CHAPTER–1 NUMBER SYSTEMSRead More➔ Worksheet: Number Systems Instructions: Section A: Multiple Choice Questions Which of the following numbers is a rational number? a) √2 b) -5 c) 0.333… d) π Identify the type of the number: -3 a) Natural number b) Whole number c) Integer d) Rational number Convert the recurring decimal 0.333… into a fraction. a) 1/3 b) 1/6 c) 3/9 d) 3/10 Section B: Short Answer Questions Classify the following numbers as rational or irrational: a) 5/7 b) √5 c) -3.14 d) 0.25 (1/4) Plot the following numbers on the number line: a) -2 b) 0 c) 3.5 d) √2 Section C: Application Problems The temperature at a location decreases from 15°C to -5°C. Find the change in temperature. A rectangular field is 45 meters long and 30 meters wide. Find the length of the longest rope that can be used to fence the entire field. The sum of three consecutive odd numbers is 63. Find the numbers. Section D: HOTS (Higher Order Thinking Skills) Questions Prove that √3 is an irrational number. Simplify: (4√3 + √12) / (2√2) Section E: Real-Life Application Answer Key: (Note: Provide the answer key separately to students or use it for grading purposes) Remember to format the worksheet in a visually appealing manner, and you can include relevant images or diagrams to aid comprehension if needed.
CHAPTER–2 POLYNOMIALSRead More➔ Worksheet: Polynomials Instructions: Section A: Multiple Choice Questions Which of the following expressions is a polynomial? a) 5x + 2/x b) 3x^2 – 2x + 5 c) 2x^2 – √x d) x^3 – 1/x What is the degree of the polynomial 2x^3 – 5x^2 + 3x – 1? a) 3 b) 2 c) 4 d) 1 The sum of the coefficients of the polynomial (4x – 1)(3x^2 + 2x – 5) is: a) 6 b) 9 c) 3 d) 0 Section B: Fill in the Blanks The highest power of the variable in a polynomial is called its ___________. The polynomial with three terms is called a ___________. The product of a polynomial and a monomial results in a ___________. Section C: Short Answer Questions Identify the degree and coefficient(s) of the term 7xy^2 in the polynomial 3x^2y + 5xy^2 – 2xy + 1. Perform the following operations: (2x^2 – 3x + 1) + (3x^2 + 2x – 4). Factorize the polynomial 6x^2 + 11x + 4. The area of a rectangular field is given by the polynomial 2x^2 + 5x – 3. Find the length and width of the field if its dimensions are in meters. Section D: Application-Based Questions A car rental agency charges a fixed fee of Rs. 500 per day and an additional Rs. 15 per kilometer traveled. Express the total cost (C) as a polynomial in terms of the number of kilometers (x) traveled in a day. The sum of two numbers is 20, and their product is 96. Express the two numbers as the roots of a quadratic polynomial equation. Answer Key: Section A: Section B: 4. degree Section C: 7. Degree: 3; Coefficients: 7 and 1 Section D: 11. C(x) = 15x + 500 Please note that the answers provided in the answer key are for reference purposes. Ensure that the students show their work and provide clear explanations where required. Also, you can add more questions or modify the difficulty level based on the needs and abilities of your students
CHAPTER–3 COORDINATE GEOMETRYRead More➔ Worksheet: Coordinate Geometry Instructions: Read the questions carefully. Plot the given points on the coordinate plane. Use the distance formula to calculate the distance between two points. Use the midpoint formula to find the midpoint of a line segment. Show all the calculations and steps clearly. This worksheet is to be completed individually. Plot the following points on the coordinate plane: a) A(2, 3) b) B(-4, 1) c) C(0, 0) d) D(5, -2) Calculate the distance between the following pairs of points: a) P(3, 4) and Q(7, 1) b) R(-2, 6) and S(-5, -3) c) T(0, 0) and U(8, 15) d) V(-6, -9) and W(10, 12) Find the midpoint of each line segment: a) AB with A(2, 3) and B(8, 9) b) CD with C(-1, 4) and D(5, -2) c) EF with E(0, 0) and F(6, -6) d) GH with G(-3, 2) and H(3, -4) In a rectangular park, the coordinates of two corners are (0, 0) and (12, 8). Find the coordinates of the other two corners. The vertices of a triangle are A(3, 2), B(-1, 4), and C(5, -1). Determine the perimeter of the triangle. A line segment has endpoints P(-2, 3) and Q(6, -4). Find the point on the segment that divides it in the ratio 2:3. On a coordinate plane, plot the points A(4, 7), B(7, -3), C(-2, 6), and D(-5, -4). Join the points to form a quadrilateral. Is the quadrilateral a square? Give reasons for your answer. In a city map, the location of the school is marked at coordinates (10, 5) and the library at coordinates (4, 8). How far is the school from the library? The coordinates of two opposite vertices of a square are given as (-3, 5) and (5, 5). Find the coordinates of the other two vertices. Find the midpoint of the line segment joining the points (2, 1) and (-4, 7). Also, find the distance between these two points. Note: The above worksheet is designed to assess students’ understanding of coordinate geometry concepts, including plotting points, calculating distances, finding midpoints, and applying the concepts to real-life scenarios.
CHAPTER–4 LINEAR EQUATIONS IN TWO VARIABLESRead More➔ Name: _______________________ Date: ______________ Instructions: Attempt all the questions. Show all your work and calculations clearly. Write the equations of lines in slope-intercept form (y = mx + b) wherever possible. Graph the lines on the provided coordinate grid. Check your answers wherever possible. The worksheet is worth 20 marks. Solve the following linear equations in two variables: a) 2x + 3y = 8 b) 5x – 2y = 7 c) 4y = 12 – 3x d) 3(x – 2) = 2(y + 4) Graph the following linear equations on the coordinate plane: a) y = 2x + 3 b) 3x + y = 5 c) y = -2x – 1 d) 2y + 4 = 8 – x Write the equations of the following lines in slope-intercept form (y = mx + b): a) Line passing through (2, 5) and (4, 9) b) Line parallel to y = 3x + 2 and passing through the point (1, 7) c) Line perpendicular to y = -2x + 5 and passing through the point (-3, 2) Solve the word problems: a) The sum of two numbers is 15. Their difference is 3. Find the numbers. b) The length of a rectangle is 5 meters more than its width. The perimeter of the rectangle is 54 meters. Find its length and width. c) The cost of 4 pens and 5 pencils is Rs. 67, while the cost of 7 pens and 10 pencils is Rs. 112. Find the cost of one pen and one pencil. Graph the system of linear equations and find the point of intersection (if any): a) y = x – 3 y = -2x + 4 b) 2x + y = 5 y = 3x + 1 Solve the following system of equations using the method of your choice: a) 3x + 2y = 14 5x – y = 9 b) 2(x + y) = 10 3x – 2y = 4 The cost of 2 kg of apples and 3 kg of oranges is Rs. 140. The cost of 5 kg of apples and 4 kg of oranges is Rs. 260. Find the cost per kg of each fruit. Coordinate Grid: (Use the space below for graphing the lines in question 2 and 5) Please note that this is a sample worksheet, and the complexity and number of questions can be adjusted based on the level of students’ understanding and the time available for the assessment. The questions cover a range of topics, including solving linear equations, graphing lines, finding slopes, and solving word problems involving linear equations in two variables.
CHAPTER–5 INTRODUCTION TO EUCLID’S GEOMETRYRead More➔ Worksheet: Introduction to Euclid’s Geometry Instructions: Define the following terms: a) Point b) Line c) Line Segment d) Ray State Euclid’s First Postulate and provide an example illustrating it. Write down Euclid’s Third Postulate and explain its significance in geometry. Identify the number of dimensions for each of the following: a) Point b) Line c) Plane d) Solid Draw a line segment AB of length 6 cm. Using a compass, construct a line segment CD of the same length. Construct an equilateral triangle XYZ with each side measuring 5 cm. Given: Triangle PQR with angle PRQ = 90° and PQ = 8 cm, QR = 6 cm. Using the Pythagorean theorem, find the length of side PR. Prove that the sum of the angles in any triangle is 180°. In the diagram below, find the value of angle x: (Insert a diagram of two parallel lines cut by a transversal, with angle x marked) Using Euclid’s axioms and postulates, prove that the opposite sides of a rectangle are equal and parallel. A circular garden has a radius of 7 meters. Calculate the area of the garden. Find the perimeter of a regular hexagon with each side measuring 12 cm. Note: The answers to these questions may vary depending on the approach used by the students. Provide appropriate marks for each question, and make sure to include sufficient space for the students to write their answers.
CHAPTER–6 LINES AND ANGLESRead More➔ Worksheet: Lines and Angles Name: ___________________________________ Date: _______________ Instructions: Section A: Multiple Choice Questions Which of the following types of lines will never intersect? a) Parallel lines b) Perpendicular lines c) Intersecting lines d) None of the above The sum of the angles of a triangle is: a) 90 degrees b) 180 degrees c) 270 degrees d) 360 degrees What is the measure of a straight angle? a) 90 degrees b) 180 degrees c) 270 degrees d) 360 degrees Identify the type of angle shown below: [Image with an acute angle] a) Acute angle b) Obtuse angle c) Right angle d) Straight angle Section B: Short Answer Questions Define parallel lines and give an example from real-life situations. If the measure of one angle of a triangle is 60 degrees, and another angle is a right angle, what is the measure of the third angle? Draw an obtuse angle and bisect it using a compass and ruler. Name the bisected angle. Section C: Long Answer Questions In a quadrilateral ABCD, ∠A = 70°, ∠B = 110°, and ∠C = 80°. Find the measure of ∠D. Draw two intersecting lines and label the point of intersection as O. Name four pairs of vertically opposite angles in the figure. A flagpole casts a shadow of 15 meters long on the ground when the angle of elevation of the sun is 60 degrees. Find the height of the flagpole. Section D: Problem Solving In a right-angled triangle XYZ, ∠Y = 90°. If the measure of ∠X is three times the measure of ∠Z, find the measure of each angle. A line segment AB measures 8 cm. Using a ruler and compass, construct a perpendicular bisector of AB and name the point of intersection as O. Section E: Justification and Proof Prove that the opposite sides of a parallelogram are equal. Using the angle sum property of a triangle, prove that the sum of the angles of a triangle is 180 degrees. Section F: True or False Two obtuse angles can be supplementary. (True/False) All right angles are congruent. (True/False) Section G: Practical Application Note:
[Image with two parallel lines AB and CD, with transversal EF intersecting them, forming angles ∠A, ∠B, ∠C, ∠D, and ∠E]
CHAPTER–7 TRIANGLESRead More➔ Worksheet: Triangles Name: ___________________ Date: ________________ Instructions: 1. Identify the Triangle: Classify each triangle based on its angles and sides. Write “Acute,” “Obtuse,” “Right-angled,” “Equilateral,” “Isosceles,” or “Scalene” in the blanks provided. a) Triangle ABC with ∠A = 70°, ∠B = 60°, ∠C = 50°. Type: _______________ b) Triangle PQR with PQ = QR = PR. Type: _______________ c) Triangle XYZ with ∠X = 90°, XY = XZ. Type: _______________ 2. Triangle Properties: Using the given information, solve the following problems: a) In triangle DEF, ∠D = 50° and ∠E = 70°. Find ∠F. ∠F = ___________ degrees. b) In triangle LMN, LM = MN, and ∠M = 40°. Find ∠N. ∠N = ___________ degrees. c) If the angles of a triangle are in the ratio 2:3:4, find the measures of the angles. ∠A = ___________ degrees ∠B = ___________ degrees ∠C = ___________ degrees 3. Applying Triangle Inequality: Determine whether the following side lengths form a valid triangle. Write “Yes” or “No” in the blanks provided. a) Side lengths: 5 cm, 8 cm, 15 cm. Valid Triangle: ___________ b) Side lengths: 3 cm, 4 cm, 7 cm. Valid Triangle: ___________ 4. Constructing Triangles: Use a ruler and compass to construct the following triangles. Clearly label the steps. a) Construct a triangle PQR with PQ = 6 cm, QR = 5 cm, and ∠P = 75°. b) Construct a triangle XYZ with XY = 4 cm, ∠X = 45°, and ∠Y = 75°. 5. Area of a Triangle: Calculate the area of the following triangles: a) Triangle ABC with base AB = 8 cm and height CD = 5 cm. Area = ___________ square cm. b) Triangle XYZ with base XY = 12 cm and height ZW = 9 cm. Area = ___________ square cm. 6. Problem-Solving: Solve the following problems: a) The measure of the third angle of a triangle is 20° less than the sum of the other two angles. If one of the angles is 60°, find the measure of the third angle. Third angle = ___________ degrees. b) In triangle MNO, ∠M = 40°, and ∠N = 80°. Find the measure of ∠O. ∠O = ___________ degrees. 7. Real-Life Applications: Find and draw an example of a right-angled triangle from your surroundings. Label the sides and angles. Triangle Name: ________________ Side Lengths: ______________________ Note: Diagrams and figures are not to scale. Answer Key: a) Obtuse b) Equilateral c) Right-angled a) ∠F = 60° b) ∠N = 70° c) ∠A = 40°, ∠B = 60°, ∠C = 80° a) No b) Yes a) (Steps will be provided by the student) b) (Steps will be provided by the student) a) Area = 20 square cm b) Area = 54 square cm a) Third angle = 80° b) ∠O = 60° Note: This is a sample worksheet template. Please add visual elements and formatting as required to make it suitable for classroom use.
CHAPTER–8 QUADRILATERALSRead More➔ Title: Quadrilaterals Worksheet Instructions: Read the questions carefully. Show all your work and calculations. Justify your answers with proper reasoning wherever required. Write the answers in the space provided. Use a ruler and protractor for accurate measurements. Classify the following quadrilaterals based on their properties: a) Parallelogram or not: [2] i) ABCD with AB || CD and AD = BC ii) PQRS with PQ || SR and PS = SR b) Rectangle or not: [2] i) WXYZ with WX = 8 cm and WY = 6 cm ii) ABCD with ∠A = 90° and AD = 10 cm c) Square or not: [2] i) EFGH with EF = 7 cm and ∠E = 90° ii) MNOP with NO = 5 cm and ∠N = 90° Calculate the value of ‘x’ in the following quadrilaterals: [3] a) In quadrilateral LMNO, ∠L = 70°, ∠M = 100°, and ∠O = x°. b) In quadrilateral PQRS, ∠P = 80°, ∠Q = 2x°, and ∠R = 3x°. Given that ABCD is a parallelogram with AB = 8 cm, BC = 12 cm, and ∠B = 110°, find the length of AD. [3] In quadrilateral PQRS, PQ = 6 cm, QR = 8 cm, ∠Q = 110°, and ∠R = 70°. Determine the length of the diagonal PS. [3] The diagonals of quadrilateral LMNO intersect at point X. If LX = 4 cm, MX = 6 cm, and NO = 10 cm, find the length of XO. [3] A kite KLMN has diagonals KL = 10 cm and MN = 12 cm. Find the length of the sides KM and LN. [4] The lengths of the sides of a trapezium PQRS are: PQ = 8 cm, QR = 12 cm, PS = 15 cm, and ∠P = 90°. Find the length of the side RS. [4] The perimeter of a quadrilateral ABCD is 48 cm. If AB = 10 cm, BC = 12 cm, and AD = 8 cm, find the length of side CD. [4] Solve the following word problem: [5] The lengths of the sides of a rhombus are 5 cm, 5 cm, 10 cm, and 10 cm. Find the length of its diagonals and the measures of its angles. Challenge Question (Optional): [5] In the quadrilateral ABCD, AB || CD, and AD = 5 cm, BC = 8 cm, ∠A = 40°, and ∠D = 130°. Find the measures of ∠B and ∠C, and determine the type of quadrilateral ABCD. Answer Key: a) i) Parallelogram; ii) Not a parallelogram b) i) Rectangle; ii) Not a rectangle c) i) Square; ii) Not a square a) x = 110° b) x = 20°, ∠P = 80°, ∠Q = 40°, ∠R = 60° AD = 8 cm PS = 8 cm XO = 8 cm KM = 8 cm, LN = 6 cm RS = 9 cm CD = 18 cm Diagonals: 14 cm, Angles: 90°, 90°, 90°, 90° ∠B = 40°, ∠C = 70°, Quadrilateral ABCD is a parallelogram. Note: The challenge question is optional and can be used to extend the learning for advanced students.
CHAPTER–9 CIRCLESRead More➔ Worksheet: Circles Name: ___________________________ Class: 9 Date: _______________________ Instructions: A Measure of arc AB = ______ degrees Two circles have radii of 3 cm and 5 cm, respectively. Find the distance between their centers if they are concentric circles. Distance between centers = ______ cm A circular garden has a circumference of 88 meters. Find the area of the garden. (Take π = 22/7) Area = ______ square meters A wheel of a bicycle has a diameter of 70 cm. How many complete revolutions will the wheel make to cover a distance of 154 meters? (Take π = 22/7) Number of revolutions = ______ In the figure below, O is the center of the circle. If ∠ACB = 50°, find the measure of angle AOB. A Measure of ∠AOB = ______ degrees The circumference of a circle is equal to the perimeter of a square. If the circle has a radius of 7 cm, find the side length of the square. (Take π = 3.14) Side length of the square = ______ cm Find the length of a chord in a circle with a radius of 10 cm and a distance of 5 cm from the center of the circle. Chord length = ______ cm A circular park has a diameter of 42 meters. Find the area of the park. (Take π = 22/7) Area = ______ square meters In the figure below, O is the center of the circle. If ∠ACB = 110°, find the measure of angle AOB. A Measure of ∠AOB = ______ degrees Note: You can add or modify the questions based on the topics covered in the chapter and the level of complexity suitable for your class. Make sure to provide enough space for students to show their work and calculations.
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CHAPTER–10 HERON’S FORMULARead More➔ Name: ___________________ Date: _________________ Class: 9 Subject: Mathematics Chapter: 10 – Heron’s Formula Instructions: Attempt all questions. Show all the steps of calculations. All answers should be in proper units. Find the area of the following triangles using Heron’s Formula: a) Triangle ABC has side lengths: AB = 8 cm, BC = 6 cm, AC = 10 cm. Area = ___________________ b) Triangle XYZ has side lengths: XY = 5 cm, YZ = 12 cm, ZX = 13 cm. Area = ___________________ c) Triangle PQR has side lengths: PQ = 7 cm, QR = 9 cm, RP = 12 cm. Area = ___________________ The sides of a triangle are given below. Determine whether the triangle is acute, obtuse, or right-angled. Use Heron’s Formula to find the area in each case. a) Side lengths: 5 cm, 7 cm, 8 cm Type of Triangle: ________________ Area = ___________________ sq. cm b) Side lengths: 9 cm, 12 cm, 15 cm Type of Triangle: ________________ Area = ___________________ sq. cm c) Side lengths: 4 cm, 7 cm, 9 cm Type of Triangle: ________________ Area = ___________________ sq. cm The sides of a triangle are in the ratio 3:4:5, and its perimeter is 144 cm. Use Heron’s Formula to find the area of the triangle. Area = ___________________ sq. cm The sides of a triangle are given as a = 12 cm, b = 20 cm, and c = 24 cm. Find the area of the triangle using Heron’s Formula. Area = ___________________ sq. cm The sides of a triangle are 7 cm, 8 cm, and x cm. If the area of the triangle is 24 sq. cm, find the value of x. x = ___________________ cm The perimeter of an isosceles triangle is 40 cm, and its two equal sides are 12 cm each. Find the area of the triangle using Heron’s Formula. Area = ___________________ sq. cm The area of an equilateral triangle is 36√3 sq. cm. Find the length of one side. Side length = ___________________ cm A triangular park has sides measuring 90 m, 72 m, and 50 m. A gardener has to sow grass in this park. Calculate the cost of sowing grass at the rate of ₹20 per square meter. Cost = ___________________ ₹ A triangle has sides of length 10 cm, 12 cm, and 16 cm. Determine whether it is possible to form a triangle with these side lengths. If yes, find the area using Heron’s Formula. Area = ___________________ sq. cm The sides of a triangle are given below. Use Heron’s Formula to find the area of the triangle. a = 15 cm, b = 17 cm, c = 8 cm Area = ___________________ sq. cm Answers: a) Area = 24 sq. cm b) Area = 30 sq. cm c) Area = 26.83 sq. cm a) Acute-angled triangle Area = 17.32 sq. cm b) Right-angled triangle Area = 54 sq. cm c) Obtuse-angled triangle Area = 13.42 sq. cm Area = 216 sq. cm Area = 96 sq. cm x = 10 cm Area = 64.56 sq. cm Side length = 12 cm Cost = ₹3600 It is possible to form a triangle. Area = 48 sq. cm Area = 60 sq. cm (Note: The answers are provided for reference and may vary depending on the accuracy of calculations.)
CHAPTER–11 SURFACE AREAS AND VOLUMESRead More➔ Name: _______________________ Date: ________________________ Instructions: Find the lateral surface area and total surface area of a cube whose edge measures 6 cm. (2 marks) The dimensions of a rectangular box are 10 cm, 6 cm, and 4 cm. Calculate its volume and total surface area. (3 marks) The height of a cylinder is 14 cm, and the radius of its base is 7 cm. Find the volume and curved surface area of the cylinder. (4 marks) A sphere has a diameter of 14 cm. Calculate its volume and total surface area. (4 marks) A cylindrical water tank has a radius of 5 meters and a height of 10 meters. Determine the volume of water (in liters) the tank can hold. (3 marks) The base radius of a cone is 8 cm, and its slant height is 17 cm. Calculate the total surface area and the volume of the cone. (5 marks) A cylindrical container has a diameter of 12 cm and a height of 15 cm. If it is full of water, find the capacity of the container in liters (1 liter = 1000 cm³). (3 marks) The given figure is a cube. Calculate its volume. (2 marks) A solid metal cone with a base radius of 6 cm and height 10 cm is melted to form a sphere. Calculate the radius of the sphere. (4 marks) A toy rocket is in the shape of a cylinder surmounted by a cone. The total height of the rocket is 36 cm, and the radius of the base of the cone is 5 cm. If the rocket is painted with red color, the cost of painting is Rs. 60 per 100 cm². Find the total cost of painting the rocket. (5 marks) Total Marks: ________ Please submit your answers to the respective questions after completing the worksheet. Good luck!
CHAPTER–12 STATISTICSRead More➔ Name: ______________________ Date: ______________________ Instructions: Solve the following questions related to statistics. Given the following data, find the mean, median, and mode: 12, 15, 18, 21, 25, 12, 21, 18, 15, 12, 25, 21, 12 Mean: ___________ Median: ___________ Mode: ___________ The heights (in cm) of 10 students in a class are as follows: 165, 158, 172, 160, 168, 155, 160, 175, 170, 165 a) Calculate the mean height of the students. Mean: ___________ b) Find the median height of the students. Median: ___________ The ages (in years) of children attending a summer camp are as follows: 8, 9, 10, 11, 12, 9, 10, 12, 8, 10, 11, 9, 8 a) Calculate the mode of the ages of the children. Mode: ___________ b) Find the range of the ages (highest age – lowest age). Range: ___________ The data shows the number of goals scored by a soccer team in its last 10 matches: 2, 1, 3, 0, 4, 2, 3, 1, 0, 2 a) Calculate the mean number of goals scored per match. Mean: ___________ b) Represent the data using a bar graph. The test scores (out of 20) of a class of 30 students in Mathematics are given below: 15, 18, 14, 16, 17, 12, 20, 13, 19, 17, 10, 16, 15, 18, 19, 11, 12, 13, 14, 15, 16, 17, 18, 14, 15, 16, 17, 18, 19, 20 a) Calculate the mode of the test scores. Mode: ___________ b) Represent the data using a histogram with appropriate class intervals. The marks obtained (out of 50) by 25 students in a Science test are as follows: 42, 34, 48, 39, 41, 37, 46, 50, 43, 36, 40, 45, 48, 49, 38, 44, 40, 47, 50, 36, 45, 49, 50, 42, 37 a) Calculate the mean marks scored by the students. Mean: ___________ b) Find the median of the marks. Median: ___________ c) Determine the mode of the marks. Mode: ___________ From the following data on the number of students in various extracurricular activities, calculate the mean and mode: Drama Club: 20 students Music Club: 15 students Chess Club: 12 students Art Club: 20 students Dance Club: 18 students Mean: ___________ Mode: ___________ The following data represents the number of hours spent by students on their smartphones in a day: 4, 5, 2, 6, 3, 5, 4, 2, 5, 3 a) Calculate the mean number of hours spent on smartphones. Mean: ___________ b) Find the mode of the data. Mode: ___________ Remember to show all the steps and workings in your calculations. Best of luck! (Note: The questions in this worksheet are created for educational purposes only and may not reflect the actual CBSE examination pattern. The numbers and examples used are fictional.)