Download Oman College of Management and Technology Practice Work 1 Q1

Oman College of Management and Technology
Practice Work 1
Q1.
Differentiate between Rational and Irrational Numbers
i.
ii.
iii.
iv.
v.
vi.
vii.
viii.
ix.
x.
xi.
xii.
2.5
22 ∕ 7
√2
3.66666
5 ∕ 3
3 ∕ 5
7 ∕5
6.8 ∕ 3.4
√93
56
7 ∕ 3
3 ∕ 7
Q2.
Complete the followings












Set of Natural Numbers:
N
=
Set of Whole Numbers:
W
=
Set of Odd Numbers:
O
=
Set of Even Numbers:
E
=
Set of Prime Numbers:
P
=
Set of Integers :
Z
=
Q3.
Enlist different operations on sets
Q4.
If
Q5.
If
U={11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
A={11, 12, 13, 14, 15, 16}
B={15, 16, 17, 18, 19, 20}
Then find A  B, A  B, A – B, B – A, Ac , Bc , Ac  Bc , (A  B) c
U={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A={5, 6, 7, 8, 9}
B={1, 2, 3, 4, 5, 8, 9, 10}
Then find A  B, A  B, A – B, B – A, Ac , Bc , Ac  Bc , (A  B) c
Oman College of Management and Technology
Practice Work 2
Q1.
If
U={11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
A={11, 12, 13, 14, 15, 16}
B={15, 16, 17, 18, 19, 20}
Then find A  B, A  B, A – B, B – A, Ac , Bc , Ac  Bc , (A  B) c
Q2.
If
U={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A={5, 6, 7, 8, 9}
B={1, 2, 3, 4, 5, 8, 9, 10}
Then find A  B, A  B, A – B, B – A, Ac , Bc , Ac  Bc , (A  B) c
Q3. Rationalize the denominator of
(i)
(ii)
1
11
3
11
Q4. Rationalize the denominator of
(i)
(ii)
(iii)
(iv)
(v)
1
5 2
1
11  7
3
7 2
1
9 2
1
11  3
Oman College of Management and Technology
Practice Work 3
Q1.
Simplify the followings:
i.
ii.
23
35
iii.
27 3
iv.
32 5
v.
64 2
1
1
1
vi.
vii.
125
9
1
3
3
2
2
5
viii.
32
ix.
16 4
x.
xi.
xii.
125 3
23 × 24
3 2 × 3 7
xiii.
22 ×22
3
1
1
3
1
xiv.
73
7
xv.
7
3
11
1
2
1
11 4
Oman College of Management and Technology
Practice Work 4
Q1.
Write types of following polynomials (Linear or Quadratic or Cubic):
i.
ii.
iii.
iv.
v.
vi.
vii.
x2 + x
x - x3
y + y2 + 4
1+x
3t
r2
7x 3
Q2.
i.
ii.
iii.
iv.
v.
vi.
Find value of
x2 + 5
at x = 4
3
x – 5x
at x = -1
5
4
x -x +3
at x = 2
5
4
5x - 3x + 3
at x = 2
2
2
x + 2xy - y
at
x = 3 and y = -2
Find value of
C=2  r
at
r = 14 cm
Q3.
i.
ii.
iii.
iv.
v.
Solve the following linear equations
x+7=4
4x - 3 = 9
6(x + 3) = 9
13x + 15 = 5x – 9
4x - 3 = 4 + 3x
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



Oman College of Management and Technology
Practice Work 5
Q1. Solve the followings
i.
ii.
iii.
iv.
v.
vi.
vii.
viii.
ix.
x.
xi.
Q2.
x3 = 6
x + 4 = 15
5x  4 + 3 = 1
2
x3 = 6
5
3
x4 = 4
2
2x  3 x  2

5
2
2x  5 x  3

6
4
2x x 1
 
5 4 5
2x  1 x  2

3
3
2
2x 4 x  2

5
3
2
x 1 2 x 1

3
4
6
Solve the followings linear inequalities
i.
( n W )
4n  1  7
ii.
(aZ )
7  5a  32
x  5 25  4 x

iii.
( xN )
10
5
7  5x 1  x

iv.
( xR)
3
2
Oman College of Management and Technology
Practice Work 6
Q1.
When 8 is added to a number, the result is equal to 21. Find the number
Q2. When 67 is subtracted from 2 times of a number, the result is equal to 33. Find the
number
Q3. 5 is subtracted from 4 times a number and the result is doubled. If the answer is equal
to 6, what is the number?
Q4. What is the number which when multiplied by 2 and added to 8 gives same result as
when it is divided by 2 and added to 32
Q5.
The sum of three consecutive natural numbers is 192. Find the numbers.
(Hint: three consecutive natural numbers are x - 1, x, x + 1)
Q6.
The sum of three consecutive odd numbers is 279. Find the numbers.
(Hint: three consecutive natural numbers are x - 2, x, x + 2)
Oman College of Management and Technology
Practice Work 7
Q1.
Add the followings:
2 x 3  4 x 2  13 x  17
7 x 3  2 x 2  4 x  23
_________________
i.
9 x 3  2 x 2  9 x  40
_________________
ii.
2x3  4x 2
 7 x 2  5x  7
________________
2 x 3  3x 2  5 x  7
________________
Q2.
Subtract the followings:
2 x 3  4 x 2  13 x  17
7 x 3  2 x 2  4 x  23
i.
_________________
 5 x 3  6 x 2  17 x  6
_________________
ii.
2x3  4x 2
 7 x 2  5x  7
________________
2 x 3  11x 2  5 x  7
Q3. Multiply 4x – 3 with 5x
Q4. Multiply 4x – 3 with 5x + 7
Q5. Multiply
Q6. Multiply
x 2  3x  9
x3
3x 2  7 x  5
4x 2  2x  1
Oman College of Management and Technology
Practice Work 8
Q1. Divide the followings
8x 5  4 x 3
i.
64 x 12  4 x 6
ii.
iii.
8 xy5  4 xy3
iv.
24 x 4 y 3 z 5  4 x 2 y 3
v.
16 x 5 y 7 z 2  16 x 4 y 6 z
Q2. Divide the followings:
8x 5  8x 3  4 x 3
i.
ii.
(24 x 3  12 x)  3x
iii.
( x 2  5 x  6)  ( x  2)
iv.
( x3  x 2  14 x  24)  ( x  2)
v.
( x 3  19 x  30)  ( x  3)
vi.
( x 3  2 x  4)  ( x  2)
vii.
( x 5  y 5 )  ( x  y)
Oman College of Management and Technology
Practice Work 9
Q1. Find remainder by Remainder Theorem when ( x 3  6 x 2  11x  8)  ( x  1)
Q2. Find remainder by Remainder Theorem when (4 x 3  3x 2  2 x  5)  ( x  5)
Q3. Find remainder by Remainder Theorem when ( x 3  x 2  14 x  24)  ( x  2)
Q4. Find remainder by Remainder Theorem when ( x 4  2 x 2  3x  3)  ( x  3)
Q5. Find by means of factor Theorem whether or not x – 2 is a factor of ( x 3  x 2  14 x  24)
Q6. Factorize the followings
x2  x
i.
ii.
x3 y  x2
iii.
x4 y2  x2 y
49 x 3  7 x 2
iv.
x3  2x 2  4x
v.
7 x 3  14 x 2  21x
vi.
x 2  11x  6 x  66
vii.
6 x 2  2 x  15 x  5
viii.
x 2  12 x  10 x  120
ix.
x3  x2  x  1
x.
Practice Work 10
Oman College of Management and Technology
Q1. Factorize the followings
x 2  7 x  10
i.
3x 2  7 x  4
ii.
4x 2  2x  6
iii.
5x 2  8x  3
iv.
Q2. Solve by Quadratic Formula
i.
ii.
iii.
iv.
v.
vi.
x 2  7 x  12  0
x 2  10 x  171  0
x 2  7 x  10
3x 2  7 x  4
4x 2  2x  6
5x 2  8x  3
Practice Work 11
Oman College of Management and Technology
Q1. Define Line, Ray and Line Segment
Q2. What are different types of a triangle
Q3. What are different types of angles
Q4. Find distance between (-1,2) and (-2,3)
Q5. Find distance between (2,-1) and (4,-5)
Q6. Write the respective Quadrant of each point.
Points
Quadrant (I or II or III or IV)
(- 3, 4)
(- 5, - 7)
(3 , -5)
(5, 9)
Q7. Draw graph of 2 x  3 y  6
Q8. Draw graph of x  2 y  4
Q9. Draw graph
Q10. Draw graph
x  2y  4
2x  y  6
Practice Work 12
Oman College of Management and Technology
Q1. Convert 12 km into meters
Q2. Convert 3.5km per hour to metre per second
Q3. how many seconds are there in 2.5 days
Q4. Convert 5600 kg into grams
Q5. Convert 6300 m into km
Q6. Convert 125 g into kg
Q7. how many centimetres are there in 5 m
Q8. how many days are there in 36 weeks
Q9. Convert 3600 m per second into km per hour
Q10. How many $ are there in 3600 RO. If 1 RO = 2.8 $
Practice Work 13
Oman College of Management and Technology
Q1. Find Circumference of circle if
(i) r = 4cm
(ii) r = 5.9cm
(iii) d = 14cm
Q2. Find Area of circle if
(i) r = 5cm
(iii) d = 4.6cm
(ii) r = 9.2cm
Q3. Draw a circle with radius 5cm
Q4. Draw a circle with daimeter 6 cm
Q5. Convert into radians measures
(i) 60 
(ii) 135 
Q6. Convert into degree measures

2
rad
rad
(i)
(ii)
3
4
Practice Work 14
(iii) 75
(iii)

4
rad
Oman College of Management and Technology
Q1. Find Length of arc if radius of circle is 3 cm and  = 2 rad.
Q2. Find Length of arc if radius of circle is 5 cm and  = 60  .
Q3. Find Area of sector if radius of circle is 6 cm and  = 5 rad.
Q4. Find Area of sector if radius of circle is 6 cm and  = 45 .
Q5. In a right angle triangle, If Base = 5 cm and Perpendicular = 12 cm then
find Hypotenuse.
Q6. In a right angle triangle, If Base = 2.9 cm and Hypotenuse = 11.7 cm then
find Perpendicular.
Q7. In a right angle triangle, If Hypotenuse = 21 cm and Perpendicular = 7 cm
then find Base.
Practice Work 15
Oman College of Management and Technology
Q1. Write down all trigonometric identities
Q2. Find values without using calculator
i.
ii.
iii.
iv.
v.
2 sin 60 cos 60
2 sin 45  2 cos 45
sin 60 cos 30  cos 60 sin 30
tan 30 cot 30  1
5 cos 45  3sin 45
Q3. Find values of
i.
(1  sin  )(1  sin  )  cos 2 
ii.
(1  cos  )(1  cos  )  sin 2 
iii.
(sec   1)(sec   1)  tan 2 
iv.
1  tan 2   sec
v.
1  cot 2   cos ec
2
, then find the remaining trigonometric ratios when  lies in the
3
first quadrant.
Q4 If sin  
Oman College of Management and Technology
Practice Work 16
Q1. A ladder makes an angle of 60 with the ground and reaches a height of 10m along the
wall. Find the length of the ladder
Q2. Angle of elevation of the top of a flag post from a point on the ground 40 m away from
the flag post is 60. Find height of the post
Q3. A tree is 72 m high. Find the angle of elevation of its top 100 m away on the ground level
Q4. Find the measure of angle of elevation of the Sun, if tower 300 m high casts a shadow
450 m long.
Q5. Calculate the value of x in the below figure.
.
12 cm
B
C
x
20 cm
A