MATHEMATICS CLASS IX PRE BOARD

Sister Nivedita school Ameerpet, Hyderabad CLASS 09 - MATHEMATICS Mathematics Time Allowed: 3 hours Maximum Marks: 80 General Instructions: 1. This question paper contains two parts A and B. 2. Both Part A and Part B have internal choices. Part – A consists 20 questions 1. Questions 1-16 carry 1 mark each. Internal choice is provided in 5 questions. 2. Questions 17-20 are based on the case study. Each case study has 5 case-based sub-parts. An examinee is to attempt any 4 out of 5 sub-parts. Part – B consists 16 questions 1. Question No 21 to 26 are Very short answer type questions of 2 mark each, 2. Question No 27 to 33 are Short Answer Type questions of 3 marks each 3. Question No 34 to 36 are Long Answer Type questions of 5 marks each. 4. Internal choice is provided in 2 questions of 2 marks, 2 questions of 3 marks and 1 question of 5 marks. Part - A [1] 1. Simplify the expression: (5 + √7–)( 2 + √5–) OR −1 Simplify: (625) 4 2. Find the value of k, if x – 1 is a factor of 4x3 + 3x2 – 4x + k. [1] 3. 1500 families with 2 children were selected randomly, and the following data were recorded : [1] Number of girls in a family 21 0 Number of families 475 814 211 Compute the probability of a family, chosen at random, having 2 girls 4. Construct an equilateral trianagle each of whose sides measures 5cm. [1] 5. The height of an equilateral triangle measures 9 cm. Find its area, correct to 2 places of [1] decimal. (Take – = 1.732) √3 OR The base of an isosceles triangle measures 80 cm and its area is 360 cm2. Find the perimeter of the triangle. 6. A cube and a sphere are of the same height. Find the ratio of their volume. [1] 7. Evaluate: (32)3 [1] Pre board-1 1/8

OR [1] Express 0.99999....in the form p , where p and q are integers and q ≠ 0. [1] q 8. Which one of the following options is true, and why? y=3x+5 has (i) a unique solution, (ii) only two solutions, (iii) infinitely many solutions 9. Find the volume of the right circular cone with radius 6 cm and height 7 cm. OR A matchbox. What will be the volume a packet containing 12 such boxes? 10. Expand: (3a + .1 3 [1] ) 4b 11. Write the equation in the form ax + by + c = 0 and indicate the values of a, b, c in case: 3x - 8 = [1] 5y 12. Factorise: x5 + x2. [1] 13. Find the measure of an angle which is 24° more than its complement. [1] 14. The weight of a man is four times the weight of a child. Write an equation in two variables for [1] this situation. 15. Write the equation of a line passing through the point (0, 4) and parallel to x-axis. [1] [1] −− 16. Classify the number √ 3 as rational or irrational. Give reasons to support your answer. 81 OR Insert a rational number and an irrational number between .0001 and .001 17. Read the Source/Text given below and answer any four questions: [4] Rohit was putting up one of his paintings in his living room. Before this Rohit had put a grid on the wall where each unit measured equal to a foot. The upper-left corner of the frame is at point C (1,8) and the upper-right corner at D (7,8). The bottom-left corner is at A (1,2) and the bottom-right corner at B (7,2). Please answer the following questions: i. What is the width of the painting plus frame? Pre board-1 2/8

a. 5 feet b. 8 feet c. 9 feet d. 6 feet ii. What is the length of the painting plus frame? a. 9 feet b. 8 feet c. 6 feet d. 5 feet iii. Which sides of the painting are parallel to x-axis? a. AB and CD b. AC and BD c. Diagonals AD and BC d. No one iv. Which sides of the painting are parallel to y-axis? a. AB and CD b. AC and BD c. Diagonals AC and BD d. No one v. Point A, B, C and D lie in which quadrant? a. I b. II c. III d. IV 18. Read the Source/Text given below and answer any four questions: [4] Four friends decided to play a game, Meena advised instead of playing physical game let's play a geometry game. Meena Drew a ΔABC. Rohit found the midpoint of side AB and marked it as D. Now the third student Mathew, from D drew a line DE||BC, for this, he made ∠ADE = ∠ABC. Further, the fourth friend Veena from the point E drew a line parallel to AB, She observed that this line cuts Bc at New point F. Veena found that EF = BD. As marked in the given picture. Now all the friends were trying to prove that △ADE ≅ΔEFC. Now answer the following questions: 3/8 Pre board-1

i. In the ΔADE and ΔEFC, AD =? [4] a. CE b. FC c. EF d. AE ii. In the ΔADE and ΔEFC, ∠1 =? 1. ∠r 2. ∠q 3. ∠E 4. ∠A iii. In the ΔADE and ΔEFC, ∠2 =? a. ∠r b. ∠q c. ∠E  d. ∠A iv. ΔADE and ΔEFC are congruent according to which criteria: a. SSS b. SAS c. ASA d. RHS v. AE is equal to which side? a. AD b. DE c. BD d. EC 19. Read the Source/Text given below and answer any four questions: There was a circular park in Defence colony At Delhi. For fencing purpose Poles A, B, C and D were installed at the circumference of the park. Ram tied wires From A to B to C and C to D, He managed to measure the  ∠A =100° and ∠D = 80° The point O  in the middle of the park is the center of the circle. Now answer the following questions: Pre board-1 4/8

i. What is the value of ∠B? [4] a. 80° b. 100° c. 90° d. 70° ii. What is the value of ∠C? a. 80° b. 100° c. 90° d. 70° iii. What is the special type of quadrilateral ABCD? a. Square b. Rectangle c. Cyclic quadrilateral d. Trapezium iv. What is the property of cyclic quadrilateral? a. Opposite angles are supplementary b. Adjacent angles are equal c. Opposite angles are equal d. Adjacent angles are complementary v. What you will call the yellow shaded shape OBC? a. Segment b. Arc c. Chord d. Sector 20. Read the Source/Text given below and answer any four questions: There are 5 bags of seeds. If we select fifty seeds at random from each of 5 bags of seeds and sow them for germination. After 20 days, some of the seeds were germinated from each collection and were recorded as follows: Bag 12345 40 48 42 39 41 No. of seeds germinated What is the probability of germination of i. more than 40 seeds in a bag Pre board-1 5/8

a. 0.6 [2] b. 0.1 c. 0.4 d. 0 ii. 49 seeds in a bag a. 1 b. 0 c. 0.9 d. -1 iii. more than 35 seeds in a bag a. 0 b. 3.5 c. 1 d. 0.35 iv. The sum of all probabilities equal to: a. 4 b. 1 c. 3 d. 2 v. If P(E) = 0.44, then P(not E) will be: a. 0.44 b. 0.55 c. 0.50 d. 0.56 Part - B 21. In the given figure, A, B, C, and D are four points on a circle. AC and BD intersect at point E such that ∠BEC =130° and ∠ECD = 20°. Find ∠BAC. 22. Are there two irrational numbers whose sum and product both are rationals? Justify. [2] OR 21 Evaluate: ( 64 − + ( 256 − 4 .3 0 )3 ) +( ) 125 625 7 23. Use suitable identities to find the following product : (y2 + 3 )(y2 - 3 ). [2] 22 24. Parveen wanted to make a temporary shelter for her car, by making a box-like structure with [2] tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore Pre board-1 6/8

negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions 4 m × 3 m? 25. Find the area of an isosceles triangle, whose equal sides are of length 15 cm each and third [2] side is 12 cm. OR The perimeter of an isosceles triangle is 42 cm and its base is 1 1 times each of the equal sides. 2 – Find the length of each side of the triangle. (Given, √7 = 2.64.) 26. In a ||gm ABCD, if ∠A = 115o, find ∠B, ∠C and ∠D. [2] 27. In figure, ∠Q > ∠R and M is a point QR such that PM is the bisector of ∠QPR. If the [3] perpendicular from P on QR meets QR at N, then prove that ∠MPN = 1 (∠Q – ∠R) 2 28. Construct an angle of 22 1 0 at O. [3] 2 OR Construct a △ABC in which BC = 5 cm, AB = 3.8 cm and AC = 2.6 cm. Bisect the largest angle of this triangle. 29. How many cubic metres of earth must be dug out to sink a well 14 m deep and 4 m in [3] diameter ? What will it cost to plaster the inner surface at the rate of Rs. 25 per square metre ? 30. Find m and n if x - 1 and x - 2 exactly divide the polynomial x3 + mx2 − nx + 10 [3] OR Factorise: 3x3 − x2 − 3x + 1 31. A traffic signal board indicating 'school ahead' is an equilateral triangle with side 'a' find the [3] area of the signal board using heron's formula. Its perimeter is 180 cm, what will be Its area? 32. If a = xyp-1, b = xyq-1 and c = xyr-1, prove that aq-r br-p cp-q = 1 [3] 33. ABCD is a quadrilateral such that diagonal AC bisects the angles A and C. Prove that AB = AD [3] and CB = CD. 34. A random survey of the number of children of various age groups playing in a park was found [5] as follows Age (in years) Number of children 1-2 5 2-3 3 3-5 6 5-7 12 7-10 9 10-15 10 15-17 4 Draw a histogram to represent the data above. Pre board-1 7/8

OR [5] Draw the graph of the equation 2x − 3y = 5. From the graph, find [5] i. the value of y when x = 4 and ii. the value of x when y = 3 35. On one page of a telephone directory, there were 200 telephone numbers. The frequency distribution of their unit's digits is given in the following table: Unit's digit 0123456789 Frequency 22 26 22 22 20 10 14 28 16 20 Out of the numbers on the page, a number is chosen at random. What is the probability that the unit's digit of the chosen number is i. 6? ii. a nonzero multiple of 3? iii. a nonzero even number? iv. an odd number? 36. PQRS is a parallelogram. PX and QY are respectively, the perpendiculars from P and Q to SR and RS produced. Prove that PX = QY. Answer scripts to be mailed to respective subject teachers Krishna Priya - [email protected] [email protected] Jyothi - [email protected] Jeevan Jyothi - mjeevanjyot [email protected] Sreehari - [email protected] Pre board-1 8/8