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. Find the value of sin 30°
2. If tan θ =
3. Find the value of
4. If sin θ =
SecB
1. if sec θ =
2. Find the value of tan 30° × cot 60°.
SecC
1. A ladder 15 meters long is leaning against a vertical wall. If the ladder makes an angle of 60°, with the ground, find how far the ladder is from the base of the wall and the height it reaches on the wall.
2. Prove that
3. From the top of a lighthouse 100 meters high, the angle of depression of a boat is 30°. Find the distance of the boat from the foot of the lighthouse.
SecD
1. A man standing on the top of a 50-meter high tower observes two cars on the opposite sides of the tower. The angles of depression are 30° and 60°. Find the distance between the two cars.
2. Two poles of heights 6 meters and 11 meters stand on the same level ground. The distance between the poles is 12 meters. Find the angle of elevation of the top of the taller pole from the top of the shorter pole.
3. Prove the identity
Value Based Questions
Problem1
Situation: A school plans to construct a wheelchair-accessible ramp at an entrance. The length of the ramp is 12 meters, and the vertical height from the ground to the door is 2 meters. The school wants to ensure that the ramp's slope is neither too steep nor too gentle, so everyone can use it comfortably.
1. Using trigonometry, calculate the angle of elevation of the ramp.
2. Discuss how the school's decision to build this ramp reflects the values of inclusivity and accessibility.
Problem2
Situation: A company is installing solar panels on the roof of their office building. To maximize efficiency, the panels need to be tilted at an angle that captures the most sunlight. The building engineer measures the sunlight falling at an angle of 35° from the horizontal, and the roof has a vertical height of 6 meters.
1. Calculate the horizontal distance from the base of the building to the point where sunlight strikes the ground.
2. How does the company's initiative of installing solar panels reflect the value of environmental sustainability?
Problem3
Situation: A group of students is preparing for a mountain-climbing expedition. From a certain point on the ground, the angle of elevation to the top of the mountain is 45°. If the height of the mountain is 1,000 meters, they need to determine the horizontal distance they must cover before they start climbing vertically.
1. Calculate the horizontal distance the students need to cover before reaching the base of the mountain.
2. How does this scenario highlight the value of perseverance and determination?
Problem4
Situation: A government is planning to build a fence around a historical monument to protect it from erosion. The monument is located at a point 50 meters above the ground, and the angle of elevation from a point on the ground to the top of the monument is 30°.
1. Calculate the distance from the base of the monument to the point on the ground where the angle of elevation is measured.
2. How does this project reflect the value of preserving cultural heritage?
HOTS
Q1
1. A ladder is placed against a vertical wall such that the top of the ladder touches the wall at a height of 8 meters. If the angle of elevation of the ladder with the ground is 60°, find the length of the ladder.
2. How does the length of the ladder change if the angle of elevation decreases to 45°?
Q2
1. From the top of a lighthouse 50 meters high, the angle of depression to a boat is 30°. How far is the boat from the base of the lighthouse?
2. If the angle of depression increases to 45° , how does the distance change?
Q3
1. A vertical pole stands on a horizontal ground, casting a shadow 10 meters long when the angle of elevation of the sun is 30°.Find the height of the pole.
2. If the sun's angle of elevation changes to 45°, what will be the new length of the shadow?
Q4
1. A parachutist observes the angle of depression of a target on the ground to be 60°. After descending vertically 100 meters, the angle of depression becomes 45°
2. Find the height from which the parachutist initially observed the target.
Q5
1. Two planes are flying at different altitudes above the ground. From a point on the ground, the angles of elevation to the two planes are 30° 60°, respectively. If the horizontal distance from the observer to the point directly beneath both planes is the same, and the altitude difference between the two planes is 500 meters, find the horizontal distance from the observer to the planes.
NCERT Exemplar Solutions
Questions
1. The value of the expression [cosec (75° + θ) – sec (15° – θ) – tan (55° + θ) + cot (35° – θ)] is
2. If cos 9α = sina and 9α < 90°, then the value of tan5α is
3. If ∆ABC is right angled at C, then the value of cos (A+B) is
4. If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is
5. A pole 6m high casts a shadow 2√3 m long on the ground, then the Sun’s elevation is
6. If a sinθ + b cosθ = c, then prove that acosθ – bsinθ = √
7. If sinθ + cosθ = p and secθ + cosecθ = q, then prove that q(
8. Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
9. Show that tan4θ + tan2θ = sec4θ – sec2θ.
10. Simplify (1 + tan2θ) (1 – sinθ) (1 + sinθ)
11. If 2sin2θ – cos2θ = 2, then find the value of θ.
12. A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, find the height of the wall.
13. An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high. Determine the angle of elevation of the top of the tower from the eye of the observer.
14. The angle of elevation of the top of a tower from certain point is 30°. If the observer moves 20 metres towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower.
15. The angle of elevation of the top of a tower from two points distant s and f from its foot are complementary. Prove that the height of the tower is √st.
16. The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60° and the angle of elevation of the top of the second tower from the foot of the first tower is 30°. Find the distance between the two towers and also the height of the other tower.
Case Based Questions
Question 1
A trolley carries passengers from the ground level located point A to up to the top of mountain chateau located at P as shown in figure. The point A is at a distance of 2000m from point C at the base of mountain. Here α = 30°, β = 60°
Based on your understanding of the above case study, answer all the five questions below
1. Assuming the cable held tight. What will be the length of cable?
2. What will be height of the mountain?
3. what will be the slant height of mountain?
4. What will be the length of BC?
5. What will be the distance of point A to the foot of the mountain located at B?
Question 2
In structural design a structure is composed of triangles that are interconnecting. A truss is one of the major types of engineering structures and is especially used in the design of bridges and buildings. Trusses are designed to support loads, such as the weight of people. A truss is exclusively made of long, straight members connected by joints at the end of each member
Based on your understanding of the above case study, answer all the five questions below:
1. In above triangle, what is the length of AC?
2. In above triangle, what is the length of AC?
3. If sin A = sin C, what will be the length of BC?
4. Which of the following relation will satisfy for above triangle?
5. If the length of AB doubles what will happen to the length of AC?