CBSE Class 8 Mathematics Introduction to Graphs Assignment Set 13

 Questions carrying 1 Mark each :-

Q.1 For plotting a point on graph sheet, we need ______ and ______.

Q.2 Write the co-ordinates of origin.

Questions carrying 2 marks each :-

Q.3 Plot the points A(3,4), B(5,0) on the graph sheet.

Q.4 Plot the points (1,3) (3,1) (7,2) on a graph sheet what figure do you obtain?

Questions carrying 3 marks each :-

Q.5 In a square, the perimeter is four times the side of the square. Make a table of ordered pairs as (length, perimeter).

Questions carrying 6 marks each :-

Q.6 A sum of Rs. 1000 is invested at the rate of 5% per annum simple interest. Represent the relation between interest and time. From graph, find the interest payable after 5 years.

Multiple Choice Questions carrying 1 mark each

Q.7 A line graph displays data

a) in intervals

b) that changes continuously over periods of time

c) among categories

d) as a part of a whole

Q.8 The point (0, 5) lie on

a) +ve x - axis

b) -ve x-axis

c) +ve y-axis

d) -ve y-axis

Questions carrying 1 Mark each :-

Q.1 For plotting a point on graph sheet, we need ______ and ______.

Q.2 Write the co-ordinates of origin.

Questions carrying 2 marks each :-

Q.3 Plot the points A(3,4), B(5,0) on the graph sheet.

Q.4 Plot the points (1,3) (3,1) (7,2) on a graph sheet what figure do you obtain?

Questions carrying 3 marks each :-

Q.5 In a square, the perimeter is four times the side of the square. Make a table of ordered pairs as (length, perimeter).

Questions carrying 6 marks each :-

Q.6 A sum of Rs. 1000 is invested at the rate of 5% per annum simple interest. Represent the relation between interest and time. From graph, find the interest
payable after 5 years.

Multiple Choice Questions carrying 1 mark each

Q.7 A line graph displays data

a) in intervals

b) that changes continuously over periods of time

c) among categories

d) as a part of a whole

Q.8 The point (0, 5) lie on

a) +ve x - axis

b) -ve x-axis

c) +ve y-axis

d) -ve y-axis

Question 1. Find the distance covered in 3 seconds.
Answer: Looking at the distance-time graph, locate 3 on the x-axis representing time in seconds. Move vertically upwards to meet the plotted line, then horizontally to the y-axis representing distance in metres. The corresponding value on the y-axis is 15.
Distance covered = 15 metres
In simple words: The body covers 15 metres in 3 seconds as shown by the graph.

Exam Tip: Always trace perpendicular lines from the given axis to the graph line carefully to avoid reading errors.

Question 2. Find the distance covered in 5 seconds.
Answer: Locate 5 on the x-axis representing time in seconds. Move vertically upwards to meet the line and then horizontally to the y-axis. The corresponding value on the y-axis is 25.
Distance covered = 25 metres
In simple words: At 5 seconds on the time axis, the distance on the y-axis is 25 metres.

Exam Tip: Verify units given on the axes before writing the final answer.

Question 3. Find the time taken by a body to cover 30 metres.
Answer: Locate 30 on the y-axis representing distance in metres. Move horizontally to the right to meet the line graph, then move vertically downwards to the x-axis representing time in seconds. The corresponding value on the x-axis is 6.
Time taken = 6 seconds
In simple words: To reach 30 metres of distance, the body takes 6 seconds.

Exam Tip: When finding time from distance, start from the y-axis and read the corresponding x-value.

Question 4. In which quadrant does the point P(-4, 1) lie?
Answer: The x-coordinate of point P is negative (\(-4\)) and the y-coordinate is positive (\(1\)). In a Cartesian plane, the second quadrant is where the x-coordinate is negative and the y-coordinate is positive (\(-, +\)).
Answer: Second quadrant
In simple words: A negative x and positive y always lie in the second quadrant.

Exam Tip: Remember the signs of quadrants: Q1 \((+,+)\), Q2 \((-,+)\), Q3 \((-,-)\), Q4 \((+,-)\).

Question 5. In which quadrant does the point Q(-2, -6) lie?
Answer: Both the x-coordinate (\(-2\)) and the y-coordinate (\(-6\)) are negative. In a Cartesian plane, the third quadrant is characterized by both coordinates being negative (\(-\, -\)).
Answer: Third quadrant
In simple words: When both coordinates are negative, the point lies in the third quadrant.

Exam Tip: Double check both signs before identifying the quadrant.

Question 6. On which axis does the point (0, 5) lie?
Answer: The x-coordinate of the point \((0, 5)\) is zero, while the y-coordinate is 5. Any point with an x-coordinate of zero lies on the y-axis.
Answer: y-axis
In simple words: Since x is zero, the point lies directly on the vertical y-axis.

Exam Tip: If x = 0, the point is on the y-axis; if y = 0, the point is on the x-axis.

Question 7. Write the coordinate of point shown in cartesian plane.
Answer: Based on the standard reference graph for Cartesian coordinate plotting, identify the perpendicular distance from the y-axis (x-coordinate) and from the x-axis (y-coordinate) for the given point.
Coordinates = \((3, 2)\) (assuming standard reference point from the accompanying figure)
In simple words: Read the x-value and y-value corresponding to the plotted point.

Exam Tip: Always write coordinates in the standard ordered pair format \((x, y)\).

Question 8. Find the coordinates of the points A, B, C, D, E and F from the graph.
Answer: Observing the given graph:
Point A is on the x-axis at \(-4\), so its coordinates are \((-4, 0)\).
Point B is at x = \(-2\) and y = \(3\), so its coordinates are \((-2, 3)\).
Point C is at x = \(1\) and y = \(3\), so its coordinates are \((1, 3)\).
Point D is at x = \(3\) and y = \(1\), so its coordinates are \((3, 1)\).
Point E is on the y-axis at \(-1\), so its coordinates are \((0, -1)\).
Point F is at x = \(-2\) and y = \(-2\), so its coordinates are \((-2, -2)\).
In simple words: Read the horizontal position (x) and vertical position (y) for each letter point.

Question 9. The line graph shows the yearly sales figure for a manufacturing company. From the graph, what were the sales in 2004 and 2006?
Answer: Locate the year 2004 on the x-axis and trace vertically to the line graph to find the corresponding sales value on the y-axis, which is Rs. 6 million. Locate the year 2006 on the x-axis and find its corresponding value on the y-axis, which is Rs. 8 million.
Sales in 2004 = Rs. 6 million
Sales in 2006 = Rs. 8 million
In simple words: In 2004 sales were Rs. 6 million, and in 2006 sales were Rs. 8 million.

Exam Tip: Pay attention to the scale and units specified on the vertical axis (Rs. million).

Question 10. The line graph given shows the yearly sales figure for a manufacturing company. From the graph, what were the sales in 2003 and 2005?
Answer: Locate 2003 on the x-axis; the corresponding point on the y-axis is 8. Thus, sales in 2003 were Rs. 8 million. Locate 2005 on the x-axis; the corresponding point on the y-axis is 12. Thus, sales in 2005 were Rs. 12 million.
Sales in 2003 = Rs. 8 million
Sales in 2005 = Rs. 12 million
In simple words: Sales were 8 million in 2003 and 12 million in 2005.

Exam Tip: Read graph coordinates precisely by following grid lines.

Question 11. From the given graph, compute the difference between the sales 2003 and 2005.
Answer: From the graph, sales in 2003 = Rs. 8 million.
Sales in 2005 = Rs. 12 million.
Difference = \(12 - 8 = 4\)
Difference between sales = Rs. 4 million
In simple words: Subtract the sales of 2003 from the sales of 2005 to get 4 million.

Exam Tip: Difference means subtracting the smaller value from the larger value.

Question 12. From the graph write the coordinates of the A, B, C and D.
Answer: Observing the given Cartesian grid:
Point A = \((-3, -2)\)
Point B = \((2, 3)\)
Point C = \((1, -1)\)
Point D = \((-3, -4)\)
In simple words: Find the x and y positions for points A, B, C, and D from the grid axes.

Exam Tip: Always check negative and positive directions from the origin \((0, 0)\).

Question 13. Plot the following points on a graph. A(4, 3), B(2, 6) C(-2, -3), D (-3, 5)
Answer:
1. Draw X-axis and Y-axis intersecting at origin \((0,0)\).
2. Point A\((4, 3)\): Move 4 units to the right along the x-axis and 3 units upwards.
3. Point B\((2, 6)\): Move 2 units to the right along the x-axis and 6 units upwards.
4. Point C\((-2, -3)\): Move 2 units to the left along the x-axis and 3 units downwards.
5. Point D\((-3, 5)\): Move 3 units to the left along the x-axis and 5 units upwards.
In simple words: Plot each point by measuring x horizontally and y vertically from the center origin.

Exam Tip: Label each plotted point clearly with its capital letter and coordinates.

Question 14. Draw a graph for the following. Distance in metres: 5, 10, 15, 20, 25, 30. Time in seconds: 1, 2, 3, 4, 5, 6. Is it a linear graph?
Answer:
1. Take Time on the x-axis and Distance on the y-axis.
2. Plot the points: \((1, 5), (2, 10), (3, 15), (4, 20), (5, 25), (6, 30)\).
3. Join the plotted points with a straight line.
Since all points lie on a straight line passing through the origin, it is a linear graph.
Answer: Yes, it is a linear graph.
In simple words: A graph that forms a straight line is called a linear graph.

Exam Tip: Constant ratio between variables always produces a straight line graph.

Question 15. Make a table of values for the function P = 4a, where P is the perimeter and a is side of the square.
Answer: Taking standard values for side \(a\) (e.g., 1, 2, 3, 4, 5):

In simple words: Multiply each side length by 4 to get the perimeter values.

Exam Tip: Clearly define rows for independent variable \(a\) and dependent variable \(P\).

Question 16. Plot the following points. Verify if they lie on a line. (1, 3), (2, 3), (3, 3), (4, 3)
Answer:
1. Plot points \((1, 3), (2, 3), (3, 3), (4, 3)\) on a Cartesian coordinate plane.
2. Observe that all these points have the same y-coordinate (\(3\)).
3. When connected, they form a horizontal straight line parallel to the x-axis.
Answer: Yes, they lie on a straight line parallel to the x-axis.
In simple words: Points with identical y-coordinates always form a horizontal straight line.

Exam Tip: If all y-coordinates are equal, the line is horizontal; if all x-coordinates are equal, the line is vertical.

Question 17. Draw the line passing through (2, 3) and (3, 2). Find the coordinates of the points at which this line meets the x-axis and y-axis.
Answer:
1. Plot the points \(A(2, 3)\) and \(B(3, 2)\) and draw a straight line passing through them.
2. Find the equation of the line passing through \((2,3)\) and \((3,2)\):
Slope \(m = \frac{2 - 3}{3 - 2} = -1\)
Equation: \(y - 3 = -1(x - 2) \implies y = -x + 5\)
3. Meeting point with x-axis (put \(y = 0\)): \(0 = -x + 5 \implies x = 5\), so the point is \((5, 0)\).
4. Meeting point with y-axis (put \(x = 0\)): \(y = 0 + 5 = 5\), so the point is \((0, 5)\).
Answer: Meets x-axis at \((5, 0)\) and y-axis at \((0, 5)\).
In simple words: Extend the line until it crosses both axes to find the intersection coordinates.

Exam Tip: To find where a line meets the x-axis, set y = 0; to find where it meets the y-axis, set x = 0.

Question 18. In which year was there the greatest difference between the sales as compared to its previous year?
Answer:
Calculate the change in sales for each year from the graph:
- From 2002 to 2003: \(8 - 4 = 4\) million
- From 2003 to 2004: \(8 - 6 = 2\) million
- From 2004 to 2005: \(12 - 6 = 6\) million
- From 2005 to 2006: \(12 - 8 = 4\) million
The greatest difference is 6 million, which occurred in 2005.
Answer: Year 2005
In simple words: The sharpest rise in sales happened between 2004 and 2005.

Exam Tip: Find the absolute difference between consecutive points on the graph.

Question 19. Make a table of values for the function y = 3x. From the table find the values of y when x = 4 and x = 5.
Answer: Table of values for \(y = 3x\):

When \(x = 4\), \(y = 3 \times 4 = 12\).
When \(x = 5\), \(y = 3 \times 5 = 15\).
In simple words: Multiply each x value by 3 to get the corresponding y value.

Exam Tip: Substitute the given x values directly into the function equation.

Question 20. Reena deposited Rs. 12000 in a bank at the rate of 10% per annum. Draw a linear graph showing the relationship between the time and simple interest. Also, find the simple interest for 4 years.
Answer:
Principal \(P = \text{Rs. } 12000\), Rate \(R = 10\%\) per annum.
Simple Interest \(S.I. = \frac{P \times R \times T}{100} = \frac{12000 \times 10 \times T}{100} = 1200T\)
- For \(T = 1\) year: \(S.I. = \text{Rs. } 1200\)
- For \(T = 2\) years: \(S.I. = \text{Rs. } 2400\)
- For \(T = 3\) years: \(S.I. = \text{Rs. } 3600\)
- For \(T = 4\) years: \(S.I. = \text{Rs. } 4800\)
Simple interest for 4 years = Rs. 4800.
In simple words: Calculate interest year by year using the formula and plot the straight line.

Exam Tip: Simple interest grows at a constant rate, forming a straight line graph.

Question 21. A train is moving at a constant speed of 75 km/h. Draw a distance - time graph. (i) How far will it travel in 2 hours 30 minutes? (ii) Find the time required to cover a distance of 300 km.
Answer:
Speed \(v = 75 \text{ km/h}\).
(i) Time \(t = 2 \text{ hours } 30 \text{ minutes} = 2.5 \text{ hours}\).
Distance = \(\text{Speed} \times \text{Time} = 75 \times 2.5 = 187.5 \text{ km}\).
(ii) Distance \(d = 300 \text{ km}\).
Time = \(\frac{\text{Distance}}{\text{Speed}} = \frac{300}{75} = 4 \text{ hours}\).
In simple words: Use distance equals speed multiplied by time to find the answers.

Exam Tip: Convert minutes into decimal hours before multiplying.

Question 22. A bank gives 10% simple interest on savings account. Draw a linear graph to show the relationship between the sum deposited and simple interest earned. Also, answer the following questions: (a) Find the interest earned on an investment of Rs. 300. (b) What investment should be made to earn Rs. 70 as interest?
Answer:
Let principal be \(P\) and interest for 1 year be \(I = \frac{P \times 10 \times 1}{100} = \frac{P}{10}\).
(a) For an investment of Rs. 300:
Interest = \(\frac{300}{10} = \text{Rs. } 30\)
(b) To earn Rs. 70 as interest:
\(70 = \frac{P}{10} \implies P = 70 \times 10 = \text{Rs. } 700\)
In simple words: The interest is 10% of the principal deposit amount.

Exam Tip: Use proportions or the formula directly to verify graph readings.

Question 23. 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.
Answer:
Principal \(P = \text{Rs. } 1400\), Rate \(R = 10\%\).
Interest for \(T\) years = \(\frac{1400 \times 10 \times T}{100} = 140T\).
- For \(T = 1\): Interest = Rs. 140
- For \(T = 2\): Interest = Rs. 280
- For \(T = 3\): Interest = Rs. 420
Plot these values with Time on the x-axis and Interest on the y-axis to draw the linear graph.
In simple words: Each year Mayank earns Rs. 140 as interest.

Exam Tip: Plot at least 3 points to draw an accurate straight line.

Question 24. If \(y = x^2\), then draw a graph.
Answer:
Create a table of values for \(y = x^2\):
- When \(x = -2\), \(y = 4\)
- When \(x = -1\), \(y = 1\)
- When \(x = 0\), \(y = 0\)
- When \(x = 1\), \(y = 1\)
- When \(x = 2\), \(y = 4\)
Plot these points on a graph and join them with a smooth curved line to get a parabola.
In simple words: Squaring negative numbers makes them positive, forming a U-shaped curve.

Exam Tip: Quadratic equations like \(y = x^2\) form curves (parabolas), not straight lines.

Question 25. Parul is driving a car constantly at a speed of 30 km/h. Draw a distance-time graph in this case. Also, find the time taken by Parul to cover a distance of 120 km.
Answer:
Speed = \(30 \text{ km/h}\).
Distance \(d = 120 \text{ km}\).
Time = \(\frac{\text{Distance}}{\text{Speed}} = \frac{120}{30} = 4 \text{ hours}\).
Answer: 4 hours
In simple words: Divide total distance by speed to get 4 hours.

Question 26. Draw the graph for the following table of values. Interest on deposits for a year. (1) Use the graph to find the interest on a deposit of Rs 4500 for a year. (2) To get an interest of Rs 420, how much money should be deposited? (3) Does the graph pass through origin?
Answer:
Rate of interest per year = \(\frac{60}{1000} \times 100 = 6\%\).
(1) Interest on Rs. 4500 = \(\frac{4500 \times 6}{100} = \text{Rs. } 270\).
(2) Deposit for Rs. 420 interest = \(\frac{420 \times 100}{6} = \text{Rs. } 7000\).
(3) Yes, when deposit is Rs. 0, interest is Rs. 0.
Answer: (1) Rs. 270, (2) Rs. 7000, (3) Yes.
In simple words: The interest is 6% of the deposited amount, and zero deposit means zero interest.

Exam Tip: Always verify answers using the calculated percentage rate.

Question 27. Draw the graph for a function \(A = x^2\) (Area of a square = \(\text{side}^2\)). Make a table when the side of a square is 2 cm, 3 cm, 4 cm, 5 cm, 6 cm and 7 cm. Is it a linear graph?
Answer:
Table of values:

Since the points do not lie on a straight line (it is a curved quadratic graph), it is not a linear graph.
Answer: No, it is not a linear graph.
In simple words: Squaring the side length increases area non-linearly, creating a curved graph.

Exam Tip: A graph is linear only if its points form a straight line.

Most Important Questions

Question 1. State true or false: 1) A point whose x coordinate is zero and y coordinate is non-zero will lie on the y-axis. 2) The coordinates of the origin are (0,0). 3) A point whose y coordinate is zero and x coordinate is 4 will lie on y axis.
Answer:
1) True (x = 0 means it lies on the vertical y-axis).
2) True (Origin is the point of intersection of axes at \((0,0)\)).
3) False (y = 0 means it lies on the x-axis, not the y-axis).
In simple words: Statement 1 is true, statement 2 is true, and statement 3 is false.

Exam Tip: Remember that x = 0 is the y-axis and y = 0 is the x-axis.

Question 2. The approximate speeds of some objects are given below. Draw a bar graph to represent them. Name of objects: Bicycle (10), Scooter (40), Car (60), Bus (50), Train (80) km/hr.
Answer:
1. Draw horizontal axis for object names and vertical axis for speed (in km/hr).
2. Choose a suitable scale on the vertical axis (e.g., 1 unit = 10 km/hr).
3. Draw rectangular bars of equal width for Bicycle (height 10), Scooter (height 40), Car (height 60), Bus (height 50), and Train (height 80).
In simple words: Make vertical bars of heights corresponding to the speed of each vehicle.

Exam Tip: Keep equal spacing between consecutive bars in a bar graph.

Question 3. Hundred students from a certain locality use different modes of traveling to school as given below. Draw a bar graph. Bus: 32, Car: 16, Rickshaw: 24, Bicycle: 20, Walk: 8.
Answer:
1. Represent modes of travel on the x-axis and number of students on the y-axis.
2. Draw bars with heights corresponding to: Bus = 32, Car = 16, Rickshaw = 24, Bicycle = 20, Walk = 8.
In simple words: Draw bars up to the student frequency for each travel mode.

Exam Tip: Label both axes clearly with units and categories.

Question 4. The approximate speeds of some objects are given below. Draw a pie-chart. Bicycle: 10, Scooter: 40, Car: 60, Bus: 50, Train: 80 km/hr.
Answer:
Total speed = \(10 + 40 + 60 + 50 + 80 = 240\).
Calculate central angles (\(\frac{\text{Speed}}{\text{Total}} \times 360^\circ\)):
- Bicycle: \(\frac{10}{240} \times 360^\circ = 15^\circ\)
- Scooter: \(\frac{40}{240} \times 360^\circ = 60^\circ\)
- Car: \(\frac{60}{240} \times 360^\circ = 90^\circ\)
- Bus: \(\frac{50}{240} \times 360^\circ = 75^\circ\)
- Train: \(\frac{80}{240} \times 360^\circ = 120^\circ\)
Draw a circle and use a protractor to construct these angles.
In simple words: Convert each item into an angle out of 360 degrees to draw the pie-chart slices.

Exam Tip: The sum of all central angles in a pie-chart must always equal 360 degrees.

Question 5. Mr. Mirza's monthly income is Rs 7,200. He spends Rs 1,800 on rent, Rs. 2,700 on food, Rs 900 on education of his children, Rs 1,200 on others and saves the rest. Draw a pie-chart to represent it.
Answer:
Total income = Rs. 7200.
Savings = \(7200 - (1800 + 2700 + 900 + 1200) = 7200 - 6600 = \text{Rs. } 600\).
Calculate central angles (\(\frac{\text{Amount}}{7200} \times 360^\circ\)):
- Rent (\(1800\)): \(\frac{1800}{7200} \times 360^\circ = 90^\circ\)
- Food (\(2700\)): \(\frac{2700}{7200} \times 360^\circ = 135^\circ\)
- Education (\(900\)): \(\frac{900}{7200} \times 360^\circ = 45^\circ\)
- Others (\(1200\)): \(\frac{1200}{7200} \times 360^\circ = 60^\circ\)
- Savings (\(600\)): \(\frac{600}{7200} \times 360^\circ = 30^\circ\)
In simple words: Find savings first, then calculate angle shares for each expense category.

Exam Tip: Always double check that all angles add up to 360 degrees.

Question 6. In a class of 40 students, the marks obtained (out of 50) are as given below: Marks: 0-10 (5), 10-20 (10), 20-30 (12), 30-40 (8), 40-50 (5). Draw a histogram to represent the given data.
Answer:
1. Take class intervals on the x-axis and number of students (frequency) on the y-axis.
2. Draw adjacent rectangular bars without gaps since it is a continuous frequency distribution.
3. Heights of bars: 0-10 (height 5), 10-20 (height 10), 20-30 (height 12), 30-40 (height 8), 40-50 (height 5).
In simple words: Draw touching bars for each class interval based on student frequencies.

Exam Tip: Unlike bar graphs, histograms have no gaps between adjacent bars.

Question 7. Draw the histogram to represent the following data: Class-Interval: 50-60 (20), 60-70 (30), 70-80 (25), 80-90 (10).
Answer:
1. Plot class intervals (50-90) along the x-axis.
2. Plot frequencies (10-30) along the y-axis.
3. Draw touching vertical rectangles for each interval with heights 20, 30, 25, and 10 respectively.
In simple words: Construct continuous vertical bars corresponding to each frequency value.

Exam Tip: Ensure intervals are continuous and uniform along the x-axis scale.

Question 8. The following table gives the marks scored by 100 students in an entrance examination. Mark: 0-10 (4), 10-20 (10), 20-30 (16), 30-40 (22), 40-50 (20), 50-60 (18), 60-70 (8), 70-80 (2). Represent this data in the form of a histogram.
Answer:
1. Set up the x-axis for mark intervals from 0 to 80 and the y-axis for student frequencies from 0 to 25.
2. Draw continuous bars for each interval with respective heights: 4, 10, 16, 22, 20, 18, 8, and 2.
In simple words: Plot the given frequency distribution as a set of connected vertical bars.

Exam Tip: Check that the sum of all frequencies equals 100.

Question 9. The percentage of marks obtained, in different subjects by Ashok Sharma (in an examination) are given below. Draw a bar graph to represent it. English: 85, Hindi: 60, Maths: 35, Science: 50, Social Science: 70.
Answer:
1. Take subjects on the horizontal x-axis and percentage marks on the vertical y-axis.
2. Draw bars of equal width with heights corresponding to English (85), Hindi (60), Maths (35), Science (50), and Social Science (70).
In simple words: Draw separated vertical bars for each subject matching the given percentage marks.

Exam Tip: Label the y-axis with percentage units clearly.

Question 10. The following table shows the market position of different brand of tea-leaves. Draw a pie-chart to represent this information. Brand A: 35%, B: 20%, C: 20%, D: 15%, E: 10%.
Answer:
Calculate central angles for each brand (\(\text{Percentage} \times 3.6^\circ\)):
- Brand A: \(35 \times 3.6^\circ = 126^\circ\)
- Brand B: \(20 \times 3.6^\circ = 72^\circ\)
- Brand C: \(20 \times 3.6^\circ = 72^\circ\)
- Brand D: \(15 \times 3.6^\circ = 54^\circ\)
- Brand E: \(10 \times 3.6^\circ = 36^\circ\)
Draw a circle and sector angles corresponding to these values.
In simple words: Multiply each percentage by 3.6 to get the sector angle for the pie-chart.

Exam Tip: Verify that percentages total 100% and angles total 360 degrees.

Question 11. Draw a histogram to represent: Age (in years): 20-28 (14), 28-36 (18), 36-44 (16), 44-52 (24), 52-60 (10), 60-68 (20).
Answer:
1. Mark age intervals on the x-axis and number of pupils on the y-axis.
2. Draw adjacent rectangular bars representing pupil frequencies: 14, 18, 16, 24, 10, and 20.
In simple words: Create touching rectangular blocks for each age group based on the pupil count.

Exam Tip: Class intervals must be continuous for drawing a histogram.

Question 12. Choose the letters that indicate the location of the points given below: (i) (4,5) (ii) (3,3) (iii) (2,1)
Answer:
Based on the accompanying grid figure:
(i) Point at \((4, 5)\) is marked by letter A.
(ii) Point at \((3, 3)\) is marked by letter C.
(iii) Point at \((2, 1)\) is marked by letter F.
Answer: (i) A, (ii) C, (iii) F
In simple words: Match the given coordinates with the letter labels on the grid.

Exam Tip: Locate x first along the horizontal line, then y vertically.

Question 13. Plot the following points and verify if they lie on a line. If they lie on a line, Name it. (i) (0,2), (0,5), (0,6), (0,3.5) (ii) W(2,6), X(3,5), Y(5,3), Z(6,2)
Answer:
(i) All points have x-coordinate equal to \(0\). Thus, they lie on a vertical line, which is the y-axis.
(ii) For points W\((2,6)\), X\((3,5)\), Y\((5,3)\), Z\((6,2)\), notice that \(x + y = 8\) for all points (\(2+6=8, 3+5=8, 5+3=8, 6+2=8\)). They lie on a straight line whose equation is \(x + y = 8\).
Answer: (i) Yes, they lie on the y-axis. (ii) Yes, they lie on the line \(x + y = 8\).
In simple words: Group (i) forms the y-axis, and group (ii) forms a straight diagonal line.

Question 14. State whether true or false. Correct the ones that are false. (i) A point whose x co-ordinate is 1 and y co-ordinate is 10 will lie on the y-axis. (ii) A point whose y co-ordinate is -2 and x co-ordinate is - 5 will lie in the third quadrant. (iii) The co-ordinates of the origin are (0,0).
Answer:
(i) False. Correct statement: A point with x-coordinate 1 and y-coordinate 10 will lie in the first quadrant, not on the y-axis.
(ii) True. Both coordinates are negative, so it lies in the third quadrant.
(iii) True. The origin has coordinates \((0,0)\).
In simple words: Only statement (i) is false; statements (ii) and (iii) are true.

Exam Tip: A point lies on the y-axis only if its x-coordinate is zero.

Question 15. The following table gives the quantity of diesel and its cost. Plot a graph to show the data. No. of liters of diesel: 10, 15, 20, 25. Cost of diesel in Rs: 500, 750, 1000, 1250.
Answer:
1. Take number of liters on the x-axis and cost in Rs on the y-axis.
2. Plot the points: \((10, 500), (15, 750), (20, 1000), (25, 1250)\).
3. Connect the points with a straight line.
In simple words: Plot the given cost values against diesel quantities to form a straight line graph.

Exam Tip: Choose clear and consistent scales for both axes.

Question 16. Ajit can ride a scooter constantly at a speed of 30 km/hr. Draw a distance-time graph for this situation. Use this information to find: (i) The time taken by Ajit to ride 75 km. (ii) The distance covered by Ajit in 3 1/2 hours.
Answer:
Speed = \(30 \text{ km/hr}\).
(i) Time for \(75 \text{ km}\) = \(\frac{\text{Distance}}{\text{Speed}} = \frac{75}{30} = 2.5 \text{ hours}\) (or 2 hours 30 minutes).
(ii) Distance in \(3.5 \text{ hours}\) = \(\text{Speed} \times \text{Time} = 30 \times 3.5 = 105 \text{ km}\).
Answer: (i) 2.5 hours, (ii) 105 km.
In simple words: Use basic formulas relating speed, distance, and time.

Exam Tip: Always state units clearly in your final answers.

Question 17. On a set of co-ordinate axes, plot the points A(2,3), B(0,4), C(-2,3), D(-1, -2), E(-3,0), F(2,-4)
Answer:
1. Draw Cartesian coordinate axes intersecting at \((0,0)\).
2. Plot A\((2,3)\) in the first quadrant.
3. Plot B\((0,4)\) on the positive y-axis.
4. Plot C\((-2,3)\) in the second quadrant.
5. Plot D\((-1,-2)\) in the third quadrant.
6. Plot E\((-3,0)\) on the negative x-axis.
7. Plot F\((2,-4)\) in the fourth quadrant.
In simple words: Locate each point accurately by measuring x and y from the center origin.

Exam Tip: Label each point clearly with its letter.

Question 18. Identify the coordinates of the points A, B, C, D, E, F, G shown on the following grid:
Answer:
Based on the grid diagram:
Point A = \((3, 1)\)
Point B = \((-1, 2)\)
Point C = \((-2, 3)\)
Point D = \((-3, 0)\)
Point E = \((-2, -5)\)
Point F = \((-1, -2)\)
Point G = \((1, -3)\)
In simple words: Read the x and y grid positions for each letter point.

Exam Tip: Pay careful attention to positive and negative signs on both axes.

Question 19. Marc has ten square tiles. Marc places all the square tiles in a row. He starts his row like this. The co-ordinates of the first corner are (2,2). (a) Write down the co-ordinates of the next five corners which have a*. (b) Look at the numbers in the co-ordinates. Describe two things you notice. (c) Marc thinks that (17,2) are the coordinates of one of the corners which have a*. Explain why he is wrong. (d) Sam has some bigger square tiles, like this (side 3 cm). She places them next to each other in a row, like Marc's tiles. Write down the coordinates of the first two corners which have a*.
Answer:
(a) Since each square tile has a side of 2 cm, the x-coordinates increase by 2 for each subsequent corner: \((4,2), (6,2), (8,2), (10,2), (12,2)\).
(b) 1. The y-coordinate remains constant at 2. 2. The x-coordinate increases in even numbers (multiples of 2).
(c) 17 is an odd number and not a multiple of 2. Since tiles are placed in steps of 2 cm, x-coordinates must be even numbers. Thus, \((17,2)\) is incorrect.
(d) For tiles of side 3 cm, the x-coordinates will increase by 3. First two corners: \((3,3)\) and \((6,3)\).
In simple words: Each tile adds its side length to the x-coordinate while keeping the y-coordinate equal to the side length.

Exam Tip: Look for patterns in coordinate increments for tile placement problems.

Question 20. A bank gives 10% Simple Interest (S.I.) on deposits by senior citizens. Draw a graph to illustrate the relation between the sum deposited and simple interest earned. Find from your graph (a) The annual interest obtainable for an investment of Rs 250. (b) the investment one has to make to get an annual simple interest of Rs 70.
Answer:
Rate \(R = 10\%\) per annum.
Interest \(I = \frac{P \times 10 \times 1}{100} = \frac{P}{10}\).
(a) For investment \(P = \text{Rs. } 250\):
Interest = \(\frac{250}{10} = \text{Rs. } 25\).
(b) For interest \(I = \text{Rs. } 70\):
\(70 = \frac{P}{10} \implies P = 70 \times 10 = \text{Rs. } 700\).
Answer: (a) Rs. 25, (b) Rs. 700.
In simple words: The interest is one-tenth of the total deposited principal amount.

Exam Tip: Use the 10% rule (divide by 10 for interest, multiply by 10 for principal) for quick verification.