LILAVATIBAI PODAR HIGH SCHOOL - ISC STD: VIII HOLIDAY HOMEWORK

LILAVATIBAI PODAR HIGH SCHOOL - ISC
STD: VIII
HOLIDAY HOMEWORK
SUBJECT : MATHEMATICS
1. Factorise:
i.
4(2a+b)²- (a-b)²
ii.
x²-(b-2)x-2b
iii.
5 – 4x(1+3x)
iv.
12 (a+b)2 – (a+b) – 35
v.
𝟏
9x2 – 𝟏𝟔
vi.
x4 – 5x2 – 36
vii.
64a2b − 144b3
viii.
35a3b2c + 42ab2c2
ix.
x2 –y2 −2yz−z2
x.
(123)2 – (77)2
xi.
(27.4)2 –(2.6)2
xii.
1−3x−3y − 4(x+y)2
2. Plot the points A (4,5), B(-1,5), C(-1,-2) and D(4,-2) on a graph paper. Join AB, BC,
CD andDA. Give a special name to the quadrilateral ABCD obtained. Also find its
area and perimeter.
3. A(1,0), B(-2,0) and D(1,-3) are the vertices of a square ABCD. By plotting the given
points on a graph paper find the co-ordinates of the unknown vertex C.
4. Plot the points A(1,-1), B(-1,4) and C(-3,-1) on a graph paper to obtain the triangle
ABC. Give a special name to the triangle ABC and, if possible, find its area and
perimeter.
5. Plot the points (2,1), (2,-2), (-1,1) and (-1,-2) join them with straight lines . give a
special name to the figure obtained and find its area and perimeter.
6. A and B can paint a room in 2days. A alone can do it in 3days. How many days
would B require working alone to paint the room?
1
7. One tap fills a tank in 20 minutes and another tap fills it in 12 minutes. The tank
being empty and if both taps are opened together, in how many minutes the tank
will be full?
8. If 3 women or 5 girls take 17 days to complete a piece of work, how long will 7
women and 11 girls working together take to complete the work?
9. A pipe can fill a tank in 12 hours. By mistake, a waste pipe in the bottom is left
opened and the tank is filled in 16 hours. If the tank is full, how much time will the
waste pipe take to empty it?
1
Hint: portion of the tank emptied by the waste pipe in one hour = 12 -
1
16
=
1
48
10. A and B together can build a wall in 10 days; B and C working together can do it
in 15 days; C and A together can do it in 12 days. How long will they take to finish
the work, working all together? Also find the number of days taken by each to do
the same work, working alone.
11 (3x+5)(4x-7)
12 (5x+9)(5x-9)
13
2𝑎 − 3𝑏
14 (3a+7b)
2𝑎 − 3𝑏
2
15 If a+b = 7 and ab =10 find the value of a2 + b2
16 If a2 +b2 = 34 and ab =15 find the value of i) a+b, ii) a-b
17 Using identities find the value of the following
a. (501)2
b. (9.8)2
18 If a+b+c =9, ab+bc+ca= 15 find the value of a2+b2+c2
19 a+b =5 and ab= 6 find a3 + b3
20 If 3p-4q=5 and pq=3 find the value of
27p3 – 64q3
21 (x2 y2)5
22 (x-3 y-3)-1
23
24 4
25
a5 × b5
a3 × b2 Type equation here.
𝑥 5𝑦 6
𝑥 4𝑦 2
a7 b9
a6 b12
26 271/3 × 81/3
2
EQUATIONS
SOLVE
1)Four less than 3 times a certain number is 8 more than twice the number.Find the
number.
2)The difference between the squares of two consecutive numbers is 141.Find the
numbers.
3)The base of an isosceles triangle is 3 cm longer than each of the other two sides.If
the perimeter is 54 cm,find the length of the sides.
4)Ravi has 20 coins worth Rs 85.If he has only 5 rupee and 2 rupee coins,find the
number of each type of coin.
5)In 5 years from now Shyam will be twice as old as he was 9 years ago.Find his
present age.
6)The digit in the tens place of a two digit number is 3 times the digit in the 3units
place.If the digits are reversed the number decreases by 36.Find the number.

UNITARY METHOD--- TIME AND WORK
1: A and B can paint a room in 2days. A alone can do it in 3days. How many days
would B require working alone to paint the room?
2: One tap fills a tank in 20 minutes and another tap fills it in 12 minutes. The
tank being empty and if both taps are opened together, in how many minutes the
tank will be full?
3: If 3 women or 5 girls take 17 days to complete a piece of work, how long will 7
women and 11 girls working together take to complete the work?
4: A pipe can fill a tank in 12 hours. By mistake, a waste pipe in the bottom is left
opened and the tank is filled in 16 hours. If the tank is full, how much time will
the waste pipe take to empty it?
1
Hint: portion of the tank emptied by the waste pipe in one hour = 12 -
1
16
=
1
48
5: A and B together can build a wall in 10 days; B and C working together can do
it in 15 days; C and A together can do it in 12 days. How long will they take to
finish the work, working all together? Also find the number of days taken by
each to do the same work, working alone.
3