Blogger Widgets APEX INSTITUTE : MATHEMATICS Question bank FOR CLASS -VIII SUMMATIVE ASSESSMENT-II 2014

Monday, January 6, 2014

MATHEMATICS Question bank FOR CLASS -VIII SUMMATIVE ASSESSMENT-II 2014














Q.1
Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.
Q.2
A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length is 1 m.
Q.3
Simplify 3x (4x −5) + 3 and find its values for
Q.4
Using a2 − b2 = (a + b) (a − b), find
(i)   512 − 492
(ii)  (1.02)2 − (0.98)2
(iii) 1532 − 1472
(iv)  12.12 − 7.92
Q.5
Solve: x - 2 = 7
Q.6
A batch of bottles was packed in 25 boxes with 12 bottles in each box. If the same batch is packed using 20 bottles in each box, how many boxes would be filled?
Q.7
Find the amount which Ram will get on Rs 4,096, he gave it for 18 months at  per annum, interest being compounded half yearly.
Q.8
Find and correct the errors in the statement: (a - 4) (a - 2) = a2 - 8
Q.9
Shobo’s mother’s present age is six times Shobo’s present age. Shobo’s age five years from now will be one third of his mother’s present age. What are their present ages?
Q.10
A factory required 42 machines to produce a given number of articles in 63 days. How many machines would be required to produce the same number of articles in 54 days?
Q.11
The population of a place increased to 54000 in 2003 at a rate of 5% per annum
(i)  find the population in 2001
(ii) what would be its population in 2005?
Q.12
Simplify and solve the linear equation 3(5z - 7) - 2(9z - 11) = 4(8z - 13) - 17
Q.13
Simplify.
(i)    (a2 − b2)2
(ii)   (2x +5)2 − (2x − 5)2
(iii)  (7m − 8n)2 + (7m + 8n)2
(iv)  (4m + 5n)2 + (5m + 4n)2
(v)   (2.5p − 1.5q)2 − (1.5p − 2.5q)2
(vi)  (ab + bc)2 − 2ab2c
(vii) (m2 − n2m)2 + 2m3n2
Q.14
Find and correct the errors in the statement: x + 2x + 3x = 5x
Q.15
Find and correct the errors in the statement: (3x + 2)2 = 3x2 + 6x + 4
Q.16
Vasudevan invested Rs 60000 at an interest rate of 12% per annum compounded half yearly. What amount would he get
(i) after 6 months?
(ii) after 1 year?
Q.17
A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of metal. How much sheet of metal is required?
Q.18
Calculate the amount and compound interest on
(a) Rs 10800 for 3 years at  per annum compounded annually.
(b) Rs 18000 for  years at 10% per annum compounded annually.
(c) Rs 62500 for  years at 8% per annum compounded half yearly.
(d) Rs 8000 for 1 year at 9% per annum compound half yearly.
(e) Rs 10000 for 1 year at 8% per annum compounded half yearly.
Q.19
Top surface of a raised platform is in the shape of a regular octagon as shown in the figure. Find the area of the octagonal surface.
Q.20
The floor of a building consists of 3000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor, if the cost per m2 is Rs 4.
Q.21
Given a cylindrical tank, in which situation will you find surface area and in which situation volume.


(a) To find how much it can hold
(b) Number of cement bags required to plaster it
(c) To find the number of smaller tanks that can be filled with water from it.
Q.22
Carry out the multiplication of the expressions in each of the following pairs.
(i)   4p, q + r
(ii)  ab, a − b
(iii) a + b, 7a2b2
(iv) a2 − 9, 4a
(v)  pq + qr + rp, 0
Q.23
Q.24
Factorise the following expressions
(i)   p2 + 6p + 8
(ii)  q2 − 10q + 21
(iii) p2 + 6p − 16
Q.25
Simplify and solve the linear equation 3(t - 3) = 5(2t + 1)
Q.26
One of  the two digits of a two digit number is three times the other digit. If you interchange the digits of this two digit number and add the resulting number to the original number, you get 88.What is the original number?
Q.27
Complete the table of products.
First monomial →
Second monomial↓
2x-5y3x²-4xy7x²y-9x²y²
2x4x²...............
-5y......-15x²y.........
3x²..................
-4xy..................
7x²y..................
-9x²y²...................
Q.28
Simplify and solve the linear equation 0.25(4f - 3) = 0.05(10f - 9)
Q.29
Show that (3x + 7)2 − 84x = (3x − 7)2
Q.30
A milkman sold two of his buffaloes for Rs 20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss.
(Hint: Find CP of each)
Q.31
Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively.
(a) (p, q)
(b) (10m, 5n)
(c) (20x2, 5y2)
(d) (4x, 3x2)
(e) (3mn, 4np)
Q.32
The lateral surface area of a hollow cylinder is 4224 cm2. It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet?
Q.33
Water is pouring into a cubiodal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 m3, find the number of hours it will take to fill the reservoir.
Q.34
Find the area of a rhombus whose side is 6 cm and whose altitude is 4 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.
Q.35
The sum of three consecutive multiples of 8 is 888. Find the multiples.
Q.36
Lakshmi is a cashier in a bank. She has currency notes of denominations Rs 100, Rs 50 and Rs 10, respectively. The ratio of the number of these notes is 2:3:5. The total cash with Lakshmi is Rs 4, 00,000. How many notes of each denomination does she have?
Q.37
Solve: 6x = 12
Q.38
A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. In the following table, find the parts of base that need to be added.
Parts of red pigment1471220
Parts of base8............
Q.39
Solve and check result: 5x + 9 = 5 + 3x
Q.40
The area of a trapezium is 34 cm2 and the length of one of the parallel sides is 10 cm and its height is 4 cm. Find the length of the other parallel side.
Q.41
The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?
Q.42
Find and correct the errors in the following mathematical statement. Substituting x = -3 in
(a) x2 + 5x + 4 gives (-3)2 + 5 (-3) + 4 = 9 + 2 + 4 = 15
(b) x2 - 5x + 4 gives (-3)2 - 5 (-3) + 4 = 9 - 15 + 4 = -2
(c) x2 + 5x gives (-3)2 + 5 (-3) = -9 - 15 = -24
Q.43
Q.44
Solve: y + 3 = 10
Q.45
The price of a TV is Rs 13,000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it,
Q.46
Find the side of a cube whose surface area is 600 cm2.
Q.47
Identify the terms, their coefficients for each of the following expressions.
(i)   5xyz2 − 3zy
(ii)  1 + x + x2
(iii)  4x2y2 − 4x2y2z2 + z2
(iv)  3 − pq + qr − rp

(vi)  0.3a − 0.6ab + 0.5b
Q.48
A shopkeeper buys 80 articles for Rs 2,400 and sells them for a profit of 16%. Find the selling price of one article.
Q.49
Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.
Q.50
Three consecutive integers add up to 51. What are these integers?
Q.51
A company packages its milk powder in cylindrical container whose base has a diameter of 14 cm and height 20 cm. Company places a label around the surface of the container (as shown in the figure). If the label is placed 2 cm from top and bottom, what is the area of the label.
 
Q.52
The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?
Q.53
Q.54
Diagram of the adjacent picture frame has outer dimensions = 24 cm × 28 cm and inner dimensions 16 cm × 20 cm. Find the area of each section of the frame, if the width of each section is same.
Q.55
A VCR and TV were bought for Rs 8,000 each. The shopkeeper made a loss of 4% on the VCR and a profit of 8% on the TV. Find the gain or loss percent on the whole transaction.
Q.56
A loaded truck travels 14 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours?
Q.57
Factorise
(i)   (l + m)2 − (l − m)2
(ii)  9x2y2 − 16
(iii) (x2 − 2xy + y2) − z2
(iv)  25a2 − 4b2 + 28bc − 49c2
Q.58
Complete the table:
First expressionSecond expressionProduct
(i)
(ii)
(iii)
(iv)
(v)
a
x + y -5
p
4p2q2
a + b + c
b + c + d
5xy
6p2 - 7p + 5
p2 - q2
abc
...
...
...
...
...
Q.59
If a box of sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the number of the children is reduced by 4?
Q.60
The diagonals of a rhombus are 7.5 cm and 12 cm. Find its area.
Q.61
I purchased a hair-dryer for Rs 5,400 including 8% VAT. Find the price before VAT was added.
Q.62
There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate Rs 100 per meter it will cost the village panchayat at Rs 75000 to fence the plot. What are the dimensions of the plot?
Q.63
Subtract the following.
(a) 4a − 7ab + 3b + 12 from 12a − 9ab + 5b − 3
(b) 3xy + 5yz − 7zx from 5xy − 2yz − 2zx + 10xyz
(c) 4p2q − 3pq + 5pq2 − 8p + 7q − 10 from 18 − 3p − 11q + 5pq − 2pq2 + 5p2q
Q.64
Following are the car parking charges near a railway station up to
                      4 hours        Rs 60
                      8 hours        Rs 100
                      12 hours      Rs 140
                      24 hours      Rs 180
Check if the parking charges are in direct proportion to the parking time.
Q.65
Using identities, evaluate.
(i)   712
(ii)  992
(iii) 1022
(iv)  9982
(v)  (5.2)2
(vi)  297 × 303
(vii) 78 × 82
(viii) 8.92
(ix)  1.05 × 9.5
Q.66
A scooter was bought at Rs 42,000. Its value depreciated at the rate of 8% per annum. Find its value after one year.
Q.67
The organizers of an essay competition decide that a winner in the competition gets a prize of Rs 100 and a participant who does not win gets a prize of Rs 25. The total prize money distributed is Rs 3000. Find the number of winners, if the total number of participants is 63.
Q.68
Factorise the expressions and divide them as directed.
(i)  (y2 + 7y + 10) ÷ (y + 5)
(ii) (m2 - 14m - 32) ÷ (m + 2)
(iii) (5p2 - 25p + 20) ÷ (p - 1)
(iv)  4yz(z2 + 6z - 16) ÷ 2y(z + 8)
Q.69
Q.70
Simplify.
(i)    (x2 − 5) (x + 5) + 25
(ii)   (a2 + 5) (b3 + 3) + 5
(iii)  (t + s2) (t2 − s)
(iv)  (a + b) (c − d) + (a − b) (c + d) + 2 (ac + bd)
(v)   (x + y) (2x + y) + (x + 2y) (x − y)
(vi)  (x + y) (x2 − xy + y2)
(vii) (1.5x − 4y) (1.5x + 4y + 3) − 4.5x + 12y
(viii) (a + b + c) (a + b − c)
Q.71
In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 12 m high. If the length of the ship is 28 m, how long is the model ship?
Q.72
Find the product.
(i)   (5 − 2x) (3 + x)
(ii)  (x + 7y) (7x − y)
(iii) (a2 + b) (a + b2)
(iv) (p2 − q2) (2p + q)
Q.73
Using (x + a) (x + b) = x2 + (a + b) x + ab, find
(i)  103 × 104
(ii)  5.1 × 5.2
(iii) 103 × 98
(iv)  9.7 × 9.8
Q.74
Q.75
A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?
(a)
(b)
Q.76
Multiply the binomials.
(i)     (2x + 5) and (4x − 3) (ii) (y − 8) and (3y − 4)
(iii)   (2.5l − 0.5m) and (2.5l + 0.5m) (iv) (a + 3b) and (x + 5)
(v)    (2pq + 3q2) and (3pq − 2q2)
Q.77
Divide as directed.
(i)   5(2x + 1) (3x + 5) ÷ (2x + 1)
(ii)  26xy(x + 5) (y - 4) ÷ 13x(y - 4)
(iii) 52pqr (p + q) (q + r) (r + p) ÷ 104pq(q + r) (r + p)
(iv) 20(y + 4) (y2 + 5y + 3) ÷ 5(y + 4)
(v)  x(x + 1) (x + 2) (x + 3) ÷ x(x + 1)
Q.78
Find and correct the errors in the statement:
Q.79
The ages of Rahul and Haroon are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?
Q.80
Find and correct the errors in the statement: (2x)2 + 5x = 4x + 5x = 9x
Q.81
Q.82
Solve and check result: 3x = 2x + 18
Q.83
Simplify and solve the linear equation 15(y - 4) - 2(y - 9) + 5(y + 6) = 0
Q.84
An ant is moving around a few food pieces of different shapes scattered on the floor. For which food - piece would the ant have to take a longer round? Remember, circumference of a circle can be obtained by using the expression c = 2πr, where r is the radius of the circle.
(a)
(b)
(c)
Q.85
Q.86
Solve: 6 = z + 2
Q.87
Q.88
Find and correct the errors in the statement: 2x + 3y = 5xy
Q.89
Factorise the expressions
(i)  (lm + l) + m + 1
(ii)  y(y + z) + 9(y + z)
(iii) 5y2 − 20y − 8z + 2yz
(iv) 10ab + 4a + 5b + 2
(v)  6xy − 4y + 6 − 9x
Q.90
Find and correct the errors in the statement: 5y + 2y + y - 7y = 0
Q.91
Find and correct the errors in the statement:
Q.92
Find the common factors of the terms
(i)    12x, 36
(ii)    2y, 22xy
(iii)   14pq, 28p2q2
(iv)   2x, 3x2, 4
(v)    6abc, 24ab2, 12a2b
(vi)   16x3, −4x2, 32x
(vii)  10pq, 20qr, 30rp
(viii)  3x2y3, 10x3y2, 6x2y2z
Q.93
Find the product.
Q.94
Use the identity (x + a) (x + b) = x2 + (a + b)x + ab to find the following products.
(i)    (x + 3) (x + 7)
(ii)   (4x +5) (4x + 1)
(iii)  (4x − 5) (4x − 1)
(iv)  (4x + 5) (4x − 1)
(v)   (2x +5y) (2x + 3y)
(vi)  (2a2 +9) (2a2 + 5)
(vii) (xyz − 4) (xyz − 2)
Q.95
If Chameli had Rs 600 left after spending 75% of her money, how much did she have in the beginning?
Q.96
Factorise the expressions and divide them as directed.
(i)  5pq(p2 - q2) ÷ 2p(p + q)
(ii) 12xy(9x2 - 16y2) ÷ 4xy(3x + 4y)
(iii) 39y3(50y2 - 98) ÷ 26y2(5y + 7)
Q.97
Describe how the two figures at the right are alike and how they are different. Which box has larger lateral surface area?
Q.98
Mohan wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along the road. It the area of this field is 10500 m2 and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.
Q.99
Find the amount and the compound interest on Rs 10,000 for   years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?
Q.100
Solve and check result: 8x + 4 = 3(x − 1) + 7
Q.101
Solve and check result: 5t − 3 = 3t − 5
Q.102
Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.
Q.103
A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time -
(i)  the length of the shadow cast by another pole 10 m 50 cm high
(ii) the height of a pole which casts a shadow 5 m long.
Q.104
Add the following.
(i)   ab − bc, bc − ca, ca − ab
(ii)  a − b + ab, b − c + bc, c − a + ac
(iii) 2p2q2 − 3pq + 4, 5 + 7pq − 3p2q2
(iv) l2 + m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl
Q.105
Q.106
A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle?
Q.107
Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72 km. What would be her distance covered in the map?
Q.108
Arif took a loan of Rs 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after years if the interest is
(i)  Compounded annually
(ii) Compounded half yearly
Q.109
Work out the following divisions.
(i)   (10x − 25) ÷ 5
(ii)  (10x − 25) ÷ (2x − 5)
(iii) 10y(6y + 21) ÷ 5(2y + 7)
(iv)  9x2y2(3z − 24) ÷ 27xy(z − 8)
(v)   96abc(3a − 12)(5b − 30) ÷ 144(a − 4) (b − 6)
Q.110
Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them?

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