DELHI PUBLIC SCHOOL, FARIDABAD

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1 DELHI PUBLIC SCHOOL, FARIDABAD Class-VII Maths Assignment Unit-ll TOPICS : 1.Linear Equations 2.Ratio and Proportion 3.Percentage and its Applications 4.. Lines & Angles SIMPLE EQUATIONS Section-A Multiple Choice Questions - Tick (/) mark the right answer: 1.The sum of the angles of a triangle is 180. If the angles are (2x+15), 85 and (x+20), the value of x is a. 60 c An example of linear equation in one variable is b. d a. 2x+1=3y b. x2-x=0 c. 2x+4=3 3.The equation whose solution is x=5 is d. -+x=0 X a. 3x = 15b. x - 4 = -2 3 c.2x-3=1d. -x + 1 = 4 4.The value of y for whcih the expressions (y-15) and (2y+1) become equal is a. 0b. 16 c. 8d The solution of the equation ax+b=0 is a. ^b. -b b -bb c. d. - aa 6.Two supplementary angles are such that one is 60 less than the other. The greater of the two angles is a. 60b. 80 c. 100d

2 7.' You alongwith four of your friends are eating a chocolate cake which is divided into 20 pieces. If everyone eats equal number of pieces then the number x each one eats is given by 11 a. T*=20b. ^x=20 c. 4x=20d. 5x=20 8.If - = 3, then the value of 3x+2 is a. 20b c. d. 8 Section-B 9.Solve the following equations and check the result. 2x + 3 3( 3 ax^ a'2x-3 5{ X 2 b. 0.06X (15-x) = 0.07 (15) 10.Find the value of p if the value of x4-3x3-px-5 is equal to 23 when x=-2 11.A son's present age is half the present age of his mother. 10 years ago, the mother was thrice as old as her son. What are their present ages? If of a number is 4 more than of the number, then what is the number? 13.The sum of three consecutive multiples of 7 is 273. Find the numbers. 14.Find a number which exceeds its one-third by added to 5 times a number equals 2 subtracted from 7 times the number. Find the number. 16.Two complementary angles differ by 40. Find the angles. Section-C 17.Solve the following equation : 18.Length of the rectangle is 4m less than 5 times its breadth. If the perimeter of the rectangle is 40 cm, find the length and breadth of the rectangle. 19.Number of four legged pets in a locality were 2 more than three times the number of two legged pets. If the total number of legs of the pets in the locality is 358, then find the number of 4 legged pets. 20.The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. What is the lowest score? 21.The difference between two numbers is 7. Six times the smaller number plus the larger number is 77. Find the numbers. 22.The ratio of the present ages of Pawan and Sushil is 3:1. After 2 years, the ratio of their ages will be 2:1. Find their present ages. 24

3 23.Two equal sides of a triangle are each 5m less than twice the third side. If the perimeter of the - triangle is 55m, find the lengths of its sides. 24.In an examination, a student requires 40% of the total marks to pass. If Rupa gets 185 marks and fails by 15 marks, find the total marks. 25.Solve the following equations : Section-D 3 - x _ 3(x -1) x I^ _ ii. (2x+5)+^ (4x-1) = 9 26.One fourth of a herd of deer went to the forest and half the total number were grazing in a field. If the remaining 12 were drinking water in a pond, find the total number of deer. 27.The denominator of a fraction exceeds the numerator by 12. If 2 is subtracted from the numerator, the fraction is equal to -. Find the fraction. 28.A man left one fourth of his money to his wife, two-fifth to his son and donated balance amount of to a Charitable fund. How much money did he have? How much money was received by his wife and son separately? 29.A labourer is engaged for 30 days on the condition that he will receive for each day he works and will be fined for 7 20 for each day he is absent. If he receives in all, for how many days did he remain absent? 30.A number consists of 2-digits. The sum of the digits is 9. If 91 is subtracted from the number, the digits change their places. Find the number. 31.Rahul has a sum of is in the form of denominations of 7 5 and 710. He has three times as much 75 notes as the had 710 notes. Find the number of notes of each type. 32.Five years ago a man was seven times as old as his son. Five years hence, the father will be three times as old as his son. Find their present ages. 33.Divide 84 into two parts such that of one part is equal to of the other part. 34.Construct 3 equations having solution a. p = b. x=-3 o 35.A man travelled two fifth of his journey by train, one-third by bus, one-fourth by car and the remaining 3km on foot. What is the length of his total journey? RATIO & PROPORTION Multiple Choice Questions - Section-A Tick (/) mark the right answer: 1. Two numbers are in the ratio 4 : 5. On subtracting 10 from each, the ratio becomes 2 : 3. The smaller number is a. 54b. 20c. 35d

4 2.A hiker covers 16 km in 4 hours. In 7 hours, distance he will cover is a. 28 kmb. 9- kmc. 8 kmd. 82 km 3.If 3 bananas cost 77.50, then cost of 20 bananas is a. 775b. 7105c. 7150d The missing element in proportion x: 12:30:24 is a. 72b. 30c. 60d The mean proportional between 4 and 49 is a. 13b. 14c. 15d The ratio between income and expenses of a person are 7:5. The ratio between total income and savings is a. 12:2b. 5:2c. 2:7d. 7:2 7.The simplest form of the ratio 1 day to 300 minutes is a. 12:2b. 24:5c. 2:7d. 17:3 8.The ratio between length and breadth of a rectangular field is 5:3. If the length is 120m, the breadth is a. 24mb. 72mc. 15md. 40m Section-B 9.A dozen cakes of soap weigh 1 kg. What will be the weight of 60 cakes? 10.Find x in the following proportions: a.21 : 28 = x : 52 b.x : 45 = 24 : Which of the following are in continued proportion? a.4,12,36 b.2,7,16 12.Find the third proportional to a.12 and 18 b.7 and For what value of x, are the following in continued proportion? a.4, 12, x b.2, x, 8 14.In a class one out of every six students fail. If there are 42 students in the class, how many pass? 15.Which is a better buy : 12 kg tomatoes for 7132 or 16 kg tomatoes for 7168? 16.Express the following ratios to simplest form : a b.6 to

5 Section-C 17.= Find the mean proportional between a.3 and 27 b.0.4 and If A:B = 1 :3andB:C = 2:3, find a.a:c b.a : B : C Divide 7180 in the ratio-:-: The yield of wheat from 6 hectares is 280 quintals. Find the number of hectares required for yield of 175 quintals. 21.The ratio of monthly income of a person to his savings is 7:2. If his savings of one year are , find his expenditure per month. 22.Compare 3 : 5 and 4 : 7 23.A certain sum of money has been divided into two parts in the ratio 9:13. If the second partis 760, find the total amount If a jet plane flies 2700 km in 3 hours, what distance would it travel in 7 hours? 25.Find x so that a.x, 12-x, 10, 30 are in proportion b.5, x+2, 4, x are in proportion Section-D 26.A student did six of twenty problems correctly. a.what is the ratio of the number of right to the number of wrong? b.for every two answers that were wrong, how many answers were right? 27.Shalu can type 920 words in 20 minutes, and Maria can type 1290 words in 30 minutes. Who is faster at typing? 28.The weight of 20m of copper wire is 0.9 kg. Find the weight of 170m of the same wire. 29.A house map is a 1:25 scale. What is the measurement of Maria's room if the dimensions on the map are 16cm and 12 cm? 9 30.A water pipe can fill a 250 litre tank in 2 hours 30 minutes. In how much time will it fill of the tank? chairs cost How many chairs can we buy for 77936? people can be seated in 19 buses comfortably a.find the number of people that can be seated in 25 buses. b.how many buses are required to accommodate exactly 2214 people? 33.Arrange the following ratios in ascending order: a.(5:6), (8:9), (11 :18) b.(11 :14), (17:21), (5: 7) and (2: 3) 27

6 Percentage and its Applications Section - A 1.Neha has a collection of bangles. She has 12 red bangles, 8 green bangles and 4 gold bangles. The percentage of gold bangles is a. 50%b. 16%c. 33^%d. 60% 33 2.On selling on article for 765, Renu gain 30%. The cost price of the article IS a. 750b c. 755d A basket has 350 eggs out of which 42 are rotten. The per cent of rotten eggs is a. 4%b. 8%c. 10%d. 12% 4.If 20% students in a class of 80 students like mathematics, then the percentage of students who do not like it is a. 4%b. 16%c. 25%d. 75% 5.The number whose 45% is 9 is a b. 25c. 20d The price of an article is increased from 7400 to The percentage increase in price is a. 2.5%b. 5%c. 10%d. 15% 7 In 10 years at the simple interest of 4% p.a will amount to a b c d What percent of - is? 7 35 a. 20%b. 25%c. 30%d. 40% Section-B 9.Find 3 % of 1 hour in minutes Find 5% less than % of the teachers in a school are males and the number of female teachers is 42. Find the number of teachers in the school. 12.Chalk contains calcium, carbon and oxygen inthe ratio 10:3: 12. a.find the percentage of carbon in the chalk. b.if in a stick of chalk, carbon is 3 g, what is the weight of the chalk stick? 13.The population of a city decreased from 25,000 to 24,500. Find the percentage decrease. 14.Vimla bought a used car for and spent on its overhauling. But she had to sell it for Find her loss/gain percent. 15.How much Ravi will pay to his friend if he borrowed at 6% per annum for 145 days? 16.In how many years will amount to at 5% p.a. simple interest. 28

7 Section-C 17.By selling a fan for 7 900, Rahul loses For how much should he sell it to gain 10%? 18.A stationery shopkeeper sold 600 pens at a profit of 15%.If a pen costs him 76, find the S.R of all the pens. 19.A man bought 5 dozens of bananas for 79 a dozen and sold for 76 a dozen. Find the loss% or gain%. 20.A shop reduces all its prices by 20%. What is the new price of a cycle which originally costs 71750? 21.In how many days will earn an interest of 7144 at the rate of 8%? 22.At what rate percent per annum will the simple interest on be in 2 years 6 months? 23.In a school 18% of students play tennis and 32% play football. If 432 actually play tennis, how many students. a.are there in the school? b.play football? 24.A real estate agent purchased a house for and sold at a loss of 22%. Find a.his actual loss in rupees b.selling price Section-D 25.A person borrows an amount of 720,000 at 8% rate for 5 years. He lends this amount to a client for 5 years at a rate of 14%. How much money does he gain in the transaction after 5 years? 26.Rajesh lent to his friend. He charged 12% per annum on and 15% on the rest. How much interest does he earn in 3 years? 27.Ajay borrowed from a money lender at 12% per annum simple interest. At the end of 3 years he settled the account after paying Rs. 40,000 cash and a motor cycle. Find the value of the motor cycle. 28.A TV and a refrigerator were bought for 720,000 each. The shopkeeper made a loss of 6% on the TV and profit of 7% on the refrigerator. Find his total gain or loss percent in the whole transaction. 29.By selling a fan for 71200, Karim loses At what price must he sell it to gain 10%? 30.Bananas are bought at 11 for 710 and sold at 10 for 711. What is the gain percent? 31.A man left 25% of his money to his mother, 55% to his daughter and the remaining to his brother. How much money did he leave? Find the shares of his mother and daughter. 32.The S.R of 20 pens is equal to the C.R of 15 pens. Find the loss % or gain %. 33.A grocer buys 10 dozen eggs at 718 per dozen. Out of these, 10 eggs were found broken and had to be thrown away. At what price per egg should he sell so as to make a profit of 10%? 34.At what rate percent per annum simple interest will a sum treble itself in 16 year? 29

8 Lines and Angles Section - A Multiple Choice Questions - Tick (/) mark the right answer: 1. Look in fig. and find which of the following pairs of angles are not adjacent? a. ZAOB, ZBOCb.ZAOB, ZBOD c. ZBOC, ZCODd.ZAOB, ZCOD Two angles, z 1 and z 2 form a linear pair. If we increase the measure of z 1, then z 2 will a. increaseb.decrease c. remain unchangedd.become acute The angles x and 90-x are a. c. Supplementaryb.Complementary Vertically opposited.making a Linear pair In fig. ZAOD = a. 144 c. 72 In the adjoining figure CEIIBA, then Z ABC = b. d a. 60 b. 65 c. 70 d

9 6. The supplement of the angle measuring 80 is a. 10b.80 c. 100d Angles which are both supplementary and vertically opposite are a. 95, 85b.90, 90 c. 100, 80d.45, Angles shown in figure are not a. acute angles b. complementary c. adjacent angles d. linear pair Section-B 9. Find b and c 10. State whether I is parallel to m or not 99 a. 7 b. 11. Findx Q 12. Find x, y, z 31

10 13. The arms of two angles are parallel as shown in Fig. If z 1=85, find Z2. B 14. In fig. find a, b, c and d if PQ II RS In fig. find a, b, c if m II n II t. 16.Two supplementary angles are such that one is of the other. Find them. o Section-C 17.ABCD, AD II BC. Find the values of x, y, z and t. ^t7b 32

11 18. ^_ Find the value of reflex ZABC where p II q 19. Find x, y, z where l II m II n y-80v.x V 20. In this figure III m, find the value of x. 21. Findx *- 2x+157/i 'GQ ^ RH7 \X In Fig. show that AB II CD. 33

12 23. In fig. AB II CD & AD II BC. Find the values of x, y, z and w 24. In fig. DE NBC. Find e, f, g h. 50 B^-t-^C Section-D 25. A ABC is an equilateral triangle. Through A, a line PQ is drawn parallel to RS. Find the measures of z 1, z 2 and z 3. Give reasons. R B S c 26. In the given figure, AB II CD, Z ABE=120, Z ECD=95. Find the value of x. 27. AB II CD and AE II CF, ZFCG=90 and ZBAC=120. Find the values of x, y and z. 34

13 28. In the following figure, find the values of x and y In the gives figure, PQ and RS intersect each other at O. If z SOT=75, find the value of a, b and c. 30. In figure PQ II RT. Find the value of i. a + b ii. a - 2b 31. In the figure, find the value of z BOC, if points A, O and B are collinear. O 32. In the given figure, AOB is a straight line and the ray DC stands on it. If zaoc=(2x-10) and ZBOC=(3x+20), find the value of x. Also find ZAOC and ZBOC. O (3x+20) + 35

14 HOTS 1.45% of x is p and 35% of x is q, what is p+q in terms of x? 2.A certain sum of money doubles itself in 8 years. In how much time it becomes 4 times of itself at the same rate of simple interest? 3.Find the value of all the unknowns in the given fig. Given lines Him find the measure of x in the given fig. A fruit vendor purchased four bunches of bananas consisting of 540 fruits in all for He sold 15 dozens at 2 bananas a rupee, another 15 dozens at 3 bananas a rupee and the remaining at 5 bananas a rupee. Find his loss or gain percentage. To make each column addition and row-addition true, each symbol will have a particular value. Findout the value of each. it 62 <( yyjo </ yyjo A train travels between two stations A and B, a distance of 108 km in 45 minutes. It passes through a station C, 40 minutes after leaving A. What is the distance between B and C? 36

15 8.A 60 - litre tank was full of oil. Sam used 40% of it and poured the rest into a 40 litre tank. 4 a.what percent of the 40 litre tank was filled with oil? b.if Sam used 3 litres of oil daily, what percent of oil in the 40 litre tank would be used in 10 days? 9.A sum of amount to in 4 years. What will it amount to, if the rate of interest is increased by 2% p.a.? 10.The sum of the squares of three numbers which are in the ratio 2:3:4 is 725. What are the numbers? 37

4. QUADRATIC EQUATIONS

4. QUADRATIC EQUATIONS . QUADRATIC EQUATIONS Important Terms, Definitions and Results The roots of a quadratic equation ax + bx + c = 0 An equation of the form ax + bx + c = 0, where a, b, c are real numbers and a 0, is called