PIONEER GUESS PAPER 9 th CBSE (SA-II) MATHEMATICS TIME: 2:0 HOURS MAX. MARKS: 80 GENERAL INSTRUCTIONS & MARKING SCHEME All questions are compulsory. The questions paper consists of 4 questions divided into four sections A, B, C and D. Section A contains 10 questions of 1 mark each, which are multiple choice type questions, Section B contains 8 questions of 2 mark each, Section C contains 10 questions of marks each, Section D contains 6 questions of 4 marks each. There is no overall choice in the paper. However, internal choice is provided in one question of 2 marks, questions of marks and two questions of 4 marks. Use of calculators is not permitted. NAME OF THE CANDIDATE PHONE NUMBER L.K. Gupta (Mathematics Classes) FOR SOLUTIONS KINDLY VISIT www.pioneermathematics.com (In Latest Updates) 1
Section A 1. x = 5, y = 2 is a solution of the linear equation (A) x + 2 y = 7 (B) 5x + 2y = 7 (C) x + y = 7 (D) 5 x + y = 7 2. The equation x = 7, in two variables, can be written as (A)1. x + 1. y = 7 (B) 1. x + 0. y = 7 (C) 0. x + 1. y = 7 (D) 0. x + 0. y = 7. Three angles of a quadrilateral are 75 0, 90 0 and 75 0. The fourth angle is (A) 90 0 (B) 95 0 (C) 105 0 (D) 120 0 4. The figure obtained by joining the mid-points of the sides of a rhombus, taken in order, is (A) a rhombus (B) a rectangle (C) a square (D) any parallelogram 5. ABCD is a trapezium with parallel with sides AB = a cm & DC = b cm. E & F are the midpoints of the non-parallel sides. The ratio of ar(abfe) & ar (EFCD) is (A) a : b (C) (a+b) : (a+b) (B) (a+b) : (a+b) (d) (2a+b) : (a+b) 6. Diagonals of a parallelogram ABCD intersect at O. If 0 0 BOC = 90 and BDC = 50,then OABis (A) 90 0 (B) 50 0 (C) 40 0 (D)10 0 7. AD is a diameter of a circle and AB is a chord. If AD = 4 cm, AB = 0 cm, the distance of AB from the centre of the circle is : (A) 17cm (B) 15cm (C) 4cm (D) 8cm 8. With the help of a ruler and a compass, it is possible to construct an angle of : (A)5 0 (B)40 0 (C)7.5 0 (D)47.5 0 9. The radius of a sphere is 2r, then its volume will be (A) 4/π r (B) 4π r (C) 8π r / (D) 2/ π r 10. The class-mark of the class 10 150 is : (A)10 (B)15 (C)140 (D)145 2
SECTION B Question numbers 11 to 18 carry 2 marks each. 11. Determine the point on the graph of the equation 2x + 5y = 20 whose x-coordinate is 5 2 times its ordinate. 12. Three angles of a quadrilateral ABCD are equal. Is it a parallelogram? 1. ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ (Fig. 1). If AQ intersects DC at P, show that ar (BPC) = ar (DPQ) 14. In the Fig. 2, OD is perpendicular to the chord AB of a circle whose centre is O. If BC is a diameter, show that CA = 2OD. 15. Draw a line segment AB of length 5.8 cm. Draw the perpendicular bisector of this line segment. 16. A cylindrical pillar is 50 cm in diameter and.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of 12.50 per m 2. 17. A soft drink is available in two packs (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having of 15 cm and (ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much? 18. Calculate the mean for the following distribution: x: 5 6 7 8 9 f: 4 8 14 11
SECTION C Question numbers 19 to 28 carry marks each. 19. Draw a graph of each of the following equations : (i) x + 2 = 0 (ii) 2y + = 0 (iii)4x 6 = 0 20. If the point (, 4) lies on the graph of y = ax + 7, then find the value of a. 21. In a quadrilateral ABCD, CO and DO are the bisectors of Cand Drespectively. Prove that 1 COD = ( A + B). 2 22. If ABCD is a parallelogram, the prove that ar ( ABD) = ar ( BCD) = ar ( ABC) = ar ( ACD) = ar ( gm ABCD) 2. Find the length of a chord which is at a distance of 5 cm from the centre of a circle of radius 10 cm. 24. How many liters of water flow out of a pipe having an area of cross-section of 5 cm 2 in one minute, if the speed of water in the pipe is 0 cm/sec? 25. A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all around it to a width of 7.5 m to form an embankment. Find the height of the embankment. 26. The ages of ten students of a group are given below. The age have been recorded in years and months: 8 6, 9 0, 8 4, 9, 7 8, 8 11, 8 7, 9 2, 7 10, 8 8 (i) What is the lowest age? (ii) What is the highest age? (iii) Determine the range? 1 2 4
27. Following are the ages of 60 patients getting medical treatment in a hospital on a day: Construct a Cumulative frequency distribution Age (in years): 10 20 20 0 0 40 40 50 50 60 60 70 No. of Patients : 90 50 60 80 50 0 28. The percentage of marks obtained by a student in monthly unit tests are given below : Unit test : I II III IV V Percentage of marks obtained: 69 71 7 68 76 Find the probability that the student gets: (i) more than 70% marks (ii) less than 70% marks (iii) a distinction. 5
Section D Question numbers 29 to 4 carry 4 marks each 29. Draw the graphs of the lines represented by the equations x + y = 4 and 2x y = 2 in the same graph. Also, find the coordinates of the point where the two lines intersect. 0. ABCD is a square E, F, G and H are points on AB, BC, CD and DA respectively, such that AE = BF = CG = DH. Prove that EFGH is a square. 1. In a ABC, P and Q are respectively the mid-points of AB and BC and R is the mid-point of AP. Prove that: (i) ar( PBQ) = ar ( ARC) 1 2 (ii) ar( PRQ) = ar ( ARC) =. 8 (iii) ar( RQC) ar ( ABC) 2. Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F 0 A 0 B 0 C respectively. Prove that the angles of DEF are90,90 and90. 2 2 2. A circus tent is cylindrical to a height of metres and conical above it. If its diameter is 105 m and the slant height of the conical portion is 5 m, calculate the length of the canvas 5 m wide to make the required tent. 4. The time taken, in seconds, to solve a problem by each of 25 pupils is as follows: 16, 20, 26, 27, 28, 0,, 7, 8, 40, 42, 4, 46, 46, 46, 48, 49, 50, 5, 58, 59, 60, 64, 52, 20 (A) Construct a frequency distribution for these data using a class interval of 10 seconds. (B) Draw a histogram to represent the frequency distribution. 6
7
Online services [ (9 th, 10 th, +1, +2, CBSE, ICSE, IIT-JEE, AIEEE, SAT, NTSE, OLYMPIAD) Ask a teacher. NCERT solutions. Discussion of R.D. Sharma, R.S. Aggarwal etc. Discussion of T.M.H., A. Das Gupta, S. L. Loney, Hall & knight, Thomas Finney etc. Mathematics Olympiad (RMO, INMO, IMO). Objective chapter wise tests with immediate result & review. Objective practice + smart solutions. Vedic mathematics (Meaningful& applicable). Test series for IIT-JEE and AIEEE. IIT-JEE sure shot Tips & Tricks. AIEEE (Twisters, Tips & Tricks). Boards, IIT-JEE, AIEEE previous year papers and solutions. Latest sample papers for boards, IIT-JEE & AIEEE. Correspondence course (9 th /10 th CBSE/ICSE SA-I, SA-II, +1, +2 IIT-JEE, AIEEE) Self study material (For AIEEE + IIT-JEE). Maths projects. Personality development, IQ sharpeners, jokes etc. And many more L.K.Gupta (M.Sc. Mathematics) Introduces www.pioneermathematics.com (Individual Approach Guaranteed) 8