Enhanced Curriculum Support
This is a comprehensive educational resource designed to provide students with the tools and guidance necessary to excel. This support system is structured to cater to various aspects of learning, ensuring that students are well-prepared for academic challenges and practical applications of mathematical concepts. Some are the key benefits are mentioned below:
Comprehensive Learning: This holistic approach helps students gain a thorough understanding of the subject. Practical Application: The resources encourage students to apply mathematical concepts to real-life scenarios, enhancing their practical understanding and problem-solving skills.
Critical Thinking and Reasoning: Value-Based and HOTS questions promote critical thinking and reasoning abilities. These skills are crucial for students to tackle complex problems and make informed decisions.
Exam Preparedness: Sample Question Papers and NCERT Exemplar Solutions provide ample practice for exams. They help students familiarize themselves with the exam format and types of questions, reducing exam anxiety.
Ethical and Moral Development: Value-Based Questions integrate ethical and moral lessons into the learning process, helping in the overall development of students' character and social responsibility. By incorporating these diverse elements, Enhanced Curriculum Support aims to provide a robust and well-rounded knowledge, preparing students for both academic success and real-world challenges.
Sample Questions/ Previous Year Questions
SecA
1. A line segment has?
2. The point where two sides of a triangle meet is called?
3. How many diagonals can be drawn in a rectangle?
SecB
1. Draw a rough sketch of a triangle and label its vertices as A, B, and C. Name the sides and angles of the triangle.
2. List out the differences between a square and a rectangle.
SecC
1. Draw a quadrilateral and name it. Identify and name its sides, vertices, and angles. What do you observe about the sum of its interior angles?
2. What is a polygon? Explain different types of polygons based on the number of sides and give examples of each.
3. Consider a pentagon ABCDE. How many diagonals can be drawn in it? Explain the method you used to determine this.
4. Explain the different types of angles (acute, obtuse, right, straight, and reflex). Draw one example of each type of angle, label the vertex and arms, and mention the measure of each angle. Discuss how angles are used in real-life situations, giving at least two examples.
SecD
1. If a rectangle and a square have the same perimeter, which one will have a larger area? Provide reasoning with a mathematical explanation.
2. Draw a circle with a radius of 4 cm. Label the center as O. Mark two points A and B on the circumference of the circle. Draw the following:
a) The diameter passing through O.
b) The chord AB.
c) A tangent to the circle at point A.
3. Define a quadrilateral. Draw a parallelogram PQRS. Show that opposite sides of a parallelogram are equal. If one angle of the parallelogram is 70°, find the measures of all other angles. Also, explain why the sum of the interior angles of any quadrilateral is always 360°.
4. Define a line, line segment, and ray. Draw a line segment AB of length 6 cm. Mark a point C on AB such that AC = 4 cm. Extend the line segment beyond B to form a ray. Label the ray as BD. Now, explain the differences between a line, line segment, and ray using your diagram.
Value Based Questions
Problem1
Situation: Seema wants to place her bookshelf at a specific point in her room where it does not block the window or the door.
1. If Seema's room is rectangular, with the window at point A and the door at point B, how can she decide where to place the bookshelf using the concept of points?
2. What should she consider to ensure the bookshelf is placed correctly?
Problem2
Situation: Raj is helping his father measure the length of the garden's fence.
1. Raj’s father asks him to measure the length of a straight section of the garden’s fence using a measuring tape. How can Raj represent this section of the fence as a line segment?
2. What does the length of this line segment represent?
Problem3
Situation: An architect is designing a city layout with roads, parks, and buildings.
1. If two roads in the city are designed to never intersect, what type of lines do they represent? If a road crosses another road at a 90-degree angle, what type of lines are they?
2. How does understanding these concepts help in city planning?
Problem4
Situation: Kavita is designing a circular flower bed for her garden.
1. Kavita wants to create a circular flower bed with a radius of 2 meters. How can she use the concepts of center, radius, and diameter to plan her flower bed?
2. Why is it important to understand these terms when designing circular shapes?
Problem5
Situation: Tina wants to hang a painting in her room so that it is perfectly straight.
1. Tina measures the angle between the top of the painting and the ceiling. What angle should she be looking for to ensure the painting is perfectly horizontal?
2. How does understanding angles help in everyday activities like this?
HOTS
Q1
1. Draw an equilateral ∆ABC of any size. Draw AD as its median and an altitude AM.
(i) Does AD coincide with AM?
(ii) Name the point on the median which divides it in the ratio 1:2.
(iii) What is the measure of ∠ADC and ∠ADB?
(iv) Are D and M the same points?
Q2
1. Draw a rough sketch of:
(a) open curve
(b) closed curve
Q3
1. Draw a rough sketch of closed curve made up of line segments.
2. Draw two different angles having common point and a common arm.
Q4
1. How many lines can pass through
(i) one given point?
(ii) two given points?
(iii) three non-collinear points?
Q5
1. Draw an equilateral ∆ABC of any size. Draw AD as its median and an altitude AM.
(i) Does AD coincide with AM?
(ii) Name the point on the median which divides it in the ratio 1:2.
(iii) What is the measure of ∠ADC and ∠ADB?
(iv) Are D and M the same points?
NCERT Exemplar Solutions
Questions
1. Draw a rough sketch of closed curve made up of line segments.
2. Draw two different angles having common point and a common arm.
3. Rectangle is a ……… curve.
4. A closed figure made up of entirely of line segments is called a?
5. The length of boundary of a circle is called its?
6. A curve which does not cross itself is called a ……… curve?
7. Triangle has ……… angles and three ……… .
8. ……… is the largest chord of a circle.
9. ……… divides the circle into two equal semi circles.
10. Only one line can be drawn through ……… points.
11. ……… number of lines can pass through a given point.
Case Based Questions
Question 1
Geometry has a long and rich history. The term ‘Geometry’ is the English equivalent of the Greek word ‘Geometron’. ‘Geo’ means Earth and ‘metron’ means Measurement. According to historians, the geometrical ideas shaped up in ancient times, probably due to the need in art, architecture and measurement. These include occasions when the boundaries of cultivated lands had to be marked without giving room for complaints. Construction of magnificent palaces, temples, lakes, dams and cities, art and architecture propped up these ideas. Even today geometrical ideas are reflected in all forms of art, measurements, architecture,engineering, cloth designing etc.
Based on the figure, answer the following questions:
1. Name the line containing point M.
2. Name the line containing three points.
3. Write two pairs of intersecting lines.
Question 2
The students were asked to draw a closed figure with few points inside the figure, few points outside the figure and few on the boundary of the figure. One of the child drew a figure like this:
Based on the above figure, answer the following questions:
1. Write the points which lie in the interior of the figure.
2. Write the points which lie on the boundary of the figure.
3. Draw two rough diagrams to illustrate the open figure.