Question Bank IX MATHS. CHAPTER 1 Unit 1 - Square Root

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1 1 Question Bank IX MATHS I. Choose the correct answer: CHAPTER 1 Unit 1 - Square Root 1. If a perfect square has n digits, then its square root has digits. (if n is odd) a) 2n b) 4n c) d) 2. If a perfect square has n digits, then its square root has digits (if n is even ) a) 2n, b) n 2 c) d) 3. + = a) 21 b) 19 c) d) 4. Area of an equilateral triangle is a) (Side) 2 b) c) d) r 2 5. If a = b 2, then b is the of a a) Cube b) cube root c) square d) square root 6. - = a) 13 b) 2 c) 15 d) = a) 42 b) 40 c) 13 d) = a) b) ab c) d) a 2 b II. Fill in the blanks: 9. A is the product of two equal numbers. 10. If a perfect square has 4 digits, its square root has digits. 11. If a perfect square has 5 digits, its square root has digits = 13. = 14. = 15. The least number to be added to make 62 a perfect square is 16. The least number to be subtracted to make 70 a perfect square is 17. = = 19. = 20. =

2 2 III. Do as directed: 2M 21. Find the square root of the following numbers by the factorization numbers: Find the square root of the following numbers by the factorization numbers: Find the square root of the following numbers by the factorization numbers: Find the square root of the following numbers: Find the square root of the following numbers: Find the square root of the following numbers by division method: Find the square root of the following numbers by division method: Find the square root of the following numbers by division method: Find the square root of the following numbers by division method: Find the least number to be added to get a perfect square: Find the least number to be added to get a perfect square: Find the least number to be added to get a perfect square: Find the least number to be added to get a perfect square: Find the least number to be subtracted from the following numbers to get a perfect square: Find the least number to be subtracted from the following numbers to get a perfect square: Find the least number to be subtracted from the following numbers to get a perfect square: Find the least number to be subtracted from the following numbers to get a perfect square: Find the square root of the following numbers using division method: Find the square root of the following numbers using division method: Find the square root of the following numbers using division method:

3 3 41. Find the square root of the following numbers using division method: Find the square root of the following numbers correct to 2 decimal places: Find the square root of the following numbers correct to 2 decimal places: Find the square root of the following numbers correct to 2 decimal places: Find the square root of the following numbers correct to 2 decimal places: Find the square root of the following numbers correct to 2 decimal places: Find the square root of the following numbers correct to 2 decimal places: Find the square root of the following numbers correct to 2 decimal places Find the square root of the following numbers correct to 2 decimal places Find the square root of the following numbers correct to 2 decimal places Find by division method. 52. Find by division method. 53. Round off the following numbers to 3 decimal place (i) (ii) Find by division method. 55. Round off to 3 decimal places (i) (ii) Find by division method. 57. Find by division method. 58. Find the squares of 9, 10, 99, 100, 999, Tabulate these numbers. 59. Find the least number to be subtracted from 1234 to make it a perfect square. IV. Solve the problems: 3m 60. A person has three rectangular plots of dimensions 112 m X 54 m, 84 m X 68 m and 140 m X 87 m at different places. He wants to sell all of them and buy a square plot of integral length of maximum possible area approximately equal to the sum of these plots. What would be the dimensions of such a square plot? How much area he may have to lose? 61. A square garden has area m 2. A trench of one meter wide has to be dug along the boundary inside the garden. After digging the trench, what will be the area of the left out garden? 62. Find perfect consecutive perfect squares between which 4567 lie? 63. Find the least number to be added to make a perfect square? 64. Find by division method. 65. Find by division method. 66. Find by division method. 67. Find the square root of 12 and correct to 3 decimal places.

4 4 68. Find and correct to 3 decimal places. 69. Find the least number to be subtracted from to get a perfect square. 70. Find the square root of Find the square root of 8 and correct to 2 decimal places. V. Solve the problems: 4m 72. A square garden has area 900 m 2. Additional land measuring equal area surrounding it, has been added to it. If the resulting plot is in the form of square, what is its side? (correct to 2 decimal places) CHAPTER 1 Unit 2 Real Numbers I. Choose the correct answer: 1m 1. (-1) x (-1) = a) -1 b) 1 c) 0 d) 2 2. = a) 15 b) c) 1 d) = a) b) c) d) In the decimal expansion , length = a) 0 b) 1 c) 3 d) 2 5. In the decimal expansion , is the non repeating part a) 4 b) 0 c) 004 d) nil 6. In the decimal expansion , is the repeating part a) 32 b) 1532 c) 15 d) nil 7. In the decimal expansion , is the integer part a) 8 b) 3 c) 6 d) 68 II. Fill in the blanks: 1. The set of rational and irrational numbers are called 2. The repeating part of a rational number is called 3. In a rational number the no of digits in the period is called 4. The decimal expansion of 1 is 5. The square of a real number is always 6. In a real number system is the additive identity. 7. In real number system is the multiplicative identity. 8. Additive inverse of 1 + is 9. Multiplicative inverse of is 10. Every irrational number has an decimal expansion. III. Solve the following: 2m 1. Write the additive inverse of the following nos. a) b) 1 + c) d) 7 +

5 5 2. What are the properties of R used in the following a) a + ( + c) = (a + ) + c b) 1 = c) (1 + ) = 2 + d) 8 7 = Write the multiplicative inverse of the following. a) 3 + b) - c) 4. Write down as the decimal expansion of 5. Write down the decimal expansion of 6. Write the rational number for Write the rational number for Write the rational number for Write the rational number for 5.8 (5.8 ) 10. Write the rational number for 0.00 IV. Solve the following: 3m 1. Find 3 irrational numbers between and 2. Find 5 irrational numbers between 4 and Find 2 rational numbers between and 4. Find 2 rational numbers between and V. Solve the following: 4m 1. Represent on number line. 2. Represent on number line. 3. Represent on number line. 4. Represent on number line. I. Choose the correct answer: CHAPTER 1 Unit 3 Surds d) In 5, order is a) 5 b) 3 c) 4 d) 2 2. In 6, radicand is a) 6 b) 4 c) 5 d) 2 3. = a) b) c) d) 4. ( ) = a) 2 b) 8 c) 3 d) = a) a -n b) a c) a n d)

6 6 II. Fill in the blanks: 1. let a and b be positive real numbers, and let r 1 and r 2 be two rational number then. = 2. the simplest form of is 3., 4 and 10 are surds. 4., 3 and 4 are surds. 5. and are surds. 6. The index form of is. III. Solve the following: 2m 1. Define surds? Give two examples. 2. Define mixed surds? Write two examples. 3. Define like and unlike surds? 4. Simplify: 5. Simplify: ( ) 6. Write into simplest form a) b) 7. Write into simplest form a) b) 8. Reduce into same order 9. Reduce into same order 10. Reduce into same order 11. Find which is larges: 3 and Find which is smaller and 13. Write in ascending order. 14. Write in descending order. and IV. Solve the following: 3m 1. Simplify: (16) (64) 4/3 2. Simplify: (0.25) 0.5 (0.01) Simplify: (6. 25) (100) -1/2 (0.01) Classify into like surds.,,,, 5. Classify into like surds:,,,,, 6. Write the following into descending order,, 7. Arrange into ascending order:, and

7 7 V. Solve the following: 4m 1. [, ( ) - ] Find the value. 2. Simplify *,( ) -, ( )-+ I. Choose the correct answer: CHAPTER 1 Unit 4 Sets 1. Founder of set theory a. George b. George Cantor c. Aryabatta d. Pythogram 2. The objects in sets are called a. Elements or members b. Integers c. Numbers d. None of these 3. The visualize operations of sets using diagram are called diagram. a. Graph b. Venn diagram c. Pictorial representation d. Power point 4. Which of the following is a set? a. All students of your school b. Good teachers of your school c. Honest students of your school d. Disciplined students of the school 5. Here A B is a. 1,3 b. 5,6 c. 2,4 d. 1,2,3,4,5,6 6. Let U={1,3,4,5,6,7,8} & B={1,3,4}. The compliment of B is a. {1,3,5} b. {5,6,7,8} c. {1,2,4} d. { } 7. Let A={3,6,15,9,12,18,21,24} B={4,8,12,16,20,24} A\B= a. {4,8,16,20}

8 8 b. {3,6,9,15,18,21} c. {4,5,21,22} d. {3,6,5,21,22} 8. If A={1,2,3} then 2 A is a. 2 3 b. 2 1 c. 2 4 d. 2 B 9. If is A subset of U, then U\A = a. A b. A c. U d. U II. Fill in the blanks: 10. Representing a set by writing all elements is called method 11. Set builder method is also called method 12. Venn diagram are introduced by 13. Two sets A and B are said to be if no element of B is in A and no element of A is in B. 14. The sets containing only one element is called a 15. Two sets A&B are disjoint if only if A B = 16. In the adjacent diagram AUB is 17. A set of all vowels A = {a, e, I, o, u} represent the above in set builder method 18. In the adjacent Venn diagram find & write the elements of B/A is 19. is subset of every set. 20. In the adjacent diagram find A B 21. If A = {1,3,5,7} and B is {5,7,8} then A/B = 22. If A = {p, q, r, s} and B = r, s, t} then B/A = 23. If A = {1, 2, 3, 4, 5, 6} and B is {6, 7, 8} then AΔB = 24. If A = {a, b, c, d} U = {a, b, c, d, e, f} find A in U 25. If A = {x/x is a even number less than 10} and B = {x/x is a square number less than 10} find A B

9 9 26. In the set A, B & C A B C is 27. In the set A, B & C find AUBUC is 28. State whether the set is finite or infinite set of points on a line is set 29. The colour of rainbow if we represent the set in roaster method the elements are 30. If A = {P,Q, R, S} and B = {S, T, U, W} the intersection of A and B is 31. A = {1, 4, 9, 16, 25, 36} if we represent the set in rule method the statement is written as III. Solve the following: 2m 32. If A ={ 1,2,3,4}, U= {1,2,3,4,5,6,7,8}, find A in U and draw Venn diagram. 33. If U={x x 25, x N}, A={ x x U, x 15 }and B = { x x U, 0 x 25},list the elements of the following sets and draw Venn diagram: A in U 34. If U={x x 25, x N}, A={ x x U, x 15 }and B = { x x U, 0 x 25},list the elements of the following sets and draw Venn diagram : B in U 35. If U={x x 25, x N}, A={ x x U, x 15 }and B = { x x U, 0 x 25},list the elements of the following sets and draw Venn diagram :A \ B 36. If U={x x 25, x N}, A={ x x U, x 15 }and B = { x x U, 0 x 25 },list the elements of the following sets and draw Venn diagram : A B 37. Suppose U= {3,4,5,6,7,8,9,10,11,12,13}, A= {3,4,5,6,9}, B = {3,7,9,5}and C= {6,8,10,12,7}. Write down the following sets and draw Venn diagram : A 38. Suppose U= {3,4,5,6,7,8,9,10,11,12,13}, A= {3,4,5,6,9}, B = {3,7,9,5}and C= {6,8,10,12,7}. Write down the following sets and draw Venn diagram : B 39. Suppose U= {3,4,5,6,7,8,9,10,11,12,13}, A= {3,4,5,6,9}, B = {3,7,9,5}and C= {6,8,10,12,7}. Write downthe following sets and draw Venn diagram : C 40. Suppose U= {3,4,5,6,7,8,9,10,11,12,13}, A= {3,4,5,6,9}, B = {3,7,9,5}and C= {6,8,10,12,7}. Write down the following sets and draw Venn diagram : ( A ) 41. Suppose U= {3,4,5,6,7,8,9,10,11,12,13}, A= {3,4,5,6,9}, B = {3,7,9,5}and C= {6,8,10,12,7}. Write down the following sets and draw Venn diagram : ( B ) 42. Suppose U= {3,4,5,6,7,8,9,10,11,12,13}, A= {3,4,5,6,9}, B = {3,7,9,5}and C= {6,8,10,12,7}. Write down the following sets and draw Venn diagram : ( C ). 43. Suppose U= {1,2,3,4,5,6,7,8,9}, A= {1,2,3,4}, B = {2,4,6,8}.write down the following sets and draw Venn diagram: A 44. Suppose U= {1,2,3,4,5,6,7,8,9}, A= {1,2,3,4}, B = {2,4,6,8}.write down the following sets and draw Venn diagram: B

10 Suppose U= {1,2,3,4,5,6,7,8,9}, A= {1,2,3,4}, B = {2,4,6,8}.write down the following sets and draw Venn diagram: A B 46. Suppose U= {1,2,3,4,5,6,7,8,9}, A= {1,2,3,4}, B = {2,4,6,8}.write down the following sets and draw Venn diagram: A B 47. Suppose U= {1,2,3,4,5,6,7,8,9}, A= {1,2,3,4}, B = {2,4,6,8}.write down the following sets and draw Venn diagram: A B 48. Suppose U= {1,2,3,4,5,6,7,8,9}, A= {1,2,3,4}, B = {2,4,6,8}.write down the following sets and draw Venn diagram: A B 49. Find (A/B) and (B/A) for the following sets and draw Venn diagram: A={a,b,c,d,e,f,g,h} and B = {a,e,i,o,u} 50. Find (A/B) and (B/A) for the following sets and draw Venn diagram: A = {1,2,3,4,5,6} and B = {2,3,5,7,9} 51. Find (A/B) and (B/A) for the following sets and draw Venn diagram: A = {1,4,9,16,25} and B = {1,2,3,4,5,6,7,8,9} 52. Find (A/B) and (B/A) for the following sets and draw Venn diagram: A = {x x is a prime number less than 5} and B = {x x is a square number less than 16} 53. Find A B and draw Venn diagram when: A = {a, b, c, d} and B = {d, e, f} 54. Find A B and draw Venn diagram when: A = {1, 2, 3, 4, 5} and B = {2, 4} 55. Find A B and draw Venn diagram when: A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4, 5, 6} 56. Find A B and draw Venn diagram when: A = {1, 4, 7, 8} and B = {4, 8, 6, 9} 57. Find A B and draw Venn diagram when: A = {a, b, c, d, e} and B = {a, c, e, g} 58. Find A B and draw Venn diagram when: A = {1, 2, 3, 4, 5} and B = {1, 3, 5, 7} 59. Find union of A and B, and represent it using Venn diagram: A = {1, 2, 3, 4, 8, 9}, B = {1, 2, 3, 5} 60. Find union of A and B, and represent it using Venn diagram: A = {1, 2, 3, 4, 5,}, B = {4, 5, 7, 9} 61. Find union of A and B, and represent it using Venn diagram: A = {1, 2, 3}, B = {4, 5, 6) 62. Find union of A and B, and represent it using Venn diagram: A = {1, 2, 3, 4, 5}, B = {1, 3, 5} 63. Find union of A and B, and represent it using Venn diagram: A = {a, b, c, d}, B = {b, d, e, f} 64. Find the intersection of A and B, and represent it by Venn Diagram: A = {a, b, d,e}, B = {b, d, e, f} 65. Find the intersection of A and B, and represent it by Venn Diagram: A = {1, 2, 4, 5}, B = {2, 5, 7, 9} 66. Find the intersection of A and B, and represent it by Venn Diagram: A = {1, 3, 5, 7}, B = {2, 5, 7, 10 12}

11 Find the intersection of A and B, and represent it by Venn Diagram: A = {1, 2, 3}, B = {5, 4, 7} 68. Find the intersection of A and B, and represent it by Venn Diagram: A = {a, b, c}, B = {1, 2, 9} 69. Find A B and A B when: A is the set of all prime number and B is the set of all composite natural numbers. 70. Find A B and A B when: A is the set of all positive real numbers and B is the set of all negative real numbers 71. Find A B and A B when: A = N and B = Z 72. Find A B and A B when: A = {x x Z and x is divisible by 6} and B = {x x Z and x is divisible by 15} 73. Give examples to show that A A Aand A A A IV. Do as directed: 3m 74. Find A Δ B and draw venn diagram if A = {1, 3, 5, 7} and B = {5, 7, 8} 75. If U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 5, 8} and B = {0, 1, 3, 5, 6}. Find i) ( A B) ii) ( A B). Draw venn diagram. 76. Find A Δ B if A = {a, b, c, d, e} and B = {a, c, e, g}. Draw venn diagram. 77. If U = { X : X N and X 9}, A = { X : X is a prime number less than 9}, B= { X : X is perfect square less than 10} then find (A B) and draw venn diagram. 78. If A = { X/X is a prime number less than 5} and B= { X/X is a multiples of 2 than 10} then find A\ B and B \ A and also find A Δ B, draw venn diagram for A Δ B. 79. If U = {a, b, c, d, e, f, g, h, i}, A = {a, d, f, h, i} and B = {a, b, d, h} show that ( A B) = A B 80. If U = {0, 1, 2, 3, 4, 5, 6, 7}, A={0, 2, 4,5} and B={0, 1, 2, 5,7} then show that ( A B) = A B V. Solve the following: 4m I. Choose the correct answer: CHAPTER 1 Unit 5 Statistics 1. The difference between the highest and lowest scores in a given distribution is called a) Mean b) range c) median d) mode 2. The most repeated score in an ungrouped data is called a) Mean b) median c) mode d) range 3. The average of the scores is called a) Mean b) median c) mode d) deviation 4. Among the following, which is not a measure of dispersion? a) Range b) median c) quartile deviation d) mean deviation

12 12 5. Mean of the following scores 3, 5, 7, 8, 10 is a) 5 b) 6 c) 6.6 d) The mode of the scores 18, 17, 20, 5, 22, 20, 23 is a) 18 b) 5 c) 17 d) Co efficient of range is given by a) b) ( ) c) d) ( ) 8. The mean deviation is calculated by a) b) c) d) 9. The event will not occur, if the probability is a) 1 b) 0.5 c) 0 d) 0.9 II. Fill in the blanks: 1. is a mathematical measure of uncertainly of events 2. Half of the inter quartile range is called 3. Quartile divide the distribution into parts. 4. Range = is calculated by using the formula 5. The formula to calculate mean is 6. Quartile deviation is calculated by using the formula 7. The difference between the upper and lower quartile values is called 8. In a histogram are marked on s-axis 9. The collection of numerical facts is called 10. The graph obtained by plotting frequency against mid point of the class interval is III. Solve the following: 2m 1. What are the measuresof dispersion? 2. Calculate the range and coefficient of range for the following data. 122, 144, 154, 101, 168, 118, 155, 133, 160, Marks scored by 10 students in a test 31, 18, 27, 19, 25, 28, 49, 14, 41, 22, 33, 13. Calculate range and coefficient of range. 4. Number of trees planted in 6 months 186, 234, 465, 861, 290, 142. Calculated range and coefficient of range. 5. Calculate quartile deviation for the following data 3, 5, 8, 10, 12, 7, The runs scored by a batsman in five innings are 28, 60, 85, 58, 74, 20, 90. Find Q1, Q2, Q3 and Quartile deviation. 7. Calculate mean deviation about mean for the following data 14, 21, 28, 21, Find the mean deviation about mean for the following data 15, 18, 13, 16, 12, 24, 10, Find the mean deviation about medium for the following data 18, 23, 9, 11, 26, 4, 14, A dice has the faces numbered 2, 4, 6, and 12. It is thrown once. What is the probability that an even numbered face shown up?

13 In a pack of 52 playing cards, a card was selected at random. What is the probability that the card selected was both red and black? IV. Do as directed: 3m 1. Calculate quartile deviation for the data: 30, 18, 23, 15, 11 29, 37, 42, 10, Calculate quartile deviation for the data 3, 5, 8, 10, 12, 7, 5 3. Find the mean deviation about mean 14, 21, 28, 21, Find the mean deviation about mean 15, 18, 13, 16, 12, 24, 10, Construct histogram of variable width of the data CI f Construct histogram CI f Draw 0 gives (cumulative frequency curves) for the data C-I Frequency Construct frequency polygon for the data C-I Frequency Draw 0 gives (cumulative frequency curves) C-I Frequency Runs scored by 22 batsmen in a test match are given here. Runs & along No. of batsman Find the probability that a batsman selected at random scored runs.

14 14 a) Between 0 and 9? b) Between 20 and 39 and c) Above 50 V. Solve the following: 4m 1. The heights of 100 students in 9 th standard are given below. Height (cm) No. of students (f) Find quartile deviation. 2. Calculate mean deviation about mean for the given frequency distribution. Class Interval Frequency The distribution of the ages (in years) of 20 persons in a locality are recorded as follows. Age (in years) No. of persons Calculate mean deviation about mean. 4.The following frequency distribution shows the daily wages earned by 15 workers. Wage (Rs) No.of workers Calculate mean deviation about mean. II. Fill in the blanks: CHAPTER 2 UNIT 1 BANKING 1. is an institution that carries out the business of accepting the deposit, lending money and investing money. 2. Single account and joint account are the types of account. 3. On opening SB account, a small book called saving bank is issued by the book. 4. A is an unconditioned order to the bank to pay the money on demand in favour of a person/institution. 5. A is a form of cheque that is issued and guaranteed by the bank. 6. At present the interest is calculated on product basis. IV. Solve the following: 3m 7. The details of the entries of the passbook of Louis are given here. Calculate the interest at rate of 4% per annum he gets the month on daily product basis.

15 15 Date Particulars Cheque No. Debit Credit Balance Balance Forward By Cheque By cash To Ravi By draft Entre the following particulars into a saving Bank Pass book. a) Balance brought forward Rs b) By Cash : Rs 3,500 on c) To self : Rs. 1,250 on d) By bank draft : Rs. 4,800 on e) By cheque no: Rs. 750 on The entries in an SB account pass book are given below. Calculate the interest at 4% per annum for the month on daily product basis. Date Particulars Cheque No. Debit Credit Balance Balance Forward By cash To Geetha To self By Cheque The entries in an SB account pass book are given below. Calculate the interest at 4% per annum for the month on daily product basis. Date Particulars Cheque No. Debit Credit Balance Balance forward By cash To cheque By cash By Cheque By Cheque CHAPTER 2 UNIT 2 COMPOUND INTEREST I. Choose the correct answer: 1. In compound interest principal for every period of time a) Increases b) decreases c) remains d) same 2. In fixed deposits, we get interest a) Zero b) simple c) compound d) unit 3. For appreciation, the growth factor is a) 1 b) greater than 1 c) less than 1 d) zero 4. For depreciation, the growth factor is a) 1 b) greater than 1 c) less than 1 d) zero

16 16 5. When the interest is compounded at different rates for successive years, amount is a) ( ) b) ( ) c) ( ) ( ) d) ( ) II. Fill in the blanks: 1. The formula to find simple interest is 2. The interest calculated on the principal and the accrued interest is called 3. The formula to find amount when interest is compound annually is 4. The formula to find amount when interest compounded half yearly (semi-annually) is 5. The formula to find amount when interest compounded quarterly is 6. The population after n years is calculated using the formula 7. Formula for depreciation or cost of vehicles after n years is III. Solve the following: 2m 1. Find the compound interest when principal is Rs. 7000, at 6% p.a and period is years (compounded annually) 2. Calculate the compound interest that Shwetha gets by investing Rs for 2 years at 9% p.a (compounded annually) 3. Sanju deposited Rs. 700 in a bank for 2 years at 10% p.a Find compound interest (compounded annually) IV. Solve the following: 3m 1. Calculate amount & compound interest Rs. 12,000 for 2 years at 10% compounded annually. 2. Calculate amount & compound interest Rs. 20,00 for 2 years at 8% compounded annually. 3. Calculate amount & compound interest Rs for 1 year at 4% compounded semi annually. 4. Rs. 10,000 for years at 5% compounded half yearly. 5. Rs. 500 for 1 year at 2% compounded annually. 6. The present population of a village is 18,000. It is estimated that the population grows by 3% per year. Find the population after 2 years. CHAPTER 2 UNIT 3 Hire Purchase And Installment Buying I. Solve the following: 2m 1. Mention the difference between hire purchase and installment. II. Solve the following: 3m

17 17 1. The cost of a cell phone is Rs. 8,000 and the down payment is Rs. 1,000. The balance amount is to be paid in 8 equal installment of Rs. 1,000. Find the rate of interest. 2. A washing machine costs Rs. 10,200 cash down payment of Rs. 2,000 and the balance was agreed to be paid in 6 equal monthly installments of Rs. 1,500 each. Find the rate of interest. 3. The cost of a motor bike is Rs. 48,000. The company offers it in 30 months of equal installments at 10% rate of interest. Find the equated monthly installment. 4. The cost of a set of home appliances is Rs. 36,000. Siri wants to buy them under a scheme of 0% interest and by paying 3 EMI in advance. The firm changes 3% as processing charges. Find the EMI and the total installment for a period of 24 months. 5. Define: a) down payment b) installment c) equated monthly installment (EMI) CHAPTER 2 UNIT 4 RATIO AND PROPORTION I. Choose the correct answer: 1m 1. The simplest form of 14:21 is. a) 2:3 b) 4:1 c) 1:2 d) 7:7 2. The simplest form of 20:100 is. a) 2:10 b) 1:5 c) 5:20 d) 40: The third proportion of 16 and 8 is. a) 2 b) 4 c) d) The fourth proportion of 5, 7, 15 is. a) 21 b) c) 17 d) In the proportion x:5 = 3:6, x =. a) 10 b) 2.5 c) 5 d) 3 II. Fill in the blanks: 1m 1. In the ratio a : b, the first term a is called and the second term b is called. 2. Ratio tells how many times the is there in the second term. 3. A proportion is equality of two. 4. In the proportion a : b = c : d, we say a, d are. 5. In the proportion a : b = c : d, we say b, c are. 6. If three terms a, b, c are such that a : b = b: c we say is the mean proportion. 7. If three terms a,b,c are such that a : b = b : c we say c is the. 8. In a proportion a : b = c : d, we say is the fourth proportion of a, b, c. 9. If a : b = c : d and a b then (a b) : (a b) =. 10. If A can do a job in m units of time and B can do the same job in n units of time, then A and B can do the job in t units of time where =.

18 In a school there are 850 pupils and 40 teachers. Then the ratio of teachers to pupils is. III. Solve the following: 2m 1. On a map a distance of 5 cm represents an actual distance of 15 km. Write the ratio of the scale of the map. 2. What number should be added to the terms of 49 : 68 to get the ratio 3: 4? 3. Find the mean proportion between 4 and Find the mean proportion between 0.3 and Find the mean proportion between 16 and Find the third proportion of 16 and Find the third proportion of 5 and Find the fourth proportion of 5, 7, Find the fourth proportion of 3, 1, In a map cm represents 25km. If two cities are 2 cm apart on the map, what is the actual distance between them? 11. Suppose 30 out of 500 components of a computer were found defective at this rate how many defective components would be found in 1600 components? 12. Suppose A alone can finish a piece of work in 15 days and B alone can do it in 20 days. If both of them work together, how much time will they take to finish it? 13. Tap A can fill a tank in 8 hours while tap B can fill it in 4 hours. In how much time will the tank be filled if both A and B are opened together? 14. There are two pipes A and B connected to a tank. It is know that A can fill the tank in 4 hours while B can empty the tank in 6 hours. If both the pipes are opened together how much time will it take to fill up the tank? IV. Solve the following: 3m 1. Find the value of x a) x : 5 = 3 : 6 b) 13 : 2 = 6.5 : x 2. Find the value of y a) 4 : y = 16 : 20 b) 2 : 3 = y : 9 3. Suppose A and B together can do a job in 12 days. While B alone can finish it in 30 days. In how many days A alone finish the work? 4. Suppose A is twice as good a work-men as B and together they can finish a job in 24 days. How many days A alone takes to finish the job. 5. Suppose B is 60% more efficient than A. If A can finish a job in 15 days, how many days B needs to finish the same job. V. Solve the following: 4m I. Choose the correct answer: 1. 2x 3 is a polynomial CHAPTER 3 Unit 1 Multiplication of Polynomials

19 19 a) Linear b) Constant c) Quadratic d) Zero 2. 8x x + 3 is a polynomial. a) Linear b) Quadratic c) Constant d) Zero 3. (x + 5) (x -2) = a) X 2 7x + 10 b) x 2 + 3x 10 c) x 2 + 3x + 10 d) x 2 3x (a + b+ 2c) 2 = a) a 2 + b 2 + c 2 + 2ab + 2bc + 2ac b) a 2 + b 2 +4c 2 + 2ab + 4bc + 4ac c) a 2 + b 2 + 4c 2-2ab - 4bc - 4ac d) a 2 + b 2 + c 2-2ab - 2bc - 2ac 5. If a + b + c = 0, then = a) abc b) 3 c) 3abc d) 1 6. An identity is valid for all values of the in it. a) Variables b) constants c) terms d) coefficients 7. x 3 8 = (x 2 + 2x + 4) a) x + 2 b) x 2 c) (x+2) (x 2) d) (x 2 2x + 4) 8. If a+b+c = 0 then a) 3abc b) -3 c) 3 d) a+b+c 9. (x-a) (x-b) (x-c) = a) x 3 (a+b+c) x 2 + (ab + bc + ac) x abc b) x 3 + (a+b+c) x 2 + (ab + bc + ac) x + abc c) x 3 - (a+b+c)x 2 + (ab + bc + ac) x + abc d) x 3 + (a+b+c) x 2 + (ab + bc + ac) x abc. II. Fill in the blanks: 1. Degree of a constant polynomial is 2. Degree of a linear polynomial is 3. Degree of a quadratic polynomial is 4. (x + a) (x + b) = 5. 9x 2 25y 2 = 6. (a + b) 3 = 7. (a b) 3 = 8. a 3 b 3 = 9. a 3 + b 3 = 10. (x + b) (x + b) (x + c) = III. Solve the following: 2m 1. Evaluate the following products:(x + 3)(x + 2) 2. Evaluate the following products: (x + 5)(x 2) 3. Evaluate the following products: (y 4)(y + 6) 4. Evaluate the following products:(a 5)(a 6) 5. Evaluate the following products:(2x + 1) (2x 3) 6. Evaluate the following products:(a + b)(c + d) 7. Evaluate the following products:(2x 3y)(x y)

20 20 8. Evaluate the following products:( x + )( x + ) 9. Evaluate the following products: (2a + 3b)(2a 3b) 10. Evaluate the following products: (x 2 + y 2 )(x 2 y 2 ) 11. Evaluate the following products:(6xy 5)(6xy + 5) 12. Evaluate the following products:( + 3)( 7) 13. Expand the following using appropriate identity:(a + 5) Expand the following using appropriate identity:(2a + 3) Expand the following using appropriate identity:(x + ) Expand the following using appropriate identity:( a + b) Expand the following using appropriate identity:( + ) Expand the following using appropriate identity:(y 3) Expand the following using appropriate identity: (3a 2b) Expand the following using appropriate identity:(y - ) Expand the following using appropriate identity: ( x - y) Expand the following using appropriate identity: ( - ) Expand the following using appropriate identity: (2x + 3)(2x +5) 24. Expand the following using appropriate identity:(3x 3)(3x + 4) 25. Expand: (x + 3)(x 3) 26. Expand: (3x 5y)(3x + 5y) 27. Expand: ( + )( - ) 28. Expand: (x 2 + y 2 ) (x 2 - y 2 ) 29. Expand: (a 2 +4b 2 )(a + 2b)(a 2b) 30. Expand: (x - 4)(x + 4)(x 3)(x + 3) 31. Expand: (x a)(x + a)( - )( + ) 32. Find the product of : (x+4)(x+5)(x+2) 33. Find the product of : (a+2)(a-3)(a+4) 34. Find the product of : (x-5)(x-6)(x-1) 35. Find the cube of (2x+y) 36. Find the cube of (4a+3b) 37. Find the cube of (x+1/x) 38. By using the identity find the cube of Find the product of Find the product of Expand (a+b+2c) ². 42. Expand (p+q-2r) ². 43. Expand (m-3-1/m) ². 44. Find the cube of (x-1/x).

21 Find the cube of (2x- 5). 46. Find the cube of 108 by using the identity. 47. If x+1/x=3 prove that x³+1/x³= If p + q=5 and pq=6 find p³+q³. 49. If a-b=3 and ab=10 find a³-b³. 50. If a+b+c=12 and a²+b²+c²=50 find ab+bc+ca. 51. If a, b, c are non-zero numbers such that a+b+c=0 prove that a+b/c + b+c/a + c+a/b = If a+b+c=abc prove that (1+a²)=(1-ab)(1-ac) 53. If a+b+c=0 prove that (b+c)(b-c)+a(a+2b)=0 54. If a+b+c=0 prove that (ab+bc+ca)²=a²b²+b²c²+c²a². 55. If a+b+c=0 prove that (a+b)(a-b)+ca-cb= If a+b+c=0 prove that a²/bc + b²/ca + c²/ab = If a+b+c=0 prove that (b²-4ac) is a square. 58. If a+b+c=2s prove that s(s-a)+s(s-b)+s(s-c)=s². 59. If a+b+c=2s prove that s²+(s-a)²+(s-b)²+(s-c)²=a²+b²+c². 60. If x²-3x+1=0 prove that x²+ 1/x² =7. IV. Solve the following: 3m 1. Simplify the following: (2x 3y) xy 2. Simplify the following: (3m + 5n) 2 (2n) 2 3. Simplify the following: (4a 7b) 2 (3a) 2 4. Simplify the following: (x + ) 2 -(m - ) 2 5. Simplify the following: (m 2 + 2n 2 ) 2 4m 2 n 2 6. Simplify the following: (3a 2) 2 (2a 3) 2 7. Find the volume of the cuboid with dimensions (x-1),(x-2) and (x-3). 8. The length,breadth and height of a cuboid are (x+3),(x-2) and (x-1) respectively. Find its volume. 9. The length,breadth and height of a metal box are (x+5),(x-2) and (x-1) respectively. Find its volume. 10. If a²+ 1/a²=20 and a³+ 1/a³=30. Find a+ 1/a. 11. Simplify (3x+4y+5)²- (x+5y-4)².

22 Simplify (a-b+c)² (a-b-c)². 13. (2m-n-3p)² + 4mn 6np + 12pm. 14. If a+b+c=0 prove that a(b-c)²+b(c-a)²+c(c-b)²= -9abc. 15. If a+b+c=2s prove that (s-a)(s-b)+(s-b)(s-c)+(s-c)(s-a)+s²=ab+bc+ca. I. Choose the correct answer: CHAPTER 3 Unit 2 Factorisation 1. (5x 2 20xy) = - (x 4y) a) 5x b) x y c) 5x 4y d) x 2. 7xa 70xb = 7x( ) a) (a b) b) (a 10b) c) (a b) d) (7a 10b) 3. a 3 b 3 = (a b) ( ) a) (a 2 + ab + b 2 ) b) (a 2 b 2 ) c) (a 2 ab + b 2 ) d) (a 2 + b 2 ) 4. If a + b + c = 0 then a 3 + b 3 + c 3 =. a) 3 b) 3abc c) abc d) 0 5. a 4 + a 2 b 2 + b 4 = (a 2 +b 2 + ab) ( ) a) (a 2 + b 2 ) b) (a 2 + b 2 ab) c) (a + b + c) d) a 2 b 2 II. Fill in the blanks: 1. The process of writing a given algebraic expressions as a product of two or more expressions is called. 2. Factors of 9x xy are and (3x + 4y). 3. Factors of 25 50p 100q are (1 2p 4q) and. 4. a 3 + b 3 =. 5. a 3 + b 3 + c 3 3abc =. 6. (a + b + c) 3 a 3 b 3 c 3 =. III. Solve the following: 2m 1. Factorise: a 2 ba + ac bc 2. Factorise: 3x 3 5x 2 + 3x Factorise: y 4 2y 3 + y 2 4. Factorise: 25x 2 64y 2 5. Factorise: 12m 4 75n 4 6. Factorise: (x + 4y) 2-4z 2 7. Factorise: x x Factorise: 2x 2-7x Factorise: x 2 + 9x Factorise: 15x 2 x Factorise: x Factorise: 27t 3 343

23 Factorise: Factorise: 32x Factorise: x 7 + xy 6 IV. Solve the following: 3m 1. If x+y+4=0 find the value of x 3 +y 3-12xy If x=2y+6 find the value of x 3-8y 3-36xy Factorise x 3 8y xy. 4. Factorise a 3 +27b 3 + 8c 3 18abc. 5. Factorise 8a b 3 64c abc 6. Find the prime factorization of Find the prime factorization of Without actually calculating the cubes find the value of (-12) Without actually calculating the cubes find the value of (-10) If a + b = 6 and ab = 8 find the value of a 3 +b Factorise: 3(x+y) 3 + (xy) Factorise: x 6 y Factorise: a 3 b 3 a+b 14. Factorise: x 6 26 x Factorise: 64 a Factorise: 3 x y Factorise: 2 (x + y) 2 9(x+y) Factorise: 9 (2x y) 2 4 (2x y) Factorise: 4x 4 + 7x Factorise: 8x 3 2x 2 y 15xy The radices of a circle are 13cm in which a chord of 10cm is drawn. Find the distance of the chord from the center of the circle. 22. Prove that (1+ )(1 - ) (1 + ) (1 + ) + ( ) = Factorise by adding and subtracting appropriate quantity. x x Factorise by adding and subtracting appropriate quantity. x 2 + 2x - 1 V. Solve the following: 4m CHAPTER 3 Unit 3 HCF and LCM I. Choose the correct answer: 1. HCF of (a + b), (a + b) 2 and (a +b) 3 is a) (a + b) b) (a + b) 2 c) (a + b) 3 d) a 3 + b 3 2. LCM of 8x 4 a 2 and 48x 2 b 4 is a) 8x 2 b 2 b) 8x 4 b 4 c) 48x 2 a 2 b 2 d) 48 x 4 a 2 b 4 3. HCF of 9x 2 y 2 z 3 and 15x 3 y 2 z 4 is

24 24 a) 3x 2 y 2 z 3 b) 9x 2 y 2 z 3 c) 15x 3 y 2 z 4 d) 45x 3 y 2 z 4 4. HCF of 2x, 4y and 6z is a) 24xyz b) 2xyz c) 2 d) 12xyz 5. HCF of 2a, 3b, and 5c is a) 1 b) 30 c) abc d) 30 abc 6. LCM of (a b) and (a 3 b 3 ) is a) (a-b) b) a 3 -b 3 c) (a-b)(a 3 -b 3 ) d) (a+b) 3 7. LCM of a 2 bc, b 3 c 3 and ab 2 c 2 is a) a 2 b 2 c 2 b) a 2 b 3 c 3 c) b 3 c 3 d) abc 8. LCM of 2a, 3b and 5c is a) 1 b) 30abc c) abc d) 30 II. Fill in the blanks: 1. If there are two or more common factors then the product of the common factors will be the of the given expressions. 2. If there are no common factors, then is the HCF of the given expressions. 3. is a factor of LCM 4. If p(x) and q(x) are two polynomials with integer coefficients and if h(x) and m(x) are respectively thus HCF and LCM. Then h(x) m(x) = III. Solve the following: 2m 1. Find the HCF of : x and x Find the HCF of : x 2 -xy and x 2 -y 2 3. Find the HCF of : 2x 2 -x and 4x Find the HCF of : x 3 + y 3 and 3x 2-3y 2 5. Find the HCF of : a and a Find the HCF of : 4x 2 1 and 4x 2 +4x+1 7. Find the HCF of : 6x 2 2x and 9x 2-3x 8. Find the LCM of: a 2 b + ab 2 and a 3 + a 2 b 9. Find the LCM of: x 4 + x and x 3 -x 10. Find the LCM of: 3x 2 75 and 2x Find the LCM of: m 2 -n 2 and 3m 2-3mn 12. Find the LCM of: (xy) 2, (xy) 3, a 2 (xy) 13. Find the LCM of: (a+b) (b+c), (b+c)(c+a), (c+a) (a+b) IV. Solve the following: 3m 1. Find the HCF of: x 2 + 2x 15 and x 2 7x Find the HCF of: x 2 -xy-2y 2 and x 2 +3xy + 2y 2 3. Find the HCF of: a 4 b ab 4, a 4 b 2 - a 2 b 4 and a 2 b 2 (a 4 -b 4 ) 4. Find the HCF of: 6(x 2 +10x+24), 4 (x 2 -x-20) and 8(x 2 +3x 4) 5. Find the HCF of p(x) = (x 3 27) (x 2 3x +2) and q(x) = (x 2 + 3x + 9) (x 2-5x + 6) 6. Find the HCF of f(x) = x 3 +x 2 -x-1 g(x) = x 3 +x 2 +x+1 7. Find the HCF of p(x) = x 4-2x 3-15x 2 and q(x) = x 3-9x 8. If the HCF of x 2 +x-12 and 2x 2 -kx 9 is (x-k) find the value of k

25 25 9. Find the LCM of the following: x 2 +4x + 4 and x 2 + 5x Find the LCM of the following: 6m 2 3m 45 and 6m 2 +11m Find the LCM of the following: a 2-3a + 2, a 3-4a + 4 and a(a 3-8) 12. Find the LCM of the following: 4x 3 + 4x 2 x 1, 8x 3-1 and 8x 2 - x Find the LCM of the following: 6(x 2 + 2xy 3y 2 ), 4(x 2 3xy + 2y 2 ) 14. Find the LCM of the following: a 2-1, a 4-1 and a Find the LCM of the following: 21(x-1) 2, 35(x 4 -x 2 ), 14 (x 4 -x) 16. Verify p(x) q(x) = h(x) m(x) for HCF and LCM of two polynomials p(x) = 12(x 4-36) and q(x) = 8 (x 4 +5x 2-6) 17. Find the HCF h(x) and the LCM m(x) for the polynomials p(x) = x 6-1, q(x) = x 4 +x 2 +1 and prove that p(x) q(x) = h(x) m(x). 18. Verify p(x) q(x) = h(x) m(x) for HCF and LCM of two polynomials p(x) = 2x 2 + 7x + 5 and q(x) = 8x Find h(x) of 3x 2 +5x 2 and 3x 2-7x + 2 by using h(x) find m(x) 20. Find h(x) of 16 4x 2 and x 2 + x 6 by h(x) find m(x) 21. If (x-3) is the HCF of p(x) = x 3 +ax 2 +bx-6 and q(x) = x 3 -x(b-4) + a. find the value of a and b 22. If p(x) = (x 3) (2x 2 ax +2), q(x) = (x+4) (x 2 +bx -6) and h(x) = x 2-5x + 6, find the values of a and b. I. Choose the correct answer: CHAPTER 3 Unit 4 Division 1. Standard form of x 2 + x 5 2x x is. a) x 5 + 2x x + x 2 c) x 5 + 2x 3 + x 2 + 3x 2 b) 2 + 3x + x 2 + 2x 3 + x 5 d) x 5 + 2x 3 + x 2 + 3x Standard form of x 8 + x + x 12 3x 7 + x is a) x 8 + x 9 + x 12 + x 3x c) x + x 8 + x 9 + x 12 3x b) x 12 + x 9 + x 8 3x 7 + x + 1 d) x 3x 7 + x 8 + x 9 + x The area of a triangle is 10x 2 and its base is 2x, then its length of altitude is a) 10x b) 2x c) 5x d) 20x 4. (-9 a 10-3a 9 ) = a) 3a b) 3a 2 c) 3 d) ( ) ( ) = a) b) 2 x 3 c) d) 32 x 3 6. If x 4 a 4 is divisible by x + a, then the remainder = a) 0 b) -2a 2 c) x a d) none of these. II. Fill in the blanks: 7. Addition of two polynomials always give a 8. Subtraction of two polynomials always give a 9. Multiplication of two polynomials always give a 10. Dividend = divisor * quotient +

26 = 12. ( x 8 ) (5x 5 ) = 13. The area of a rectangle is 800 x 2 and its length is 40x, then its breadth is III. Solve the following: 2m 14. Divide: 3x 2 + 4x 4 by x Divide: 6x 3 23x + x by 2x Divide: 2x 2 7x + 6 by x Divide: 3x 2 + x by x Divide: x 3 1 by x Find the remainder when x 3 + px 2 + qx + r is divided by x 2 + px +q. IV. Solve the following: 3m 20. Divide: 4x 5 + 7x x 3 + 3x 2-8x + 6 by x 2 + 3x Divide: x 3 + 5x 2 + 4x 4 by x 2 + 3x Divide: x 4 4x x + 9 by x 2 + 2x Divide: 2x 5 7x 4-2x x 2 3x 8 by x 3 2x Divide: x 5 + a 5 by x + a 25. Divide: x 7 y 7 by x y 26. Divide: x 9 + y 6 by x 3 + y What should added to x 5 1 to be completely divisible by x 2 + 3x + 1? 28. What should be added to a 6 64 to be completely divisible by a 4 16? V. Solve the following: 4m CHAPTER 3 UNIT 5 Simultaneous linear equations I.Choose the correct answer: 1m 1. If the two graph lines of the given equation intersect at a point, then it gives a solution. a) Unique b) Infinite c) Finite d) Zero 2. An equation in which the variable occur to the first degree is called equation. a) Quadratic b) Linear c)pure d) Adfected 3. If x 15 = 0, the value of x is. a) 2 b) -15 c) 0 d) If x + 9 = 20, then the value of x is. a) 11 b) 20 c) -9 d) If 5x 30 = 0, the value of x is. a) 0 b) 30 c) -5 d) 6 6. If 7x = 49, the value of x is. a) 3 b) 7 c) 8 d) Which of the following is a linear equation having two variables? a) 3x + 2y = 9 b) x + 3 = 5 c) x 2 4 = 0 d) y 2 + 2y 1 = 0

27 27 II. Fill in the blanks: 1m 8. The general form of linear equation is. 9. If the two graph lines of the given equation are parallel, then the equations have solution. 10. If two graphs coincide, we get solutions. 11. If two graphs intersect at a point, then it has solution. 12. x + 3 = 7 is a equation. III. Do as directed: 2m 13. Solve: x + y = 10 x y = Solve: x + y = 3 3x y = Solve: 2x + y = 0 3x y = Solve: 3x + y = 7 x y = Solve: 2x y = 6 3x + y = 9 IV. Solve the following: 3m 18. Solve 3x 7y =7 11x + 5y = Solve: 3x 4y = 10 4x + 3y = Solve: 5x + 4y 4 = 0 x 20 = 12y 21. Solve: 2p + 3q = -5 3p 2q = Solve: 100 x + 200y = x y = Solve: 41x + 53y = x + 41y = 147

28 The sum of two numbers is 40. If the smaller number is doubled, it becomes 14 more than the larger number. Find the numbers. 25. Two numbers are such that twice the smaller number added to 2 gives the larger number. Also, double the larger number is 1 less than five times the smaller number. Find the numbers. 26. Find the fraction which becomes when denominator is increased by 4 and when the numerator is diminished(decreased) by There is a number which is equal to 4 times the sum of its digits. If 27 is added to the number, the number s digits get reversed. Find the number. 28. Solve the following: i) 7x + 5y = 10 3x + y = 2 ii) 3a 2b = 12 4a 5b = Solve: i) 2x + y = 7 2x 3y = 3 ii) 5x 4y = -14 3x + 2y = Solve: i) 3x + 2y = 5 5x 4y = 23 ii) 2x + 3y = 13 4x + y = 11 V. Solve the following: 4 Marks 31. Solve graphically x + y = 7 2x 3y = Solve graphically 2x + y = 6 x 2y = Solve graphically x + y = 3 2x + 5y = Solve graphically x y = -2 x y = Solve graphically x y = 1 2x 2y = Solve graphically 3x y 2 = 0 2x + y 8 = 0

29 29 CHAPTER 3 UNIT 6 VARIATION I. Choose the correct answer: 1m 1. If y varies directly as x and y=10 when x = 5, then the constant of proportionately is a) b) 50 c) 2 d) 0 2. If x varies as y and if x = 6 when y =3 then the value of x when y = 10 is a) 20 b) 18 c) 60 d) If p varies as q and if p = 5 when q =10 then the value of q when p = 20 is a) 50 b) 40 c) 30 d) If x varies directly as y and if x = 4 when y = 20. Then the value of y when x = 12 is a) 40 b) 50 c) 60 d) If y varies directly as and y = 24 when x = 3 then the value of y when x = 16 is a) b) 32 c) 192 d) If Q inversely varies as square of P and if Q = 8 when p = 2, then the value of Q when p = 2 a) b) c) d) 32 II. Fill in the blanks: 1m 7. A quantity which takes different values is called. 8. Variation means. 9. If the product of two variables is constant, then one variable varies as the other. 10. The symbol used to denote variation is. III. Solve the following: 2m 11. The volume of sphere varies as the cube of its radius and its volume is cm 3 when radius is 3.5cm. Find the volume when radius is 1.75cm. 12. The distance through which a body falls from rest varies as square of time it takes to fall that distance. It is known that the body falls 64cm in 2 seconds. How far does that body fall in 6 seconds. 13. If 35 men can do a piece of work in 30 days, in how many days will 21 men can do it. 14. If 7 pipes can fill a tank in 1 hour 24 minutes, how long will it take to fill the tank if 6 pipes of the same type as used. 15. If 7 workers can build a trench in 25 hours. How many workers will be required to do the same work in 35 hours. 16. A farmer has a stock of food enough to feed 28 animals for 9 days. He buys 8 more animals which takes same quantity of food. How long would the food last now. 17. Suppose that y varies inversely with the square of x and y = 50 when x = 4. Find y when x = 5. IV. Solve the following: 3m 18. If 195 men working 10 hours a day can finish a job in 20 days, how many men, working 13 hours a day, should be employed to finish the job in 15 days. 19. If z varies jointly as x and the square not of y, and if z = 6. When x = 3 and y = 16. Find z when x = 7 and y = If 36 men can build a wall of 140m long in 21 days, how many men are required to build a similar wall of length 50m in 18 days.

30 If the total wages of 15 laborers for 6 days is Rs Find the wages of 21 labourers for 5 day. 22. Tap A can fill a cistern in 8 hours and tap B can empty it in 12 hours. How long will it take to fill the cistern if both of them are opened together? V. Solve the following: 4m I. Choose the correct answers: CHAPTER 4 UNIT 1 Polygons 1. If the exterior angle of a polygon is 60 o then the number of sides of a polygon is. (a) 5 (b) 6 (c) 8 (d) If a polygon has 8 sides then the number of triangles are formed by fixing a vertex are. (a) 10 (b) 9 (c) 7 (d) 6 3. If a polygon has 10 sides, then the number of triangles are formed by fixing a vertex are. (a) 8 (b) 9 (c) 10 (d) If the exterior angle of a polygon is 120 o, then the number of sides of a polygon is. (a) 5 (b) 4 (c) 3 (d) 6 5. If the exterior angle of a polygon is 72 o then the polygon is named as. (a) Hexagon (b) Square (c) Pentagon (d) Octagon 6. If the exterior angle of a polygon is 45 o then the polygon is named as. (a) Hexagon (b) Heptagon (c) Octagon (d) Nanogon 7. The sum of exterior angle and interior angle is equal to (a) One right angle (b) 2 right angle (c) 3 right angle (d) 4 right angles 8. The sum of all exterior angles is equal to (a) 4 right angles (b) 6 right angles (c) 2 right angles (d) 8 right angles 9. In a regular n-gon all its interior angles are equal to (a) (n-2)π (b) ( )π (c) ( )π (d) (n+2)π 10. In a regular n-gon all its exterior angle are equal to (a) 2πn (b) (c) (d) 11. The sum of the interior angles of a n-gon is (a) (n+2)π (b) (n+2) right angles (c) (n-2)π (d) II. Fill in the blanks: 12. A rectilinear figure bounded by three or more sides is called. 13. In a polygon if one angle is a reflex angle then it is called. 14. In a polygon if no angle is reflex angle then it is called. 15. If a polygon has 10 sides then it is called. 16. If a polygon has 4 sides then it is called.

31 An example for regular quadrilateral. III. Solve the following: 2m 18. Find the number of sides of a regular polygon if each exterior angle is 30 o. 19. Find the number of sides of a regular polygon if each exterior angle is Find the number of sides of a regular polygon if each exterior angle is Find the number of sides of a regular polygon if each exterior angle is Find the sum of the interior angles of a octagon. 23. Find the sum of the interior angles of a pentagon. 24. If the sum of interior angles of a polygon is Find the number of sides of the polygon. 25. If the sum of interior angles of a polygon is 7 straight angles. Find the number of sides of the polygon. 26. Find the number of sides of a polygon whose sum of interior angles is Find the measure of each exterior angle of a regular polygon with the sides Find the number of sides of a regular polygon if its exterior angle is Find the number of sides of a regular polygon if its exterior angle is 120. IV. Solve the following: 3m 30. Find the number of sides of a regular polygon if each exterior angle is equal to its interior angle. 31. Find the number of sides of a regular polygon if each exterior angle is equal to half its interior angle. 32. Find the number of sides of a regular polygon if each exterior angle is equal to twice its interior angle. 33. Find the number of sides of a regular polygon of its interior angle is equal to four times exterior angle. 34. Find the sum of interior angles of a hexagon. 35. The angles of a convex polygon are in the ratio 2:3:5:9:11. Find the measure of each angle. CHAPTER 4 UNIT 2 Quadrilaterals I. Choose the correct answer: 1. The sum of 4 interior angles of a quadrilateral is equal to a) 2 right angles b) 3 right angles c) 4 right angles d) 8 right angles. 2. A quadrilateral in which all 4 sides are equal and all four angles are right angles is a) Rectangle b) Rhombus c) square d) trapezium 3. The minimum elements needed for the construction of a quadrilateral is a) 4 b) 5 c) 6 d) 8 4. The line joining the mid points of a quadrilateral forms a) Square b) rectangle c) kite d) parallelogram