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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 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. x3 = 6 x + 4 = 15 5x 4 + 3 = 1 2 x3 = 6 5 3 x4 = 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. (aZ ) 7 5a 32 x 5 25 4 x iii. ( xN ) 10 5 7 5x 1 x iv. ( xR) 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 x3 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