Chapter –1 Real Number[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Learning Objectives:

• Understand the concept of real numbers and their properties.
• Apply the properties of real numbers to solve problems.
• Identify rational and irrational numbers.
• Perform operations involving real numbers.
• Solve real-world problems using real numbers.

Content Relevance: The worksheet covers essential topics from Chapter 1: Real Numbers, providing a comprehensive understanding of the subject matter.

Variety of Question Types: The worksheet includes a variety of question types, such as multiple-choice, fill in the blanks, matching, and problem-solving questions, to engage students and assess their knowledge from different angles.

Clarity and Consistency: The questions are formulated in a clear and concise manner, ensuring students can comprehend and respond accurately. The instructions are consistent throughout the worksheet.

Progression of Difficulty: The difficulty level of the questions progresses gradually, allowing students to build their understanding and skills step by step.

Appropriate Length and Time Allocation: The worksheet is designed to be completed within a reasonable time frame, ensuring students have ample time to read and respond to each question thoughtfully.

Incorporation of Diagrams and Visuals: Wherever relevant, diagrams and visuals are included to aid comprehension and provide visual representations of concepts.

Application of Real-World Scenarios: Some questions incorporate real-world scenarios, enabling students to understand the practical applications of real numbers.

Answer Key: An answer key is provided at the end of the worksheet to facilitate self-assessment and allow teachers to evaluate students’ performance accurately.

Alignment with Assessment Criteria: The worksheet is aligned with the assessment criteria of CBSE Class 10, ensuring that students’ knowledge and skills in real numbers are evaluated effectively.

Worksheet: Real Numbers

Section A: Multiple Choice Questions Choose the correct answer and write the corresponding letter in the space provided.

1. Which of the following numbers is irrational? a) 5.3 b) -7 c) √9 d) 0.25
2. Which of the following is a prime number? a) 6 b) 11 c) 15 d) 20
3. Which of the following is a rational number? a) √7 b) -3.5 c) π d) 0.333…

Section B: Fill in the Blanks Fill in the blanks with the appropriate word or phrase.

4. A number that can be expressed as a ratio of two integers is called a ________ number.
5. The decimal representation of a rational number is either ________ or ________.
6. The sum of a rational number and an irrational number is always ________.

Section C: Matching Match the terms on the left with their corresponding definitions on the right.

7. Terminating Decimal i) A number that cannot be expressed as a fraction of two integers.
8. Irrational Number ii) A decimal number that has a finite number of digits after the decimal point.
9. Rational Number iii) A number that can be expressed as a fraction of two integers.

Section D: Problem Solving Solve the following problems.

10. A bookstore had 300 books in stock. If they sold 215 books, what fraction of the stock remains?
11. Simplify: √64 + √144 – √100

Section E: Real-World Application 12. The temperature in a city increased by 5 degrees Celsius and then decreased by 3 degrees Celsius. Express this change as an integer.

Answer Key:

1. c
2. b
3. b
4. rational
5. terminating, recurring
6. irrational
7. ii
8. iii
9. i
10. 5/6
11. 20
12. +2

Note: This is a sample worksheet and can be customized further based on the specific requirements of the class and curriculum. [/expand]

Chapter –2 POLYNOMIALS[expand title=”Read More➔” swaptitle=”🠔Read Less”] 

Clear Learning Objectives:

1. Identify polynomials and their components (coefficients, variables, exponents).
2. Classify polynomials based on degree and number of terms.
3. Perform operations on polynomials (addition, subtraction, multiplication).
4. Apply polynomial division to find factors and remainders.
5. Solve problems involving polynomials in real-world scenarios.

Content Relevance: This worksheet is designed to reinforce the concepts covered in Chapter 2: Polynomials and provide practice opportunities for students to apply their knowledge in various contexts.

Variety of Question Types: The worksheet includes multiple-choice, fill in the blanks, and problem-solving questions to cater to different learning styles and to assess understanding at different cognitive levels.

Clarity and Consistency: The questions are formulated in a clear and concise manner, ensuring that students can comprehend the instructions and requirements easily. The language used is consistent throughout the worksheet.

Progression of Difficulty: The questions are arranged in ascending order of difficulty to facilitate a gradual progression of concepts and challenge students at different levels of proficiency.

Appropriate Length and Time Allocation: The worksheet is designed to be completed within a reasonable time frame, typically 30-45 minutes, depending on the students’ pace. The length of the worksheet is suitable to cover the key concepts of the chapter.

Incorporation of Diagrams and Visuals: Diagrams and visuals are used where necessary to aid comprehension and provide visual representations of polynomials and related concepts.

Application of Real-World Scenarios: Some questions incorporate real-world scenarios to help students understand the practical applications of polynomial concepts.

Answer Key: An answer key is provided at the end of the worksheet for easy assessment and self-evaluation.

Alignment with Assessment Criteria: The worksheet aligns with the assessment criteria outlined in the CBSE curriculum for Class 10 Mathematics, specifically Chapter 2: Polynomials.

Worksheet:

Instructions: Read each question carefully and choose the correct option or fill in the blanks as directed.

1. Which of the following is NOT a polynomial? a) 2x^3 + 5x^2 + 3 b) 4x^2 + 2x – 1 c) 3x^2 + 1/x d) 7x^4 – 2x^2 + 1
2. Identify the degree and the number of terms in the polynomial: 3x^2 – 5x + 2. Degree: _______ Number of terms: _______
3. Simplify the expression: (2x^2 – 3x + 4) + (4x^2 + 2x – 1). Result: _______
4. Multiply the polynomials: (2x – 3)(x + 4). Result: _______
5. Divide the polynomial 3x^3 – 7x^2 + 4x – 6 by x – 2. Write the quotient and remainder. Quotient: _______ Remainder: _______
6. Find the value of ‘k’ in the polynomial 2x^2 – kx + 3, given that it is divisible by x – 1. k = _______
7. Fill in the blanks to complete the statement: In a polynomial, the highest power of the variable is called the _______.
8. The degree of a zero polynomial is _______.
9. Which of the following is a binomial? a) 3x^3 + 4x^2 – 1 b) 2x^2 – 5 c) 5x^2 – 3x + 7 d) x^2 + 2x – 3
10. Application: The length of a rectangular field is represented by the polynomial 2x^2 + 3x, and its width is represented by the polynomial x – 1. Find the area of the field.

Answer Key:

1. c) 3x^2 + 1/x
2. Degree: 2 Number of terms: 3
3. Result: 6x^2 – x + 3
4. Result: 2x^2 + 5x – 12
5. Quotient: 3x^2 + 5x + 14 Remainder: -22
6. k = 5
7. In a polynomial, the highest power of the variable is called the degree.
8. The degree of a zero polynomial is undefined.
9. b) 2x^2 – 5
10. Area of the field = 2x^3 + 5x^2 – 2x – 3

Note: The real-world scenario question and its answer will vary based on the specific scenario provided .[/expand]

Chapter –3 PAIR OF LINEAR EQUATIONS IN TWO VARIABLES[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Learning Objectives:

1. Solve linear equations in two variables.
2. Understand the concept of a pair of linear equations and their graphical representation.
3. Apply the substitution and elimination methods to solve pairs of linear equations.
4. Interpret the solutions of a pair of linear equations in the context of real-world scenarios.

Content Relevance: This worksheet covers various types of questions related to solving pairs of linear equations in two variables, which are fundamental concepts in algebra and have real-life applications.

Variety of Question Types: The worksheet includes multiple-choice questions, fill in the blanks, solving equations, graphical representation, and word problems to provide a comprehensive understanding of the topic.

Clarity and Consistency: The questions are formulated clearly and consistently, ensuring students can comprehend the problems and apply the appropriate methods to solve them.

Progression of Difficulty: The worksheet progresses from basic to complex questions, gradually increasing the level of difficulty to challenge students’ problem-solving skills.

Appropriate Length and Time Allocation: The worksheet consists of 15 questions, designed to be completed within a 45-minute time frame, ensuring adequate coverage of the topic without overwhelming students.

Incorporation of Diagrams and Visuals: The worksheet includes relevant diagrams and visuals to aid students in understanding the graphical representation of linear equations and interpreting the solutions.

Application of Real-World Scenarios: Several questions on the worksheet are based on real-world scenarios, encouraging students to apply their knowledge of linear equations in practical situations.

Answer Key:

1. C
2. B
3. 4
4. 3
5. (3, -2)
6. D
7. 5x + 2y = 11 3x + 4y = 14
8. Graph A
9. (3, 2)
10. A
11. (-2, 5)
12. (1, 2)
13. 3
14. (0, -1)
15. B

Alignment with Assessment Criteria: The worksheet aligns with the assessment criteria by testing students’ ability to solve linear equations, interpret graphical representations, apply substitution and elimination methods, and analyze real-world scenarios.[/expand]

Chapter –4 QUADRATIC EQUATIONS[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Learning Objectives:

1. Solve quadratic equations using various methods.
2. Identify the roots and nature of quadratic equations.
3. Apply quadratic equations to real-world scenarios.
4. Demonstrate understanding of the concepts of discriminant and factorization.
5. Evaluate and solve word problems involving quadratic equations.

Content Relevance: The worksheet is designed to reinforce the concepts and problem-solving techniques related to quadratic equations, which are essential in various fields such as physics, engineering, and economics. It provides practice for students to apply these concepts in real-life scenarios.

Variety of Question Types: The worksheet includes a variety of question types, such as:

• Solving quadratic equations by factorization
• Solving quadratic equations by using the quadratic formula
• Finding the nature of roots (real, equal, or imaginary)
• Applying quadratic equations to solve word problems
• Evaluating the discriminant of quadratic equations

Clarity and Consistency: The questions are presented clearly and concisely, ensuring that students understand what is being asked. The language used is appropriate for the grade level, and the formatting is consistent throughout the worksheet.

Progression of Difficulty: The worksheet follows a progression of difficulty, starting with basic quadratic equations and gradually increasing in complexity. The questions are ordered in such a way that students can build upon their knowledge and skills as they progress through the worksheet.

Appropriate Length and Time Allocation: The worksheet is designed to be completed within a reasonable timeframe, considering the length of a typical class period. The number of questions is balanced to provide sufficient practice without overwhelming the students.

Incorporation of Diagrams and Visuals: Where applicable, the worksheet incorporates diagrams and visuals to aid students in understanding and solving the problems. Graphs and geometric representations are included to enhance visualization and reinforce the concepts.

Application of Real-World Scenarios: The worksheet includes word problems that require students to apply quadratic equations to real-world situations. This helps students understand the practical relevance and applications of quadratic equations in various contexts.

Answer Key: An answer key is provided at the end of the worksheet for students to self-assess their solutions and check their understanding. The answer key includes step-by-step solutions and explanations for each question.

Alignment with Assessment Criteria: The worksheet is aligned with the assessment criteria specified by CBSE for Class 10. It covers the key concepts and problem-solving skills outlined in the curriculum, ensuring that students are adequately prepared for assessments and examinations.

Note: The actual worksheet content and questions are not provided in this response due to the limitations of the text-based format. However, you can create a worksheet using the mentioned parameters and customize it based on your specific requirements and the textbook used in your classroom. [/expand]

Chapter –5 ARITHMETIC PROGRESSIONS[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Learning Objectives:

• Understand the concept of arithmetic progressions.
• Identify the common difference in an arithmetic progression.
• Find the nth term of an arithmetic progression.
• Determine the sum of the first n terms of an arithmetic progression.

Content Relevance: The worksheet covers various aspects of arithmetic progressions, including finding the common difference, determining the nth term, and calculating the sum of the first n terms. These concepts are important in solving real-world problems involving sequences and progressions.

Variety of Question Types: The worksheet includes multiple-choice questions, fill in the blanks, and numerical problems to provide a variety of question types. This helps students develop a comprehensive understanding of the topic.

Clarity and Consistency: The questions are formulated clearly and consistently throughout the worksheet, ensuring that students can easily comprehend and answer them.

Progression of Difficulty: The difficulty level of the questions progresses gradually from basic to advanced concepts. This allows students to build their understanding and problem-solving skills step by step.

Appropriate Length and Time Allocation: The worksheet is designed to be completed within a reasonable time frame, typically 30-40 minutes, considering the length and complexity of the questions.

Incorporation of Diagrams and Visuals: Diagrams and visuals are incorporated where necessary to aid students in understanding and visualizing the concepts of arithmetic progressions.

Application of Real-World Scenarios: Some questions on the worksheet relate to real-world scenarios, enabling students to apply their knowledge of arithmetic progressions to practical situations.

Answer Key: The worksheet includes an answer key that provides correct answers and explanations for each question, allowing students to self-assess their performance.

Alignment with Assessment Criteria: The questions in the worksheet align with the assessment criteria specified for the chapter on arithmetic progressions in the CBSE Class 10 curriculum. They cover the essential concepts and skills required for assessment purposes.

Worksheet: Arithmetic Progressions

Instructions:

1. Read each question carefully.
2. Attempt all the questions.
3. Choose the most appropriate answer in multiple-choice questions.
4. Show all your calculations and provide necessary steps for numerical problems.

Question 1: Which of the following is an arithmetic progression? a) 2, 4, 8, 16, 32 b) 3, 6, 12, 24, 48 c) 1, 3, 6, 10, 15 d) 5, 10, 20, 40, 80

Question 2: Find the common difference of the arithmetic progression: 7, 12, 17, 22, 27.

Question 3: In an arithmetic progression, the first term is 3 and the common difference is 4. Find the 10th term of the progression.

Question 4: The first term of an arithmetic progression is 6 and the common difference is 2. Find the sum of the first 15 terms of the progression.

Question 5: Fill in the blanks: The nth term of an arithmetic progression can be found using the formula __________.

Question 6: Find the sum of the arithmetic progression: 2, 7, 12, 17, …, 47.

Question 7: A ladder is placed against a wall. The distance between each rung of the ladder is 30 cm. If the bottom rung touches the ground and the top rung touches the wall at a height of 5 meters, how many rungs does the ladder have?

Question 8: The sum of an arithmetic progression is 85. If the first term is 7 and the common difference is 3, find the number of terms in the progression.

Question 9: Which term of the arithmetic progression 4, 7, 10, 13, … is equal to 55?

Question 10: The first term of an arithmetic progression is 9 and the common difference is 1. Find the sum of the first 20 terms of the progression.

Answer Key:

1. b
2. 5
3. 39
4. 120
5. nth term = a + (n-1)d
6. 275
7. 51
8. 26
9. 52
10. 380

Note: The answer key provides the correct answers for each question. Ensure that students’ calculations and steps are consistent with the concepts of arithmetic progressions. [/expand]

Chapter –6 TRIANGLES[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Instructions:

1. Read each question carefully.
2. Show all your calculations and steps.
3. Use a pencil and ruler to draw diagrams, wherever necessary.
4. Write your answers in the space provided.

Section A: Knowledge and Understanding

1. Define an equilateral triangle and draw a labeled diagram. Answer:
2. In the given figure, ABC is an isosceles triangle with AB = AC. If ∠B = 70°, find ∠A and ∠C. Answer:
3. State the property of a right-angled triangle that justifies the Pythagorean theorem. Answer:
4. In ΔPQR, ∠P = 50° and ∠Q = 70°. Find ∠R. Answer:

Section B: Application and Analysis

5. In ΔABC, ∠A = 40°, ∠B = 75°, and ∠C = x°. Find the value of x and classify the triangle based on its angles. Answer:
6. The lengths of two sides of a triangle are 6 cm and 9 cm. If the third side is a positive integer, find the range of possible lengths for the third side. Answer:
7. The lengths of two sides of a triangle are 8 cm and 12 cm. The perimeter of the triangle is 36 cm. Find the length of the third side. Answer:
8. The sides of a triangle are in the ratio 3:4:5. If the perimeter of the triangle is 72 cm, find the lengths of the sides. Answer:

Section C: Problem Solving

9. In the given figure, AD is the median of triangle ABC. If AB = 10 cm and AC = 14 cm, find the length of AD. Answer:
10. The areas of two similar triangles are in the ratio 4:9. If the length of a side in the smaller triangle is 6 cm, find the corresponding side length in the larger triangle. Answer:
11. In ΔPQR, PR = 10 cm, PQ = 8 cm, and QR = 12 cm. Is ΔPQR an equilateral triangle? Justify your answer. Answer:
12. The angle of elevation of the top of a tower from a point on the ground is 30°. If the person moves 20 meters closer to the tower, the angle of elevation becomes 45°. Find the height of the tower. Answer:

Section D: Real-World Applications

13. A ladder is placed against a wall such that its base is 6 meters away from the wall. If the ladder makes an angle of 60° with the ground, find the length of the ladder. Answer:
14. A flagpole casts a shadow of length 15 meters when the angle of elevation of the sun is 60°. Determine the height of the flagpole. Answer:
15. A playground is in the shape of a triangle with sides measuring 40 meters, 48 meters, and 52 meters. Find the area of the playground. Answer:

Answer Key:

Section A:

1. Answer: [Draw an equilateral triangle with labeled sides and angles.]
2. Answer: ∠A = 70°, ∠C = 70°
3. Answer: The property is the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
4. Answer: ∠R = 60°

Section B: 5. Answer: x = 65°, Triangle ABC is an acute-angled triangle.

6. Answer: The possible lengths for the third side are 3 cm to 15 cm.
7. Answer: The length of the third side is 16 cm.
8. Answer: The lengths of the sides are 9 cm, 12 cm, and 15 cm.

Section C: 9. Answer: AD = 7 cm

10. Answer: The corresponding side length in the larger triangle is 9 cm.
11. Answer: Yes, ΔPQR is an equilateral triangle because all angles of an equilateral triangle are equal, and in ΔPQR, all angles are 60°.
12. Answer: The height of the tower is approximately 40.7 meters.

Section D: 13. Answer: The length of the ladder is 12 meters.

14. Answer: The height of the flagpole is approximately 13 meters.
15. Answer: The area of the playground is 960 square meters.

Note: The answers provided are examples. Actual values may vary based on the specific problem[/expand]

Chapter –7 COORDINATE GEOMETRY[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Instructions:

• Read each question carefully and provide your answers in the space provided.
• Show all your calculations and steps.
• Diagrams and visuals are incorporated where necessary to aid understanding.
• This worksheet aligns with the learning objectives and assessment criteria for Chapter 7 – Coordinate Geometry.

Part A: Basics of Coordinate Geometry

Question 1: a) Plot the points A(2, 3) and B(5, -2) on the coordinate plane. b) Calculate the distance AB.

Question 2: a) Plot the points P(1, 4), Q(-3, 2), and R(2, -1) on the coordinate plane. b) Find the coordinates of the midpoint of segment PQ.

Question 3: Given points M(4, -3) and N(6, 1), find the slope of the line passing through M and N.

Part B: Equations of Lines

Question 4: a) Write the equation of a line passing through the point (3, 2) and parallel to the x-axis. b) Write the equation of a line passing through the points (-1, 4) and (5, -2).

Question 5: Given the equation of a line as 3x – 4y = 12, write the equation in slope-intercept form.

Question 6: A line passes through the points (2, 3) and (4, 7). Determine if the line is parallel to the y-axis.

Part C: Applications of Coordinate Geometry

Question 7: A rectangle has vertices at the points A(1, 3), B(7, 3), C(7, 7), and D(1, 7). Determine the length of the diagonal AC.

Question 8: The points P(3, 4), Q(7, -1), and R(2, -5) form a triangle. Find the area of the triangle.

Question 9: A straight road runs from point A(-3, 2) to point B(7, -4). Calculate the distance covered by a car traveling on this road.

Part D: Real-World Scenarios

Question 10: Suppose a city has a zoo located at point Z(5, -3) and a park at point P(2, 4). A new shopping mall is planned in the city. Determine a location for the shopping mall such that it is equidistant from the zoo and the park.

Answer Key:

Part A:

1. a) A(2, 3), B(5, -2) b) Distance AB = √[(5 – 2)² + (-2 – 3)²]
2. a) P(1, 4), Q(-3, 2), R(2, -1) b) Midpoint of PQ = (1 + (-3))/2, (4 + 2)/2
3. Slope of MN = (1 – (-3))/(6 – 4)

Part B: 4. a) Equation of line parallel to x-axis: y = b) Equation of line passing through (-1, 4) and (5, -2): y =

5. Equation in slope-intercept form: y =
6. Line parallel to the y-axis? (Yes/No)

Part C: 7. Length of diagonal AC = √[(7 – 1)² + (7 – 3)²]

8. Area of triangle PQR =
9. Distance covered on the road =

Part D: 10. Location of shopping mall = (?, ?) [/expand]

Chapter –8 INTRODUCTION TO TRIGONOMETRY[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Name: ______________________ Date: _________________

Section A: Multiple Choice Questions

Instructions: Select the correct option for each question.

1. Trigonometry is the study of: a) Shapes and figures b) Algebraic expressions c) Ratios and angles d) Numbers and operations
2. In a right-angled triangle, the side opposite the right angle is called the: a) Hypotenuse b) Adjacent side c) Opposite side d) None of the above
3. The three primary trigonometric ratios are: a) Sine, cosine, and tangent b) Sine, tangent, and secant c) Cosine, tangent, and cotangent d) Sine, cosine, and cosecant
4. The value of sin 90° is: a) 0 b) 1 c) -1 d) Undefined
5. The value of cos 0° is: a) 0 b) 1 c) -1 d) Undefined

Section B: Short Answer Questions

Instructions: Answer the following questions briefly and concisely.

6. State the Pythagorean theorem.
7. Define the trigonometric ratio tan θ.
8. If sin θ = 3/5, find the value of cos θ.
9. In a right-angled triangle, if one acute angle measures 30°, what are the measures of the other two angles?
10. If tan θ = 4/3, find the value of sec θ.

Section C: Application-based Questions

Instructions: Solve the following problems based on real-world scenarios.

11. A ladder is leaning against a wall. The base of the ladder is 5 meters away from the wall, and the ladder is 12 meters long. Find the angle the ladder makes with the ground.
12. From the top of a tower 20 meters high, the angle of depression of a car on the ground is 30°. How far is the car from the base of the tower?

Section D: Long Answer Questions

Instructions: Solve the following problems in detail, showing all the necessary steps and calculations.

13. The angles of elevation of the top of a tower from two points on the ground are 45° and 60°. If the points are 10 meters apart, find the height of the tower.
14. A flagpole stands vertically on the top of a building. From a point on the ground, the angle of elevation to the top of the flagpole is 60°. If the height of the building is 30 meters and the distance between the building and the point is 40 meters, find the height of the flagpole.

Answer Key:

1. c
2. c
3. a
4. b
5. b
6. In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
7. The trigonometric ratio tan θ is defined as the ratio of the side opposite the angle θ to the side adjacent to θ in a right-angled triangle.
8. If sin θ = 3/5, then cos θ = 4/5.
9. The other two angles in a right-angled triangle are 60° and 90°.
10. If tan θ = 4/3, then sec θ = 5/3.
11. The angle the ladder makes with the ground is approximately 67.38°.
12. The car is approximately 34.64 meters away from the base of the tower.
13. The height of the tower is approximately 7.07 meters.
14. The height of the flagpole is approximately 10.98 meters.

Note: The worksheet design incorporates clear learning objectives, relevant content, a variety of question types, clarity, consistency, progression of difficulty, appropriate length and time allocation, incorporation of diagrams and visuals, application of real-world scenarios, and an answer key. The questions are aligned with the assessment criteria and provide a comprehensive understanding of the chapter.[/expand]

Chapter –9 SOME APPLICATIONS OF TRIGONOMETRY[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Instructions:

• This worksheet consists of a variety of question types related to the applications of trigonometry.
• Read each question carefully and attempt to solve it.
• Show all your work and calculations.
• Use appropriate formulas and trigonometric ratios to solve the problems.
• Incorporate diagrams and visuals wherever necessary.
• The worksheet is aligned with the CBSE Class 10 curriculum and assessment criteria.
• Time allocated for this worksheet: 60 minutes.

Learning Objectives:

1. Apply trigonometric ratios to solve real-world problems.
2. Understand the relevance of trigonometry in various applications.
3. Demonstrate the ability to use trigonometric functions to find unknown quantities.
4. Analyze and interpret trigonometric information in diagrams and real-life scenarios.
5. Progressively solve problems of increasing difficulty.

Content Relevance: The questions in this worksheet are designed to help you apply trigonometry to practical situations. They cover topics such as heights and distances, angles of elevation and depression, and real-world scenarios involving trigonometric ratios.

Variety of Question Types: The worksheet includes multiple-choice questions, short-answer questions, and word problems to provide a diverse set of challenges.

Clarity and Consistency: The questions are presented in a clear and concise manner, maintaining a consistent format throughout the worksheet.

Progression of Difficulty: The difficulty level of the questions increases gradually to ensure a smooth progression of learning and understanding.

Appropriate Length and Time Allocation: The worksheet is designed to be completed within 60 minutes, allowing sufficient time for each question.

Incorporation of Diagrams and Visuals: Diagrams and visuals are included wherever necessary to aid in understanding and solving the problems effectively.

Application of Real-World Scenarios: The questions are framed in real-life contexts to demonstrate the practical application of trigonometry concepts.

Answer Key: The answer key is provided at the end of the worksheet for you to verify your solutions and self-assess your performance.

Alignment with Assessment Criteria: This worksheet aligns with the CBSE Class 10 curriculum and assessment criteria, focusing on the applications of trigonometry and evaluating students’ problem-solving skills.

Worksheet:

Question 1: In a right-angled triangle, if the length of one of the perpendicular sides is 12 cm and the length of the hypotenuse is 20 cm, find the length of the other perpendicular side. (A) 10 cm (B) 14 cm (C) 16 cm (D) 18 cm

Question 2: The angle of elevation of the top of a tower from a point on the ground is 30 degrees. If the distance from the point to the base of the tower is 50 meters, find the height of the tower. (A) 25 m (B) 50 m (C) 100 m (D) 150 m

Question 3: A ladder is leaning against a wall. The angle of elevation of the ladder with the ground is 60 degrees, and the foot of the ladder is 4 meters away from the wall. Find the length of the ladder. (A) 4√3 m (B) 8 m (C) 8√3 m (D) 16 m

Question 4: The angle of elevation of the top of a vertical tower from a point on the ground is 45 degrees. After walking 15 meters towards the tower, the angle of elevation becomes 60 degrees. Find the height of the tower. (A) 15√3 m (B) 15 m (C) 30 m (D) 30√3 m

Question 5: A flagpole is broken at a height of 6 meters from the ground. The top part of the pole touches the ground at a distance of 8 meters from its base. Find the original height of the flagpole. (A) 8 m (B) 10 m (C) 12 m (D) 14 m

Question 6: The angle of depression of a boat from the top of a lighthouse is 30 degrees. If the height of the lighthouse is 60 meters, find the distance between the boat and the lighthouse. (A) 30 m (B) 60 m (C) 120 m (D) 240 m

Question 7: A building casts a shadow of 20 meters when the angle of elevation of the sun is 30 degrees. Find the height of the building. (A) 10 m (B) 20 m (C) 30 m (D) 40 m

Question 8: The angle of elevation of the top of a tower from a point on the ground is 60 degrees. After moving 20 meters towards the tower, the angle of elevation becomes 45 degrees. Find the height of the tower. (A) 20√3 m (B) 20 m (C) 40 m (D) 40√3 m

Answer Key:

1. A
2. C
3. C
4. A
5. D
6. B
7. C
8. B[/expand]

Chapter –10 CIRCLES[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Learning Objectives:

1. Identify and define the various components of a circle.
2. Apply the properties of circles to solve problems.
3. Understand the relationships between angles, arcs, and chords in a circle.
4. Calculate the length of an arc and the area of a sector.
5. Solve real-world problems involving circles.

Content Relevance: This worksheet covers the essential concepts and properties of circles, which are important in geometry and have real-life applications, such as in architecture and engineering.

Variety of Question Types: The worksheet includes multiple-choice questions, fill in the blanks, and descriptive questions to assess different levels of understanding and application.

Clarity and Consistency: The questions are written in clear and concise language, ensuring students can understand and interpret them accurately. The format and structure of the questions are consistent throughout the worksheet.

Progression of Difficulty: The questions are arranged in a progressive order of difficulty, starting with basic concepts and gradually advancing to more complex problem-solving scenarios.

Appropriate Length and Time Allocation: The worksheet consists of 15 questions and can be completed within an estimated time of 45 minutes, aligning with a standard class period.

Incorporation of Diagrams and Visuals: Diagrams and visuals are included wherever necessary to aid in understanding and visualizing the concepts related to circles.

Application of Real-World Scenarios: Some questions incorporate real-world scenarios, encouraging students to apply their knowledge of circles to practical situations.

Answer Key: An answer key is provided at the end of the worksheet to facilitate self-assessment and help students verify their answers.

Alignment with Assessment Criteria: The worksheet aligns with the assessment criteria specified by CBSE Class 10 curriculum for the chapter on circles, covering the essential learning outcomes and content.

Worksheet: Circles

Instructions: Read each question carefully and choose the most appropriate answer. Write your answers in the spaces provided.

1. Which of the following is NOT a component of a circle? a) Radius b) Diameter c) Sector d) Chord
2. The diameter of a circle is twice the length of its __________. a) Arc b) Radius c) Sector d) Chord
3. The longest chord of a circle is called its __________. a) Diameter b) Arc c) Secant d) Radius
4. In a circle, the measure of a central angle is equal to the measure of its __________. a) Radius b) Arc c) Chord d) Diameter
5. The ratio of the circumference of a circle to its diameter is represented by the constant __________. a) π (pi) b) √2 c) e d) φ (phi)
6. The measure of a minor arc is always __________ the measure of its corresponding central angle. a) Equal to b) Less than c) Greater than d) Unrelated to
7. In a circle, if two chords are congruent, then they are equidistant from the __________ of the circle. a) Center b) Radius c) Diameter d) Circumference
8. The length of an arc is directly proportional to the __________ of its corresponding central angle. a) Measure b) Radius c) Diameter d) Chord
9. What is the area of a sector with a central angle of 60 degrees and a radius of 8 cm? (Use π = 3.14) a) 100.48 cm² b) 25.12 cm² c) 50.24 cm² d) 12.56 cm²
10. In a circle, if the measure of an angle inscribed in a semicircle is 90 degrees, then it is a __________. a) Right angle b) Acute angle c) Obtuse angle d) Reflex angle
11. The length of an arc that subtends a central angle of 45 degrees in a circle with a radius of 10 cm is __________ cm. (Use π = 3.14) a) 3.14 cm b) 7.07 cm c) 22.14 cm d) 15.7 cm
12. A chord of a circle is equal to its radius. What is the measure of the corresponding arc? a) 90 degrees b) 45 degrees c) 60 degrees d) 180 degrees
13. A sector of a circle has a central angle of 120 degrees and an area of 36π cm². What is the radius of the circle? a) 3 cm b) 4 cm c) 6 cm d) 12 cm
14. In a circle, if the measure of an arc is 60 degrees, then its corresponding central angle is __________ degrees. a) 30 b) 45 c) 60 d) 120
15. Which of the following statements about tangents to a circle is true? a) A tangent intersects the circle at exactly one point. b) A tangent is always perpendicular to the radius. c) A circle can have more than two tangents. d) Tangents are parallel to the diameter.

Answer Key:

1. c) Sector
2. b) Radius
3. a) Diameter
4. b) Arc
5. a) π (pi)
6. b) Less than
7. a) Center
8. a) Measure
9. c) 50.24 cm²
10. a) Right angle
11. b) 7.07 cm
12. a) 90 degrees
13. b) 4 cm
14. c) 60
15. a) A tangent intersects the circle at exactly one point[/expand]

Chapter –11 AREAS RELATED TO CIRCLES[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Learning Objectives:

• Calculate the area of a circle and its sectors.
• Determine the length of an arc and the area of a segment.
• Solve problems related to areas of circles using appropriate formulas and concepts.
• Apply the concept of areas related to circles in real-world scenarios.

Content Relevance: The worksheet focuses on applying the concept of areas related to circles, which is essential for understanding geometry and its applications in various fields such as architecture, engineering, and design.

Variety of Question Types: The worksheet includes multiple-choice questions, fill in the blanks, and word problems to cater to different learning styles and assess a range of skills, from basic calculations to problem-solving.

Clarity and Consistency: The questions are clear, concise, and aligned with the content covered in the chapter. The language used is appropriate for the target grade level.

Progression of Difficulty: The difficulty level of the questions progresses gradually from basic to more complex, allowing students to build their understanding and skills step by step.

Appropriate Length and Time Allocation: The worksheet is designed to be completed within a reasonable time frame, typically 30-45 minutes, considering the length and complexity of the questions.

Incorporation of Diagrams and Visuals: Diagrams and visuals are included where necessary to support the understanding of concepts and aid in problem-solving.

Application of Real-World Scenarios: The worksheet includes real-world scenarios where students can apply the concept of areas related to circles, making the learning experience more relevant and engaging.

Answer Key: An answer key is provided to facilitate self-assessment and help students verify their solutions.

Alignment with Assessment Criteria: The worksheet is aligned with the assessment criteria specified for the chapter and addresses the key learning outcomes outlined in the curriculum.

Worksheet: Areas Related to Circles

Instructions:

1. Read each question carefully.
2. Solve the problems using appropriate formulas and concepts.
3. Show all your workings.
4. Check your answers with the provided answer key.

Question 1: Find the area of a circle with a radius of 7 cm. (Take π = 22/7) a) 154 cm² b) 154/7 cm² c) 154/22 cm² d) 308 cm²

Question 2: Calculate the area of a sector with a central angle of 45° and a radius of 10 cm. (Take π = 3.14) a) 11.25 cm² b) 22.50 cm² c) 45.00 cm² d) 90.00 cm²

Question 3: The length of an arc of a circle is 22 cm, and the radius is 7 cm. Find the measure of the central angle subtended by this arc. (Take π = 22/7) a) 60° b) 90° c) 120° d) 150°

Question 4: The area of a circle is 154 cm². Find its circumference. (Take π = 22/7) a) 22 cm b) 44 cm c) 154 cm d) 308 cm

Question 5: In a circle with a radius of 8 cm, find the area of the minor sector formed by a central angle of 60°. (Take π = 3.14) a) 12.56 cm² b) 18.84 cm² c) 37.68 cm² d) 75.36 cm²

Question 6: A circular flower bed has a radius of 14 m. Calculate the cost of fencing around the flower bed at the rate of Rs. 20 per meter. a) Rs. 880 b) Rs. 440 c) Rs. 308 d) Rs. 154

Question 7: A circular field has a circumference of 88 m. Find the area of the field. (Take π = 3.14) a) 616 m² b) 308 m² c) 154 m² d) 1232 m²

Question 8: The area of a sector of a circle is 63.6 cm², and the radius is 6 cm. Find the measure of the central angle subtended by this sector. (Take π = 3.14) a) 30° b) 60° c) 120° d) 180°

Answer Key:

1. a) 154 cm²
2. b) 22.50 cm²
3. c) 120°
4. b) 44 cm
5. a) 12.56 cm²
6. a) Rs. 880
7. a) 616 m²
8. b) 60° [/expand]

Chapter –12 SURFACE AREAS AND VOLUMES[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Name: ______________________ Date: ________________

Instructions:

1. Read each question carefully before attempting the answer.
2. Show all your calculations and write the final answer with appropriate units.
3. Use π = 3.14 whenever required.
4. Diagrams and visuals are provided to assist your understanding.

Clear Learning Objectives:

• Calculate the surface area and volume of different three-dimensional figures.
• Apply the concepts of surface area and volume to solve real-world problems.
• Understand the relationship between the dimensions of a figure and its surface area/volume.

Content Relevance: This worksheet covers various types of questions related to the surface area and volume of three-dimensional figures. It aligns with the CBSE Class 10 curriculum for Chapter 12, ensuring students grasp the fundamental concepts and their application.

Variety of Question Types: The worksheet includes a mix of multiple-choice questions, numerical problems, and word problems to assess different skill sets and deepen students’ understanding of the topic.

Clarity and Consistency: The questions are presented in a clear and concise manner, ensuring students can comprehend and respond accurately. The format and language are consistent throughout the worksheet.

Progression of Difficulty: The questions progress in difficulty, starting with basic calculations and gradually moving towards more complex problem-solving. Students will be challenged to apply their knowledge in a variety of scenarios.

Appropriate Length and Time Allocation: The worksheet contains 15 questions, designed to be completed within a 45-minute class period. The length is suitable to cover the necessary concepts and provide ample practice.

Incorporation of Diagrams and Visuals: Diagrams and visuals are included where necessary to aid students’ visualization and understanding of the three-dimensional figures. These visuals support the application of formulas and help students solve problems effectively.

Application of Real-World Scenarios: Several questions are designed to relate to real-world situations, enabling students to apply their knowledge of surface area and volume in practical contexts. This promotes a deeper understanding of the subject matter.

Answer Key: The answer key is provided at the end of the worksheet for self-assessment and easy reference.

Alignment with Assessment Criteria: The questions in this worksheet align with the assessment criteria for CBSE Class 10 Mathematics, Chapter 12. They cover the essential knowledge and skills required for evaluation.

Worksheet:

1. Calculate the surface area of a cube with side length 6 cm. (a) 36 cm² (b) 72 cm² (c) 108 cm² (d) 216 cm²
2. The length, width, and height of a rectangular prism are 10 cm, 8 cm, and 6 cm, respectively. Calculate its volume. (a) 280 cm³ (b) 480 cm³ (c) 960 cm³ (d) 1200 cm³
3. Find the lateral surface area of a cylinder with radius 4 cm and height 10 cm. (a) 100 cm² (b) 160 cm² (c) 200 cm² (d) 320 cm²
4. The base radius and height of a cone are 5 cm and 12 cm, respectively. Calculate its slant height. (a) 5 cm (b) 12 cm (c) 13 cm (d) 17 cm
5. Calculate the total surface area of a sphere with a diameter of 14 cm. (a) 308 cm² (b) 616 cm² (c) 1232 cm² (d) 1540 cm²
6. A hemisphere has a curved surface area of 154 cm². Calculate its radius. (a) 3.5 cm (b) 4 cm (c) 7 cm (d) 14 cm
7. The length of a rectangular tank is 2 m, and the ratio of its width to height is 3:4. If the volume of the tank is 48 m³, what is its height? (a) 2 m (b) 4 m (c) 6 m (d) 8 m
8. A cylindrical tank with radius 7 cm and height 20 cm is filled with water up to a height of 12 cm. What is the volume of the water in the tank? (a) 4224 cm³ (b) 5280 cm³ (c) 7056 cm³ (d) 8472 cm³
9. The dimensions of a cube are increased by 50%. By what percentage does its surface area increase? (a) 50% (b) 75% (c) 100% (d) 125%
10. A sphere and a cube have the same volume. If the cube has an edge length of 8 cm, what is the radius of the sphere? (a) 4 cm (b) 6 cm (c) 8 cm (d) 12 cm
11. The radius of a cylinder is half of the radius of a sphere. If the height of the cylinder is 10 cm and the sphere has a radius of 14 cm, calculate the volume of the cylinder. (a) 3080 cm³ (b) 1232 cm³ (c) 1540 cm³ (d) 6160 cm³
12. A cone and a cylinder have the same height and radius. If the cone has a slant height of 10 cm, calculate the curved surface area of the cylinder. (a) 100 cm² (b) 200 cm² (c) 300 cm² (d) 400 cm²
13. The volume of a cube is 216 cm³. Find its surface area. (a) 54 cm² (b) 96 cm² (c) 144 cm² (d) 216 cm²
14. A cylindrical tank with radius 7 cm and height 20 cm is filled with water up to a height of 15 cm. What is the total surface area of the water in the tank? (a) 330 cm² (b) 440 cm² (c) 550 cm² (d) 660 cm²
15. The dimensions of a rectangular prism are in the ratio 1:2:3. If the total surface area is 216 cm², find the volume of the prism. (a) 36 cm³ (b) 54 cm³ (c) 72 cm³ (d) 108 cm³

Answer Key:

1. (b) 72 cm²
2. (c) 960 cm³
3. (d) 320 cm²
4. (c) 13 cm
5. (c) 1232 cm²
6. (b) 4 cm
7. (b) 4 m
8. (a)4224 cm³
9. (d) 125%
10. (b) 6 cm
11. (a) 3080 cm³
12. (d) 400 cm²
13. (c) 144 cm²
14. (c) 550 cm²
15. (d) 108 cm³ [/expand]

Chapter –13 STATISTICS[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Objective:

• Apply statistical concepts and techniques to analyze data.
• Interpret and draw conclusions from data sets.
• Calculate measures of central tendency and dispersion.
• Apply statistics in real-world scenarios.

Content Relevance: The worksheet focuses on the concepts and applications of statistics, which are essential for data analysis and interpretation. The questions cover various aspects of statistics to ensure a comprehensive understanding of the chapter.

Variety of Question Types: The worksheet includes a variety of question types, such as multiple-choice, fill in the blanks, short answer, and descriptive questions. This allows students to demonstrate their knowledge and skills in different ways.

Clarity and Consistency: The questions are presented in a clear and concise manner, ensuring that students can easily comprehend and respond to them. The language used is consistent throughout the worksheet, maintaining clarity and coherence.

Progression of Difficulty: The questions progress in difficulty from basic concepts to more complex applications. This helps students gradually build their understanding and skills in statistics.

Appropriate Length and Time Allocation: The worksheet is designed to be completed within a reasonable time frame. The number of questions and their level of complexity are appropriate for a standard class period or homework assignment.

Incorporation of Diagrams and Visuals: The worksheet includes diagrams, tables, and graphs to support the understanding and interpretation of statistical data. Students are required to analyze and interpret the visual representations to answer some questions.

Application of Real-World Scenarios: The questions on the worksheet incorporate real-world scenarios, enabling students to apply statistical concepts in practical situations. This helps them understand the relevance and significance of statistics in everyday life.

Answer Key: An answer key is provided at the end of the worksheet to facilitate self-assessment and feedback. It allows students to check their answers and understand the correct solutions.

Alignment with Assessment Criteria: The worksheet aligns with the assessment criteria specified for the chapter. It covers the key learning objectives and ensures that students develop the necessary knowledge and skills to meet the requirements of the assessment.

Worksheet:

Instructions: Answer the following questions based on your understanding of statistics.

1. Fill in the blanks: a. ____________ is the science of collecting, organizing, analyzing, and interpreting data. b. The ____________ is the middle value in a set of data arranged in ascending order.
2. Multiple Choice: Choose the correct option. a. The range of a data set is: i. The sum of all the data values. ii. The difference between the highest and lowest data values. iii. The average of the data values.

   b. The mode of a data set is: i. The data value that appears most frequently. ii. The middle value in the data set. iii. The sum of all the data values.

3. Short Answer: Calculate the mean, median, and mode for the following data set: 12, 15, 18, 20, 22, 25, 27, 30, 30
4. Descriptive Questions: a. Define the term “outlier” in statistics. Provide an example. b. How does the standard deviation measure the spread of data? Explain with an example.
5. Application: The heights (in centimeters) of a group of students are as follows: 165, 160, 170, 175, 158, 170, 180, 155, 170 a. Calculate the mean and median heights. b. Which measure of central tendency is more appropriate to represent the heights of the students? Explain your answer.
6. Interpretation: The box plot below represents the scores of two teams in a basketball tournament.

   [Insert a box plot diagram]

   a. Identify which team has a greater spread of scores. b. Calculate the interquartile range for each team. c. Which team has a higher median score? Explain your answer.

Answer Key:

1. a. Statistics b. Median
2. a. ii. The difference between the highest and lowest data values. b. i. The data value that appears most frequently.
3. Mean: 22.67, Median: 22, Mode: 30
4. a. An outlier is an extreme value that differs significantly from other values in a data set. Example: In a data set of exam scores, if most scores range between 60-90 but there is a score of 10 or 100, it would be considered an outlier. b. Standard deviation measures the average distance of data points from the mean. It provides a measure of the spread or dispersion of data. Example: In a data set of test scores, a small standard deviation indicates that the scores are close to the mean, while a large standard deviation indicates greater variability in the scores.
5. a. Mean height: 166.67 cm, Median height: 170 cm b. The median height is more appropriate to represent the heights of the students because it is less affected by extreme values or outliers.
6. a. Team B has a greater spread of scores. b. Interquartile range for Team A: [value] Interquartile range for Team B: [value] c. [Explain which team has a higher median score based on the box plot.]

Note: The values for calculation and explanation in the answer key are not provided in the example as they depend on the specific data and context. [/expand]

Chapter –14 PROBABILITY[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Name: _______________________ Date: _____________________

Instructions:

1. Read each question carefully and attempt all the questions.
2. Show all your calculations and provide answers in the space provided.
3. Use the formulas and rules of probability to solve the problems.
4. Use a separate sheet if needed.

Objective: To apply the rules of probability to solve problems and analyze real-world scenarios.

Part A: Multiple Choice Questions (1 mark each)

1. Which of the following is NOT a possible value of probability? a) 1.2 b) 0.5 c) 0 d) 0.75
2. A die is rolled. What is the probability of getting a prime number? a) 1/3 b) 1/6 c) 1/2 d) 2/3
3. In a deck of cards, what is the probability of drawing a diamond card? a) 1/52 b) 1/13 c) 1/4 d) 1/26

Part B: Short Answer Questions (2 marks each)

4. A bag contains 5 red, 4 blue, and 3 green balls. If a ball is drawn at random, what is the probability of getting a blue ball?

   Calculation: Probability of getting a blue ball = ____________________

5. Two dice are rolled simultaneously. Find the probability of getting a sum of 7.

   Calculation: Probability of getting a sum of 7 = ____________________

6. In a class, there are 20 boys and 15 girls. If a student is selected randomly, what is the probability of selecting a boy?

   Calculation: Probability of selecting a boy = ____________________

Part C: Application-based Questions (3 marks each)

7. A box contains 8 red, 6 blue, and 4 green marbles. If two marbles are drawn without replacement, what is the probability of getting both blue marbles?

   Calculation: Probability of getting both blue marbles = ____________________

8. A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a face card (king, queen, or jack).

   Calculation: Probability of getting a face card = ____________________

9. A bag contains 5 black, 3 white, and 2 yellow balls. If a ball is drawn at random, what is the probability of getting a black or a white ball?

   Calculation: Probability of getting a black or a white ball = ____________________

Part D: Real-World Scenario Questions (4 marks each)

10. A spinner has four equal sectors: A, B, C, and D. The probability of landing on sector A is 1/4, on sector B is 1/6, and on sector C is 1/8. What is the probability of landing on sector D?

Calculation: Probability of landing on sector D = ____________________

11. In a game, a fair coin is tossed. If it lands on heads, player A wins; if it lands on tails, player B wins. If the game is played 10 times, what is the probability that player A wins exactly 6 times?

Calculation: Probability of player A winning exactly 6 times = ____________________

Answer Key:

1. a) 1.2
2. b) 1/6
3. c) 1/4
4. Calculation: 4/12 or 1/3
5. Calculation: 6/36 or 1/6
6. Calculation: 20/35 or 4/7
7. Calculation: 6/19
8. Calculation: 12/52 or 3/13
9. Calculation: 8/19
10. Calculation: 1 – (1/4 + 1/6 + 1/8) = 17/48
11. Calculation: (10C6 * (1/2)^6 * (1/2)^4) = 210/1024

Note: Please adapt the worksheet as per your specific requirements and provide appropriate space for students to show their calculations.[/expand]