Question 1

(i) Choose data from any 3 states you find interesting and present it through a line graph using an appropriate scale.
(ii) What do you find interesting in this data? Share your observations.
(iii) Compare the price variation in Gujarat and Uttar Pradesh.
(iv) In which state has the price increased the most from 2016 to 2025?
(v) What are you curious to explore further?

Accepted Answer

Solutions will vary depending on the states chosen and observations made. A sample solution is as follows:

(i) Select 3 states, for example, Gujarat, Uttar Pradesh, and Maharashtra. Using the given data, plot the prices for each year from 2016 to 2025 on a graph with years on the x-axis and price on the y-axis. Use an appropriate scale to clearly show trends.

(ii) Observations might include trends such as steady increase or fluctuations in prices, differences in price levels among states, or any anomalies.

(iii) Compare the price variation by noting the starting and ending prices for Gujarat and Uttar Pradesh, and observe the trend lines for increases or decreases.

(iv) Identify the state with the greatest increase by subtracting the 2016 price from the 2025 price for each state and comparing.

(v) Curiosities might include reasons for price changes, impact of policies, or comparison with other commodities. — Plotting the data on a line graph helps visualize trends over time. Comparing prices between states involves calculating differences and observing patterns. Observations and curiosities encourage critical thinking about data.

Question 2

Referring to the graph below, which of the following statements are valid? Why?

(i) In 1983, the majority in rural areas used kerosene as a primary lighting source while the majority in urban areas used electricity.
(ii) The use of kerosene as a primary lighting source has decreased over time in both rural and urban areas.
(iii) In the year 2000, 10% of the urban households used electricity as a primary lighting source.
(iv) In 2023, there were no power cuts.

Accepted Answer

(i) Valid: In 1983, the graph shows majority rural households used kerosene and urban households used electricity.
(ii) Valid: The graph indicates a decrease in kerosene use over time in both rural and urban areas.
(iii) Invalid: The graph shows electricity use in urban areas was higher than 10% in 2000.
(iv) Invalid: The graph does not provide information about power cuts in 2023. — By analyzing the graph, one can verify the trends and percentages for each statement. Statements (i) and (ii) align with the data, while (iii) and (iv) do not.

Question 3

Answer the following questions based on the line graph.

(i) How long do children aged 10 in urban areas spend each day on hobbies and games?
(ii) At what age is the average time spent daily on hobbies and games by rural kids 1.5 hours?

(a) 8 years
(b) 10 years
(c) 12 years
(d) 14 years
(e) 18 years

(iii) Are the following statements correct?

(a) The average time spent daily on hobbies and games by kids aged 15 is twice that of kids aged 10.
(b) All rural kids aged 15 spend at least 1 hour on hobbies and games everyday.

Accepted Answer

(i) Children aged 10 in urban areas spend approximately 1.5 hours daily on hobbies and games as per the graph.

(ii) The average time spent daily on hobbies and games by rural kids is 1.5 hours at age 14 years (Option d).

(iii)(a) Correct: The graph shows that kids aged 15 spend about twice the time compared to kids aged 10.
(iii)(b) Incorrect: The graph shows average time, individual times may vary; not all rural kids aged 15 spend at least 1 hour daily. — By reading the graph, the time spent by children of different ages in urban and rural areas can be estimated. The multiple-choice question (ii) is answered by locating the age where rural kids spend 1.5 hours. The true/false statements are verified by comparing values on the graph.

Question 4

Individual project: Make your own activity strip for different days of the week.

(i) Do you eat and sleep at regular times every day? Typically how long do you spend outdoors?
(ii) Calculate the average time spent per activity. Represent this average day using a strip.
(iii) Similarly, track the activities of any adult at home. Compare your data with theirs.

Accepted Answer

This is a project-based question requiring students to track their daily activities and those of an adult at home.

(i) Students note their eating, sleeping, and outdoor times each day.
(ii) Calculate average time spent on each activity over the week and represent it visually as an activity strip.
(iii) Compare the student's activity strip with that of an adult, noting similarities and differences. — Tracking and representing daily activities helps understand time management and differences between children and adults. The activity strip is a visual tool to summarize data.

Question 5

Small group project: Make a group of 3–4 members. Do at least one of the following:

(i) Track daily sleep time of all your family members for a week. Daily sleep time includes night sleep, naps, and any sleep during the day.

(a) Represent this on strips.
(b) Put together the data of all your group members. Calculate the average and median sleep time of children, adults, elderly.
(c) Share your findings and observations.

(ii) When do schools start and end? On a weekday, Manoj’s school starts at 9:30 am and ends at 4:30 pm, i.e., 7 hours which include class time and breaks. Collect information on the daily timings of different schools for Grade 8, including class time and break time (the schools can be anywhere in the country. You can ask your neighbours, relatives, parents and friends to find out). Analyse and present the data collected.

Accepted Answer

This is a group project involving data collection and analysis.

(i)(a) Track and represent sleep times on strips for each family member.
(i)(b) Combine data from group members and calculate average and median sleep times for children, adults, and elderly.
(i)(c) Discuss findings such as sleep patterns, differences among age groups.

(ii) Collect school timing data for Grade 8 from various schools, analyze start and end times, class and break durations, and present findings. — The project encourages collaborative data collection, statistical calculations, and presentation skills. It helps understand sleep patterns and school schedules.

Question 6

The following graphs show the sunrise and sunset times across the year at 4 locations in India. Observe how the graphs are organised. Are you able to identify which lines indicate the sunrise and which indicate the sunset?

Answer the following questions based on the graphs:

(i) At which place does the sun rise the earliest in January? What is the approximate day length at this place in January?
(ii) Which place has the longest day length over the year?
(iii) Share your observations—what do you find interesting? What are you curious to find out?

Accepted Answer

(i) The sun rises earliest in January at the location where the sunrise line is lowest on the graph for January. For example, if the graph shows Chennai, Delhi, Mumbai, and Kolkata, Chennai typically has the earliest sunrise in January.
The approximate day length can be found by calculating the difference between sunset and sunrise times from the graph, usually around 10-11 hours.

(ii) The place with the longest day length over the year is generally the one with the greatest variation between sunrise and sunset times, often Delhi or a northern location.

(iii) Observations may include seasonal variations in day length, differences between locations, and curiosity about how these affect daily life or agriculture. — By analyzing the sunrise and sunset graphs, one can determine earliest sunrise times and day lengths. Observations encourage understanding of Earth's tilt and seasonal effects.

Question 7

We all know the typical sunrise and sunset timings. Do you know when the moon rises and sets? Does it follow a regular pattern like the sun? Let's find out. The following graph shows the moonrise and moonset time over a month:

(i) Find out on what dates amavasya (new moon) and purnima (full moon) were in this month.
(ii) What do you notice? What do you wonder?

Accepted Answer

(i) Amavasya (new moon) occurs when the moon is not visible, typically when moonrise and moonset times coincide or the moon is absent. Purnima (full moon) occurs when the moon is fully visible, typically when moonrise and moonset times are approximately 12 hours apart.
By examining the graph, identify the dates where these conditions occur.

(ii) Notice that moonrise and moonset times shift daily and do not follow a fixed pattern like the sun. One might wonder about the causes of this variation and its effects on tides and calendars. — The moon's rise and set times vary daily due to its orbit around Earth. Identifying new and full moon dates from the graph involves understanding these patterns.

Question 8

Which of the following best describes a line in geometry?

Accepted Answer

A one-dimensional figure extending infinitely in both directions — In geometry, a line is defined as a one-dimensional figure that extends infinitely in both directions without any endpoints. Unlike line segments or rays, lines have no endpoints.

Question 9

Identify the type of line segment that has exactly one endpoint and extends infinitely in the other direction.

Accepted Answer

Ray — A ray has exactly one endpoint and extends infinitely in one direction. This distinguishes it from a line segment (which has two endpoints) and a line (which extends infinitely in both directions).

Question 10

Which of the following pairs of lines will never meet, no matter how far they are extended?

Accepted Answer

Parallel lines — Parallel lines lie in the same plane and never meet, regardless of how far they are extended. Intersecting lines meet at a point, and perpendicular lines are intersecting lines at right angles. Skew lines are non-coplanar and do not intersect but are not parallel.

Question 11

Two lines intersect at a point forming a right angle. What type of lines are these?

Accepted Answer

Perpendicular lines — Perpendicular lines are intersecting lines that meet at a right angle (90 degrees).

Question 12

What is a transversal in geometry?

Accepted Answer

A line that intersects two or more lines at distinct points — A transversal is a line that crosses two or more other lines at distinct points, often used to study angle relationships formed by these intersections.

Question 13

Explain the difference between intersecting lines and parallel lines.

Accepted Answer

Intersecting lines are lines that meet or cross each other at a point. For example, two roads crossing at a junction are intersecting lines. Parallel lines are lines in the same plane that never meet, no matter how far they are extended. For example, railway tracks are parallel lines. — Intersecting lines cross each other at a point, whereas parallel lines maintain a constant distance and never intersect. This distinction is fundamental in geometry and real-life applications.

Question 14

What property do perpendicular lines have that distinguishes them from other intersecting lines?

Accepted Answer

Perpendicular lines intersect at right angles, meaning they form an angle of exactly 90 degrees. For example, the corner of a rectangular table where two edges meet is a right angle formed by perpendicular lines. — Perpendicular lines are a special case of intersecting lines characterized by their right angle intersection, which is important in constructions and design.

Question 15

When a transversal cuts two parallel lines, which pair of angles are equal and lie on the same side of the transversal but inside the two lines?

Accepted Answer

Interior angles on the same side of the transversal — Interior angles on the same side of the transversal lie inside the two parallel lines and on the same side of the transversal. These angles are supplementary (sum to 180°), not equal.

And Lines

And Lines — Study Notes

Introduction

Types of Lines

Angles formed by a Transversal

Practice Questions — And Lines

All 7 Chapters in Ganita Prakash Part-II