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CBSE Class 9 Exam 2026 : Mathematics : Final Exam 2025 Maths

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ST. XAVIER S SENIOR SECONDARY SCHOOL, DELHI 110 054 Std. 9 18-2-2025 Time : 3 hrs. Max. Marks : 80 Final Examination MATHEMATICS General Instructions: i) This Question Paper has 5 Sections A, B, C, D, and E. ii) Section A has 20 Multiple Choice Questions (MCQs) carrying 1 mark each. iii) Section B has 5 Short Answer-I (SA-I) type questions carrying 2 marks each. iv) Section C has 6 Short Answer-II (SA-II) type questions carrying 3 marks each. v) Section D has 4 Long Answer (LA) type questions carrying 5 marks each. vi) 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. vii) All Questions are compulsory. However, an internal choice in 2 Questions of 5 marks, 2 Questions of 3 marks and 2 Questions of 2 marks has been provided. An internal choice has been provided in the 2marks questions of Section E. viii) Draw neat figures wherever required. Take = 22/7 wherever required if not stated. Section A (20 x 1 mark = 20 marks) 1. The product of any two irrational numbers is: A. always an irrational number B. C. always an integer D. 2. Factors of 2 30 are A. ( 6) ( +5) C. (2 3) (3 +2) B. D. (2 2) ( 3) (2 +3) (3 2) 3. The linear equation 3 11y = 10 has: A. Unique solution C. Infinitely many solutions B. D. Two solutions No solutions 4. Abscissa of a point is negative in A. Quadrant IV only C. Quadrant I and IV B. D. Quadrant II and III Quadrant I only 5. For two triangles, if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the congruence rule is A. SSS B. ASA C. SAS D. None of the above 6. D and E are the mid points of sides AB and AC of a ABC. If BC = 5.6 cm, find DE. A. 2.8 cm B. 3 cm C. 2.9 cm D. 2.5 cm 7. The sides of a triangle are in the ratio of 3 : 4 : 5. If its semi perimeter is 18 cm, then its longest side is A. 5 cm B. 12 cm C. 15 cm D. 9 cm 8. = 2, y = 3 is a solution of the linear equation A. + 2y = 8 B. C. - + y = 8 D. always a rational number sometimes rational, sometimes irrational 1 1 1 1 1 1 1 1 +y=8 2 + y = 8 9. Which one of the following is not the graphical representation of statistical data? A. bar graph B. histogram C. frequency polygon D. tally marks 1 10. 0.01233333 .. can be expressed in rational form as A. 900/111 B. 111/9000 C. 123/100 1 11. A polynomial of two terms is called A. quadratic B. binomial 12. The linear equation +0y+9 = 0 in two variables is A. parallel to -axis B. parallel to y-axis C. passing through origin D. none of these 1 13. The ordinate of any point on -axis is A. 0 B. -1 1 14. Which is not the criteria of congruency of triangles? A. SSS B. AAS C. AAA 15. Three angles of a quadrilateral are 75 , 90 and 75 . The fourth angle is A. 90 B. 95 C. 105 D. 120 C. C. monomial 1 D. D. 111/900 cubic D. any number D. SAS 1 1 1 Std. 9 -2- MATHEMATICS 16. If the perimeter of an equilateral triangle is 60 cm, then what is its area? A. 200 2cm2 B. 100 2cm2 C. 100 3cm2 D. 200 3cm2 1 17. The expanded form of (3 5)3 is A. 27 3 + 135 2 + 225 125 C. 27 3 135 2 + 225 125 1 18. B. D. 27 3 + 135 2 225 + 125 None of the above How many linear equations can be satisfied by = 5 and y = -1? A. Only one B. infinitely many C. two D. none of these 1 DIRECTION: In question number 19 and 20, a statement of Assertion(A) is followed by a statement of Reason(R). Choose the correct option. 19. Assertion (A): Degree of a non-zero constant polynomial is zero. Reason (R): Polynomial having two terms is called binomial. A. Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). B. Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). C. Assertion (A) is true but reason (R) is false. D. Assertion (A) is false but reason (R) is true. 20. Assertion (A): Reason (R): A. B. C. D. 2 + 6 is an irrational number. Sum of a rational number and an irrational number is always an irrational number. 1 Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). Assertion (A) is true but reason (R) is false. Assertion (A) is false but reason (R) is true. SECTION B (5 x 2 marks = 10 marks) 21. Factorise : 22. The surface areas of two spheres are in the ratio 1:4. Find the ratio of their volumes. (OR) Find the capacity of a conical vessel with height 12 cm and slant height 13 cm. [ = 3.14] 8 3 (2 )3 2 23. Write the coordinates of the point: i) Which lie on both and y axes? ii) Whose ordinate is 5, which lies on y-axis? 24. In the given figure, ray OS stands on a line POQ, ray OR and ray OT are angle bisectors of POS and SOQ respectively. If POS = , find ROT. (OR) If two lines intersect each other, then prove that the vertically opposite angles are equal. 25. 1 2 1 1 2 2 How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold? SECTION C 2 2 (6 x 3 marks = 18 marks) 26. Locate 6.3 on a number line. 3 27. Simplify: 3 ( + y + z)2 ( y z)2 (OR) 2 2 If + y = 49 and y = 3 then find the value of 3 y3 28. AB, CD and EF are three concurrent lines passing through the point O such that OF bisects BOD. If BOF = 35 , find EOC, BOC and AOD. 3 3 Std. 9 29. -3- MATHEMATICS Prove that the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. (OR) If the non-parallel sides of a trapezium are equal, then prove that it is cyclic. 3 3 30. State and prove ASA congruence rule. 3 31. The perimeter of an isosceles triangle is 42 cm. The ratio of the equal side to its base is 3: 4. Find the area of the triangle. [Take 0.2 = 0.45] 3 SECTION D 32. 33. (4 x 5 marks = 20 marks) In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see Fig.). Show that: i) APD CQB ii) AP = CQ iii) AQB CPD iv) AQ = CP v) APCQ is a parallelogram. (OR) ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that: i) D is the mid-point of AC. ii) MD AC 1 iii) CM = MA = 2 AB i) 5 5 In the given figure, POQ is a line. Ray OR PQ, OS and OR . is another ray lying between rays OP 1 Prove that ROS = 2 ( QOS POS) ii) It is given that XYZ = 64 and XY is produced to point P. Draw a figure from the given bisects ZYP, find XYQ and reflex QYP. information. If ray YQ 2+3 (OR) If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then prove that the two lines are parallel. 5 34. The diameter of moon is approximately one-fourth the diameter of earth. Find the ratio of their surface areas and what fraction of the volume of the earth is the volume of the moon? 35. The following table gives the lifetimes of 400 neon lamps. LIFE TIME ( IN HOURS ) 300 400 400 500 500 600 600 700 700 800 800 900 900 1000 i) ii) 5 NUMBER OF LAMPS 14 56 60 86 74 62 48 Illustrate the given information with the help of a histogram. How many given lamps have a lifetime of more than or equal to 800 hours? 4 1 Std. 9 -4- MATHEMATICS SECTION E 36. (3 x 4 marks = 12 marks) To judge the preparation of students of class 9th on the topic rationalization of irrational numbers, Mathematics teacher defined rationalization saying that when the denominator of an expression contains the term with the square root, the procedure of converting it to an equivalent expression whose denominator is rational is called rationalizing that denominator. Based on the above information answer the following questions: 1 3+ 2 a) Rationalize b) Classify the following as rational or irrational number (6 27) ( 27 8) 1 c) Simplify ( 14 2 2)2 2 1 (OR) c) 37. 38. Rationalize the denominator of 7 11 5 Ankit visited a mall with his father. He sees that three shops are situated at P, Q, R as shown in the figure from where they have to purchase things according to their need. Distance between shop P and Q is 8m and distance between shop P and R is 6m. Considering O as centre of the circle, answer the following questions: a) Find the measure of QPR b) Find the measure of QSR c) Find the radius of the circle. (OR) c) Find the perimeter of the circle. 2 1 1 2 2 In the current scenario, people use such door whose top half part is made of glass and bottom half part is wooden. The glass portion of the door is having length and width in the ratio of 5:3. The wooden frame around the glass portion adds 11 inches to the total width and 14 inches to the total length. Consider the length of the glass portion as 5 inches: On the basis of the above information, solve the following questions: a) Find the total length of the glass portion of the door (in inches) is represented in terms of . b) Find the total width of the glass portion of the door (in inches). c) If the area of the door is 6 2 + 5 6, then find its dimensions. (OR) c) Find the zero(s) of the polynomial representing the area of the glass portion. -x-x-x-x-x-x- 1 1 2 2

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