph for the above data. Also, find:
Litres of petrol filled
2 4 6 8 10 12
Cost of petrol (in ₹)
70 140 210 280 350 420
(i) The cost of 5 litres of petrol.
(ii) How many litres of petrol can be filled for ₹385.
Answer
Scale:
x-axis: 1 unit = 2 litres
y-axis: 1 unit = ₹70
\(
\begin{align*}
(i) \color{magenta} \text{ Cost of 5 litres petrol?} \\ \\
\text{ Cost of 1 L petrol}& = \text{₹} 35 \\
\text{ Cost of 5 L petrol}& = 35 \times 5 \\
\color{green} \text{ Cost of 5 L petrol} &= \color{green} \text{₹}175 \\ \\
\end{align*}
\)
\(
\begin{align*} \\
(ii) \color{magenta} \text{ Litres of petrol for ₹385} & = \frac{385}{35} \\ \\
&= \color{green} 11 \ litres \\
\end{align*}
\)
26.
The side of a square and its perimeter are given in the following table:
Draw a graph to show this information.
Side of square (in cm)
2 3 3.5 5 6
Perimeter (in cm)
8 12 14 20 24
Answer
Scale:
x-axis: 1 unit = 1 cm
y-axis: 1 unit = 4 cm