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Class & section: VIII FIRST TERMINAL EXAMINATION -SEPTEMBER -2013 Time: 3 hours Roll No: _____________________ Name of the Student: ______________ Signature of the invigilator: ________ Marks Obtained: Total Marks: 100 Signature of the evaluator: ______ SUBJECT: MATHEMATICS I. Choose the correct answer: [1 x 14 =14] 1. The digits in the units place of a perfect square number can never be ________________________ a. 2&3, b. 0&1, c.5&6, d. 6&9 2. The multiplicative inverse of 3 is _________________________ 5 a. 5 , b. 5 , c. 3 , d. 3 3 3 5 5 3. An article costing Rs.600 is sold for Rs.750. the gain percent is __________________________ a.20, b. 25, c. 30, d. 35 4. The rational number each of which is equal to its reciprocal is __________________________ a.1 & –1, b.0 & 2, c. 0 &1, d.2 & –2 5. Discount is equal to ___________________________ a.M.P – S.P, b. S.P – C.P, c. C.P – S.P, d. M.P – C.P.] 6. The 8thtriangular number is [a. 10, b. 28, c. 36, d. 48 ] ___________________________ 7. The value of 3 2197 is [a. 23, b. 27, c. 13, d. 17] ___________________________ 8. If 4 is added to a number and the sum is multiplied by 3, the result is 30, then the number is __ [a.3, b. 4, c.5, d.6] ___________________________ 9. The simplified form of 7 x 9 y 3 3x 5 y 8 is ___________________________ a. 4 x 4 y 11, b. 4 x 14 y 11 , c. 4 x 4 y 11 , d. 3x+5y-11] 10. If 2 x (3x 4) 3x 5, then x a. 4 , b. 9 , c. 3 , d. 2 9 4 2 3 ___________________________ 11. The factors of a 2 b 4 b 2 a 4 is ___________________________ a. a 2 b 2 , b. (a 2 b 2 )( a 2 b 2 ) , c. a 2 b 2 a b(a b) , d. a 2 b 2 a b a b 12. The difference of 4.5 1.5 simplifies to a. 18 b. 81 c. 108 d. 801 __________________________ 13. If pq = 32, p+q= – 12, then p & q are-a. 8, 4 b. 16, 2 c.–8, – 4, d. – 16, 2 _______________________ 14. 3 y 6 5x is-a. 30 xy 15 x b.15 xy 30 x, c. 30 xy 15 x d. 15 x 30 xy ________________________ II. Fill in the blanks: [ 1 x 7 = 7] 1. The property used in the following statement is 2 9 = 9 2 is _______________ 2. Nine percent of Rs.700 is ______________________________________________ 2 2 3. The sum of first 26 odd numbers is ______________________________________ 4. If x y 3 & xy 4 , then the value of x 2 y 2 is _____________________________ 5. The factors of ax bx ay by is _______________________________________ 6. The sum of 2b 4a and 4a b is ___________________________________ 7. An article marked Rs.,800 is sold for Rs.704. the discount percent is ____________ III. Solve: [12 x 2 = 24) 1. Find the Square root of 11664 by factor method. 2. How many perfect cubes are there from 1 to 500. How many of them are perfect square? 22 36 6 3. Simplify: 5 5 7 4. Write the following in ascending order. 2 , 5 5 , 6 15 10 , , 8 11 6 13 , 9 4 5. The salary of an employee is increased by 15%. If the new salary is Rs.12,650, what was his salary before enhancement? 6. The marked price of a shirt is Rs.750 and the shopkeeper offers 20% discount on it, what would be the S.P of the shirt? 7. Factorize: p 2 24 p 144 . 8. Viji is twice as old as his brother Deepu. If the difference of their age is 11 years, find their present ages. 9. Find three consecutive odd numbers, whose sum is 219. 1 10. Find the product: m 2 1 1 m 3 2 11. Evaluate using Identity: 53 55. 12. Solve: 3 4 x 1 x 3 . 1 1 2 1 m 3 4 9 IV. Solve: [3 x 4 =12] 1. A square yard has area 1764 m2. From a corner of this yard, an another square part of area 784m2 is taken out for public utility. The remaining portion is divided into 5 equal square parts. What is the perimeter of each of these equal parts? 2. (a) Check and verify a b c a b c for the values of a 2 , 3 (b) Represent the rational number 9 2 b 3 4 and c 3 5 on the number line. 3. The sides of a rectangle are 2 x 3 y and 3x 2 y from this a square of side x y is removed. What is the area of the remaining region? 4. Factorize: x 8 y 8 . V. Solve: [3 x 4 =12] 1. The sum of the digits of a two digit number is 12. if the new number formed by reversing the digits is greater than the original number by 18. Find the original number. Check your solution. 2. A man sold two houses for Rs.2970 each. On one he gains 10% while on the other he loses 10% . How much percent does he gains or loss on the whole transaction? GEOMETRY: I. Choose the correct answer: [1 X 6=6] 1. In an equilateral triangle, each exterior angle is _____________________ [a. 600, b. 1200 c. both (a) &(b) d. 1500] 2. Two line segments are congruent if they have same ______________________ [a. length, b. endpoints, c. both (a)&(b), d. none of these.] 3. Angles which coincide on superposition are called ____ angles of congruent ______________________ triangles. [a. adjacent b. corresponding c. consecutive d. vertically opposite angles] 4. In a triangle, if A=800 and AB=AC, then B= ___ [a. 200, b. 1200, c. 500, d. 800] ________________ 5. The general statements which are particular to Geometry and are accepted without questions are called [a. axioms b. Postulates c. propositions d. enunciation] ________________ 6. The measure of an angle which is 3 times its supplement is [a.1440, b.1150, c.1500, d.1350] ______________________ II. Fill in the blanks: [1 x 3 = 3] 1. In an isosceles triangle, the angle bisector of the ________ angle is the perpendicular bisector of the base. 2. The value of ‘b’ in the given figure is ____________ 3. In the adjoining figure, if AC=CE and ∆ ABC ∆ DEC then D= ____________ and A = _______________ III. Do as directed: [2 x 6 = 12] 1. Two parallel lines and m are intersected by another pair of parallel lines p and q as in the figure; show that ∆ ABC ∆ ADC. 2. In the adjoining figure, COA – BOC = 700, find these angles. 3. The angles of a triangle are x 40 0 , x 20 0 & 1 x 15 0 , find the values of x. 2 4. In the adjoining figure, AB = CD & AD = BC, show that ADB = DBC. 5. Find the values of ' x' in the given figure. 6. The angles of a triangle are in the ratio 1: 2: 3. Determine the three angles. IV. Solve: [3 x 2 = 6] 1. Prove that if a side of a triangle is produced the exterior angle so formed is equal to the sum of the corresponding interior opposite angles. 2. (a) State ASA Postulate. (b) In a ∆ ABC, AB = AC and the altitude AD bisects BC. Prove that ∆ ADC ∆ ADB. V. Solve: [4 x 2 = 8] 1. a) Prove that in a triangle the angles opposite to equal sides are equal. b) In a quadrilateral ACBD, AC=AD and AB bisects A. Show that ∆ ABC ∆ ABD. 2. a) Find the value of ' y ' in the given figure. b) Find the value of ' p ' in the given figure. Class & section: IX_ FIRST TERMINAL EXAMINATION SEPTMBER2013 Time: 3 hour Roll No :_____________________ Marks Obtained : Name of the Student :______________ Total Marks : 100 Signature of the invigilator : ______ MATHEMATICS Signature of the evaluator :______ I. Choose the correct answer & fill in the blanks: 1x17=17 1. The additive inverse of 3+ 8 is __________ a) -3+ 8 b) 1 c) 3 - 8 d) – 3 - 8 3 8 2. (- 12 ) 3 + 7 3 + 5 3 = ___________ a) 1260 b) – 1260 c) 0 d) – 480 3. The square and square root of 10.24 will have ___ & ___decimal digits respectively. a) 2&4 b) 2&1 c) 1&2 d) 2&2 2 4. The coefficient of x in (2x + 1) (2x – 2) (2x – 5) is _______ a) – 6 b) + 16 c) – 24 d) +24 2 3 5. The irrational number between & is ________ a) 0.66…….. b) 0.657…….. c) 0.67…….. d) 3 4 0.76………. 2 2 2 6. If a + b+ c = 12, a + b + c = 50 , then ab + bc + ca = _________ a) 62 b) 124 c) 47 d) 94 7. Two surds are said to be like surds if ____________ a) their order & radicand are same b) their order & Coefficient are same c) their radicand & Co-efficient are same d) only order or radicand are same. 8. The factors of x 2 +xy + x + y are ________ & ________ a) (x+1) (y+1) b) (x+1) (x+y) c) (x+y) (y+1) d) (x+y) (x+y) 9. A = { 1, 2, 3, 4, 5, 6 } can also be expressed as __________ a) { x : x W & 0 x 6 } b) { x : x W & 0 x 6} c) { x : x W & 0 x 6 } d) { x : x W & 0 x 6 } 5 5 4 3 4 3 2 3 5 10. The HCH of 24a b c , 30a b c & 36a b c is ____ a) 6a 2 b 3 c 3 b) 2 a 2 b 3 c 3 c) 3 a 2 b 3 c 3 d) 6a 5 b 5 c 5 1 1 1 1 11. The index form of the surd 2 4 5 is ________ a) (10) 4 b) (5) 4 c) 80) 4 d) (80) 5 12. If AB = QR, BC = PR and CA = PQ, then __________ a) ABC QRP b) CBA PQR c) ABC PQR d) PQR BCA 13. A regular polygon of 12 sides will contain _________ triangles. a) 12 b) 10 c) 6 d) 14 14. In quadrilateral ABCD, AB = BC and CD = DA, then the quadrilateral is a _____________ a) Parallelogram b) rhombus c) kite d) trapezium 15. In ABC, D, E & F are the midpoints of sides BC, CA & AB respectively, then __________ AB AC BC a) DE = b) DE = 2AB c) DE = d) DE = 2 2 2 16. ABCD is a parallelogram. X and Y are the midpoints of sides AB & CD respectively. Then, the quadrilateral AXCY Is a ___________ a) parallelogram b) rectangle c) rhombus d) square 17. Which of the following statement is correct? ___________________ a) a trapezium is a parallelogram b) every rectangle is a parallelogram c) every parallelogram is a rectangle d) every rhombus is a square II. Fill in the blanks: 1x13=13 1. The 70.56 is ____________ 2. The simplified form of (2x – 3y) 2 + 12xy is _________ 3. Complete the equation : (A B) 1 = __________ 4. The cube of ( 3x - 2 ) = _________ 5. The rational form of 0.1 6 is ________ 6. The factors of 4(a + b) 2 - 6 (a+b) are ______ & _______ 7. If A B, then A B & A B are ________ & ________ respectively. 8. The LCM of 6x 2 - 2x & 9x 2 - 3x is ________ 4 9. The simplest form of ( 16 ) 0.75 x (64) 3 is __________ 10. The expansion of (x – y – z ) 3 - x 3 + y 3 + z 3 = _________ 11. A polygon in which one of its angle is a reflex angle is called a ____________ polygon. 12. If one pair of opposite sides are equal and parallel in a quadrilateral, it is a ___________ 13. In parallelogram PQRS, Q - S is equal to ___________ degree. III. Do as directed: 2x18=36 1. For any subset A of , prove that (A ) = A 2. Find the product of 105 x101 x102 using identity. 3. Represent 2+ 8 on a number line. 4. If (a + b + c ) = 0. Show that 2a 2 + bc = ( a – b ) ( a – c ) . 123 5. Write the decimal expansion of & mention its period. 35 1 1 1 6. If a 2 + 2 = 20 and a 3 + 3 = 30, find a+ . a a a 7. What is the least number to be subtracted from 4321 to get a perfect square? 8. Factorise: 4x 4 + 25y 4 + 10x 2 y 2 9. Which is greater? 3 3 3 or 4 4 4 10. Resolve into factors using identity: 2 2 a 3 + 16 2 b 3 + c 3 - 12abc 11. Find the square root of 12.34 upto two decimal places. 12. Factorise x 2 + 10x + 8 by adding & subtracting required quantity. 13. In a regular polygon, the interior angle is 9 times the exterior angle. Find the number of sides of the polygon. 14. Calculate the measure of each interior angle of an octagon. 15. The angles of a quadrilateral are in the ratio 1: 2: 4: 5. Find all the angles of the quadrilateral. 16. In the figure ABCD, is a parallelogram of area 128 cm 2 . If CF = 16cm, find the length of AD. 1 1 17. In the figure ABCD is a parallelogram in which E & F are the points on DA & DC respectively. Show that area of triangle ABF is equal to area of BEC. 18. Prove that if the diagonals of a parallelogram are equal, then it is a rectangle. IV. Solve: 3x6=18 1. Group into like surds: 24 , 128 , 375 , 648 3 686 , 2000 2. If a + b + c = 2s, prove that (s – a ) 3 + (s – b ) 3 + 3c (s – a ) (s – b ) = c 3 . 3 3 3 3 3 3 6 , 3 4 12 , 4 8 3. Write the following surds into descending order: 4. Find the LCM of 8x 3 - y 3 , ab ( 4x 2 + 2x + y 2 ) and bc ( 4x 2 - y 2 ) 5. ABCD is a parallelogram in which diagonals bisect each other. If AD = x+2y, BC = 2x+3, DC = x+7 and AB = 3y +2. Find the measure of the sides of the parallelogram. 6. Construct a quadrilateral ABCD with the given measurements: AB = 4cm, BC = 8cm, BD = 9.5cm, CD = 7cm, & AD=6cm. V. Solve: 4x4=16 1. Let A={3, 6, 9, 12, 15, 18, 21, 24 }, B= { 4, 8, 12, 16, 20, 24 }. Find i) A B ii) A B iii) A\B iv) A B and represent each with Venn diagram. 2 2. The HCF of ( x+1 ) ( x + ax + 4 ) & ( x+4) ( x 2 + bx + 2 ) is ( x 2 + 5x + 4 ). Find the values of ‘a’ & ‘b’. 3. In a parallelogram PQRS, PQ = 4x and QR = 3x+2. If the perimeter is 88cm and area is 120cm 2 , find the length of the altitude from S to PQ. 4. State and prove the mid point theorem for a triangle. FIRST TERMINAL EXAMINATION -SEPTEMBER -2013 Class & section: X. Roll No: _____________________ Name of the Student: ______________ Signature of the invigilator: ________ Time: 3 hours Marks Obtained: Total Marks: 100 Signature of the evaluator: _____ SUBJECT: MATHEMATICS I. Multiple Choice Questions: [20 x 1 = 20] 1. The roots of (x-3) (x+8) are a. –3 & 8 b. 3 & –8 c. 5 & –24 d. ±3 & ±8 2. In a G.P. if S10 : S5=33:1 then the common ratio is a. 33 b. 2 c. 32 d. 34 3. If a b c 2S then S 2b a c 2b a c 3b d. 2 2 4. If G.M & H.M of two number a & b are 4 3 and 6 then a. a c 3b b. b c a _______________________ _______________________ _______________________ c. A.M of those two number is ___a. 8 b. 6 c. 24.3 d. 4.3 _______________________ 5. If 5 2 6 x y then x y & xy are _____ & _____ _______________________ a. 5 & 6, b. 6 & 5, c. 7 & 6, d. 7 & 30 6. The product of m n m n and its conjugate is _______________________ a. 2n, b. – 2n c. 2 m d. – 2m 7. If AM, GM & HM of two numbers are A, G & H, then the relation among them is _______________________ a. A=G=H, b. A> G> H c. G=AH, d. A ,G ,H 8. If H.C.F. of x 3 3x 2 px 24 and x 3 7 x 2 Qx 15 is x 3 _______________________ then the value of p is : a. 8, b.10, c.12, d. not possible to find the value. 9. In a sequence, if Tn3 n 5 then Tn _______________________ a. n 2 , b. n 8 , c. n 3 , d. n 8 10. A BUC A B A C This statement represents _______________________ a. intersection of sets over Union of sets b. Union of sets over intersection of sets c. Distributive d. Associative Property. With reference to the given figure, _______________________ 11. which of the following is not correct. 2 2 2 a. AC BC AB b. CP 2 PN 2 CN 2 c. AN 2 AP 2 PN 2 d. AC 2 AN 2 CN 2 2 AN .CN 12. In ∆ ABC, A 90 AD BC then AB2 = _______________________ 2 2 2 2 a. BC.DB b. AD +BD c. BC – AC d. All the above. 13. Which of the following is not a Pythagorean triplet? _______________________ a. 8, 15, 17, b. 36, 15, 39 c. 25, 24, 18 d. a b , a b ,2 ab , where a & b are 2 numbers. 14. The number of common tangents to a pair of externally touching circle is ----- a. 3 b. 4 c. 2 d. 1 _______________________ 15. The correct formula to find the length of transverse _______________________ Common tangent is a. d 2 t 2 R r 2 b. t 2 d 2 R r 2 c. t R r 2 t 2 d. t d 2 r 2 16. The simplest index form of 4 324 is _______________________ a. 34 3 b. 33 4 c. 93 4 d. none of these. 17. If 5 2 2 3 is subtracted from 3 3 2 2 , the _______________________ resultant is - a. 3 7 2 , b. 3 2 3 , c. 2 3 , d. 5 3 3 2 18. If one factor of a 3 b 3 c 3 3abc is a b c, then the other _______________________ 3 3 3 2 2 2 factor is _ a. a b c b. a b c ab bc ac c. 3abc d. a 2 b 2 c 2 2ab 2bc 2ac 19. If the H.C.F of two expressions with Product 15 x 2 y 3 z 4 is _______________________ 2 2 3 4 2 3 4 3 5 xy z then their L.C.M is - a. 3x y z b. 75x y z c. 3xyz d. 15 x 2 y 3 z 4 1 2 x 2 20. 0 1 0 if the given matrix is a scalar matrix then the 36 value of ' x' is - a. 4, b. 3, c. ± 3 d. 3 2 _______________________ 21. Among 25 passengers 15 can speak Kannada 12 speak both Kannada & English. [10 x 1=10] The number of passengers who can speak only English is _______________________ 22. ∆ ABC ||| ∆ DEF. If a side of ∆ ABC is twice the corresponding side of ∆ DEF, the area of ∆ DEF is _______________________ In the given figure, ∆ CDP ||| ∆ BLP. 23. then BL2 BP 2 CD 2 CP 2 24. In Quadrilateral ABCD, AD ||BC the diagonals intersect at ‘O’, then the pair of triangles which are similar is 25. The space between diameter and an arc of a circle is _______________________ _______________________ _______________________ 26. If a b c 12 and a 2 b 2 c 2 50 then the value of ab bc ac is _____________________ 27. If Tn 2n 4 95 and, Tn 257, then n _______________________ 28. The standard form of adfected Quadratic equation is _______________________ 29. If the nth term of H P is 27 35 , then nth term the A.P is _______________________ 30. State the converse of Basic Proportionality theorem. II. Answer the following: [18 x 2 = 36] 31. In a G.P. the sum of first and second term is 18 and the sum of second and third term is 90. Find the first term. 32. If a H and b are in H P, prove that H = 2ab a b . 33. How many terms of 3+7+11+………… make the sum 666 ? 34. If b, a, c are in AP, c, b, a are in G.P show that a, c, b are in H P. 35. In a G.P. if fourth and seventh terms are 3 8 and 3 64 find the first term. 36. The sum of four terms of an AP is 40, and the product of their extremes is 91, find the common difference. 37. If t 2 d 2 r 2 solve for ‘ r ’if d=25, t=24, find ‘r’. 38. Solve 2a 2 5a 6 by formula method. 39. Find the length of diagonal of a square of side 10 cm. 40. Rationalize the denominator of 5 32 5 5 32 5 . 41. Which is a greater surd? 4 6 or 3 4. 42. Find the roots of 42 m 2 13m 42 by factorization method. 43. Find the H.C.F. of 6 x 3 5 x 2 3x 2 and 3 x 3 7 x 2 4 . 44. In ∆ PQR, PQ=PR and QS PR. Prove that QR2 =2 PR.RS. In ∆ ABC, B =900, DE AC=12 cm, find DE. 45. 46. In ∆ ABC, AP BC, BQ AC, if BC = 18 cm, AD=5 cm, AC. AP and BQ intersect at ‘O’. Prove that A of AOQ OQ 2 OP 2 A of BOP 47. In ∆ ABC, XY || BC, AX= p+3, BX=3p-1, AY CY 2 3 , find the value of ‘p’. 48. Draw tangents to a circle of radius 3.5 cm, so that the angle between them is 75. 49. U is a set of digits, A and B are subsets of U, A is a set of even digits more than 3, B={ x x U 5 x <8}. Verify Demorgan’s laws. 50. The three numbers are in the ratio 2:5:7. If 7 is subtracted from the second, the resulting numbers are in A.P find the numbers. [6 x 3 = 18] 51. Prove that the Areas of two similar triangles are Proportional to the square on their corresponding sides. 52. Draw a pair of tangents of length 6 cm to a circle from the point which is 7.5 cm away from the centre. 53. If 2 x 2 8 x 3 0. Find the value of 4 x 2 9 . x2 54. Solve: y y 1 25 . y 1 y 12 2 3 x 3 4 1 6 3 55. Find the value of x & y . 4 1 y 7 56. Find L.C.M of 40 y 3 18xy2 3x 2 y x 3 and 30 y 3 11xy2 4 x 2 y x 3 [4x4=16] 57. Draw Direct common tangents to two circles of radii 4 cm and 2.5 cs. whose centers are 10.5 cm apart. Measure their lengths. 58. State and prove Pythagoras theorem.