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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 2 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. 1. In the figure A, B, C and D are concyclic points. Which of the following is definitely a true statement? 2. a) CBE = BCD b) ABC = ADC c) BAD = EBC d) CBE = ADC An isosceles right triangle has the hypotenuse measuring a) 2 3. b) 1 c) 2 cm. The area in cm2 is 1 2 d) 4 The class marks of a frequency distribution are given as follows : 15, 20, 25, ... The class corresponding to the class mark 20 is : a) 12.5 17.5 4. b) 17.5 22.5 c) 18.5 21.5 d) 19.5 20.5 ABCD is a square. Name the congruency criterion which cannot be used to show PCD = PBA. a) SAS b) SSS c) RHS d) ASA 5.1. The bisectors of any two adjacent angles of a parallelogram intersect at a) 30 b) 45 c) 60 d) 90 Page 1 of 7 6. The diameter of the base of a closed right circular cylinder is equal to its height h then its TSA is a) 2 h 2 7. b) 3 2 h 2 c) 4 2 h 3 d) h 2 If x 62 62 is divided by x 1 then the remainder is a) 0 b) 63 c) 59 d) 60 8.2. Which of these is a factor of x 2 4 y 2 9z 2 4 xy 12 yz 6xz ? a) x 2 4 y 2 9z 2 9. b) x 2 y 3z c) x 2 y 3z d) x 2 y 3z 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) : A cyclic quadrilateral with one right angle is always a rectangle. Reason (R) : A quadrilateral with all right angles is a rectangle. 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) : 3 2 5 multiplied with 3 2 5 gives a rational number. Reason (R) : An irrational number multiplied with its conjugate always gives a rational number. 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. Answer the following questions: 11. 2 1.41, what is the value of 1 ? 2 Page 2 of 7 12. Find the value of x in the given figure. O 13. AB and BC are two equal arcs of a circle with centre O. If AOB 20 , x A find the value of x. C B 14. Find the equation of the line which passes through the points. 2 , 2 , 0 , 0 , 2 , 2 . 15. 1. In the given figure, if AC is the bisector of A and C and BAC BCA . In order to prove A C , state the Euclid s Axiom used. 16. 2. In a parallelogram ABCD, if A 3x 20 , C x 40 find x . 17. The area of an equilateral triangle with side 2 3 cm is _________________. 2 18. If p x x 2 2x 1 what is p 2 2 ? 19. Two right circular cylinders of equal volume have their heights in the ratio 1 : 2. The ratio of their radii is______________. 20. Give an example of a polynomial in one variable , which is a binomial of degree 4. Page 3 of 7 SECTION B Section B consists of 5 questions of 2 marks each. Answer the following questions: 21. 1. If x k 1 , y 2k 1 is a solution of the equation 3x 2 y 7 0 . Find k . 22. In the given figure, BC = AC. What is the measure of BAD? 23. The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 60 . Find all the angles of the parallelogram. 24. Find the value of a , if 2x a is a factor of x 3 ax2 2x a . 25. Find the volume of water in ml that is displaced by a solid spherical ball of diameter 4.2 cm when it is completely immersed in water. SECTION C Section C consists of 6 questions of 3 marks each. Answer the following questions: 26. Simplify : 64 2 3 125 27 3 2 3 25 9 1 2 27. If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, prove that the chords are equal. A 28. In the figure AB = AC. DBC DCB . D Show that AD bisects BAC . B C Page 4 of 7 29. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle. 30. The diameter of the internal surface of a hollow hemispherical metal bowl is 6cm and the thickness of the bowl is 3cm. Find the volume of the metal used to make the bowl. 1. 31. 2. Draw the graph of the linear equation x 2 y 6 . 3. SECTION D Section D consists of 4 questions of 5 marks each. Answer the following questions: 32. a) Express 3.525252 . as a rational number . b) If x 2 1 2 1 and y 2 1 2 1 , then find the value of x 2 y 2 . 33. Find the value of a) x 3 y 3 12 xy 64 , when x y 4 b) Factorise : 32a3 108b3 34. Draw a histogram and a frequency polygon on the same graph to represent the following data which shows the daily wages of workers in a company. Daily wages in Rs. No. of workers 340-380 380-420 420-460 460-500 500-540 540-580 16 9 12 2 7 4 4. 35. 5. a) Prove that the line segment joining the midpoints of the two sides of a triangle is parallel to the third side and half of it. b) In ABC, D, E and F are the midpoints of BC, CA and AB respectively. If the lengths of side AB, BC and CA are 7 cm, 8 cm and 9 cm respectively, find the perimeter of DEF. 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 IX 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) [1] What is the volume of the tent? 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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