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CBSE Class 9 Exam 2025 : Mathematics

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Subject : Mathematics Marks : 80 Time : 3 Hrs. Date : 12.02.2024 FINAL EXAMINATION {2023-24} SET 1 Class : 9 Instructions : 1. All questions are compulsory. 2. The question paper consists of five sections A , B , C , D and E . 3. Section A has 20 questions carrying 1 mark each. 4. Section B has 5 questions carrying 2 marks each. 5. Section C has 6 questions carrying 3 marks each. 6. Section D has 4 questions carrying 5 marks each. 7. Section E has 3 case based questions carrying 4 marks each. SECTION A Section A consists of 20 questions of 1 mark each. Choose the correct option: 1. In the figure below, P, Q, R and S are points on the circle and T is a point inside the circle on PQ. PQR 80 . Which of the following is definitely true? 2. a) PTR = 80 b) PSR = 100 c) PTR = 100 d) PSR = 80 An isosceles right triangle has area 1 cm2 . The length of its hypotenuse is a) 3. 2 b) 1 2 c) 1 2 d) 2 In a frequency distribution, the class mark of a class interval is 10 and the class size is 6. The lower limit of the class is : a) 6 4. b) 7 c) 8 In the figure BC = DE. Name the congruency used to show AD = CF. a) SAS b) ASA c) SSS d) RHS d) 12 F A B C D E Page 1 of 7 5. If x 61 61 is divided by x 1 then the remainder is a) 0 6. b) 1 c) 59 d) 60 A right circular cylindrical tunnel of diameter 2 m and height 40 m is to be constructed from a sheet of iron. The area of iron sheet required in m 2 is : d) 100 c) 80 b) 60 a) 40 7.1. 9a 2 16b 2 25c 2 24 ab 40bc 30ac is the expansion of a) 3a 4b 5c 2 b) 3a 4b 5c 2 c) 3a 4b 5c d) 3a 4b 5c 2 2 8.2. Diagonals necessarily bisect opposite angles in a a) kite 9. b) parallelogram c) square d) isosceles trapezium 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) : Two circles can intersect at maximum two points . Reason (R) : Only two circles can be drawn through two given distinct points 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. 10. Assertion (A) : Reason (R) 3 2 5 added to 3 2 5 gives an irrational number. : Irrational numbers are closed under addition. 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. Page 2 of 7 Answer the following questions: 11. 5 2.24 , what is the value of 1 ? 5 12. Find the measure of EOB in the given figure. B 13. AB and BC are two equal arcs of a circle with centre O. Find the value of x. if OCA 35 O x A 14. 1. Find the equation of the line which passes through the points 3 , 3 , 0 , 0 , B C 7 , 7 . 15. 2. In the given figure AB = AD and AC = AD. In order to prove AB = AC, state the Euclid s Axiom used. 16. ABCD is a trapezium with AB CD. If A 2x 10 , D x 20 17. The length of each side of an equilateral triangle having an area of 9 find x . 3 cm2 is __________. 18. If p x x 2 2 2x 1 what is p 2 2 ? 19. Two right circular cones of equal volume have their heights in the ratio 1 : 2. Find the ratio of their radii. 20. Give an example of a polynomial in one variable, which is a trinomial of degree 2. Page 3 of 7 SECTION B Section B consists of 5 questions of 2 marks each. Answer the following questions: D A 21. Two equilateral triangles ABC and DEF lie on a straight line as shown below. What is the measure of x ? P B E x C F 22. The radius of a spherical balloon is inflated from 1.5 cm to 2.5 cm by pumping more air in it. Find the ratio of surface areas of the resulting balloon to the original one. 23. If x 1 and y 1 is a solution of the equation 2x 3 a 1 y 1 0 . Find a . 24. The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 50 . Find all the angles of the parallelogram. 25. Find the value of a , if 2x a is a factor of x3 ax2 2x a . SECTION C Section C consists of 6 questions of 3 marks each. Answer the following questions: 64 26. Simplify : 125 2 3 1 256 625 1 4 25 3 64 0 27. If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords. 28. Find the area of a triangle whose perimeter is 36 cm. Two sides are in the ratio 3 : 2 and the third side measures 11cm. Page 4 of 7 29. ABC is an isosceles triangle in which AC = BC. AD and BE are respectively two altitudes to sides BC and AC. Prove that AE = BD. 30. The diameter of the internal surface of a hollow hemispherical metal bowl is 6 cm and the thickness of the bowl is 2 cm. Find the volume of the metal used to make the bowl. 31. Draw the graph of the linear equation 2x y 6 . SECTION D Section D consists of 4 questions of 5 marks each. Answer the following questions: 32. a) Express 2.525252 .. as rational number . b) If x 3 2 3 2 and y 3 2 3 2 , then find the value of x 2 y 2 . 1. 33. 2. a) Prove that the diagonals of a square bisect each other at right angles and are equal. b) ABCD is a square. A line segment DX cuts side BC at X and the diagonal AC at O such that OXC 60 . Find the value of a . 34. a) Find the value of x 3 8 y 3 36 xy 216 when x 2 y 6 . b) Factorise 54 x 6 2x 3 y 3 . 35. Following is the frequency distribution of total marks obtained by the students of different sections of Class IX. Draw a histogram and frequency polygon for this data on the same graph. Marks 100 150 150 200 200 250 250 300 300 350 Number of students 60 100 100 80 180 Page 5 of 7 SECTION E Section E consists of 3 case based questions of 4 marks each. Answer the following questions: 36. A circular park with centre O and radius 6 cm has three parallel paths as shown in the figure. ABCD is a rectangle with DC = 8cm . Observe the figure and answer the following questions. a) Find the length AD. [2] b) If the angle subtended by the minor arc DC on any point of the remaining part of the circle is 85 , what is the respective angle at the centre ? [1] c) Which chord AB Or EF subtends a bigger angle at the centre ? Why? [1] 37. To promote cooperation, culture, creativity, sharing, self-confidence and other social Values a Student Adventure Camp was organised by the school for class 9 students and accommodation was planned by the teacher. Students were given 500 m 2 cloth. As shown in the figure they were asked to make a tent with the height 15 m and diameter 16 m. The remaining cloth was used as a carpet. Consider 3.14 a) Find the slant height of the tent. [1] b) What is the area of the cloth used as a carpet? [2] c) What is the volume of the tent? [1] 15 m 16 m Page 6 of 7 38. Ladakhi Mandalas are also known as Architecture of Enlightment. The word mandala comes from the Sanskrit word mand means to mark off and la means circle. A number of circles and squares are used in drawing this. Basic outline of one such Mandala is drawn on the graph sheet as shown below. Observe the graph and answer the following questions. a) Find the coordinates of reflection of point V in x axis. [1] b) Name a point in the 3rd quadrant which is at a distance of 1 unit from x axis and 4 units from y axis. [1] c) Find the area enclosed between ABCD and the circle. Consider 3.14 [2] *******Good Luck****** Page 7 of 7

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