CBSE Class 8 Mathematics Introduction To Graphs Worksheet Set 03

1. Tick the correct alternative :

i. The point of intersection of co-ordinate axes is called
(a) Common point
(b) Zero point
(c) Origin
(d) Null point
Answer: (c) Origin
The point where the x-axis and y-axis intersect is defined as the origin, with coordinates \((0, 0)\).
In simple words: The starting point of a graph where both axes cross is called the origin.

Exam Tip: Always remember that the coordinates of the origin are always \((0, 0)\).

ii. x-coordinate of a point on y-axis is
(a) x
(b) 1
(c) y
(d) 0
Answer: (d) 0
Every point lying on the vertical y-axis has a horizontal distance (x-coordinate) equal to 0.
In simple words: On the y-axis, you do not move left or right, so the x-coordinate is zero.

Exam Tip: Equation of the y-axis is \(x = 0\).

iii. The point (-1, -5) lies in
(a) First quadrant
(b) Second quadrant
(c) Third quadrant
(d) Fourth quadrant
Answer: (c) Third quadrant
Both coordinates are negative (\(x < 0, y < 0\)), which places the point in the third quadrant.
In simple words: When both x and y are negative, the point is in the bottom-left region, which is the third quadrant.
Exam Tip: Quadrants follow the counter-clockwise order: I (+, +), II (-, +), III (-, -), IV (+, -).

iv. The point (0, -4) lies on
(a) +ve x-axis
(b) +ve y-axis
(c) -ve y-axis
(d) -ve x-axis
Answer: (c) -ve y-axis
Since the x-coordinate is 0 and the y-coordinate is negative (\(-4\)), the point lies on the negative side of the vertical y-axis.
In simple words: Since x is 0 and y is negative, it lies straight down on the negative y-axis.

Exam Tip: A point with a zero x-coordinate always lies on the y-axis.

2. The following graph shows the maximum temperature in the first week of April.
a) What was the temperature on Thursday?
Answer: Looking at the graph for Thursday, the temperature corresponding to the point on the curve is \(35^\circ\text{C}\).
In simple words: Find Thursday on the bottom axis and look up to see the temperature value of \(35^\circ\text{C}\).

Exam Tip: Always check the scale on the axes before reading values.

b) When was the maximum temperature \(35^\circ\text{C}\)?
Answer: The maximum temperature of \(35^\circ\text{C}\) was recorded on Thursday.
In simple words: Trace \(35^\circ\text{C}\) on the vertical temperature axis across to the line graph to find the day, which is Thursday.

3. The following line graph shows the sale of capacitors in the last 5 years. Read the graph and answer the questions that follow:
a) What were the sales in (i) 2004 (ii) 2006?
Answer:
(i) Sales in 2004 = 150 capacitors
(ii) Sales in 2006 = 300 capacitors
In simple words: Read the corresponding y-axis values for the years 2004 and 2006 from the line graph.

Exam Tip: Note that each unit on the y-axis represents 50 capacitors according to the given scale.

b) In which year was the sale maximum?
Answer: The sale was maximum in the year 2007 (reaching 400 capacitors).
In simple words: Look for the highest point on the line graph, which corresponds to the year 2007.

Exam Tip: The highest point on a line graph represents the maximum value.

c) Compute the difference between the year when the sales were maximum and the year in which the sales were minimum.
Answer:
Year of maximum sales = 2007 (Sales = 400)
Year of minimum sales = 2004 (Sales = 150)
Difference in years = 2007 - 2004 = 3 years
In simple words: Subtract the year with the lowest sales from the year with the highest sales: \(2007 - 2004 = 3\) years.

Exam Tip: Ensure you subtract the years, not the sales figures, since the question asks for the difference between the years.

4. Ruchi is the school topper. Her predicted marks in class X boards and her actual marks are shown in the graph below. The dotted line represents the predicted marks and the solid line represents the actual marks.
a) In which subject were the actual marks and the predicted marks equal?
Answer: The actual marks and predicted marks are equal where the solid line and dotted line intersect, which is in Science.
In simple words: Find the subject where both lines meet, which is Science.

Exam Tip: Intersection points of two lines indicate equal values for both quantities.

b) What were the maximum marks scored by Ruchi (actually) and in which subject?
Answer: The maximum actual marks scored by Ruchi were 100 in Maths.
In simple words: Find the highest point on the solid line, which reaches 100 in Maths.

Exam Tip: The solid line represents actual marks; look for its highest peak.

c) In which subject did the actual marks differ the most from the predicted marks?
Answer: The actual marks differed the most from the predicted marks in English (where the vertical gap between the solid and dotted lines is the largest).
In simple words: Look for the subject with the largest vertical distance between the two lines, which is English.

Exam Tip: Greater vertical separation signifies a larger difference between the two datasets.

5. The graph shows the path of a cyclist. Answer the questions given below.
a) What is the average speed during the first part of the journey?
Answer:
Distance covered in the first part = 20 m
Time taken for the first part = 4 seconds
Average speed = \(\frac{\text{Distance}}{\text{Time}} = \frac{20\text{ m}}{4\text{ s}} = 5\text{ m/s}\)
In simple words: Divide the total distance traveled in the first section (20 meters) by the time taken (4 seconds) to get 5 m/s.

Exam Tip: Speed is calculated as distance divided by time.

b) For how long did he rest?
Answer: The cyclist rested during the horizontal flat portion of the graph from \(t = 4\) seconds to \(t = 9\) seconds.
Duration of rest = \(9 - 4 = 5\) seconds.
In simple words: A flat horizontal line means distance is not changing, indicating a rest period of 5 seconds.

Exam Tip: A zero slope (flat line) on a distance-time graph represents zero speed (resting).

c) What was the average speed during the second part of the journey?
Answer:
Initial distance at start of second part = 20 m at \(t = 9\) s
Final distance at end of journey = 40 m at \(t = 13\) s
Distance covered in second part = \(40 - 20 = 20\) m
Time taken for second part = \(13 - 9 = 4\) seconds
Average speed = \(\frac{20\text{ m}}{4\text{ s}} = 5\text{ m/s}\)
In simple words: The cyclist covered another 20 meters in 4 seconds, giving a speed of 5 m/s.

Exam Tip: Consider only the interval of the second part when calculating its specific speed.

6. The graph represents the journey of a camel in the Thar Desert. Read and answer the following questions:
a) What is the average speed of the camel?
Answer:
Total distance = 40 km
Total time = 4 hours
Average speed = \(\frac{\text{Total Distance}}{\text{Total Time}} = \frac{40\text{ km}}{4\text{ hours}} = 10\text{ km/h}\)
In simple words: Divide total distance (40 km) by total time (4 hours) to get 10 km/h.

Exam Tip: Overall average speed is always total distance divided by total time.

b) In what time did the camel travel first 25 km?
Answer: Looking at the graph, a distance of 25 km corresponds to 2.5 hours (or 2 hours 30 minutes).
In simple words: Find 25 km on the horizontal axis and trace up to the graph to find the corresponding time of 2.5 hours.

Exam Tip: Read fractional grid units carefully between major tick marks.

c) What was his speed during the last one hour?
Answer:
Distance at \(t = 3\) hours = 30 km
Distance at \(t = 4\) hours = 40 km
Distance covered in the last 1 hour = \(40 - 30 = 10\) km
Speed = \(\frac{10\text{ km}}{1\text{ hour}} = 10\text{ km/h}\)
In simple words: The camel traveled 10 km in the final 1 hour, so its speed was 10 km/h.

Exam Tip: Speed over an interval is the change in distance divided by the change in time.

7. Plot the points on a graph paper. Verify if they lie on a line.
a) A(0, 2), B(-2, 2), C(2, 2)
Answer:
Plotting the points: \(A(0, 2)\), \(B(-2, 2)\), and \(C(2, 2)\).
All three points have the exact same y-coordinate (\(y = 2\)).
Therefore, they all lie on the horizontal line given by the equation \(y = 2\).
In simple words: Since all points have a y-coordinate of 2, they form a straight horizontal line.

Exam Tip: Points with identical y-coordinates form a horizontal line parallel to the x-axis.

b) A(3, 3), B(4, 3), C(3, 1)
Answer:
Plotting the points: \(A(3, 3)\), \(B(4, 3)\), and \(C(3, 1)\).
Points A and B lie on the horizontal line \(y = 3\), while point C lies at \(x = 3, y = 1\).
Since a straight line can only pass through two points at a time and C does not share the y-coordinate or lie on the horizontal line connecting A and B, they do not all lie on the same straight line.
In simple words: These three points form a triangle rather than a single straight line.

Exam Tip: Collinear points must satisfy a single linear equation connecting all of them.

8. I. Write the abscissa (x-coordinate) of each of the following:
a) (6, 5)
Answer: Abscissa = 6
In simple words: The x-coordinate is the first number in the coordinate pair, which is 6.

Exam Tip: Abscissa refers to the x-coordinate, and ordinate refers to the y-coordinate.

b) (0, -3)
Answer: Abscissa = 0
In simple words: The first number is 0.

Exam Tip: Always state the first value of the ordered pair \((x, y)\).

c) (8, 2)
Answer: Abscissa = 8
In simple words: The x-coordinate is 8.

Exam Tip: Abscissa is always written before the ordinate.

8. II. Write the abscissa (x-coordinate) of each of the following:
a) (2, 3)
Answer: Abscissa = 2
In simple words: The first element is 2.

Exam Tip: Read carefully to extract only the x-coordinate.

b) (7, -3)
Answer: Abscissa = 7
In simple words: The first element is 7.

c) (5, -5)
Answer: Abscissa = 5
In simple words: The first element is 5.

Exam Tip: Double-check the ordered pair structure.

Q 9-13 What value do you inculcate from the graphs?

9. The following table shows the marks obtained by a student in various class tests. Plot a graph using the table below:

Answer:
To plot the graph, take Unit Tests (I, II, III, IV) along the horizontal x-axis and Marks (30, 42, 60, 80) along the vertical y-axis. Plot the ordered pairs: \((I, 30)\), \((II, 42)\), \((III, 60)\), and \((IV, 80)\), and connect them with line segments to form a trend line showing academic progress.
Value inculcated: Analyzing performance graphically helps in understanding progress, identifying areas of improvement, and maintaining consistent academic growth.
In simple words: Represent test scores on a graph to visually track how marks improve over time.

Exam Tip: Choose an appropriate scale on the y-axis (e.g., 1 unit = 10 marks) to fit all data points neatly.

10. Iron is heated and its temperature is noted at different intervals of time as given in the following table. Plot a graph using the figures in the table.

Answer:
Plot Time (in seconds) along the x-axis and Temperature (in \(^\circ\text{C}\)) along the y-axis. The coordinate points to plot are \((0, 20)\), \((2, 22)\), \((6, 27)\), \((12, 32)\), and \((14, 39)\). Connect these points consecutively with line segments.
Value inculcated: Scientific observation and graphical representation teach patience, precision in data recording, and understanding cause-and-effect relationships in physics.
In simple words: Plot time and temperature values to see how heating increases the temperature steadily.

Exam Tip: Label both axes clearly with units and maintain uniform spacing for time intervals.

11. The following graph shows the side of a square and its perimeter. Read the graph and answer the following questions:
a) What is the perimeter of the square when the side is 4 cm?
Answer: Perimeter = \(16\text{ cm}\).
In simple words: Since perimeter is \(4 \times \text{side}\), for a side of 4 cm, the perimeter is \(4 \times 4 = 16\text{ cm}\).

Exam Tip: Verify graphically by locating 4 on the side axis and tracing up to the line graph.

b) What is the side of the square if the perimeter is 12 cm?
Answer: Side = \(3\text{ cm}\).
In simple words: Divide the perimeter by 4: \(12 \div 4 = 3\text{ cm}\).

Exam Tip: Use the formula \(\text{Side} = \frac{\text{Perimeter}}{4}\) to cross-verify.

12. A bank gives interest on deposits. Draw a graph to illustrate the relation between the number of years and the simple interest earned when the sum deposited is Rs 100.
Answer:
Let the principal \(P = \text{Rs } 100\), rate of interest \(R = 20\%\) per annum (as given in previous context or standard annual interest).
Simple Interest (SI) for \(T\) years = \(\frac{P \times R \times T}{100} = \frac{100 \times 20 \times T}{100} = 20T\).
Calculate points: - For \(T = 1 \text{ year}, \text{SI} = \text{Rs } 20\) -> Point \((1, 20)\) - For \(T = 2 \text{ years}, \text{SI} = \text{Rs } 40\) -> Point \((2, 40)\) - For \(T = 3 \text{ years}, \text{SI} = \text{Rs } 60\) -> Point \((3, 60)\) - For \(T = 4 \text{ years}, \text{SI} = \text{Rs } 80\) -> Point \((4, 80)\)
Plot Time (years) on the x-axis and Simple Interest (Rs) on the y-axis, and join the points with a straight line.
Value inculcated: Financial literacy, understanding savings, and realizing the benefits of long-term investments.
In simple words: Draw a straight-line graph showing how interest money grows steadily each year.

Exam Tip: Simple interest grows linearly, so the resulting graph will always be a straight line passing through the origin.

13. Plot the graphs for the values of the following table:
a) Cost of oranges

Answer:
Plot Number of oranges on the x-axis and Cost (in Rs) on the y-axis using coordinates \((1, 3)\), \((5, 15)\), \((7, 21)\), \((12, 36)\), and \((15, 45)\). Joining these points yields a straight line, showing direct proportionality.
Value inculcated: Understanding fair pricing, budgeting, and proportional reasoning in daily market transactions.
In simple words: Plot oranges against cost to show that buying more oranges increases the total price proportionally.

Exam Tip: Direct proportion graphs always form a straight line passing through the origin \((0, 0)\).

b) Consumption of rice by children in a hostel

Answer:
Plot Number of children on the x-axis and Rice (in kg) on the y-axis with points \((10, 15)\), \((15, 22.5)\), \((20, 30)\), \((25, 37.5)\), and \((30, 45)\). Connect the points with a straight line.
Value inculcated: Resource management, planning supplies efficiently, and understanding consumption patterns.
In simple words: Graph the relationship to show how food consumption increases uniformly with more children.

Exam Tip: Plot decimal values like 22.5 precisely halfway between grid lines.

c) Distance travelled by a car and time taken

Answer:
Plot Time (in hours) on the x-axis and Distance (in km) on the y-axis with coordinates \((1, 40)\), \((2, 70)\), \((3, 100)\), \((4, 140)\), \((5, 190)\), and \((6, 250)\). Join the points with a smooth curve or line segments.
Value inculcated: Safety awareness in travel, understanding speed variations, and practical time-distance estimation.
In simple words: Plot time against distance to observe how a car travels further as time progresses.

Exam Tip: Ensure correct assignment of independent (time) and dependent (distance) variables to standard axes.

Students must free download and practice these worksheets to gain more marks in exams. CBSE Class 8 Mathematics Worksheet - Introduction to Graphs