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CBSE Class 10 Sample / Model Paper 2024 : Mathematics

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Sanjay Sharma
St. Francis ICSE School, Chamrajanagar
12 mathematics
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CBSE ADDITIONAL PRACTICE QUESTIONS MATHEMATICS STANDARD (041) Class X | 2023 24 Time allowed: 3 Hours Maximum marks: 80 General Instructions: 1. This Question paper contains - five sections A, B, C, D and E. 2. Section A has 18 MCQs and 02 Assertion-Reason based questions of 1 mark each. 3. Section B has 5 Very Short Answer (VSA)-type questions of 2 marks each. 4. Section C has 6 Short Answer (SA)-type questions of 3 marks each. 5. Section D has 4 Long Answer (LA)-type questions of 5 marks each. 6. Section E has 3 case based integrated units of assessment (4 marks each) with sub parts of the values of 1, 1 and 2 marks each respectively. 7. All questions are compulsory. However, an internal choice in 2 questions of 5 marks, 2 Qs of 3 marks and 2 questions of 2 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E. SECTION A (This section comprises of Multiple-choice questions (MCQ) of 1 mark each.) Serial No. 1 Question Which of the following could be the graph of the polynomial? (x - 1)2 (x + 2)? Marks 1 Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO (a) (b) Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO (c) (d) 2 The lines k 1 , k 2 and k 3 represent three different equations as shown in the graph below. The solution of the equations represented by the lines k 1 and k 3 is x = 3 and y = 0 while the solution of the equations represented by the lines k 2 and k 3 is x = 4 and y = 1. 1 Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO Which of these is the equation of the line k 3 ? (a) x - y = 3 (b) x - y = -3 (c) x + y = 3 (d) x + y = 1 3 What is/are the roots of 3x 2 = 6x? 1 (a) only 2 (b) only 3 (c) 0 and 6 (d) 0 and 2 4 The coordinates of the centre of the circle, O, and a point on the circle, N, are shown in the figure below. 1 Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO What is the radius of the circle? (a) 0.4 units (b) 2 units (c) 4 units (d) 42.4 5 PQR is shown below. ST is drawn such that PRQ = STQ. 1 (Note: The figure is not to scale.) If ST divides QR in a ratio of 2:3, then what is the length of ST? 10 (a) 3 cm (b) 8 cm (c) 12 cm 40 (d) 3 cm 6 Two scalene triangles are given below. 1 Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO (Note: The figures are not to scale.) Anas and Rishi observed them and said the following: Anas: PQR is similar to CBA Rishi: PQR is congruent to CBA Which of them is/are correct? (a) Only Anas (b) Only Rishi (c) Both Anas and Rishi (d) Neither of them, as two scalene triangles can never be similar or congruent. 7 Harsha made a wind chime using a frame and metal rods. She punched 8 holes in the frame, each 2 cm apart, and then hung 6 metal rods from the frame, as shown in the figure below. The ends of the metal rods are aligned over a line, shown by the dotted line in the figure. 1 Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO (Note: The figure is not to scale.) If all of the rods are straight and not swaying, then what is the length of Rod P? (a) (b) (c) (d) 8 69 7 53 5 cm cm 76 5 111 7 cm cm Two circles with centres O and N touch each other at point P as shown. O, P and N are collinear. The radius of the circle with centre O is twice that of the circle with centre N. OX is a tangent to the circle with centre N, and OX = 18 cm. 1 (Note: The figure is not to scale.) What is the radius of the circle with centre N? 18 (a) 2 cm (b) 9 cm 9 (c) 2 cm (d) 9 18 10 cm Shown below is a circle with centre O having tangents at points P, T and S. 1 Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO (Note: The figure is not to scale.) If QR = 12 cm and the radius of the circle is 7 cm, what is the perimeter of the polygon PQTRSO? (a) 26 cm (b) 31 cm (c) 38 cm (d) (cannot say with the given information.) 10 Shown below is a table with values of cosecant and secant of different angles. cosec sec (90 - ) 35 P 1.7 1 65 1.1 Q What are the values of P and Q respectively? (a) 1 and 1.7 1 1.1 (b) 1.1 and 1.7 (c) 1.7 and 1.1 (d) (cannot be found with the given information) 11 In the figure below, PQRS is a square. 1 Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO (Note: The figure is not to scale.) What is the value of sin SPT? (a) (b) 8 17 8 15 15 (c) ) 17 (d) (cannot be found with the given information) 12 Shown below is a solved trigonometric problem. 1 In which step is there an error in solving? (a) Step 1 (b) Step 2 (c) Step 3 (d) There is no error. Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO 13 A circle with radius 6 cm is shown below. The area of the shaded region in the circle is of the area of the circle. 1 (Note: The figure is not to scale.) What is the length of the circle's minor arc? (a) (b) 16 3 cm 20 3 cm (c) 16 cm (d) 20 cm 14 A regular pentagon is inscribed in a circle with centre O, of radius 5 cm, as shown below. 1 What is the area of the shaded part of the circle? (a) 2 cm2 Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO (b) 4 cm2 (c) 5 cm2 (d) 10 cm2 15 A cuboid of base area P sq units is filled with water upto a height of Q units. A sphere of volume R cu units is dropped into the cuboid such that it is completely submerged. A representation of the submerged sphere is shown below. 1 Which of these represents the increase in the height of water? (a) 0 units (b) units (c) R units (d) + units 16 Sweety, Nitesh, and Ashraf visited a hospital for their annual body checkup, which included a blood pressure evaluation. The results of their systolic blood pressure readings are as follows: 1 Sweety: 121 mmHg Nitesh: 147 mmHg Ashraf: 160 mmHg The table below depicts the systolic blood pressure ranges of all the patients who visited the hospital on the same day. Blood pressure (mmHg) Number of patients 115 - 125 10 125 - 135 9 135 - 145 12 145 - 155 19 155 - 165 10 Who among the three friends have a blood pressure reading that falls in the modal class? Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO 17 (a) Sweety (b) Nitesh (c) Ashraf (d) Both Sweety and Ashraf The table below depicts the weight of the students of class 6 of Red Bricks Public School. There are 18 students in the class that weigh above the median weight. 1 If there are no students with the same weight as median weight, how many students weigh between the range of 37 - 40 kgs? 18 (a) 5 (b) 7 (c) 18 (d) 31 Ginny flipped a fair coin three times and tails came up each time. Ginny wants to flip the coin again. 1 What is the probability of getting heads in the next coin flip? 19 (a) 0 (b) 0.25 (c) 0.5 (d) 1 A number q is prime factorised as 32 72 b, where b is a prime number other than 3 and 7. 1 Based on the above information, two statements are given below - one labelled Assertion (A) and the other labelled Reason (R). Read the statements carefully and choose the option that correctly describes statements (A) and (R). Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO Assertion (A): q is definitely an odd number. Reason (R): 32 72 is an odd number. 20 (a) Both (A) and (R) are true and (R) is the correct explanation for (A). (b) Both (A) and (R) are true but (R) is not the correct explanation for (A). (c) (A) is true but (R) is false. (d) (A) is false but (R) is true. P (-2, 5) and Q (2, -1) are two points on the coordinate plane. 1 Two statements are given below - one labelled Assertion (A) and the other labelled Reason (R). Read the statements carefully and choose the option that correctly describes statements (A) and (R). Assertion (A): The midpoint (0, 2) is the only point equidistant from P and Q. Reason (R): There are many points (x, y) where (x + 2)2 + (y - 5)2 = (x - 2)2 + (y + 1)2 are equidistant from P and Q. (a) Both (A) and (R) are true and (R) is the correct explanation for (A). (b) Both (A) and (R) are true and (R) is not the correct explanation for (A). (c) (A) is true but (R) is false. (d) (A) is false but (R) is true. SECTION B (This section comprises of very short answer type-questions (VSA) of 2 marks each.) Serial No. Question Check whether the statement below is true or false. 21 Marks 2 The square root of every composite number is rational. Justify your answer by proving rationality or irrationality as applicable. 22 Kimaya and Heena started walking from the point P at the same moment in opposite directions on a 800 m long circular path as shown below. Kimaya walked to the club house at an average speed of 100 m/min and Heena walked to the badminton court at an average speed of 80 m/min. The length of the circular track between the clubhouse and the badminton court is 180 2 Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO m. (Note: The figure is not to scale.) If Heena took 1 minute more than Kimaya to reach her destination, find the time taken by Heena to reach the badminton court. Show your work. 23 Shown below is a circle with centre O and three tangents drawn at points A, E and C. AE is a diameter of the circle. The tangents intersect at points B and D. 2 Based on the above information, evaluate whether the following statement is true or false. Justify your answer. Atleast one pair of opposite sides of AEDB is parallel. 24 Shown below is a right circular cone of volume 13,600 cm3 . 2 Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO (Note: The figure is not to scale.) Find the angle which the slant height makes with the base radius. Show your work. (Note: Take as 3, 2 as 1.4 and 3 as 1.7.) OR Shown below are two right triangles. 2 (Note: The figure is not to scale.) Find the length of the unknown side marked '?'. Show your work. 25 ABCD is a rhombus with side 3 cm. Two arcs are drawn from points A and C respectively such that the radius equals the side of the rhombus. The figure is shown below. 2 Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO (Note: The figure is not to scale.) If BD is a line of symmetry for the figure, then find the area of the shaded part of the figure in terms of . Show your work. OR Wasim made a model of Pac-Man, after playing the famous video game of the 2 same name. The area of the model is 120 cm2 . Pac-Man's mouth forms an angle of 60 at the centre of the circle. A picture of the model is shown below. (Note: The figure is not to scale.) Wasim wants to decorate the model by attaching a coloured ribbon to the entire boundary of the shape. What is the minimum length of the ribbon required in terms of ? Show your work. Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO SECTION C (This section comprises of short answer type questions (SA) of 3 marks each) Serial No. Question Prime factorisation of three numbers A, B and C is given below: 26 Marks 3 A = (2r 3p 5q ) B = (2p 3r 5p ) C = (2q 3q 5p ) such that, p < q < r and p, q, & r are natural numbers.. The largest number that divides A, B and C without leaving a remainder is 30. The smallest number that leaves a remainder of 2 when divided by each of A, B and C is 5402. Find A, B and C. Show your work. 27 Riddhi throws a stone in the air such that it follows a parabolic path before it lands at P on the ground as depicted by the graph below. 3 (Note: The figure is not to scale.) Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO i) The above graph is represented by a polynomial where the sum of its zeroes is 1 and the sum of the squares of its zeroes is 25. Find the coordinates of P and Q. ii) If one unit on the graph represents 25 metres, how far from Riddhi does the stone land? Show your work. 28 Given below is a pair of linear equations: 3 2x - my = 9 4x - ny = 9 Find at least one pair of the possible values of m and n, if exists, for which the above pair of linear equations has: i) a unique solution ii) infinitely many solutions iii) no solution Show your work. OR (6, 0) and (0, 2) are two of the points of intersections of two lines represented by a pair of linear equations. 3 i) How many points of intersections does the pair of linear equations have in total? Justify your answer. ii) Find the equation that represents one of the lines of the above pair. Show your work. 29 In the given figure, PQ is the diameter of the circle with centre O. R is a point 3 on the boundary of the circle, at which a tangent is drawn. A line segment is drawn parallel to PR through O, such that it intersects the tangent at S. Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO Show that SQ is a tangent to the circle. OR Shown below is a circle with centre O. Tangents are drawn at points A and C, such that they intersect at point B. 30 If OA OC, then show that quadrilateral OABC is a square. Shown below is a semicircle of radius 1 unit. 3 3 (Note: The figure is not to scale.) Make necessary constructions and show that: Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO 31 Naima is playing a game and has two identical 6-sided dice. The faces of the dice have 3 even numbers and 3 odd numbers. 3 She has to roll the two dice simultaneously and has two options to choose from before rolling the dice. She wins a prize if: Option 1: the sum of the two numbers appearing on the top of the two dice is odd. Option 2: the product of the two numbers appearing on top of the two dice is odd. Which option should Naima choose so that her chances of winning a prize is higher? Show your work. SECTION D (This section comprises of long answer-type questions (LA) of 5 marks each) Serial No. Question Manu and Aiza are competing in a 60 km cycling race. Aiza's average speed 32 is 10 km/hr greater than Manu's average speed and she finished the race in hours less than Manu. Marks 5 Find the time taken by Manu to finish the race. Show your work. OR Shown below is a cuboid with water in two different orientations. The length, breadth and height of the cuboid are distinct. The cuboid has 480 cm3 of water. 5 (Note: The figures are not to scale.) Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO If the height of water in orientation II is half of that in orientation I, then find the heights of water in both orientations. Show your work. 33 In the following figure, ABC is a right-angled triangle, such that: 5 AC = 25 cm PT || AB and SR || BC (Note: The figure is not to scale.) Find the area of PQR. Show your work. 34 Two rectangular sheets of dimensions 45 cm 155 cm are folded to make hollow right circular cylindrical pipes, such that there is exactly 1 cm of overlap when sticking the ends of the sheet. Sheet 1 is folded along its length, while Sheet 2 is folded along its width. That is, the top edge of the sheet is joined with its bottom edge in both the sheets, as depicted by the arrow in the figure below. Both pipes are closed on both ends to form cylinders. 5 (Note: The figures are not to scale.) Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO i) Find the difference in the curved surface areas of the two cylinders. ii) Find the ratio of the volumes of the two cylinders formed. Show your work. (Note: Use as 22 7 . Assume that the sheets have negligible thickness.) OR Shown below is a cylindrical can placed in a cubical container. 5 i) How many of these cans can be packed in the container such that no more cans are fitted? ii) If the capacity of one can is 539 ml, find the internal volume of the cubical container. Show your work. (Note: Take as 35 22 7 .) A car assembly unit assembles a limited number of cars daily, depending on the prevailing demand. The following table presents an analysis of the number of cars assembled by the unit over three consecutive months: 5 Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO Cars assembled per day 0-4 4-8 8 - 12 12 - 16 16 - 20 Number of days 33 18 21 11 7 i) If the demand of the cars is doubled, estimate how many cars on an average should be assembled per day such that the increased demand is met? ii) At least on how many days, less than average number of cars were assembled? Show your work. SECTION E (This section comprises of 3 case-study/passage-based questions of 4 marks each with two sub-questions. First two case study questions have three sub questions of marks 1, 1, 2 respectively. The third case study question has two sub questions of 2 marks each.) Serial No. Question Answer the questions based on the given information. 36 Marks An interior designer, Sana, hired two painters, Manan and Bhima to make paintings for her buildings. Both painters were asked to make 50 different paintings each. The prices quoted by both the painters are given below: Manan asked for Rs 6000 for the first painting, and an increment of Rs 200 for each following painting. Bhima asked for Rs 4000 for the first painting, and an increment of Rs 400 for each following painting. (i) How much money did Manan get for his 25th painting? Show your work. (ii) How much money did Bhima get in all? Show your work. 1 1 Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO (iii) If both Manan and Bhima make paintings at the same pace, find the first painting for which Bhima will get more money than Manan. Show your steps. OR (iii) Sana's friend, Aarti hired Manan and Bhima to make paintings for her at the same rates as for Sana. Aarti had both painters make the same number of paintings, and paid them the exact same amount in total. 2 2 How many paintings did Aarti get each painter to make? Show your work. 37 Answer the questions based on the given information. In the game of archery, a bow is used to shoot arrows at a target board. The player stands far away from the board and aims the arrow so that it hits the board. One such board, which is divided into 4 concentric circular sections, is drawn on a coordinate grid as shown. Each section carries different points as shown in the figure. If an arrow lands on the boundary, the inner section points are awarded. Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO (i) After shooting two arrows, Rohan scored 25 points. 1 Write one set of coordinates for each arrow that landed on the target. (ii) If one player's arrow lands on (2, 2.5), how many points will be awarded to the player? Show your work. 1 (iii) One of Rohan s arrow landed on (1.2, 1.6). He wants his second arrow to land on the line joining the origin and first arrow such that he gets 10 points for it. Find one possible pair of coordinates of the second arrow's landing mark. Show your work. OR (iii) An arrow landed on the boundary and is worth 20 points. The coordinates of the landing mark were of the form (m, -m). 2 2 Find all such coordinates. Show your steps. 38 Answer the questions based on the given information. A drone, is an aircraft without any human pilot and is controlled by a remotecontrol device. Its various applications include policing, surveillance, photography, precision agriculture, forest fire monitoring, river monitoring and so on. David used an advanced drone with high resolution camera during an expedition in a forest region which could fly upto 100 m height above the ground level. David rode on an open jeep to go deeper into the forest. The initial position of drone with respect to the open jeep on which David was riding is shown below. Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO David s jeep started moving to enter the forest at an average speed of 10 m/s. He Simultaneously started flying the drone in the same direction as that of the jeep. (i) David reached near one of the tallest trees in the forest. He stopped the drone at a horizontal distance of 5 3 m from the top of the tree and at a vertical distance of 65 m below its maximum vertical range. 1 (Note: The figure is not to scale.) If the angle of elevation of the drone from the top of the tree was 30 , find the height of the tree. Show your work. (ii) The drone was flying at a height of 30 3 metres at a constant speed in the horizontal direction when it spotted a zebra near a pond, right below the drone. The drone travelled for 30 metres from there and it could see the zebra, at the same place, at an angle of depression of from it. 1 Draw a diagram to represent this situation and find . Show you work. (iii) After 2 minutes of starting the expedition both the drone and the jeep stopped at the same moment so that the drone can capture some images. The position of the drone and the jeep when they stopped is as shown below. 2 Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO (Note: The figure is not to scale.) Find the average speed of the drone in m/s rounded off upto 2 decimal places. Show your work. OR (iii) At some point during the expedition, David kept the drone stationary for some time to capture the images of a tiger. The angle of depression from the drone to the tiger changed from 30 to 45 in 3 seconds as shown below. 2 (Note: The figure is not to scale.) What was the average speed of the tiger during that time? Show your work. (Note: Take 3 as 1.73.) Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO Click this link to buy latest Educart books on Amazon - https://amzn.to/3OFHQkO CLASS 10 BOOKS e c i t c a r P i h a S # ! i a H i r o o Zar National Best-selling Publisher Books: Question Banks & Sample Papers Latest Syllabus & Paper Pattern NCERT Textbooks with Solutions www.educart.co BUY at special discount

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