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ICSE Class IX Sample / Model Paper 2023 : Mathematics : vibgyor high

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Saachi Zanvar
Vibgyor High School, Pune (Balewadi)

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VIBGYOR HIGH Sample Paper AY 2022-2023 MATHEMATICS Grade: IX Max. Marks : 80 Date : dd/mm/2023 Time Allowed: 2 hour INSTRUCTIONS: Answers to this paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this paper is the time allowed for writing the answers. The intended marks for the questions or parts of questions are given alongside the questions. Attempt all questions from Section A and any four questions from Section B. All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer. Omission of essential working will result in the loss of marks. Geometrical figures to be constructed wherever applicable. For geometry, figures are to be copied to the answer script. SECTION A (40 marks) (Attempt all questions) Choose the correct answers to the questions from the given Question 1. [15] options: i) The rationalizing factor of 3 + 5 is: [1] a) 3 5 b) 3 5 c) 3 5 d) 3 + 5 ii) Find the amount on a sum of 800 for 3 years at 10% p.a. simple interest. a) 940 1 [1] b) 1010 c) 1020 d) 1040 iii) If = 8, = 5, find 2 + 2 . [1] a) 64 b) 65 c) 66 d) 63 iv) If tan + cot = 3, the value of 2 + 2 is: [1] a) 3 b) 9 c) 7 d) 6 v) The median of the following data: [1] 7, 8, 9, 8, 7, 6, 11, 3, 15 is: a) 7 b) 8 c) 6 d) 15 vi) If 2 = 1.4 and 3 = 1.7 ,then2 3 + 2 2 is equal to: [1] (a) 6.2 (b) 6.3 (c) 6.22 (d) None of these vii) In the given fig., ABC = 90 , CAB = , tan = 15 cm. Find the measure of AC. a) 20 cm b) 24 cm c) 25 cm d) 25.5 cm 2 3 4 and BC = [1] viii) Through which of the following points, the graph of y = passes? a) (1, 1) b) (0, 1) c) ( 1, 1) d) None of the above ix) 3+ 2 If x = 3 2 [1] [1] then which of the following is the simplest rationalizing factor for x ? (a) 3 + 2 (b) 3 2 (c) 3 2 (d) None of the above x) Find the value of a) b) c) d) xi) 2 30 [1] 2 45 2 3 2 3 3 2 3 2 Express each of the following as the logarithm of a single number . log 12 log 2 log 3 a) log 2 b) log 3 c) log 12 d) None of the above 3 [1] xii) Find the radius of a circle whose perpendicular distance to a [1] chord of length 16 cm is 6 cm. a) 11 cm b) 10 cm c) 12 cm d) 10.50 cm xiii) Find the value of sin 38 cos 52 [1] a) 10 b) 1 c) 100 d) 0 xiv) In the given figure, arc AB and arc BC are equal in length. If [1] AOB=48 , find BOC. a) 48 b) 96 c) 42 d) 66 xv) In the given figure, if area of triangle ADE = 60cm2, the parallelogram ABED is: a) 60 cm2 b) 76 cm2 4 [1] c) 120 cm2 d) 30 cm2 Question 2. a) Solve the following: [12] Find two numbers such that the larger number added to three [4] times the smaller number gives 7 and twice the larger number added to the smaller number gives 9. (Solve the equations using elimination method) b) (i) Show that ( ) + . ( ) + ( ) + = 1 [4] (ii) If log 7 (2x2 1)= 2, then find the value of x. c) Question 3. a) Construct a regular hexagon of side 3cm. [4] Solve the following: [13] Factorize: (i) (p+q) -20(p+q) -125 [4] [2] (ii) a2 +b2 -2 (ab ac + bc) [2] 2 b) The length, breadth and height of a cuboid are 30 cm, 20 cm [4] and 25 cm respectively. Find its (a) volume (b) total surface area c) (i) Plot the points P(0,-4), Q(6,2), R(3,5), and S(-3,-1) [5] (ii) Calculate the distance of PQ and RS using distance formula. (iii) Name the geometrical figure obtained. SECTION B (40 marks) (Attempt any 4 questions) Question 4. a) Solve the following: [10] Two poles of heights 6m and 11m stand vertically on a plane [3] ground. If the distance between their feet is 12m; find the distance between their tops. b) Prove that: 1 1+ + [3] 1 1+ + 5 1 1+ + =1 c) D is the mid-point of side BC of ABC and E is the mid-point of [4] BD. If O is the mid-point of AE, then prove that ar( BOE) = Question 5. a) 1 8 ar( ABC) Solve the following: [10] The sum of a two digit number and the number obtained by [4] reversing the order of its digits is 121, and the two digits differ by 3. Find the numbers. b) Calculate the following Compound interests: [6] (i) Find the difference between compound interest and simple [4] interest on Rs 12000 and 1.5 years at 10% compounded halfyearly. (ii) In how many years will 7000 amount to 9317 at 10% per [2] annum compound interest? Question 6. a) Solve the following: [10] In a pentagon ABCDE, AB is parallel to ED and B = 140o. [3] Find C and D, if C : D= 5:6. b) Construct a parallelogram ABCD in which AC = 6.4 cm, BD = [3] 8.2 cm and angle between diagonals AC and BD is 60 o. c) A solid cube of side 12 cm is cut into 8 cubes of equal 6 [4] volume. What will be the side of the new cube? Also, find the ratio between their surface areas. Question 7. a) Solve the following: [10] Find the points on the -axis whose distances from the points [3] A(7,6) and B(-3,4) are in the ratio 1:2. 2 b) If = 1+ 2, find the values of , given ( 2 < 1) [3] c) In the given figure, AD BC and BD < DC. Show that AB < AC. [4] Solve the following: [10] Find mean and median for the following observations : [3] Question 8. a) 31, 38, 27, 28, 36, 25, 35, 40 b) D is any point on the side AC of ABC with AB = AC. Show [3] that CD < BD. c) A swimming pool is 40 m long and 15 m wide. Its shallow and deep ends are 1.5 m and 3 m deep respectively. If the bottom of the pool slopes uniformly, find the amount of water in litres required to fill the pool. 7 [4] Question 9. a) Solve the following: [10] Construct a frequency polygon for the following distribution, [3] using histogram C.I. 5 15 15 25 25 35 35 45 45 55 55 65 f 8 16 18 14 8 2 b) c) 1 Simplify: 8 3 (27) Evaluate: 1 25 2 (4) 4 0 (9) + 1 125 3 ( 64 ) cos 37 .cosec 53 [3] [4] tan 5 .tan 25 .tan 45 .tan 65 .tan 85 Question 10. [10] a) (i) [6] An isosceles triangle ABC has AC = BC. CD bisects AB at D [3] and CAB = 55o. Find : (ii) i. DCB ii. CBD In the given figure, AC = CD, BAD = 110o and ACB = 74o. Prove that : BC > CD. 8 [3] b) Solve graphically the following system of linear equations (use graph sheet). From the graph find the co-ordinates of the point where the two lines intersect. 6y = 5 + 10 y = 5 15 ***** 9 [4]

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