Download 1 - Vijaya Vittala Vidyashala

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 Tn3  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. 33 4 c. 93 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 32 5
5 32 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.