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Class & section: VIII___ FINAL EXAMINATION MARCH -2012 Roll No: _____________________ Name of the Student: ______________ Signature of the invigilator: ________ Time: 3hours Marks Obtained: Total Marks: 100 Signature of the evaluator: ______ MATHEMATICS I. Multiple choice questions: 20 X 1 = 20 1. The price quoted on an article for sale is __________________[Selling price, Cost price, Marked price, Discount] 2. The statement “if 13 is taken away from one-fifth of a number, the result is IQ” mathematically written as 1 x 13 x 12 , 13 12 , 13x 1 1Q ] __________________________ [ 13 x , 5 5 5 5 3. A bank run by the students for the student is _____________________ [Nationalized Bank, Co-operative Bank, Sanchayika, Private Bank] 4. Among the following irrational number is _______________________[ 3 2 , 16 25 , 5 , 4 ] 6 25 3x 5 1 is __________________ [-1, -2, 0, 2] 5. The value of x in 2x 1 3 6. Which of the following statement is true ____________________________________________ b a b a b , a.b a b , [ ab a b , ] a b a 7. If 2% commission is given on Rs.1000, then the amount of commission is Rs._________[ 100, 2, 200, 20] 8. H.C.F. of (a 2 b 2 ) and (a 2 2ab b 2 ) is __________________ [ (a b) , a 2 b 2 , (a b) 2 , ( a b) ] 9. The point A(0,3) lies on _________________________ axis. [ ve x , ve x , ve y , ve y ] 10. The mean of 7, 9, 10, 12 and 15 is _____________________________[11.6, 10.6, 10, 11] 4 11. 0.0003416 is scientifically denoted as __________________________[ 3.416 10 , 3.416 10 4 , 0.3416 10 4 ] 0. 3416 10 4 , 12. The product of repeated factor is called the _______________ of the factor. [base, power, index, multiple] 13. The missing term to make 16a 2 ___________ ab 2 a perfect square is ___________________________ [ 12ab , 12ab , 24ab , 36ab ] In the figure l1 and l 2 intersect at ‘0’, then the value of x is _________________ 14. [800, 200, 1000 160 ] 15. In the figure ABCD D A C = __________ [ B A C , AC D , AC B , ABC ] In the figure ABC PQR then A = __________[ P , Q , R , None of the above] 17. Which of the following statement is correct? [a. only two lines can be drawn through a point b. The whole is lesser than its part, c. angle at a common and point of two opposite rays is 0 180 , d. If equals are added to unequal wholes are equal] _______________________________________________ 16. 18. Complete the statement “If a transversal intersect two parallel lines, then a pair of corresponding angles are _______________________ [complementary, are supplementary, equal, equal to 360 ] 19. The centriod divides the median in the ratio ______________________[2:3, 2:1, 1:2, 1:1] 20. Which of the following forms a linear pair____________________ 0 a. b. c. d. II. Fill in the blank with correct answer: 10 x 1 = 10 21. The simple interest for Rs.2450 at 3% for 6 months is ________________ 22. Varun’s father age is thrice as old as Varun if the father’s age is 45 yrs, then the Varun’s age is _________________ 23. The 3 consecutive even numbers whose sum is 162, then the numbers are _________________ 4 5 6 24. The order of the matrix A is ______________________ 7 8 9 25. The number which do not have multiplicative inverse is _________________________ 26. The n 2 form of 9801 is ____________________________ 27. The mid point of the class interval 60-69 is _______________________ 28. In a right angled triangle, if 29. A B C 90 0 then the longest side of the triangle is __________ Which axiom can be stated based on the given example? 30. Define ‘centroid’. III. Do as directed: 18 x 2 = 36 2 2 31. Find H C F and L C M of 9xy, 12 x y & 15xz . 32. Find the least number by which 700 must be multiplied to make it a perfect square. 33. A company sells a sewing machine for Rs.3520 by allowing discount at 12%. Calculate the Marked Price. 34. Find the co-efficient of x 2 and x in (3 x +2)(3 x + 4 y ) . 35. What is a matrix? Give an example for a matrix of order 2 3 . 36. Solve graphically. 3x y 6 (Separate graph sheet enclosed). 37. Find the square root of 3025 by factor method. 38. Factorize (1) x 2 8 x 15 (2) 6a 2 b 15ab 2 39. Find the product of 2 x 5 y 9 z 2 using suitable Identity. 40. Distinguish between S.B. account and Current account. 41. Find the Simple Interest for Rs.1500 at 4% for 3½ months. Given the interest for Rs.500 per month is Rs.1.6667. 42. Define rational numbers and prove the closure property over addition with an example. 43. The Arithmetic mean of 6, 8, 5 7 x and 4 is 7. Find the value of x . 44. In the figure l 2 stands on l1 and a b 40 . Find the value of a &b. AB is a straight line OB bisects P O Q . Show that A O P A O Q. 45. 46. In the figure AB and CD bisect each other at ‘0’ show that AC=BC. 47. In the adjoining figure, find value of ‘ x ’ and measure of A O B and A O C. 48. In the given figure PQR ABC IV. Solve the following: 49. Verify the associative Property over addition for the Rational numbers. 1 2 , 6 x 3 = 18 1 , 2 . 5 4 2 2 2 50. Subtract the sum of 8m 7n 6 p and 3m 4n p from the sum of 2m 4n 3 p and m n p . 2 x x x x x a 51. Prove that x a b b bc b c ca c a =1 52. The volume of a cube is 9261 cm3. Calculate the length of its side and find the area of one of its faces. 53. ABC is an isosceles triangle. AB=AC, and AP= AQ. Show that BQ=CP. 54. AB and CD intersect at ‘O’ perpendicularly. OX bisects A O C and OY bisects V. Answer the following: 4 x 4 = 16 2 2 2 55. Factorize: (1) 5 x 16 x 21 (2) 3a 11ab 6b 56. Calculate the mean, and median: Scores 2 7 12 17 22 27 32 37 Frequency 2 4 6 10 7 6 3 2 0 57. In any triangle, the sum of three interior angle is 180 . Prove this theorem logically. 58. Construct equilateral triangle ABC with sides 5 cms each and draw circum-circle to it. ****************************** Class & section: IX ___ FINAL EXAMINATION MARCH -2012 Time: 3 hours Roll No :_____________________ Marks Obtained : Name of the Student :______________ Total Marks : 100 Signature of the invigilator : ______ MATHEMATICS Signature of the evaluator :______ Choose the correct answer: 20x1=20 1. In post office the monthly minimum balance is called _______________________________. a) Product b) Principle c) Amount d) Interest bearing balance. 2. The number for which the reciprocal is itself is ________________. [ a) 0 b) 1 c) ½ d) 0.1 ] 3. If P= { 2,3,4,5} Q= { 4,5,6,8 } then Q-P is ___________ [ a) {2,3} b) {4,5} c) {2,3,4,5,6,8 }, d) {6, 8}] 4. The word drawer refers to _______________________[a) Account holder b) The person to whom the cheque is payable c) The bank d) Manager x 2 x 3 = 3 x 5 x 2 , This statement shows ___________________ property 3 7 2 2 3 7 a) Associative property b)Distributive property c) communicative property d) binary operation 6. The number which has no multiplicative inverse is ________________. [ a) 0 b) 1 c) -1 d) 3 ] 5. 5 7. If a+2b = 10 , ab=15 then a 3 8b 3 = _________________________ [a) 900. b) 100 c) 550 d) 990. 8. Which of the following expressions has their H.C. F as 1__________________________________ a) a b 2 a 2 b2 b) a 2 b 2 a 2 b 2 c) a b a 2 b 2 d) a b 2 2 b a 9. LCM of 5 x 2 y 2 , 10 y 2 z 2 , 15 x 2 z 2 , y 2 is ______________ a) 30 x 2 y 2 b) 15 x 2 y 2 z 2 c) 5x 2 y 2 z 2 d) 30 x 2 y 2 z 2 z 2 10. Which of the following is not B.O on the given set a) a b = a+b+2 a, b N b) a b = a-b a, b N c) ) a b = a b a, b N d) a b = HCF of a, b N 11. The trinomial which cannot be factorized _______________________________________ a) x 2 x 6 b) x 2 7 x 6 c) x 2 x 6 d) x 2 5 x 6 12. Which of the following is not in the form of a 3 b 3 is _______________________________ a) 8 x 6 b) 27x 3 y 3 z 4 c) x 4 xy 6 d) x 3 -8(b-c) 3 13. The co-ordinates of the origin are _________________________a) (x,0) b) (0, y ) c) (0.x) d) (0,0) 14, The diagonals bisect at right angles in _______________ and _________________________ a) square, Rhombus b) square parallelogram c) Rhombus , Rectangle d) square Rectangle 15. In an inscribed regular hexagon each interior angle is ___________________ the central angle a) equal b) twice c) four times d) half 16. The volume of cubical box whose T. S. A is 600cm 2 = ______ cm 3 a) 2500 b) 1000 c) 900 d) 1100 17. In Parallelogram ABCD ‘P’ is the midpoint of BC. DP and AB are Produced to meet at Q. AQ= ______ a) 2CP 18 . b) 2 AB c) 2AD d) 2DP ABCD is a Cyclic quadrilateral if CBF 130, EDC ___________________ a) 130 0 b) 65 0 c) 50 0 d) 40 0 19 . In ABC P , Q , and R are the midpoints of AB, BC and AC respectively which of the following Statement is correct ________________________________ a) Area of ABC = Area of PQR b) Perimeter of ABC = Perimeter of PQR c) Area of a PQR is half the area of ABC d) Perimeter of a ABC is twice the Perimeter of PQR In the figure if ‘O’ is the centre . OP AB OQ CD and OP = OQ then a) AB > CD b) AB =CD c) AB < CD d) no relation between AB and CD 20. II . Fill in the Blanks with correct answer: 3 21. The value of 10x1=10 64 + 3 125 + 7 is ______________________________. 22. The number to be added to x 2 6 x 7 to make it divisible by x 3 is ________________ 23. If 5: x = x : 1.25 then the value of x is _______________________ 24.The quotient of 4 x 5 z 8 8 x 4 y 4 12 x 6 y 9 z 10 is _______________________________ 25.The factors of a 2 b c are______________________ and __________________ 2 26. If a=b , b=c then a=c this indicates the property ________________________________________ 27. In the figure BOC 130 0 then BAC 28. The area of a trapezium is 400m 2 , if the parallel sides are 15m and 17 m . its altitude is ___________ 29. The angle in the major segment is always ____________________________ 30. The volume of Prism is 300cc. The volume of Pyramid with same height and base as that of the Prism is ___________________________________ Answer the following : 18x2=36 31. Find the Product of 103.102 and 98 using suitable Identity 32. Locate 5 on the number line. 33. Reduce into simplest forms and classify into set of like surds 50 45 12 20 27 34. Find the remainder when x 4 2 x 3 x 7 is divided by x 2 . without actual division 35. Find the compound interest if principle is Rs 2000. rate of interest is 10% for 2years 36. Factorise 2 x 2 27 x 63 37. Slove 5 x 3 y 7 and 3x 2 y 8 38. Find the square root of 81.5409 39. Find the HCF of x 2 x 6 x , x 2 3 x 2 40. a b ab , a ,b Z verify whether (z , ) is an algebraic structure. 2 41. Divide Rs 1750 in the ratio 12:9:4 42. If P= {2,4,6,8,10} Q= {1,2,3,4,5,6} and R= { 1,3,5,7,9,11} find (P Q) R 43. Inscribe a regular pentagon on a circle of radius 3.5cms. 300 44. construct rhombus ABCD having side AB= 5.5cm and diagonal AC= 7.6cm Measure the other diagonal . 45. In a circle of radius 10 cms there are two parallel chords of length 12cm and 16cms find the distance between then when they are either side of the centre. 46. In a parallelogram ABCD . X and Y are mid points of AB and CD respectively . Prove that BYDX is a parallelogram . Y D C A B X 47. The sides of the base of a square based pyramid is 25cm is the volume is 900cc find the height of the pyramid . 48. In the fig PQRS is a cycle quadrilateral PSQ 60 0 SPQ =85 0 , SOR 90 0 Find PQR Do as Directed 4x4=16 49. The cash price of a fan is Rs 960 is is purchased by paying Rs 160 cash down and the balance is paid in 6 monthly installment of Rs 160 each . calculate the rate of interest . 50. The entries in the S B Account pass book of a person are found to be as follows . Calculate the interest to be credited to the account on the last day of June at 6% per annum Sl no 1 2 3 4 5 6 7 8 Date Jan 3 Jan 5 March 4 March 9 March 17 April 8 April 10 April 19 Amt Deposited withdrawn B/F 4000 1000 2000 2000 800 1700 500 Balance 1000 5000 4000 6000 4000 4800 6500 6000 51. Divide 2 x 3 5 x 2 6 x 5 by x 2 52. A is 25 years older than B . After 15 years A will be twice of B . Find their present ages. 53. The base of a right prism is an equilateral triangle with perimeter 12cm and the height is 5cm . Find lateral surface Area and Total surface area . 54. i) Find the value of x ii) A Pyramidal tent is made of canvas it occupies a square area of 100 sq ms on the ground and the height 12cm . Calculate the air space inside the tent . Answer the following : 55. Calculate the mean deviation from median C.I f 20-24 2 25-29 3 30-34 5 35-39 3 40-44 2 N=15 56. State and Prove the mid . point theorem 57. Construct a quadrilateral ABCD in which BC=7.5cm AC= AD=6cm CD=5cm BD=10cm Draw the altitude AP and CQ on the diagonals DB and find the area of quadrilateral ABCD. 58. Solve graphically , 2 x y 5 and 3x y 7 ******************