Alike_maths_vi_std Entrance Guide

Mathematics Marks: 25

Time: 30 Minutes

Arithmetic • Addtion • substraction • multiplication • Division • HCF, LCM • Average of whole numbers Fraction and decimals • Addtion • substraction • multiplication • Division Commercial mathematics • Profit and loss • simple interest • Percentage Sets and algebra – Fundmental Geometry Angles, Different kinds, construction

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1. The area of few districts of our state are given in square Km. Bangalore 8005 Km Belgaum 13415 Km Chitradurga 8440 Km Chickmagalur 7201 KM Uttar Kannada 10291 KM •

Name the district which has the largest area ______________

•

What is the area of Bangalore District ___________________

•

What is the area of Utttar Kannada ___________________

•

What is the area of Chickmagalur district ______________

•

Name he district which has the smallest area ____________

Name of the place Unit Ten Hundred Thousand Ten thousand

Number form 100000 100000 100000 100000 100000

Comparison

a. Ten thousand = ___ lakh b. Hundred thousand = _________ lakh 1. Form two numbers of six digits using the digits 5,2,8 repeatedly. 2. Form the largest and smallest six digit numbers using only the digits 4,6,9 repeatedly. 3. Write the place and place value of the digit 7, present in different place in 787577

4. Approximate each number given below, nearer to tens, hundreds and thousands place. a. 964 b. 1049 c. 1009

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Chapter 2 – Fundamental operations of numbers 1. In a town, there are 38649 men, 37468 women and 13784 children. what is the total population?

2. Gopalaiah had 9642 coconuts. He sold 5324 coconuts in a village fair. He used 1021 coconuts for cooking. How many coconuts are remaining with him?

3. Priya had Rs. 235785 in her saving bank account. If she withdraws Rs. 122676 from her account, what is the balance amount in her account?

4. If 2325 books can be loaded in a lorry, how many books can be loaded in 35 such Lorries?

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5. A retail merchant has purchased 125 silk saris from a wholesale merchant. If the cost of each silk sari is Rs. 2525 what is the amount he has to pay?

6. 12 laborers earn Rs. 4248 for completing a piece of work. Find the wages earned by each laborer

7. 8500 kg of rice was distributed equally among the 35 workers, how much rice does each one get? How much rice remains?

8. The population of a village is 8687. It has 3697 men, 3579 women and the rest is children. How many children are there in the village?

9. A merchant has 253 Kg of onion. He fills it equally in 23 bags. what is the quantity of onion present in each bag?

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Chapter 3 – Fractions, Decimals and percentage a. Classify the following fraction into proper and improper fractions. ½, ¼, 5/2, 2/5, 7/3, 9/11

b. What do we call these fractions? 1½, 2¼, 5¾ Exercise 3.1 a) Give two equivalent fraction for each of fraction given below a. 1/2 b. 3/4 c. 3/10

b) Recognize the fractions which do not belong to the group a. 1/2 , 5/10, 2/3, 3/6 b. 2/8, 4/16, 2/10, 1/4 c. 1/3, 3/15, 1/5, 4/20 c) Are 10/15 and 20/30 equivalent fractions

d) a. b. c. d.

Which are the equivalent fractions in the given set of fractions? 1/5, 4/20 2/13, 4/26 4/10, 1/10 6/32, 2/4

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e) Test whether the given fraction are equivalent of not? a. 3/10, 12/50 b. 5/9, 30/54 f) Add 1/15 to 4/15

g) Girija walks 2 ¼ Km from her home and travels 4 ½ km by bus to reach the school. Find the distance from her house to school

h) Rani has 2 ¾ m of ribbon. If she gives 1 ¼ m of ribbon to her friend mary, Find the length of ribbon left with her

i) A farmer sold 1 ¼ acre, out of 5 ¾ acres of land. How many acres of land is left with him?

j) Find the sum of a. 2 ¼ + 3 ¼ + 5 ¼

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b. 5/6 + 8 / 9 + 7 / 9

k) Find the difference of a. 4 / 7 – 3/7

b. 5 1/2 – 2 1/4

1. Write the following into decimals a. 8 m and 40 cm = b. 6 KM and 785 m = c. 28 KG and 25 gm = d. Rs. 25 and 9 paise = e. 15 l and 90 ml = f. Rs. 5 and 75 paise = g. 8 liters and 250 mili-liters = h. Rs. 12 and 40 paise = i. 20 KG and 500 gm = j. 6 km and 250 m = 2. Rakesh 1.68 m, joseph 1.95 m, sheela 1.65 m

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Who is the tallest? Who is the shortest? 3. Write ascending order 1.98, 1.09, 2.9, 8.1

4. Write descending order 10.4, 8.7, 8.6, 9.12

5. There are 200 hundred bags in this lorry. Out of them 80 bags are of dal and 120 bags are of rice. Tell the bags of rice and dal in percentage

6. Express 25 paise in percent of Rupee.

7. Ram a boy of 5th standard requires a cloth of 60 cm to stitch a half pant. Write the same in percentage.

Exercise 3.3 1. Write the following in decimal form a. 7 / 10 =

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b. 98/100 = c. 76/100 = d. 9/1000 = 2. Write the following fraction in percentage a. 14/100= b. 72/100= c. 26/100= d. 48/50= e. 5/25= 3. Write the following percent as fractions. a. 15%= b. 29%= c. 89%= d. 96%= e. 65%= 4. Write the following paisa in decimal form and in percent of a rupee a. 25 paise = b. 85 paise = c. 89 paise = d. 96 paise = e. 67 paise = 5. Write the following centimeters in meters and express the same in percents using symbols (1m = 100 cm) a. 17 cm = b. 28 CM = c. 89 cm = d. 192 cm = 9

e. 42 cm = 6. Write the following things in decimal form a. The cost of a pencil is Re. 8/10 = b. The cost of an eraser is Re. 35/100 = c. The cost of book is 1950 paise = 7. Write the numbers in place value chart. a. 4.7 b. 53.09 c. 6.214 8.Encircle the larger number l) 2.8, 3.8 , 6.04, 6.4 m) 9.2, 8.90, 9.13, 9.06 9. Write the following in ascending order a. 4.28, 4.82, 4.3, 4.12 = b. 15.4, 15.31, 15.114, 15.001 = 10. Write the following in descending order a. 4.28, 4.82, 4.3, 4.12 = b. 15.4, 15.31, 15.114, 15.001 = Exercise 3.5 . 1. Write the given fractions in percentage a. 13/100 = b. 26 / 200 = c. 14 / 50 =

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2. Write each of the following in fractional form d. 13/100 = e. 26 / 200 = f. 14 / 50 = 3. Write the given paise in percent of a rupee g. 50 paise = h. 90 paise = i. 75 paise = 4. Write the following ml in percent of liter j. 450 ml = k. 320 ml = l. 900 ml = Chapter 4 – Decimals – Fundamental Operations 1. Kartik deposited Rs. 304.75, Rs. 118, Rs. 498.10 and Rs. 217.50 respectively in a bank for 4 days. What is the total amount deposited by him in 4 days.

2. In a milk co-operative society, mill collected for 4 days respectively are 1038 L 250 ml, 937 L 76 ml, 895 :L 300 ml and 904 L 150 ml. how much milk was collected in 4 days. 3.

How many millimeters are there in a meter?

4. 200.5 km + 28.750 km

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5. Raju bought a pen for Rs. 8.50 and a pencil Rs. 2 what is total cost?

6. Add the following a. 436.5 kg + 25.75 kg = ______________ b. 25.2 L + 495.211 L = _______________ c. 680 mg + 750 mg = _______________ 7. A barrel contains 205.300 L of cooking oil. If 168.500 L of this oil is sold, how much oil remains in the barrel?

8. 34600 litres of milk is used out of 40 literes of milk bought for a function. How much milk is unused?

9. Fill in the blanks a. 1 litre = __________ ml b. 1 kg = ____________ gm c. 1 km = ___________ m d. 1 m = ____________ cm e. Rs. 4 and 35 paise = ____________ paise f. 1 quintal = ___________ kg 10. If Ravi gives Rs. 4.25 and Rs. 2.35 to his friends from Rs. 10. Find the amount left with him.

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11. If gangappa sells 3.400 litres, 2.300 litres and 1.600 litres of milk from 10 litres of milk in a can, how much quantity of milk remains in his can.

Chapter 5 – Algebra Exercise 5.2 Write the numerical co-efficient and algebraic co-efficient in the blanks provided below. Algebraic Term Numerical co-efficient Algebraic co-efficient 7p 7 8a a 4x M 8mn Mn 7z 7 Find the numerical co-efficient in the given algebraic terms a. 5x ________ b. 8m _________ c. n _________ d. 6z _________ Chapter 6 – Geometry a. An angle of 90 deg is called a ________________ b. An angle less than 90 deg is called an __________ c. An angle which is more than 90 deg and less than 180 deg is called an _____________ d. An angle which measures exactly 180 deg is called a __________

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e. Kirans height is 150 cm and Deepak height is 107 cm. express their heights in metres Chapter 7 – Fractions – Fundamental operations 1.Everyday Gopal brings 1/2 litre of milk. How much milk would he bring in 10 days?

2. There are 24 biscuits in a packet. Deepa distributed 3/4 of them to her friends. How many biscuits did she distribute to her friends?

3.There is 3/4 parts of fruit. Priya eats 1/2 part of it. How much of fruit does Priya eat?

4. Divide 1/4 by 2

5. Divide 6 by 2/3 6. Divide a. 5 divide by 1/4 ------------

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b. 7 divide by 2/3 _________ c. 5/6 divide by 9 _________ 8. The cost of a chocolate is Rs. 1/4 . What is the cost of 8 such chocolates?

9. There are 12 apples. If half of an apple is distributed to each one, for how many person that can be distributed.

10. Simplify a. 4/5 x 20 = b. 7/9 x 3 = c. 15 x 4/5 = d. 12 x 5 /6 = e. 3/8 divide by 6

11. To prepare a cup of coffee, 2/3 cup of milk is required. How many cups of milk are required to prepare 25 cups of coffee?

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12. 20 m of ribbon is distributed among students. if each student gets 2/3 m of it, how many students can receive the ribbons?

13. 60 litres of milk have been supplied to a milk centre. If 1/4 litre of mil is put in eah packet, how many packets can be made out of 60 litries

Chapter 2 – Fundamental operations 1. The length and breadth of rectangular field are 235.5 m and 87 m respectively. Find the area of the field.

2. A silk merchang sold 1 kg of cocoons for Rs. 135.50. How much does he earn b selling 87.6 kg of cocoons?

3. A person consumes 2.3 litres of water in a day. How much does the person consume in 10 days?

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4. Find how many hours are there in a week.

5. Find the product of the following problems i. 698.5 x 43 ii. b. 9999 x 9.9

6.What is the quantity of oil in 25 tins, if each tin contains 16.550 litres?

7. A weaver weaves 5.30 m of silk in a day. How many metres of silk cloth can he weave in a week

8. How many grams are there in 7.3 kg? _______________

9. How many centimeters are there in a 2.4 m? ___________

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10. How man paise are there in Rs. 12.75? ______________

11. How many millimeter is there in 8.125 l _____________

12. How many metere is there in 7.125 km ______________

a. 4 children together prepared a thing and kept in their school exhibition for sale. If they earn Rs. 12.60 as profit. Find the amount earned by each child?

b. 15 L of milk is bought from a milk dairy for Rs. 175.50. Find the cost of one litre milk

c. Rs. 125.50 is equally distributed among 5 persons. What is the amount each one gets?

d. If 18.4 kg of sugar is equally filed in a 4 bags. Find the quantity of sugar filled in each bag.

e.solve

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a. 18.45 divide by 5

b. 36.47 divide by 7

f. Raju has 14 cans, each containing 8.5 liters of milk. He filled the milk in 4 big cans of equal capacity. How many litres of milk that each can contains?

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g. 8 donors purchased 34.8 m of uniform cloth each. This cloth was distributed to 3 schools equally. What is the length of the cloth received by each school?

h. Find the wages of each worker per day, if 25 worker earns Rs. 9100 for 4 days.

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Chapter 3 – Commercial Mathematics 1. If a merchant buys a 200 pages note book for Rs. 12 and sell it for Rs. 15. What profit does he get?

2. Ramappa buys a cow for Rs. 8948 and spends Rs. 158 for its transportation. Later he sells it for Rs. 8945. Find loss/profit.

3. Shiva bought 15m of cloth for Rs. 525. If he had sold each meter of cloth at Rs. 40. Find the profit or loss?

4. what is the selling price of a radio, if it is bought for Rs. 365 and sold at a loss of Rs. 20?

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5. 4 not books are bought for Rs. 32 and each book sold at Rs. 10. Find the profit or loss.

CP Rs. 427

SP

Profit Rs. 73

Rs. 328

Rs. 12 Rs. 1000

Rs. 9271 Rs. 8679

Loss

Rs. 588

3.2 Percentage 1. The population of India as per 1991 census was 85 crores. Among this 46% were women. Find the population of woman.

2. The capacity of a container is 30 litres. It is filled with 30% of water find the quantity of water in the container.

3. Pradeep scored 48 marks out of 50 in mathematics in first semester examination. Find the percentage of marks scored by him. 22

4. In a class of 60 students 40% are girls. Find the number of girls and boys.

5. Find the value of the following a. 40% of 122m b. 80% of 30 litres c. 75% of 24 hours

6. A shopkeeper sells a pen worth Rs. 10 with 25% profit and a note book worth Rs. 20 with 20% profit. Which will bring him more profit?

7. An ore of silver contains 10% silver. Find the weight of silver present in 8000 kg of the silver ore.

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8. Raj deposited Rs. 10000 which he had saved in a bank for 2 years. How much interest does he get the rate of 8% p.a? what the total amount he gets at the end of 2 years?

9. Sujatha deposits Rs. 50000 in her savings bank account. At the end of 6 years, the balance in her account was Rs. 75000. Find the interest she has earned.

10. What is the simple interest for Rs. 4250 at 10% P.a for 6 years?

11. Ganesh borrows Rs. 15000 from a bank at the rate of 10% p.a. to open a cycle shop. How much interest should he pay to the bank after 3 years?

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3.5 Average 1. In running race Sunil, Prasad, Gopal, Sharath and siril participated. They ran a particular distance in 14 seconds, 15 seconds, 16 seconds, 16 seconds and 14 seconds. Find the average time taken by them.

2. In a school, attendance of 50 students for 10 months is as follows June – 40, July – 42, Aug – 45, Sep – 48, Oct – 44, Nov – 45 , dec – 45, Jan – 48, Feb – 48, March – 45 What is the average attendance?

3. In a school garden 5th, 6th and 7th standard students grow 40, 30 and 70 saplings respectively. Find the average saplings grown by the three classes?

4. 45 students requires six iddlies on an average for breakfast. How many iddlies have to be cooked for breakfast?

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5. When we want to get a draft for Rs. 8000 from a bank, 2% commission has to be paid to the bank. Find the amount of commission.

Sl.n

Principal

Rate of Interest

Time

o 1 2 3 4

Rs, 8500 Rs. 10500 Rs. 89000 Rs. 75000

P.a 8% 12% 6.5% 9%

2 years 5 years 4 years 6 months

SI

Amount

6. A Cow gives milks per day as follows Mon = 10.5 litres

Tues = 12.5 litres

wed = 9.5 litres Thu=11.5 litre 26

Fri = 10 litres,

Sat = 12 litres

Sun = 9 litres

Find the average of the milk given by the cow per day.

7. Ravi reaps four crops of silk in a year. The profit was Rs. 25000, Rs. 38000, Rs. 12800 , and Rs. 24000. What was the average profit of crops.

Chapter 4 – sets 1. Say whether the following are finite sets or infinite sets with reason a. A = { 0,1,2,3,4,5,6} b. P = { cow, buffalo, goat, sheep} c. C = { 5,10,15,20,25,……………} d. D = {A set of flowering plants in a park} e. M = {10,20,30,40,50,…………} 2. Write the following sets using listing method a. B = {Colors of our national flag} b. C = {prime numbers between 1 and 20} c. L = {Set of even numbers} d. P = {Letters in your name}

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II. Express the following sets in rule method a. A = {2,4,6,8,10…………….} b. B = {Kannada, English, Mathematics, Science, social studies} c. Z = {chair, table, bench, stool, plank} d. P = {Kabaddi, Kho-Kho, chinnidandu, Cricket} III. State whether the following True or False a. 4 is an element of the set {3,4,7.10} b. 3 € {1,4,5,6,12} c. 6 € {1,2,3,4,5,8……….} d. {red, blue, green, saffron} is a set, expressed in Roster Method e. {a,b,c,d,e} is an infinite set IV. Mention in which method are the following sets written a. N = {letters of the English alphabet} b. T = { tiger,lion, cheeta} c. R = {set of teachers in our school} d. S = {green gram, black gram, dal, cow gram, Bengal gram}

Chapter – 5 Like and Unlike Terms 1. Mention like terms in each group

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a. 8m, 5k, 5m, 4p b. 3p, 3x, 5p, 5z c. 6x, 8y, y, 8p d. 7a, 7b, 7c, 1a, 2b 2. Add two more like terms for each group a. 8a, 4a, 3a, ______, _______ b.6pq, pq, 10pq, _______, ________ c. z, ¼ z, 8z, _______, ________ d. 6m, 8m, m, _______ , _________ 3. 8x and 8y are unlike terms. Why? 4. 3m, ½ m are like terms. Why? 5. Identify each term and say how many terms are there in the given expressions a. a + b + c b. 4 x y z c. 8m ÷ 4 d. mn + p e. a – 2b + c 6. Classify the following as monomial, binomial and trinomial expressions a. m + n b. a + b + c c. 4xyz d. 8m – 2n e. 8xyz f. 9x ÷ 4 g. 6a + b + c h. 5xp i. 2p + 3z

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3. Express the following as algebraic expressions using symbols of operation and name them a. Sum of 4x and 5y b. multiply m with n c. From the sum of a and b, subtract d. Divide 10x by 5 e. Divide 8x by 4 f. The sum of p and q g. The sum of a, b and c h. the product of x, y and z i. To the product of 5 and m, add n 4. Complete the following Sl.no

Algebraic Expression

1 2 3 4 5 6 7 8

6p + 8q 5mxn 18p ÷ 9 5p + q + 4x Ab + b + c Xyz – z 8x + 9x + 1x 3a – 2abc

Number of Terms

Name of the expression

Chapter 6 – Geometrical Figures (Perimeter, Area and volume) 1. A community hall in village is square in shape and its side is 8 m. The cost of 1 square meter is Rs. 120. Find area & the total cost.

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2. A slab is a square. one side is 30 cm. Find the perimeter of the slab.

3. If the length of a square is 5 cm. find its area.

4. Find the perimeter of the floor of a class room with length 5m and breadth 4m. How many square shaped marble slabs of 1 m are required the cover the floor.

5. The length of a stage is 12m and breadth is 7m. How many square shaped slabs of 1 sq.m are required to cover the floor? If a square slab of 1m costs Rs. 150, find the total cost to cover the stage.

6. The area of rectangle is 96 sq.cm. If the length is 12 cm. what is the breadth?

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7. The perimeter of a square is 24 cm. Find the area of the square.

8. A farmer has a rectangular field of length 250m and breadth 180m. Find the area of the field.

9. The length and breadth of a photo is 50 cm and 40 cm respectively. What length of wooden frame is needed to frame the photo?

10. A carpet is needed to cover the entire area of a room. If the length of a room is 5.2m and breadth is 5 m. Find the area of carpet required.

11. A Cuboids has length 6 cm, breadth 3 cm and height 3 cm. find its volume.

12. Find the volume of a cube of side 4 cm 13. A cube shaped sugar candy measure 5cm in length. Find its volume?

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14. An eraser has length 2cm, breadth 1cm, height 1 cm. How many such erasers can be arranged in a box, having length, breadth, and height equal to 10 cm each?

15. Solve the following a. The cost of a chocolate is Rs. 1 ¼ what is the cost of 8 such chocolates

b. The length of a tape is 6.6 m. if 9 such tapes are arranged one after the other, find the total length.

c. Sameena bought 4 balls for Rs. 54.80. Find the cost of each ball.

d. a Cuboid has length 5 cm, breadth 4 cm and height 3 cm. Find its volume.

e. Separate and write the binomials from the following i. 3x, 6mn, a+b, 8a + b, 9pq

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ii. 2x + y, ab, 3p – 2q, a – b

f. Gopinath deposited Rs. 45000 for 3 years in a bank. If the rate of interest is 10% p.a. Calculate the interest earned and total amount end of the 3 years.

g. Rama purchased a TV for Rs. 18000 and sold it for Rs. 17000. calculate the loss or profit.

h. The cost of a litre of diesel is Rs. 32.43. A farmer bought 8.5 litres of diesel and distributed equally among 5 tractors. Find the cost of diesel filled into each tractor.

i. Monthly income of a worker is Rs. 14000. Out of this he spends 60% for house hold expenses. Find the actual amount spent for household expenses. Also find the amount left with him.

15. Give the missing term

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1. Divisor x quotient + ________ = dividend 2. 16. Recognize the word which does not belong to the group a. meter, millimeter, milliliter, centimeter b. kilogram, quintal, kilometer, milligrams, c. hours, minutes, seconds, liters Question Paper 1. 3/5 x 14 = __________ 2. If 4/3 litres of milk is distributed equally among two persons then each will get __________ litres. 3. 4.5 x 0.2 = ____________ 4. In the figure, ABCD is a square of side 5 cm. The perimeter of the square is _____________ 5. The like term for 6p is _______________ ( 6q, 6r, 3p, 6z) 6. A binomial among the following is ____________ a. a+b+c

b. 4xyz

c. 3a – 2b+c

d. mn + P

7. According to railway timings 2.00 pm is expressed in hours as________ 8. 50% of 60 is ________________ 9. The symbol used to represent ‘belong to the set’ is _________ a. €

b. ¥

c. µ

d.≠

10. The number of right angles in a right angled triangle is / are …………. 11. The distance between the centres of the circle to a point on the circle is __________ Remember 5. In a rectangle two pairs of opposite sides are equal and parallel. All angels are right angels 6. All the four sides of a square are equal 7. Opposite sides of rectangle are equal

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8. All the angles of a square and rectangle are equal. Each angle is equal to 90 deg 9. opposite sides of a rectangle and a square are parallel 10. Division is the repeated subtraction of the same number. 11. The price at which a thing is bough is called the cost price 12. The price at which a thing is sold is called the selling price 13. The difference between selling price and cost price is called profit or loss. 14. Percentage means per 100 or a fraction with 100 as the denominator. 15. The same algebraic numbers which are coming in a situation always represent a definite number 16. Even though the numerical co-efficient are different, if algebraic co-efficient are same, they are called like terms. 17. If there is one term is called monomial 18. If there are two term is called binomials 19. If there are three terms are called trinomials 20. Algebraic terms, connected with + or – sign are considered separate terms. 21. Algebraic terms, connected with ‘x’ or ‘÷’ sign are considered as single term.

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