Introduction To Graphs
List the two coordinates required to fix the position of a point on a graph.
Describe how to read the information for a specific point on a line graph.
A graph showing the cost of notebooks is a straight line. Justify why this graph must pass through the origin.
A vertical line is drawn on a time-distance graph. Justify why this cannot represent the journey of an object.
Identify which axis typically represents time in a time-temperature or time-distance graph.
A time-temperature graph shows that at 3 p.m., the temperature was 28°C. Solve for the coordinates of this point, assuming time is plotted on the x-axis and temperature is plotted on the y-axis.
Propose a graphical method to compare the growth of two different saplings over a month. Describe what the axes would represent and what a point of intersection on the graph would signify.
Formulate a simple test to determine if a given graph is a linear graph.
Analyze a graph showing the relationship between the number of pens bought and their total cost. Why must this graph pass through the origin (0,0)?
Define what a line graph is.
Examine the relationship between the number of notebooks purchased and the total cost. Which quantity is the independent variable?
Examine a distance-time graph. What does a horizontal line segment on the graph indicate about the motion of an object?
Name the two axes used for plotting points on a graph sheet.
Formulate a rule to decide which variable should be on the x-axis and which on the y-axis when plotting a graph.
Evaluate whether the relationship between the side length of a square and its area will produce a linear graph.
A graph shows the volume of water in a tank (in litres) over time (in minutes). The graph is a straight line passing through the points (0, 50) and (10, 250). Calculate the rate at which the tank is being filled in litres per minute.
Recall what a horizontal line segment on a time-distance graph indicates.
Summarize the steps involved in creating a line graph from a data table.
List two examples of real-life situations where one quantity depends on another, making them suitable for graphical representation.
Explain why it is important to choose a suitable scale for the axes when drawing a graph.
Examine the possibility of a time-temperature graph that is a perfect vertical line. Is such a graph possible in a real-world scenario? Justify your answer.
Explain the primary purpose of using graphs to represent numerical data.
Describe what a linear graph looks like and what it represents.
The given line graph shows the scores of two students, Amit and Priya, in five consecutive math tests. Amit's scores are shown by a solid line and Priya's by a dashed line. Compare their performances to determine which student is more consistent and justify your reasoning.
A bank offers 8% simple interest per annum. Create a table showing the interest earned on deposits of ₹1000, ₹2000, ₹3000, and ₹4000 for one year. Demonstrate this relationship by drawing a linear graph. Use the graph to solve for the interest on a deposit of ₹3500.
Design a time-temperature graph that represents heating a pot of water, bringing it to a boil, letting it boil for some time, and then allowing it to cool down. Create three distinct questions that could be answered by interpreting your graph. Justify why your graph has a horizontal section.
The line graph for cricketer A's scores has very high peaks and very low troughs. The graph for cricketer B has smaller fluctuations and stays within a narrower range of scores. Evaluate which cricketer is more consistent and justify your reasoning.
The journeys of two cars, Car A and Car B, are shown on the same distance-time graph. The line representing Car A is steeper than the line representing Car B. Compare the speeds of the two cars and justify your answer.
The population of a small town was recorded as follows: Year 2010: 5000, Year 2012: 5500, Year 2014: 6000, Year 2016: 6500. Demonstrate this data on a line graph, explaining the choice of scale for the vertical axis.
A student plotted a graph showing the relationship between the number of hours studied and the marks obtained in a test. The graph is a straight line that passes through the origin. Evaluate the claim that studying for zero hours results in zero marks, based on this linear model. Is this a realistic representation?
A graph is drawn to show a city's population growth over 50 years. The points for each decade are plotted correctly, but the student has drawn a jagged, zig-zag line connecting them instead of a smooth curve or straight line segments. Critique this method of representation.
The distance-time graph for a car's journey is a line that gets steeper over time. Justify what this indicates about the car's speed. Then, create a small table with three data points that would produce such a graph and explain how the table reflects this change.
Design a hypothetical temperature graph for a desert location over a 24-hour period, starting from midnight. Justify the shape of your graph based on typical desert climate patterns.
A graph is plotted with the side of a square on the x-axis and its area on the y-axis. Analyze the shape of this graph and explain why it is not a straight line.
Summarize the key information that can be understood from the 'performance' graph of two batsmen shown in the source text.
Explain the difference between an independent variable and a dependent variable using an example.
A line graph shows the percentage of a mobile phone's battery charge over time. The graph passes through the points (1 hour, 80%) and (3 hours, 40%). Assuming the battery drains at a constant rate, solve for the time it will take for the battery to be completely discharged (0%).
Create a scenario for a journey between two cities, 200 km apart. Formulate a table of values for time versus distance, including a one-hour stop. Design a linear graph to represent this journey, ensuring you label the axes, choose a suitable scale, and clearly indicate the stop. Justify your choice of scale.
Explain how a graph can be used to find data that was not originally recorded in a table.
A student wants to plot the monthly sales of a company, which were Rs. 5 lakhs, Rs. 6 lakhs, Rs. 5.5 lakhs, and Rs. 1 crore. The student chooses a scale of 1 unit = Rs. 1 lakh on the y-axis. Critique this choice of scale. Propose a better approach to represent this data clearly.
Propose a graphical method to determine which of two mobile phone plans is more economical. Plan A costs a fixed Rs. 200 for 100 minutes and Rs. 2 per minute thereafter. Plan B has no fixed cost but charges Rs. 3 per minute. Design the graphs for both plans on the same axes for up to 200 minutes of usage and evaluate the point of intersection.
Contrast the graph of 'Perimeter of a square vs. its side' with the graph of 'Area of a square vs. its side'. Plot both graphs for side lengths 1, 2, 3, and 4 cm and explain the fundamental difference in the relationships they represent.
The line graph shows the quarterly sales (in crores) of a company for two years. For Year 1, sales were Q1: 20, Q2: 25, Q3: 30, Q4: 40. For Year 2, sales were Q1: 30, Q2: 40, Q3: 35, Q4: 50. Analyze the data to identify the quarter with the highest sales in Year 2. Then, calculate the total sales for Year 1 and the percentage increase in sales in Q4 of Year 2 compared to Q4 of Year 1.
A cyclist travels from Town A to Town B. The table shows the distance from Town A at various times. Plot a distance-time graph for this data. Analyze the graph to find the total travel time, identify any period of rest, and calculate the speed during the first hour. Data: Time: 8 am, 9 am, 10 am, 10:30 am, 11:30 am. Distance (km): 0, 15, 30, 30, 45.
Define the term 'direct variation' in the context of graphs.