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CBSE Class 9 Exam 2025 : Mathematics

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VIDYAPEETHII YII VIsHWA GROUP OF SCHOOLS SECONDARY EDUCATION CENTRAL BOARDOF DECEMBER (2024-25] THIRD PERIODIC TEST MATHEMATICS Date:05/12/2024 Time: 1 hour Marks: 25 Name: Class: IX Instructions: 1. This Question Paper has 5 Sections A, B, C, D, andE. 2. Section Ahas Multiple 7Choice Questions (MCQs) carrying Imark each. 3.Section Bhas 3Short Answer-I (SA-l) type questions carrying 2marks each. 4. Section C has 1 Short Answer-I1 (SA-II) type question carry ng 3 marks each. each. values of 1 Imark 5. SectionD has 1 Case-based integrated unit of assessmentt (4 marks) with sub-parts of the 6.Section Ehas lLong Answer (LA) type question carrying 5mrks each. 7. AllQuestions are compulsory. (ix7=7) SECTION A A hand fan is made by stitching 10 equal-sized triangular strips of two different types of paper (1) as shown below. The dimensions of the equal strips are 25 cm, 25 cm, and 14 cm. Find the total area of paper needed to make the hand fan. a. 840 cm? 2 b. 1680 cm c. 480cm? If the perimeter of an equilateral triangle is 180cm. Then its area will be: c.300V3 cm? a. 900 cm? b. 900V3 cm? VVP/ Third Periodic Test QP/2024-25/1 of 3 d. 7844 cm? (1) d. 600V3 cm? The angle subtcndcd by a clhord and the diameter of a circle at the center is a. 90 b. 45 c. 180 (1) d. 60 Ifthe surface arca of a sphere of radius "R" is cqual to the curved surface arca of a hemisphere () of radius "r" what is the ratio of R/r? a. b. 1/N2 d. v2 c. 2 lfaline intersects two concentric circles with centre Oat A, B, Cand D, then: a. AB =CD b. AB> CD c. AB <CD ) d. cannot be determined If aright circular cone has aradius of 4cm and aslant height of5 cm then what is its volume? (1) 6 a. 16 cm b. 14 n cm c. 12 cm d. 18 cm Assertion: there can be infinite numbers of equal chords of acircle. Reason: Acircle has only a finite number of equal chords. (1) Both A and R are true andR is the correct explanation of A. b. Both A and R are true but R is not the correct explanation of A. a. C. A is true but R is false. d. A is false butR is true. SECTION B 8 inside radius of the bowl is 5 cm. A hemispherical bowl is made of steel 0.25 cm thick. The Find the volume of steel used in making the bowl. find out the diameter of its base. The height of agiven cone is 15cm. Ifits volume is 1570cm , (Use n=3.14) at the centre. 10 Prove 'Equal chords of acircle subtend equal angles 9 SECTION C equal side to its base js 3:2. The perimeter of an isosceles triangle is 32 cm. The ratio of the Find the area of the triangle. VVP/ ThirdPeriodic Test QP/2024-25/2 of 3 (2X3-6) (2) (2) (2 (3) (3) (4) SECTION D to show Red Fort. it was a Amathematics teacher of a school took her 9th-standard students narrated the part of their Educational trip. The teacher had an interest in history as wcll. She find a can one monument this in said teacher the Then students. facts of Red Fort to 12 combination of solid figures. There are 2 cylindrical pillars. Also, 2 domes at the corners which are hemispherical.7 smaller domes at the centre. The flag hoisting ceremony on Independence Day takes place near these domes. i. How much cloth material will be required to cover 2 big domes each of radius 2.Smetres? (Take TT= 22/7) 1. 11 the dome radius is increased by 2 meters in case (i) how much extra cloth material will be required to cover 2 big domes? i1. How much is the yolume of a hemisphere if the radius of the base is 3.5m? IV. What is the ratio of the sum of volumes of tWo of radius I cm each to the hemispheres the volume ofa sphere of radius 2cm? 13 Prove that the (1) (1) (1) (1) SECTION E quadrilateral formed by the internal angle bisectors (5) of any quadrilateral is cyclic. 2 A 7 * k * *k * * k** k * * k k* k * *k * * k * * k 7 VVPIThird Pcriodic Test **** *** * QP/I2024-25/3 of3 |(5) VIDYAPEETH || Y||VISHWA GROUP OF SCHOOLS EDUCATION CENTRAL BOARID OF SECONDARY HALE-YEARLY EX AMINATION- JULY (2024-25) MATIIEMATICS (SET-2) SUBJECT CODE: 041 DATE:15-07-2024 TIME: 3 HOURS NAME: CLASS: IX MAXIMUM MARKS: 80 General Instructions : qucstions are compulsory. Thisquestion paper contains 38 qucstions. All Sections A, Band C, Dand E question paper is divided into five s ctions. This Section Acomprises 20 questions of Imark each. Scction Bcomprises 5questions of 2marks each. Section C comprises 6 questions of 3 marks each. Section D consists 4 questions for 5 marks each. Section E contains 3 case-based questions for 4 marks each. " Use of a calculator is not permitted. Section A () The coefficient of x in (2- 3x Xx- 5) is c)- 17 b) 1 2 d)- 10 If5- a5-b . then the value of 'b' is 11 3+2/5 a) 3 c) - 1 d) 2 I +- 1(x, y* 0), then the value ofx. b) 2 a)- 1 4 3 y (1) is d) 0 c) I Which of the following points does not lie on the line y= 3x +4?) - 3x--*4 a) (- 1,1) b) (1.7) c) (2.10) Ha.12) The point that lies on the x-axis at a distance of 4 units in the positive direction of x-axis 4,0) 6 b) (- 4, 0) c) (0, - 4) ( d)(0, 4) The linear equation 4x - 7y =-15 has a) no solution c) a unique solution ) () ofinfinitely many solutions d) two solutions VVP/ Half Yearly Examination QP/2024-25/1 of6 L B is the mid-point of I"Cis the mid-point of the line scgment AB and L 7 ML =AB HAL =AB c) AL =AB d) AL =AB 3 AC, then (1) (1) Postulates are assumed a) universaltruths specific togeometry universal truths in all branches of matheniatics d) definitions c) theorems many line segments can be drawn using them Givenfour distinct points in a plane. How when nothree of them are collinear? 10 If d) 12 c) 4 2 2=1.414 then y2+1) c) 0.414 b)0.621 a) 0.207 d) 2.414 (1) Every real number is a)either rational or irrational b) rational d) irrational c) neither rational nor irrational 3 (1) Ifx - 3x +3x- 7= (x+ I)(ax +bx + c), then a +btc= a) 3 12 d) 1 b) 4 a) 8 (1) Irg** =240+ 9, then x = a) 0.2 60.5 d) 0.1 c) 0.4 =||,then the value of 'm' is |If(- 2, 5)is a solution of2x + my )2 a)- 2 I6 17 c)3 (1) d)- 3 intersect one another at the point 0. If Two straight lines AB and CD 274 , then z AOD= L AOCt2 COB+t 2 BOD= c)94 d) 90 b) 137 are in the ratio 7: |1, then the angles Iftwocomplementary angles are d) 30 , 50 c) 40 , 50 b) 20 , 60 ) 35 ,55 . (1) MP then: M andN, C is the mid-point of If the point P lies in between (1) a) MC+ CN = MN c) MC+ PN = MN 18 (1) b) CP + CN = MN d) MP + CP = MN 60 36284 ratio 5:3:7, then the triangle is The angles of atriangle are in the ) an gbtuse-angled triangle X)an isosceles triangle. y)a right triangle (1) (1) Yan acute angled triangle of 6 VVP/ Half Yearly Examination QP/2024-25/2 30 Assertion (A): The points (- 3, 5) and (5, - 3) are at diflerent positios in the coordinate l) 19 plane. Rcason (R): Ifx ythen (x, y)* (y.N) a Both Aand R are tnic and R is the corect explanation of A. b) Both and R are truc but R is not the corrcct explanation ot A. c) A is true but R is falsc. d) A is false but R is truc. 20 Assertion (A): If (x+ I)is afactor of f(x)=xt ax +2. then a =- 3. Reason (R): If (x - a) is afactor of p(x). if pla) =0. a) Both Aand Rare true and Ris the correct explanation of A. b)Both A and R are true but R is not the correct cxplanation ol A. c) Ais true but R is false. Ais false but R is truc. Section B This section contains 5 questions of 2 marks cach 2 23 |Simplify the prod1er(a 3b)|3b +a+98') I (2) Findfour solutions for the following equation :2(x )+3y = 4 (2) Point C is called a midpoint of line segment AB, prove that every line scgment has onc (2) and only One mid-point. 24 From the given figure, name the tollowing: i. Three lines (2) i. One rectilinear figure iii. Four concurrent points. G A EZ 25 It is known that x + y* 10 and that x =z. Show that z + y= 10? (2 Section C This section contains 6 questions of 3 marks each 26 Draw the graphs ofy=x and y=- x in the same graph. Also find the coordinates of the(3) point where the two lines intersect. 27 Simply by rationalizing denominator 7+35 7-3/s (3) y1t 4s+2(1)(313) VVP/Half Yearly Examination QP/2024-25/3 of 6 In the given figure, LM is a line parallel to they- axis at an distance of3 units. 28 (3) 312 3/0 -2 M i. What are the coordinates of the points P, R and Q? 2 ii. What is the diference between the abscissa of the points L and M? 3 ti 29 In the given figure, Iines AB and CD intersect at O. IfZ AOC + 2 BOE =70 and 40.find z BOE and reflex z COE. BOD (3) 101 Ah D SS ota 30 In the given figure, PQ is an incident ray and QR is the reflected ray. If ZPQR = 124 then find z RQB. P 124" f1 A TTTrrrrTr OR In Fig. if PO||RS. DeterminezPQR. (Hint: draw a line parallel to P0 passing through Q) 130 110 VVP/Half Yearly Examination QP/2024-25/4 of 6 (3) 31 Factorise: 2x. 17x + 30 OR lfx - 3and x - are both factors of px +5x +r. then showthat p =1 Section D This scetion consists of 4questions of 5 marks each 32 33 (5) Represent eachof the numbers y2 and y5 on the real line. Plot the graph. by finding any five dillercnt solutions of thc cquation: 3y = 4x. (5 (5) 34 35 Factorise- (2r + 5y' +(y+)-(z + (5) arms of another Prove that if the arms of an angle are respectively perpendicular to the angle, then the angles are either equalor supplementary. OR find x. In the given figure, if AB || CD, CD|| EF and y: z = 3: 7, Section E cach This section contains 3 questions of 4 marks 36 VOTE. In India, every citizen Democracy h s given people a powerful right- that is to enjoying it as a holiday. one must over 18 years of age has the right to vote. Instead of process and bring about a vote if he/she truly wants contribute to the nation-building change. yote for a Better India 5 which /9 + 2x-2x voters wcre men and y9+2x A survey was done in a small arca Voters were women. i.What is the value of 'x' if the number of men is cqual to the numbcr of women? ii. What is the product of the variables a a ii. Simplify 75 7 7 iv, Is it true that ifr is rational and s is irrational,then r+s is irrational? vVP/HalfYearly Examination QP/2024-25/5 of 6 (4) 37 that Beti Bacho, Beti Padho (BBBP) is apersonal campaign of the Govcrnment of India for (4) of wclfare scrviccs intcnded aims lo gcnctale aWarcncss andimprovethe cfficicncy 3 3 In a sehool, a group of (x+ y) teachers, (x+ y") girls and (x +y) boys organised a campaign on Beti Bacho, Beti Padho,. i. low many teachers are there in the group ifthere are 63 girls (given xy= 9)? ii. How many girls are there in the group if there are 10 teachers and 370 boys? ii. How many boys are there in the group if thereare 10teachers and 58 girls? iv.What is the value of (x - y)ifthe number of teachersare 10 (given x - y=23)? 38 Maths teacher draws a straight line AB shown on the blackboard as per the following figure. Now he told Raju to draw another line CD as in the figure The teacher told Ajay to mark ZAOD as 2z Suraj was told to mark ZA0C as 4y Clive Made and angle ZCOE = 60 Peter marked Z BOEand BOD as y and x respectively i. What is the value of x? a) 48 c) 100 b) 96 ii. What is the value of y? a) 48 b) 96 c) 100 d) 120 d) 24 iii. What should be the value of x + 2z? a) 148 b)360 c) 180 d) 120 iv.What is the relation between yand z? a). 2y +z=90 b) 2y + z = |80 c) 4y + 2z =|20 **** VVP/Half Yearly Examination QP/2024-25/6 of 6 d) y= 2z * **%** (4)

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