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DAV PUBLIC SCHOOLS, ODISHA ZONE-II
QUESTION BANK FOR SA – I (2016 – 17)
SUB –MATHEMATICS
CLASS – VII
SECTION – A (Each Question Carries 1 Mark)
1. If x, y & z are rational numbers, then the property (x+y)+z = x+(y+z) is known as ________
(i)Commutative property
(ii) Distributive property
(iii) Associative property
(iv) Closure property
2. Value of “p” if the expression z2 + 3z – p=3 for z=2 is ______
(i) 6
(ii) 5
(iii) 7
(iv) 4
3. How many lines of symmetry does a circle have ?
(i)1
(ii) 2
(iii) 4
(iv) Infinite
4. A tetrahedron has ________ vertices.
(i) 2
(ii) 3
(iii) 4
(iv) 5
5. Find the area of a rectangle whose sides are 2a and 3a.
(a) 6a square unit
(b) 5a2sq uint
(c) 3a2 sq uint
(d) 6a2sq. Unit
6. A triangular pyramid has _________________ number of edges.
(a) 4
7.
6.4
0.2
(b) 6
(c) 8
(d) 2
= ___________________
(a) 3.2
(b) 0.32
(c) 32
(d) 2.3
8. The number of lines of symmetry of an equilateral triangle is :(a) 2
(b) 1
(c) 3
(d) 4
9. If x, y and z are rational numbers, then the property (x+y) +z = x+ (y+z) is known as –
(a) Commutative property.
(b) Associative property.
(c) Distributive property.
(d) Closure property.
2
2
2
10. (3p – 14 pq + 2r) – (14pq + 3p + 2r ) is a –
(a) Monomial.
(b) Binomial.
(c) Trinomial.
(d) None
11. A regular heptagon has ______ lines of symmetry.
(a) 5
(b) 6
(c) 7
(d) 8
12. A tetrahedron has ______ vertices.
(a) 2
(b) 3
(c) 4
(d) 5
1
13. The multiplicative inverse of 5 2 is
(a) −
11
2
2
(b ) 11
2
(c) 11
(d)
11
2
.
14. The H.C.F of the terms of the expression 18x3y2 + 36 xy4 – 24 x2y2 is
(a) 6x2y2
( b) 6 xy2
(c) 6xy
(d) none of these
15. An isosceles trapezium has ______ lines of symmetry.
(a) One
(b) two
(c) three
(d ) none of these
16. All the side faces of tetrahedron are :
(a) Triangular
(b) Square
(c) Rectangular
(d) pentagonal
17. The number of lines of symmetry of a semicircle is :
(a) 1
(b) 2
18. The additive inverse of
−4
(a)
−4
5
3
(d)
4
is:
−5
(b)
5
(c)
(c)
4
5
(d)
4
4
5
19. A rectangular prism is also called a :
(a) Cuboid
(b) cube
(c) cone
(d) none of these
20. The value of p in the expression : z2 + 3z – p = 3 , for z = 2 is:
(a) 6
4
2
(b) 5
4
5
(c) 7
(d)
4
4
21. 7 x 3 – 7 x 6 = 7 x (____ - ___ )
22. H.C.F of the terms of the expression ( 4p2q2r- 12pq2r2 + 16p2q2r2) is ___________
23. A tetrahedron has ___________ vertices.
24. How many lines of symmetry a scalene triangle has____________
1
25. What is the multiplicative inverse of 65 ?
26. What is the co-efficient of a in –6ab2 ?
27. How many line of symmetry a parallelogram has ?
28. What the figure is called which has no vertex and no edge?
29. Every rational number has an additive inverse such that their sum is equal to
(a)
-1
(b)
1
(c)
0
(d)
2
(d)
Multinomial
30. An algebraic expression having two terms is said to be as
(a)
Trinomial
(b)
Monomial
(c)
Binomial
31. The number of line of symmetry a regular Octagon is
(a)
Five
(b)
Seven
(c)
Nine
(d)
Eight
(c)
Five
(d)
Six
32. The number of faces of a tetrahedron is
(a)
Three
(b)
Four
33. A rectangle is symmetrical about
(a) a line joining the mid points of the opposite sides.
(b) Each one of its sides.
(c) Each one of its diagonals
(d) None of these.
34. A tetrahedron is also known as
(a) Triangular pyramid.
(b) Triangular prism.
(c) Square prism
(d) None of these.
1
35. The multiplicative inverse of 5 3 is
(a)
−16
−3
(b)
3
3
(c)
16
16
16
(d)
3
36. The H.C.F. of the terms of the expression : 4p3q2r – 12 pq2r2 + 16 p2q2r2 is
(a) 4 pq2r
(b) – 4 pq2r
16p3q2r2
(c)
(d) – 16 p3q2r2
SECTION – B (Each Question Carries 2 Marks)
1. What number should be added to
−𝟑
𝟕
2. Find four rational numbers between
so as to get 1 ?
−𝟖
𝟑
&|
−𝟖
𝟑
|
3. Evaluate: 182•3 + 12•65 – 23 –|0•718|
4. Factories: 9x (6x –5y) –12x2(6x –5y)
5. Write two letters of English alphabet each having :
(a) two line of symmetry
(b) No line of symmetry
6. What is the difference between a cube and a cuboid?
3
7. The sum of two rational numbers is 1.If one of the number is – 7.Find the other.
8. Simplify 5X 0.16 – 0.52 +8.263.
9. Factorise: 1 + x + xy + x2y
10. Find the two rational numbers between
1
4
3
&4
11. Write the line of symmetry of an octagon & a rhombus.
12. A tetrahedron has how many vertices and edges.
13. How many vertices, edges and faces will a cuboid have? What is the shape of its faces?
14. Write three letters of English alphabet each having –
(a) Two line of symmetry.
(b) No line of symmetry.
15. Find the HCF and factorise 8y3 + 8x3.
16. Evaluate: 25.75 + 2.09 – 13.6.
9
17. Simplify: 5 x
−2
27
7
+ 30
18. The product of two rational numbers is
8
19. Divide - 13 by
3
−26
−3
7
5
. If one of the number is21 , find the other.
.
3
7
20. Find the reciprocal of - 8 X - 13 .
21. Without actual division determine whether the following rational numbers are terminating or not.
39
a ) 24
22. Find the product
98
b)28 .
3
4
2
a2 ( 3 b2 + 8 ab ) .
23. State the number of lines of symmetry for the following figures:
a) Rhombus
b ) Regular pentagon .
24. Draw a net for a tetrahedron.
25. Give four examples of capital English alphabets with no lines of symmetry.
26. Draw the net of a square pyramid.
−3
27. What number should be added to
28. Simplify −4 (
7
3
−
9
10
7
, so as to get 1?
) and express the result in standard form.
−25
29. Find the decimal representation of
12
.
30. Factorize: ax + a y – bx – by.
31. Find the values of : -7/64 +3/16
32. What number should be added to -
3
7
so as to get 1 ?
33. Express the decimal number in the form of p/q : 586.875
34. Multiply the monomials 1.2a2 b2, 5ab4c2 and 1.1a5bc7
35. Write two letters of English alphabet each having
(a) one line of symmetry
7
(b) no line of symmetry.
1
36. Find the value: – 11 –+4
37. What should be added to –
4
11
to get 1?
38. Express as rupees using decimals : 7paise
39. Add 4x+3y–5z and –7x+5y–8z by using column method.
40. Write two English alphabets and show their line of symmetry.
41. Draw a net for a cone.
7
3
42. Find the sum of 16 and 4
3 5 3 5
43. Simplify: 7 + 7 + 7 + 7
44. Express the given rational number as decimal by using long division method: 629/125
45. Subtract (6p2-13pq+r) from (-12p2+5pq-14r) by horizontal method.
46. Write 5 English alphabets having no line of symmetry.
47. How many vertices, edges and faces will a cuboid have? What is the shape of its faces?
48. The sum of two rational numbers is – 3 . If one of the number is
49. For x =
−2
7
and y =
5
8
, verify that
𝑥×𝑦 = 𝑦 ×𝑥.
50. Write four English capital alphabets having one line of symmetry.
51. Complete the net for making a cube,
2
3
, find the other.
− 37
52. Find the decimal representation of
60
.
53. Factorize: a2 + 2a + ab + 2b.
54. The sum of two rational numbers is – 3 . If one of the number is
55. For x =
−2
7
and y =
5
3
, find the other.
𝑥×𝑦 = 𝑦 ×𝑥 .
, verify that
8
2
56. Write four English capital alphabets having one line of symmetry.
57. Complete the net for making a cube,
− 37
58. Find the decimal representation of
60
.
59. Factorize: a2 + 2a + ab + 2b.
SECTION – C (Each Question Carries 3 Marks)
1. Express :
−𝟒
𝟕
as a rational number with ; (i)Numerators 12 (ii) Denominator 42
2. Find the reciprocal of
𝟑
3. For x= 𝟒 & y =
−𝟗
𝟖
−𝟐
𝟑
x
𝟓
𝟕
+
𝟐
𝟗
÷
𝟏
𝟑
x
𝟔
𝟕
, insert a rational number between (x –y)-1 & ( x-1 – y-1)
4. Simplify : (156•25 ÷ 0•025) x 0•02 – 5•2
5. (a) Find the decimal representation of –
𝟏𝟐𝟕
𝟕
(b) Express 4•82 as rational number in standard form.
6. The perimeter of a triangle is (x2y +10) units. One of the side is (x2y – 4) units & another side is
(3 –2x2y) units. Find the third side.
7. (a) When two circles said to be congruent?
(b) What is the side included between the angles M & N of  MNP.
(c) If  ABC congruent to  EFD, then the side BC= side _____ & Lc = _______ .
8. If PQR is an isosceles triangle such that PQ = PR , then prove that the
altitude PS from P on QR bisects QR.
9. Mr Gupta has a rectangular field ABCD. He wants to make a partition on that field two equal
parts by taking one diagonal AC, then he plants half of this field by mango trees & other half by
coconut trees. (a) What is the shape of the field of portion planted by mango trees?
(b) Is triangle ABC congruent triangle CDA ? By what condition ?
(c) Write the value that you get.
10. Construct an equilateral triangle ABC. Find all its sides of triangle.
11. Arrange the following in descending order:
4
7
,
5
9
,
2
5
,
1
3
3 1
5
12. Show of 5(-7 -
14
3
=
)
×
5
−1
7
-
3
5
5
× 14
13. (x – y) -1≠ 𝑥 -1 – y-1
5
3
Here x = --7, y = 7
14. Compute the product:
12.4×15.7
15. Convert the following rational numbers into decimal form using long division method.
25
2
i) 12
ii) 7
16. Factorise:
a xy + cbxy - az - bcz
17. Draw the lines of symmetry of a square
Or
Draw any 3 English alphabets having two lines of symmetry and show their lines of symmetry.
9
18. Find the value of x: i) 15 =
𝑥
ii)
−50
36
𝑥
=-4
19. <B=<D=900 , and side BC=DC=6.5cm. Are the two triangles congruent? State the result in
symbolic form.
20. Prove that the bisector of the vertical angle of an isosceles triangle is perpendicular to the base.
21. Express
22. Simplify:
−64
256
as a rational number with denominator 8.
−11
30
8
7
- 15 + 6 +
−2
5
.
7
3
9
2
23. Verify x * y = y * x, for x = and y = .
25
24. Convert 12 into decimal.
25. Compute 6.4 ÷ 0.2.
26. Find the product of (5x + 3) (2x + 4).
Or
2
3
Simplify: p (2pq + q ) – 2q2 (p2q +5).
27. ∆ ABC is isosceles with AB = AC. AD is the altitude from A on BC.
i) Is ∆ABD≅ ∆ACD? Why?
ii) State the three pairs of matching parts you have used to answer (i).
iii) Is it true to say that BD= CD? Why?
28. Namita got a chocolate on her friend’s birthday from school. She took
it home and cut into two congruent triangles. She gave one piece to
her maid’s daughter Meenu and had the other piece herself. You are
given the way in which Namita divided the chocolate.
a) What congruence criteria did Namita use here?
b) What value of Namita is depicted here?
29. If ∆PQR is an isosceles triangle such that PQ = PR, then prove that
the altitude PS from QR bisects QR.
30. l, m, n, t are the lines of symmetry of line segments XQ, PR, XY and RY respectively.
If XP = 1.5 cm, find the length of the line segments.
(a) PQ
b) RY
c) PR
1
31. Represent the following on number line : a) 34
5
b) 5
32. Find three rational numbers in between - 3 and − 3
3
23
5
.
9
33. For x = 4 and y = - 8 verify that ( x÷ y )-1 = x-1 ÷ y-1 .
34. Simplify the following expression : 6.25 ÷ 0.5 + 2.4 X 3.5 – 5.7 .
35. Simplify and express the result as a rational number in its lowest term:
3
2
7
+ 5 + 0.015 ÷ 3 .
36. Simplify : 3x2 ( 3y2 + 2 ) – x ( x- 2xy2 ) + y ( 2x2y – 2y)
OR
( y2 -7y + 4 ) ( 3y2 – 2 ) + ( y + 1 ) ( y2 + 2y)
37. Show that the bisector of the vertical angle of an isosceles triangle bisects the base at right
angles .
38. If the given triangle PQR is an isosceles triangle such that PQ= PR,
then prove that the altitude PS from P on QR , bisects QR.
39. Show that in an isosceles triangle, angles opposite to equal sides are equal.
40. Construct an equilateral triangle ABC. Find all its lines of symmetry.
41. In an isosceles triangle ABC, AB = AC, D and E are two points on the sides AB and AC
respectively such that AD = AE. Prove that ∆ 𝐴𝐵𝐸 ≅ ∆ 𝐴𝐶𝐷
42. Represent
43. For 𝑥 =
3
4
−3
5
on the number line.
and 𝑦 =
−9
8
, insert a rational number between (x+y) and (x – y).
44. In the given figure ,PQ | | SR
PQ = SR.
(i ) Is  QPR =  SRP? Why?
(ii) Is ∆ PQR ≅ ∆ RSP ? If yes,
Justify with congruency condition.
45. 15. A rope of length 40 meters is cut in to some equal sized pieces .How many pieces can it be
cut if each piece is of length of
4
9
meter.
46. Simplify and express the result as a rational number in its lowest form.
2
5
−
1
4
+
8.1 × 2.7 ÷ 0.09
47. In the given figures,
∆ PQR ≅ ∆ XYZ. Such that
PQ = XY, PR = XZ and QR = YZ.
Find the value of a and b.
If PQR = (a – 5)° and
XZY = ( b + 5) °
PRQ = 35 ° and XYZ = 55 ° .
48. Simplify : 2x ( x – y2 ) – 3 y ( xy + 2x ) – xy ( x + y ).
OR
2
Find the product of 7 x2 ( 7y + 14 x ) and
verify the result when x = 2 and y = 3 .
49. The arrow headed line represents the
line of symmetry of a isosceles
triangle ABC, with AB = AC .
If ABC = 40 ° and OB = 4.5 cm. Find ( i) BAO (ii) Measure of OC .Give reason.
50. Ranjan has to cover distance of 30 kms. To reach his grandmother’s house. He covered 11.25
kms. by bus, 7.083 kms. by auto and the rest by foot.
(a) How much distance did Ranjan cover by foot.
(b) How is Ranjan benefited if he walks to any distance?
In what ways does it effect our environment?
51. Arrange the following in ascending order : -3/4,-5/-12,-7/16
1
52. Rohit donated of his monthly income to an Non- Government Organisation (NGO) working
5
1
1
1
for the education of the girl child, spent 4 of his salary on food, 3 on rent and 15 on other
expenses. He is left with Rs. 9000
(a) Find Rohit’s monthly salary.
(b) What values of Rohit are depicted here ?
(c) Why is the education, specially for girls , important ?
53. Insert three rational numbers between -7/10 and 11/10.
54. Evaluate it 182.3 + 12.65 – 0.23 – 10.71
55. Simplify it - 5.7 + 13.20 – 15.009 + 0.02
56. Factorise it axy + bcxy – az – bcz
OR
Find the area of a rectangle whose length is thrice its breadth, where breadth is 4x.
57. If ∆ PQR is an isosceles triangle such that PQ =PR, then
prove that the altitude PS from P on QR, bisects QR.
58. QS and RT are the altidues of ∆ PQR, and QS =RT
(i) Is ∆QRS  ∆RQT by RHS congruence condition ?
(ii) State the three pairs of corresponding parts which makes
∆QRS  ∆RQT.
59. Show that in an isosceles triangle, angles opposite to equal sides are equal.
60. If the dotted lines represents the line of symmetry of the given angles, find the value of X.
61. Compare: –
4
3
and
8
–7
.
62. By what number should –
55
18
be divided to get
63. By what number should we multiply
64. Simplify: (15.05 ÷0.05)x0.001+2.351.
65. Evaluate 182.3+12.65–0.23–10.71
–17
45
–22
9
.
so that the product is –
–51
15
?
66. Multiply (3x+2y–4)(x–y)
Or
Multiply (x2–5x+8)(x2+2)
67. In the side figure AB and CD intersect each other at O
and O is the mid-point of both AB and CD. Prove that AC=BD.
68. In the given figure AB=AD, BC=CD
a) Is ∆ABC≅∆ADC ?
b) Write the three matching parts.
69. Show that in an isosceles triangle angles opposite to equal sides are equal.
70. If the dotted lines represents lines
of symmetry of the given angle.
Find the value of y and z.
71. Represent
3
72. For x =
4
−7
3
on a number line.
and y =
−9
8
, insert a rational number between (x + y ) and (x – y).
73. Simplify and express the result as a rational number in its lowest form.
1
2
1
+ 5 + 6.25 ÷ 0.25.
74. In the figure given , PQ = PS and RQ = RS.
Find the third pair of corresponding
parts that makes ∆ PQR ≅ ∆ PSR.
75. Find the reciprocal of
76. Find the product
1
4
−2
3
5
×7+
2
9
÷
1
3
6
× 7.
a2 b ( 5b2 − 3 a b) and verify the result for a = 2 and b = − 1
OR
Simplify :
( p + q )( p2 – q2 ) + ( p – q ) ( p2 + q2 ).
77. Lines 𝑙 and m are the line of symmetry
of the line segments XY and YZ respectively.
If XA = 4 cm, and YZ = 6 cm.
Find AY, YB and XZ.
78. Given that ∆ ABC ≅ ∆ RPQ. A = 50° , B = 60°, Find  P , Q and R.
79. Raghu bought a book for Rs. 112 ½ from a shop. He gave a Rs. 500 note to the
shopkeeper. He realized that the shopkeeper had given him Rs. 72 extra. He returned
the extra money and a feeling of satisfaction. Then answer the followings:
(a) How much money had the shopkeeper returned to Raghu?
(b) What values did Raghu exhibit in the given situation? Give two points.
80. If ∆ ABC ≅ ∆ DEF. Fill in the blanks to make each statement true.
(b) C =
(a) AB = ________
(d) D=
________
________
(e) CA =
(c) EF = ________
(f) B = ________
________
SECTION – D (Each Question Carries 4 Marks)
1. (a) Represent –
29
4
on a number line. (b) Find the value of x for
𝟒
𝟐
2. (a) Find the average of the rational numbers 𝟓 ,
𝟒
,
𝟑
𝟐𝟑
𝒙
=
𝟐
–𝟖
𝟓
𝟔
𝟖
and 1 𝟓
(b) Compare : –𝟑
3. Verify that (x÷ y)-1 = x-1 ÷ y-1 by taking x=
4. (a) Divide the sum of
𝟓
𝟐𝟏
𝟒
&
&𝑦 =
−𝟑
𝟓
by thier differenc .
𝟕
𝟏
(b) Findthe value of 1 + (1 ÷ 1 +
5. Simplify & express the result as
𝟐
𝟑
)
𝟔
𝒑
𝟏
𝟏
form: (0•4 x 0•04 x 0•005) ÷ (0•1 x 10 x 0•001)– 𝟐 +𝟓
𝒒
6. (a) Without actual division : determine
𝟐𝟖
𝟐𝟓𝟎
𝟏
is terminating or non terminating decimal number .
𝟑
𝟒
(b) Simplify & express in decimal form : 𝟓 + 𝟏𝟎 + 𝟐𝟓
𝟓
7. Find the product & verify: (𝟒 x2 –
𝟑
𝟐
xy) ( x+ y + y2 ). For x= -2 y =3
8. Simplify : (a) (a2 + b 2) ( a2 + b2) – (a2 - b2) ( a2 – b2)
(b) Find the HCF of 2 x3 y2 , 10 x 2y2 , 14 x2 y3
9. Show that the bisector of the vertical angle of an isosceles triangle bisect the base at right angle.
10. QS &RT are the altitudes of triangle PQR & QS = RT
(a) Is triangle QRS congruent to triangle RQT by which condition?
(b) State the three pairs of corresponding parts which make triangle
QRS congruent to triangle RQT.
11. Show that in an isosceles triangle, angles opposite to equal sides are equal.
12. Simplify& Express the result in a lowest form.
2
5
×
3
4
+
1
25
1
2
× 2 - 10 ×
1
5
25
5
13. The product of two numbers is -16 , one number is - 4 , Find the other number.
2
14. (a) Compare − 9 and
1
−8
36
(b) Represent 53 on number line.
15. Arrange in descending order.
2
5
−1
,
2
−8
,
−3
,
15
16. (a) Convert
10
5
into decimal form.
8
(b) Simplify (6.05+5.01)-(12.5-0.09)
-6 x2 ( xy +2y2 ) - 3y 2 (2x2 +y).
17. Simplify:
18. Find the product & verify m = -2, n = 0;
(m3 + n3)(2m – 3n)
19. (a) Draw the net for a tetrahedron.
(b) Draw the Isometric sketch for a cuboid of dimensions 4X3X2.
20. Simplify & express the result as a rational number in its lowest form.
0.144÷1.2
0.016÷0.02
7
+5 -
21
8
21. Namita got a chocolate on her friend’s birthday from school. She took it home and cut into two
congruent triangles. She gave one piece to maid’s daughter Minu and had the other piece
herself. You are given the way in which Namita divided the chocolate.
(a) What congruence criteria did Namita use here?
(b) What value of Namita is depicted here?
22. Represent the rational numbers on two different number lines.
a)
3
−3
b)
4
5
23. Arrange the following rational numbers in descending order.
−3 −7
9
18
, ,
,
10 −5 −15 30
24. Divide the difference of
25. Find the reciprocal of
−2
3
12 −16
35
,
20
5
2
by their product.
1
6
x 7 + 9 ÷ 3 x 7.
26. Simplify and express the result as a rational number in its lowest terms.
2
5
3
1
1
2
1
x 4 + 25 x 2 - 10 x 5
27. Simplify the following and express the result as decimals.
(156.25÷ 0.025) x 0.02 – 5.2.
ii) (x +1)2 - 4 (x + 1)
28. Factorise: i) ax + ay – bx – by.
29. Express 1.5a2 (10 ab – 4b2) as a binomial and then evaluate it for a=-2, b=3.
30. In the given figure, AB = CD and AD = BC. Prove that ∆ADC ≅ ∆CBA.
or
QS and RT are the altitudes of ∆PQR, and QS = RT
(a) Is ∆QRS≅ ∆RQT by RHS congruence condition?
(b) State the three pairs of corresponding parts which
make Is ∆QRS≅ ∆RQT.
31. In the given figure, PQS and PRS are two triangles on a common base PS such that PQ = SR
and PR = SQ.
(i) Is ∆PSQ≅ ∆SPR? By which congruence condition?
(ii) State the three pairs of corresponding parts you
have used to answer (i).
(iii) If ∠SRP = 40o, and ∠ QPS= 110o, find ∠PSQ.
32. The given figure shows a cube surmounted by a pyramid.
How many faces, edges and vertices does it have? Name
its edges, faces and vertices. Also state the faces which
are triangles and which are squares.
33. Compare the numbers in each of the following pairs of numbers:
5
(i)
9
-7 , −13
, (ii)
8
3
−9 , −9
34. Arrange the following in descending order .
−2
,
−5
−3
4
−3
,
10
2
, -15 .
2
3
4
35. For x = 5 , y = -10 , z=15 prove that x÷ ( y-z ) ≠( x÷y) - ( x÷z) .
1
1
1
1
36. Find the product of (1-2 ) ( 1- 3 ) ( 1- 4) -----------(1-10 ) .
𝑝
37. Simplify and express the result in the form of 𝑞 .
2
5
3
1
1
2
1
X 4 + 25 X 2 - 10 X 5 .
38. Simplify and express the result as a rational number in its lowest term.
0.144÷1.2
0.016÷0.02
+
7
5
-
21
8
39. Simplify and then verify the result for the given values:
(3x- 4y ) ( 4x2y + 3 xy2 ) , for x = 2 , y = -1 .
OR
1
1
( 2p + 3q ) ( 4p + 12pq + 9q2) , for p = 2 , q = 3 .
2
40. Factorise : (i) 4 ( p+q) ( 3a- b ) + 6 (p+q) ( 2b-3a) .
(ii) axy+ bcxy - az – bcz .
41. In the given figure, P and Q are two points on equal
sides AB and AC of an isosceles triangle
ABC such that AP = AQ. Prove that BQ = CP.
42. In the given figure, ABC is an isosceles triangle in
which AB = AC. Also D is a point such that BD =CD.
Prove that AD bisects angle A and angle D.
OR
In the given figure , AD= AE ,BD= CE .
Prove that triangle AEB congruent to triangle ADC .
43. (a) Complete the given net for making a cube .
(b) Two cubes of edge 2 cm each are placed side to side to from a cuboid. Draw an oblique
sketch for the resulting figure .
44. In an isosceles triangle ABC , AB = AC, D and E are two points on the sides AB and AC
respectively such that AD = AE. Prove that ∆ 𝐴𝐵𝐸 ≅ ∆ 𝐴𝐶𝐷 .
45. Represent
46. For 𝑥 =
3
4
−3
5
on the number line.
−9
and 𝑦 =
8
,insert a rational number between (x+y) and (x – y) .
47. Evaluate : (a) 25.75 + 2.09 – 13.6
(b) 4.8 × 1.84 + 6.029
48. Simplify: ( p2 + q2 + r2 ) (p q + q r) and verify the result for p = 2 q = – 3 and r = 1.
49. In figure, the measures of some parts
of the two triangles are given. Prove the
Congruence of two triangles and by
which congruence condition they are
congruent, state the result in symbolic form.
OR
Prove that the bisector of the vertical angle of an isosceles triangle is perpendicular to the base.
50. (a) Find the equivalent forms of rational numbers having a common denominator in
–72 (– 15 – 37 – 18 ) .
(b) Simplify:
51. Show that:
3
−1
5
7
−
5
14
3
=
5
×
−1
7
−
3
5
×
5
14
.
52. Simplify and express the result as a rational number in its lowest form.
0.4 × 0.04 × 0.005
1 1
− +
0.1 × 10 × 0.001
2 5
53. In the given figure, ABC is an isosceles triangle
in which AB = AC, Also D, is a point
such that BD = DC.
Prove that AD bisects A and D.
54. Arrange the following in ascending order.
3
4
,
−5
−12
,
−7
16
,
−9
24
1 2
, ,
3
7 8 14
.
55. (a) Factorize: (a – b ) 2 + ( a – b ) .
(b) Multiply:
(0.1 p + 0.2 q ) and ( 0.2 q – 0.1 p)
−36
56. (a) With what number should we multiply
5
?
1
1+
(b) Find the value of
35
−6
so that the product be
1
6
1+
57. Draw a cuboid. How many vertices, edges and faces does it have?
What is the shape of its faces?
2
58. Arrange the following in descending order:
59. Show that :
−4
3
×
2
−7
−4
+ 10 =
5
3
2
×5 + (
,
5
−4
3
×
−1
,
2
−7
10
8
−15
,
5
6
.
).
60. Simplify and express the result as a rational number in its lowest form.
0.144 ÷ 1.2
0.016 ÷ 0.02
7
21
5
8
+ −
.
61. In the given figure , AB || DC and AB = DC.
(a) Is ∆ ACD ≅ ∆ CAB ?
(b) State three pairs of matching parts used to answer (a).
(c) Which angle is equal to CAD?
(d) Does it follow from (c) that AD || BC?
OR
Prove that in an isosceles triangle, the angles opposite to equal sides are equal.
62. (a) The product of two rational numbers is
2
(b) Subtract 6 3 from the sum of
−4
7
−3
7
. If one of the number is
5
21
, find the other.
and 2 .
63. In the given figure, PS bisects P and PS ⊥ QR
(i) Find the three pairs of matching parts to
make ∆ PSQ ≅ ∆ PSR.
(ii) Is it true that QS = SR? Why?
64. (a) Find the value of x ,if
(b) Compare:
−4
7
,
36
𝑥
= −4 .
5
−9
65. Evaluate: 37 – 16.58 + 12.25.
(b) Compute: 6.4 ÷ 0.2 + 45.2
66. Simplify ( 7 x 2 y – 3 z 2 ) ( x +y + z ) and verify the result for x = 1 y = 1 and z = −1
67. Base of the given pyramid is BCDE.
(a) Find out how many more faces does it have?
(b) Name its other faces.
(c) What is the shape of its other faces?
68. (a) Factorize : 1 + x + xy + x2y.
−1
(b) Multiply (
4
𝑎+
1
5
𝑏 ) 𝑎𝑛𝑑 (
1
4
𝑎+
1
5
𝑏).
69. Fill in the blanks
48
(i) □ / -15 = 90
(ii) 169 /□ =
70.
−13
6
Arrange the following rational numbers in descending order :
−3
10
−7
9
18
, −5 , −15 , 30
71. Verify that │ x + y │ ≤ │x │ + │y│ by taking x =2/3 ,y = -3/5
72. Check the validity of the result , (x + y)-1≠ x-1 + y-1 for x =1/3 , y=-2/7
73. Simplify it (75.05÷ 0.025) × 0.001 + 2.351
74. Simplify and express the result as a rational number in its lowest form
(0.4 x 0.04 x 0.005)/(0.1 x 10 x 0.001) – ½ + 1/5
75. Simplify the given algebraic expression :
3x2(3y2 + 2) – x( x- 2xy2) + y(2x2y – 2y)
76. Simplify and then verify the result for the given values :
(1/4 a2 +5/9 b2) ( a + b + ab) ; a =2 , b =3
77. P and Q are two points on equal sides AB and AC of
an isosceles triangle ABC such that AP = AQ. Prove
that BQ = CP.
OR
ABC is an isosceles triangle in which AB= AC. Also ,
D is a point such that BD = CD . Prove that AD
Bisects
A and
D
78. In the given figure , AB =AC, BD = EC. Prove that ∆ABE  ∆ACD and AD =AE.
79. Name all the vertices, edges and faces of the given pyramid.
4
80. Find 4 rational number between 5
and
–9
4
–3 –7
9
18
81. Arrange the following in ascending order: 10 , –5, –15, 30 .
5
82. Divide the sum of 21 and
4
by their difference.
7
3
–9
83. Find a rational number between (x–y)–1 and x–1–y–1 , if x=4 and y= 8
84. Mohan had to cover a distance of 30km to reach his grand mother’s house. He covered
11.25 km by bus , 7.063 km by auto and the rest by foot.
a) How much distance did Mohan covered by foot ?
b) How is Mohan benefitted if he walks down to any of his destination ? In what ways does it
affect our environment ?
85. Simplify:
0.144÷12
0.016÷0.02
7
21
5
8
+ –
and write it in its lowest term form.
86. Simplify and find the values for a=–1 , b=–2
–5a+10–3b–4–5b+2a
87. Factorise: i) (a–b)2–(a–b) ii) 2ax+bx+2ay+by
88. Show that the bisectors of the vertical angles of an isosceles triangle bisects the base at
right angles
Or
ABC is an isosceles triangle in which AB=AC,
also D is a point such that BD=CD.
Prove that AD bisects ∠𝐴 𝑎𝑛𝑑 ∠𝐷 .
89. In the given figure AB=CD ,AD=BC
prove that ∆𝐴𝐷𝐶 ≅ ∆𝐶𝐵𝐴
90. The base of the given pyramid is a square BCDE
i) How many more faces does it have ?
ii) What is the shape of other faces ?
iii) Name all the vertices and edges of the given pyramid.
3 5 −8 −2
91. Represent , ,
7 7 7
,
7
on number line using pencil.
92. Find x such that the rational numbers in each of the following pairs are equivalent
a)
𝑥
,
5
b)
12 6
93. Simplify:
5
36
+
−7
8
15 −3
𝑥
+
,
8
6
−72
+
−3
−12
5
94. For rational numbers x=6, y=
−7
3
2
, z=9, verify that x (y-z) =x y-x z.
95. Simplify and express the result as a rational number in its lowest form.
0.4 x0.04 x 0.0005 1 1
- +
0.1x10 x0.001
2 5
96. Megha bought a book for Rs. 112.50 from a shop. She gave 500 rupee note to the shopkeeper
and got the balance back. But, she realized that the shopkeeper had given her Rs. 72 extra.
Megha returned the extra money and had a feeling of great satisfaction.
(a) How much money had the shopkeeper returned to Megha?
(b) What values did Megha exhibit in the above situation (at least two)?
97. Simplify: (a2+b2)(a2+b2)-(a2-b2)(a2-b2)
98. Find the product of (a-b) (a2+ab+b2) and verify the result for a=2, b=-3.
99. QS and RT are the altitudes of Δ PQR, and QS=RT
(a) Is ΔQRS is congruent to ΔRQT?
If it is by which congruence?
(b) State the three pairs of corresponding parts which
make ΔQRS is congruent to ΔRQT.
OR
State the five congruence conditions to prove congruency between triangles.
100. In fig. QS bisects <PQR as well as <PSR. State the three facts needed to ensure that
ΔQRS is congruent to ΔQPS? Give reasons for each statement?
101. Sketch the following with a labeled diagram by using pencil:
(a) A cuboid of size 3x3x2
(b) A cuboid of size 3x2x1
*********