Math – 12

1 – COMPOUND INTEREST

Test Assignment 1.1.

1. Ramesh invested Rs. 12800 for three years at the rate of 10% per annum compound interest. Find:

a. the sum due to Ramesh at the end of the first year

b. the interest he earns for the second year

c. the total amount due to him at the end of three years

2. Find the amount and the compound interest on Rs. 4000 at 10% p.a. for 2 ½ years.

3. A person invests Rs. 10000 for two years at a certain rate of interest compounded annually. At the end of one year this sum

amounts to Rs. 11200. Calculate:

a. the rate of interest per annum.

b. the amount at the end of second year.

4. Nikita invests Rs. 6000 for two years at a certain rate of interest compounded annually. At the end of first year it amounts to Rs.

6720. Calculate:

a. the rate of interest

b. the amount at the end of second year

5. A man invests Rs. 5000 for three years at a certain rate of interest, compound annually. At the end of one year it amounts to Rs.

56000. Calculate:

a. the rate of interest per annum.

b. the interest accrued in the second year

c. the amount at the end of the third year.

6. If the interest is compounded half yearly, calculate the amount when the principal is Rs. 7400, the rate of interest is 5% and the

duration is one year.

7. On a certain sum, the compound interest for 2 years is Rs. 2172. If the rates of interest for successive years are 6% and 8% per

year, then find the sum.

8. The simple interest on a sum of money for 2 years at 4% per annum is Rs. 340. Find

a. the sum of money

b. the compound interest on this sum for one year payable half annum is Rs. 340. Find

9. What sum of money will amount to Rs. 3630 in two years at 10% per annum compound interest?

10. What sum of money will amount to Rs. 9261 in 3 years at 5% per annum compound interest?

11. The simple interest on a certain sum of money for 3 years at 5% p.a. is Rs. 1200. Find the amount due and the compound

interest on this sum of money at the same rate after 3 years if the interest is reckoned annually.

12. The compound interest on a certain sum of money at 5% per annum for two years is Rs 246. Calculate the simple interest on the

same sum for three years at 6% per annum.

13. On what sum will the compound interest (reckoned yearly) for 3 years at 4% per annum be Rs. 7651?

14. At what rate percent per annum compound interest will Rs. 2000 amount to Rs. 2315.25 in 3 years?

15. If Rs. 24000 amounts to Rs. 27783 in 18 months compounds semi – annually, find the rate of interest per annum.

16. In what time will Rs. 15625 amount to Rs. 17576 at 4% per annum compound interest?

17. In what period of time will Rs. 12000 yield Rs. 3972 as compound interest at 10% per annum, if compound on yearly basis?

18. In what time will a sum of Rs. 800 at 10% per annum compounded half – yearly produce Rs. 126.10?

19. On what sum of money will the difference between the compound interest and simple interest for 2 years be equal to Rs. 25 if

the rate of interest charged for both is 5% p.a.?

20. The difference between the compound interest for a year payable half-yearly and the simple interest on a certain sum of money

lent out at 10% p.a. for a year is Rs. 180. Find the sum of money lent out.

21. The difference between compound interest and simple interest in 3 years at 10% p.a. reckoned yearly is Rs. 18.60. Find the sum

and the compound interest.

22. A certain sum of money amounts to Rs. 10584 in two years and to Rs. 11113.20 in three years, interest being compounded

annually. Find the interest rate percent and the original sum.

23. The simple interest in 3 years and the compound interest in 2 years on a certain sum at the same rate are Rs. 1200 and Rs. 832

respectively. Find:

a. the rate of interest b.the principal c.the difference between C.I. and S.I. for three years.

24. The compound interest for the third year on a certain sum is Rs. 968. If the simple interest on the same sum for 3 years is Rs.

2400, find the rate of interest and the sum.

25. Mr. Kumar borrowed Rs. 15000 for two years. The rate of interest for the two successive years are 8% and 10 % respectively. If

he repays Rs. 6200 at the end of first year, find the amount outstanding at the end of second year.

26. Mr. Dubey borrows Rs. 100000 from State Bank of India at 11% per annum compound interest. He repays Rs. 41000 at the end

of first year and Rs. 47700 at the end of second year. Find the amount outstanding at the beginning of the third year.

27. A man borrows Rs. 5000 at 12% p.a. compound interest, compounded semi-annually. He repays Rs. 1800 at the end of every six

months. Calculate the third payment he has to make at the end of 18 months in order to clear the entire loan. Give your answer

correct to the nearest rupee.

Test Assignment 1.2

1. The present population of a town is 64000. If the population increases at the rate of 2 ½ % every year, what will be increase in

the population after 3 years.

2. The population of a city increases uniformly by 4% every year. If its present population is 676000, find:

a. its population 2 years hence b.its population two years ago.

3. 16000 blood donors were registered with 'red cross' at Bangalore. The number of donors increased at the rate of 5% every six

months. Find the time period at the end of which the number of blood donors increased by 2522.

4. A factory increased its production of cars from 40000 in the year 2007-08 to 46305 in 2010-11. Find the annual rate of growth

of production of cars.

5. The price of a property is increasing at the rate of 20% every year. By what percent will the price of the property increase after 3

years?

6. The cost of a washing machine depreciates by Rs. 720 during the second year and by Rs. 648 during the third year. Calculate:

a.the rate of depreciation per annum. b.the original cost of the machine. c.the value of the machine at the end of third year.

2 – SALES TAX AND VALUE ADDED TAX

Test assignment 2.1

1. Harshad purchased a car which was quoted at Rs. 270000. The shopkeeper charged sales tax at the rate of 10%. Harshad wanted

to take the car outside to the state, so the shopkeeper charged 2% extra as central sales tax. Find the total amount paid by

Harshad.

2. Deepak bought an article for Rs. 8500 and spent Rs. 500 for transportation. He marked the article at Rs. 11700 and sold it to a

customer. If the customer had to pay 12% sales tax, find:

a.the customer's price. b.Deepak's profit percent.

3. I paid Rs. 52.20 as sales tax on a watch worth Rs. 1305. Find the rate of sales tax on the watch.

4. A washing machine is available for Rs. 12840 inclusive of sales tax. If the original cost of washing machine is Rs. 12000, find

the rate of sales tax.

5. The price of a washing machine, inclusive of sales tax, is Rs. 13530. If the sales tax is 10%, find its basic price.

6. A colour T.V. is marked for sales for Rs. 17600, which includes sales tax at 10%. Calculate the sales tax in rupees.

7. The catalogue price of a colour T.V. is Rs. 24000. The shopkeeper gives a discount of 8% on the listed price. He gives a further

off season discount of 5% on the balance. But sales tax is charged at 10% on the remaining amount. Find:

a. the sales tax amount a customer has to pay. b.the final price he has to pay for the colour T.V.

8. The cataloguer price of a computer set is Rs. 45000. The shopkeeper gives a discount of 7% on the listed price. He gives a

further off – season discount of 4% on the balance. However, sales tax at 8% is charged on the remaining amount. Find:

a. the amount of sales tax a customer has to pay. b.the final price he has to pay for the computer set.

9. The price of a T.V. set inclusive of sales tax of 9% is Rs. 13407. Find its marked price. If the sales tax is increased to 13%, how

much more does the customer pay for the T.V.?

10. Ms. Chawla goes to a shop to buy a leather coat which costs Rs. 735. The rate of the sales tax is 5%. She tells the shopkeeper to

reduce the price to such an extent that she has to pay Rs. 735, inclusive of sales tax. Find the reduction needed in the price of the

coat.

11. Kiran purchase a an article for Rs. 5400 which includes 10% rebate on the marked price and 20% sales tax on the remaining

price. Find the marked price of the article.

12. A shopkeeper buys an article for Rs. 2500 and marks-up its price. A customer pays Rs. 3052 for the article, inclusive of sales tax

at the rate of 9%. Find the mark-up percentage on the price of the article.

13. Dinesh bought an article for Rs. 374, which included a discount of 15% on the marked price and a sales tax of 10% on the

reduced price. Find the marked price of the article.

Test Assignment 2.2.

1. A manufacturer sells a washing machine to a wholesaler for Rs. 15000. The wholesaler sells it to a trader at a profit of Rs. 1200

and the trader sells it to a consumer at a profit of Rs. 1800. If the rate of VAT is 8%, find:

a. the amount of VAT received by the State Government on the sale of this machine from the manufacturer and the

wholesaler. b.the amount that the consumer pays for the machine.

2. A shopkeeper buys a camera at discount of 20% from the wholesaler, the printed price of the camera being Rs. 1600 and the rate

of sales tax is 6%. The shopkeeper sells it to the buyer at the printed price and charges tax at the same rate. Find:

a. the price at which the camera can be bought. b.the VAT (Value Added Tax) paid by the shopkeeper.

3. The printed price of an article is Rs. 60000. The wholesaler allows a discount of 20% to the shopkeeper. The shopkeeper sells

the article to the customer at the printed price. Sales tax (under VAT) is charged at the rate of 6% at every stage. Find:

a. the cost to the shopkeeper inclusive of tax. b.VAT paid by the shopkeeper to the Government.

c. the cost to the customer inclusive of tax.

4. The marked price of an article is R.s 7500. A shopkeeper sells the article to a consumer at the marked price and charges sales tax

at the rate of 7%. If the shopkeeper pays a VAT of Rs. 105, find the price inclusive of sales tax of the article which the

shopkeeper paid to the wholesaler.

5. A shopkeeper bought a TV at a discount of 30% of the listed price of Rs. 24000. The shopkeeper offiers a discount of 10% of

the listed price to his customer. If the VAT (Value Added Tax) is 10%, find:

a. the amount paid by the customer b.the VAT to be paid by the shopkeeper.

6. In a particular tax period, Mr. Sunder Dass, a shopkeeper purchased goods worth Rs. 96000 and paid a total tax of Rs. 62750

(under VAT). During this period, his sales consisted of taxable turnover of Rs. 40000 of goods taxable at 6% and Rs. 480000 for

goods taxable at 12.5 %. He also sold tax exempted goods worth Rs. 95640 in the same period. Calculate his tax liability (under

VAT) for this period.

3 – BANKING

Test Assignment 3

1. Given the following details, calculate the simple interest at the rate of 6% per annum upto June 30:

Date Debit (in Rs.) Credit (in Rs.) Balance (in Rs.)

Jan. 1 ....... 24000.00 24000.00

Jan. 20 5000.00 ....... 19000.00

Jan. 29 ....... 10000.00 29000.00

March 15 ....... 8000.00 37000.00

April 3 ....... 7653.00 44653.00

May 6 3040.00 ....... 41613.00

May 8 ....... 5087.00 46700.00

2. Mr. Shiv kumar has a saving bank account in Punjab National Bank. His passbook has the following eateries:

Date Particulars Withdrawals Deposit Balance

April 1, 2001 B/F ....... ....... 3220.00

April 15 By transfer ....... 2010.00 5230.00

May 8 To cheque No. 355 298.00 ....... 4932.00

July 15 By clearing ....... 4628.00 9560.00

July 29 By cash ....... 5440.00 15000.00

Sept. 10 To self 6980.00 ....... 8020.00

Jan. 10, 2002 By cash ....... 8000.00 16020.00

Calculate the interest due to him at the end of the financial year (March 31st, 2002) at the rate of 6% per annum.

3. The entries in a Saving Bank Passbook are as given below:

Date Particulars Withdrawals Deposit Balance

01.01.03 B/F ....... ....... Rs. 14000

01.02.03 By cash ....... Rs. 11500 Rs. 25500

12.02.03 To cheque Rs. 5000 ....... Rs. 20500

05.04.03 By cash ....... Rs. 3750 Rs. 24250

15.04.03 To cheque Rs. 4250 ....... Rs. 20000

09.05.03 By cash ....... Rs. 1500 Rs. 21500

04.06.03 By cash ....... Rs. 1500 Rs. 23000

Calculate the interest for six months (January to June) at 4% per annum on the minimum balance on or after the tenth day of

each month.

4. A page from the passbook of Mrs. Rama Bhalla is given below:

Date year

2004

Particulars Withdrawals (in

Rs.)

Deposit

(in Rs.)

Balance

(in Rs.)

January 1 B/F ....... ....... 2000.00

January 9 By cash ....... 200.00 2200.00

February 10 To cheque 500.00 ....... 1700.00

February 24 By cheque ....... 300.00 2000.00

July 9 To cheque 200.00 ....... 1800.00

November 7 By cash ....... 300.00 2100.00

December 8 By cash ....... 200.00 2300.00

Calculate the interest due to Mrs. Bhalla for the period January to December 2004, at the rate of 5% per annum.

5. Mrs. Kumar has an account with the Bank of India. The following entries are from her pass book:

Date Particulars Amount Withdrawals (in

Rs.)

Amount Deposit (in Rs.)

Balance(in Rs.)

08.02.06 B/F ....... ....... 8500.00

18.02.06 To self 4000.00 ....... .......

12.04.06 By cash ....... 2238.00 .......

15.06.06 To self 5000.00 ....... .......

08.07.06 By cash ....... 6000.00 .......

Complete the above page of her pass book and calculate the interest for the six months, February to July 2006, at 4.5% per

annum.

6. Mr. Dhoni has an account in the Union Bank of India. The following entries are form his pass book:

Date Particulars Withdrawals (in Rs.)

Deposit (in Rs.)

Balance(in Rs.)

Jan 3, 07 B/F ....... ....... 2642.00

Jan 16 To self 640.00 ....... 2002.00

March 15 By cash ....... 850.00 2852.00

April 10 To self 1130.00 ....... 1722.00

April 25 By cheque ....... 650.00 2372.00

June 15 To self 577.00 ....... 1975.00

Calculate the interest from January 2007 to June 2007 at the rate of 4% per annum.

7. Mr. Mishra has a Savings Bank Account in Allahabad Bank. His pass book entries are as follows:

Date Particulars Withdrawals (in Rs.)

Deposit (in Rs.)

Balance(in Rs.)

Jan 4, 2007 By cash ....... 1000.00 1000.00

Jan 11, 2007 By cheque ....... 3000.00 4000.00

Feb 3, 2007 By cash ....... 2500.00 6500.00

Feb 7, 2007 To cheque 2000.00 ....... 4500.00

March 3, 2007 By cash ....... 5000.00 9500.00

May 25, 2007 By cash ....... 2000.00 11500.00

June 7, 2007 By cash ....... 3500.00 15000.00

Aug 29, 2007 To cheque 1000.00 ....... 14000.00

Rate of interest paid by the bank is 4.5% per annum. Mr. Mishra closes his account on 30th October, 2007. Find the interest he

receives.

8. Mrs. Kapoor opened a Saving Bank Account in State Bank of India on 9th January 2008. Her passbook entries for the year 2008

are given below:

Date year 2008

Particulars Withdrawals (in Rs.)

Deposit (in Rs.)

Balance(in Rs.)

January 9 By cash ....... 1000.00 1000.00

February 12 By cash ....... 15500 25500

April 6 To cheque 3500 ....... 22000

April 30 To self 2000 ....... 20000

July 16 By cheque ....... 6500 26500

August 4 To self 5500 ....... 21000

August 20 To cheque 1200 ....... 19800

December 12 By cash ........ 1700 21500

Mrs. Kapoor closes the account on 31st December, 2008. If the bank pays interest at 4% per annum. Find the interest Mrs.

Kapoor receives on closing the account. Give your answer correct to the nearest rupee.

9. Mr. Choudhary opened a Saving Bank Account at State Bank of India on 1st April 2007. The entries of one year as shown in his

passbook are given below:

Date Particulars Withdrawals (in Rs.)

Deposit (in Rs.)

Balance(in Rs.)

1st April 2007 By cash ....... 8550.00 8550.00

12th April 2007 To self 1200.00 ....... 7350.00

24th April 2007 By cash ....... 4550.00 11900.00

8th July 2007 By cheque ....... 1500.00 13400.00

10th Sept. 2007 By cheque ....... 3500.00 16900.00

17th Sept. 2007 To cheque 2500.00 ....... 14400.00

11th Oct. 2007 By cash ....... 800.00 15200.00

6th Jan. 2008 To Self 2000.00 ....... 13200.00

9th March 2008 By cheque ....... 950.00 14150.00

If the bank pays interest at the rate of 5% per annum, find the interest paid on 1st April, 2008. Give your answer correct to the

nearest rupee.

10. A page from the Savings Bank Account of Mr. Prateek is given below:

Date year 2006

Particulars Withdrawals (in Rs.)

Deposit (in Rs.)

Balance(in Rs.)

January 1st B/F ....... ....... 1270

January 7th By cheque ....... 2310 3580

March 9th To self 2000 ....... 1580

March 26th By cash ....... 6200 7780

June 10th To cheque 4500 ....... 3280

July 15th By clearing ....... 2630 5910

October 18th To cheque 530 ....... 5380

October 27th By self 2690 ....... 2690

November 3rd By cash ....... 1500 4190

December 6th To cheque 950 ....... 3240

December 23rd By transfer ....... 2920 6160

If he receives Rs. 198 as interest on 1st January 2007, find the rate of interest paid by the bank.

11. Saloni deposited Rs. 150 per month in a bank for 8 months under the recurring deposit scheme. What will be the maturity value

of her deposits if the rate of itnerest is 8% per annum?

12. Mrs. Goswami deposits Rs. 1000 every month in a recurring deposit account for 3 years at 8% per annum. Find the matured

value.

13. Kiran deposited Rs. 200 per month for 36 months in a bank's recurring deposit account. If the bank pays interest at the rate of

11% per annum, find the amount she gets on maturity.

14. David opened a Recurring Deposit Account in a bank and deposited Rs. 300 per month for 2 years. If he recrived Rs. 7725 at the

time of maturity, findthe rate of interest per annum.

15. Ahmed has a recurring deposit account in a bank. He deposits Rs. 2500 per month for 2 years. If he gets Rs. 66250 at the time of

maturity, find

a. the interest paid by the bank b.the rate of interest

16. Mr. R.K. Nair gets Rs. 6455 at the end of one year at the rate of 14% per annum in a recurring deposit account. Find the monthly

instalment.

17. A man has a recurring deposit account of Rs. 500 per month at 8% per annum simple interest. If he gets Rs. 24010 at the time of

maturity, find the total time for which the account was held.

4 – SHARES AND DIVIDENDS

Test Assignment – 4

1. A man bought 600 shares, each of face value Rs. 50, of a certain company, and received Rs. 2400 as dividend. Find the rate of

dividend.

2. A man wants to buy 62 shares available at Rs. 132 (par value of Rs. 100)

a. How much should he invest? b.If the dividend is 7.5%, what will be his annual income?

c. If he wants to increase his annual income by Rs. 150, how many extra shares should he buy?

3. Find the market price of 5% share when a person gets Rs. 175 by investing Rs. 3850.

4. A man invests Rs. 16800 in buying shares of nominal value Rs. 24 and selling at 12% premium. The dividend on the shares is

15% per annum.

a. Calculate the number of shares he buys b.Calculate the dividend he receives annually.

5. A man invests Rs. 9600 on Rs. 100 shares at Rs. 80. If the company pays him 18% dividend, find:

a. the number of shares he buys. b.his total dividend. c.his percentage return on the shares.

6. Amit Kumar invests Rs. 36000 in buying Rs. 100 shares at Rs. 20 premium. The dividend is 15% per annum. Find:

a. the number of shares he buys b.his yearly dividend. c.the percentage return on his investment.

7. A man invests Rs. 20020 in buying shares of nominal value Rs. 26 at 10% premium. The dividend on shares is 15% per annum.

Calculate:

a.the number of shares he buys. b.the dividend he receives annually. c.the rate of interest he gets on his money.

8. Ajay owns 560 shares of a company. The face value of each share is Rs. 25. The company declares a dividend of 9%. Calculate.

a. the dividend that Ajay will get

b. the rate of interest, on his investment, if Ajay has paid Rs. 30 for each share.

9. Mr. Tiwari invested Rs. 29040 in 15% Rs. 100 shares at a premium of 20%. Calculate:

a. the number of shares bought my Mr. Tiwari. b.Mr. Tiwari's income from the investment

c. the percentage return on his investment.

10. A company with 4000 shares of nominal value of Rs. 110 each declares an annual dividend of 15%. Calculate:

a. the total amount of divided paid by the company. b.the annual income of Shah rukh who holds 88 shares in the

company. c.If the received only 10% on his investment, find the price Shah Rukh paid for each share.

11. Mr. Parekh invested Rs. 52000 on Rs. 100 shares at a discount of Rs. 20 paying 8% dividend. At the end of one year, he sells the

shares at a premium of Rs. 20. Find:

a. the annual dividend. b.the profit earned including his dividend.

12. At what price should a 6.25% Rs. 50 share be quoted when the money is worth 10%?

13. A man invested Rs. 45000 in 15% Rs. 100 shares quoted at Rs. 125. When the market value of these shares rose to Rs. 140, he

sold some shares, just enough to raise Rs. 8400. Calculate:

a. the number of shares he still holds, b.the dividend due to him on these shares

14. Vivek invests Rs. 4500 in 8%, Rs. 10 shares at Rs. 15. He sells the shares when the price rises to Rs. 30, and invests the

proceeds in 12% 100 shares at Rs. 125. Calculate:

a. the sale proceeds. b.the number of Rs. 125 shares he buys c.the change in his annual income from dividend.

15. Which is more profitable investment: 4% Rs. 100 share at Rs. 120 or 3.5% ten – rupee share at Rs. 9?

16. Mr. Ram Gopal invested Rs. 8000 in 7% Rs. 100 shares at Rs. 80. After a year he sold these shares at Rs. 75 each and invested

the proceeds (including his dividend) in 18% Rs. 25 shares at Rs. 41. Find:

a.his dividend for the first year b.his annual income in the second year c.the percentage increase in his return on his original investment.

17.Rs.25 shares of a company are sold at a discount of Rs. 5. If the return on the investment is 15%, find the rate of dividend declared.

18. A dividend of 9% was declared on Rs. 100 shares selling at a certain price. If the rate of return is 7 ½ %, calculate:

a. the market value of the share. b.the amount to be invested to obtain an annual dividend of Rs. 630.

19. Divide Rs. 95680 into two parts such that if one part is invested in 8% Rs. 100 shares at 4% discount and the other in 9% Rs. 50

shares at 8% premium, the annual incomes are equal.

20. A man invests Rs. 6750, partly in shares of 6% at Rs. 140 and partly in shares of 5%, at Rs. 125. If his total income is Rs. 280,

how much has he invested in each?

5 – LINEAR INEQUATIONS

Test assignment 5

1. Solve x – 3 (2 + x) > (3x - 1), x {–3, –2, –1, 0, 1, 2, 3}. Also represent its solution on the number line.

2. Find the values of x, which satisfies the inequation .,6

51

3

2

2

12 Nx

x Also represent the solution on the number line.

3. If .323532, xxxsolveIx

4. Solve Rxx ,5322 and mark it on number line.

5. Given that ,Rx solve the following inequality and graph the solution on the number line: 23431 x

6. Solve the following inequation and represent the solution set on the number line: .,6

5

3

2

2

13 Rx

x

7. Solve the following inequation and graph the solution on the number line: .,3

13

3

1

3

1

3

22 Rxx

8. Given that ,Ix solve the inequation and graph the solution on the number line: .232

43

xx

9. Solve:3

13

3

1

3

22 x given that a. Nx b. Wx c. Ix

10. If ,Ix solve .35242 xxx Also represent its solution on the number line.

11. Solve the in equation ,114552 xx where .Ix Also represent the solution set on the number line.

12. Solve the following inequation and graph the solution on the number line: .,114552 Rxxx

13. Solve the following inequation and represent the solution set on the number line: .,5

22

5

3194 Rxx

xx

14. Solve .,5

2

3

132 Rxx

xxx

Also graph its solution on the number line.

15. Solve the given inequation and graph the solution on the number line: .;74132 Ryyyy

16. Solve the inequation and represent the solution set on the number line: .,23

142

3

83 Ixwherex

xx

17. If },,1215918:{},37511:{ RxxxxBandRxxxxA find the set BA and represent it on a

number line.

6 – QUADRATIC EQUATIONS

Test Assignment 6.1

1. Find the values of a and b such that x =1, x = –2 are solutions of the quadratic x2 + ax + b =0.

Solve the following equations (2 to 10) by factrisation:

2. a. 28)53(7

1 2 x b. 28

3 x

x

3. a. 02)21(2 xx b. .032534 2 xx

4. a. .0,0483 222 ababxxa b. .0,0)( 222222 abxbaxa

5. a.73

32

3

2

x

x

x

xb.

2

12

1

1

x

x

x

x

6. a.4

3

10

1

6

1

xxxb. 2

ax

b

bx

a

7. a. 0,0,11

abbababx

b

ax

ab. .0,0,0,

1111

qpqp

xqpxqp

8. a. 01282.34 3 xx b. .2655 11 xx

9. a. 24 xx b. xx 1392

10. a. 061

51

2

x

x

x

xb. 3

32

14

1

32

x

x

x

x

Solve the following equations (11 to 14) by using formula:

11. a. 0276 2 xx b. 0142 xx

12. a. 0552 2 xx b. 071367 2 xx

13. a. 044 222 baaxx b. .012)34(2 axax

14. a.32

23

3

1

x

x

x

xb. 4

2

2

2

2

x

x

x

x

15. Solve the following equations by using formula and give your answer correct to 2 decimal places:

a. 06102 xx b. 0242 xx

c. 01052 xx d. 073 2 xx

e. 5)5)(1(2 xx f. 71

2 x

x

16. Solve the following quadratic equation for x and give your answer correct to 2 decimal places: 0932 xx

17. Solve the following quadratic equation for x and give your answer correct to two decimal places: 5x (x + 2) = 3.

18. Solve the following quadratic equation and give the answer correct to two significant figures: .0274 2 xx

19. Solve the equation .618

x

x Give your answer correct to two significant figures:

20. Solve the equation 0435 2 xx and give your answer correct to 3 significant figures.

21. Discuss the nature of the roots of the following equations:

a. 0354 2 xx b. 0342 2 xx

c. 03

123 2 xx d. 04343 2 xx

e. 03753 2 xx f. 0323 2 xx

22. Without solving the following quadratic equation, find the value of 'p' for which the roots are equal: 0342 xpx .

23. Find the value(s) of k for which each of the following quadratic equation has equal roots:

a. 032 2 kxx b. 0)18()2(2)4( 2 kxkxk

24. Find the value(s) of m for which each of the following quadratic equation has real and equal roots:

a. 0)1(2)13( 2 mxmxm b. 0)5()1(22 mxmx

25. Find the values of p for which each of the following quadratic equation has real roots:

a. 0232 xpx b. 084 2 pxx

TEST ASSIGNMENT 6.2

1. The sum of two natural numbers is 18 and the sum of their squares is 170. Taking one number as x, form an equation and solve

it to find the numbers.

2. Find two consecutive integers such that the sum of their squares is 85.

3. If the product of two positive consecutive odd integers is 195, find the integers.

4. The sum of the squares of two natural numbers is 116. If the square of the larger number is 25 times the smaller number, find the

numbers.

5. Five times a certain whole number is equal to three less than twice the square of the number. Find the number.

6. If the sum of the squares of the three consecutive integers is 110, find the integers.

7. If the sum of two numbers is 15 and the sum of their reciprocals is 10

3, find the numbers.

8. The sum of the numerator and denominator of a certain positive fraction is 11. If 1 is added to both numerator and denominator,

the fraction is increased by56

3. Find the fraction.

9. The perimeter of a rectangular plot is 180 m and its area is 1800 m2. Take the length of the plot as x m. Use the perimeter 180 m

to write the value of the breadth in terms of x. Use the values of length, breadth and the area to write an equation in x. Solve the

equation to calculate the length and breadth of the plot.

10. The perimeter of a rectangular plot is 68 m and length of its diagonal is 26 m. Find its area.

11. In an auditorium, seats area arranged in rows and columns. The number of rows was equal to the number of seats in each row.

When the number of rows was doubled and the number of seats in each row was reduced by 10, the total number of seats

increased by 300. Find:

a. the number of rows in the original arrangement. b.the number of seats in the auditorium after re – arrangement.

12. A two digit number is such that the product of digits is 24. If 45 is subtracted from this number, the digits interchange their

positions. Find the number.

13. The speed of an express train is x km/hr and the speed of an ordinary train is 12 km/hr less than that of the express train. If the

ordinary train takes one hour longer than the express train to cover a distance of 240 km, find the speed of the express train.

14. A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/hr more, the time taken for the journey would

have been 1 hour 40 minutes less. Find the original speed of the car.

15. An aero plane covered a distance of 400 km at an average speed of x km/hr. On the return journey, the speed was increased by

40 km/hr. Write down an expression for the time taken for: a. the onward journey b.the return journey

If the return journey took 30 minutes less than the onward journey, write down an equation in x and find its value.

16. An aeroplane flying with a wind of 30 km/hr takes 40 minutes less to fly 3600 km, than what it would have taken to fly against

the same wind. Find the plane's speed of flying in still air.

17. A swimming pool can be filled by 2 pipes together in 6 hours. If the larger pipe alone takes 5 hours less than the smaller pipe to

fill the pool, find the time in which each pipe alone would fill the pool.

18. The hotel bill for a number of a number of persons for overnight stay is Rs. 4800. If there were 4 more persons, the bill each

person had to pay would have reduced by Rs. 200. Find the number of persons staying overnight.

19. Some students planned a picnic. The budget for the food was Rs. 480. As eight of them failed to join the party, the cost of the

food for each member increased by Rs. 10. Find how many students went for the picnic.

20. Rs. 480 is divided equally among 'x' children. If the number of children were 20 more, then each would have got Rs. 12 less.

Find x.

21. A shopkeeper buys a certain number of books for Rs. 720. If the cost per book was Rs. 5 less, the number of books that could be

bought for Rs. 720 would be 2 more. Taking the original cost of each book to be Rs. X, write an equation in x and solve it.

22. A trader bought a number of articles for Rs. 900. Five articles were damaged and he sold each of the rest at Rs. 3 more than what

he paid for it, thus getting a profit of Rs. 150 on the whole transaction. Find the number of articles he bought.

23. A boat can cover 10 km up the stream and 5 km down the stream in 6 hours. If the speed of the stream is 1.5 km/hr, find the

speed of the boat in still water.

24. One year ago, father was 8 times as old as his son. Now his age is the square of his son's age. Find their present ages.

25. Two years ago, a man's age was three times the square of his son's age. In three years' time, his age will be four times his son's

age. Find their present ages.

26. Five years ago, a woman's age was the square of her son's age. Ten years hence her age will be twice that of her son's age. Find:

a. the age of the son five years ago. b. the present ate of the woman.

27. The length (in cm) of the hypotenuse of a right angled triangle exceeds the length of one side by 2 cm and exceeds twice the

length of other side by 1 cm. Find the length of each side.

Factorization

Test Assignment – 7

1. Using remainder theorem, find the remainder when 9572 23 xxx is divided by 2x – 3.

2. Find the remainder (without division) when 8732 23 xxx is divided by x–1.

3. When 1049 23 xxkx is divided by x + 1, the remainder is 2. Find the value of the constant k.

4. What number should be added to xxx 752 23 so that the resulting polynomial leaves the remainder –3 when divided by 2x + 1.

5. When divided by x – 3, the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3) x – 6 leave the same remainder. Find the value of 'p'.

6. The polynomails 193 23 kxxx and 292 xkx when divided by 3x + 1 leave the same remainder. Find the value of k.

7. a. Show that (x – 3) is a factor of .9157 23 xxx Hence factorise .91573 xxx

b. Show that (x – 1) is a factor of .8147 23 xxx Hence, completely factorise the above expression.

8. Show that 2x + 7 is a factor of 141152 22 xxx . Hence factorise the given expression completely, using the factor

theorem.

9. Find the value of a, if (x – a) is a factor of x3 – ax2 + x +2.

10. Find the value of 'k' if (x – 2) is a factor of x3 + 2x2 – kx + 10. Hence determine whether (x + 5) is also a factor.

11. If (x – 2) is a factor for 2x3 – x2 – px – 2,

a. find the value of p. b.with this value of p, factorise the above expression completely.

12. Use factor theorem to factorise the following polynomials completely:

a. 24103 23 xxx b. 4423 xxx

13. a. Use the remainder theorem to factorise the following expression:2x3 + x2 – 13x + 6

b. Using Remainder Theorem, factorise completely the following polynomial: 3x3 2x2 – 19x + 6

14. Find the values of the constants a and b, if (x – 2) and (x + 3) are both factors of the expression x3 + ax2 + bx – 12.

15. Given that x + 2 and x + 3 are factors of 2x3 + ax2 + 7x – b. Determine the values of a and b.

16. (x – 2) is a factor of the expression x3 + ax2 + bx + 6. When this expression is divided by (x – 3), it leaves the remainder 3. Find

the values of a and b.

17. The expression 2x3 + ax2 + bx – 2 leaves remainders of 7 and 0 when divided by 2x – 3 and x+ 2 respectively. Calculate the

values of a and b. With these values of a and b, factorise the given expression completely.

18. When a polynomial f(x) is divided by (x – 1), the remainder is 5 and when it is divided by (x – 2), the remainder is 7. Find the

remainder when f(x) is divided by (x – 1) (x – 2).

Ratio and Proportion

Test Assignment 8.1

1. Find the compounded ratio of: a.5 : 7 and 9 : 10 b.2a : 3 b, 2b : 3a, a2 : b2.

2. Find the following: a.the duplicate ratio of 3 : 7 b.the triplicate ratio of 2 : 5

c. the sub – duplicate ratio of 36 : 25 d.the sub – triplicate ratio of 27 : 1 e.the reciprocal ratio of 9 : 11.

3. Divide Rs. 1162 among three children in the ratio 8

7:

3

11:

4

11 .

4. There are 36 members on a student council in a school and the ratio of the number of boys to the number of girls is 3 : 1. How

many more girls should be added to the council so that the ratio of the number of boys to the number of girls may be 9 : 5?

5. If ,3:5: ba find (5a + 8b) : (6a – 7b)

6. If ,3

7

53

53

yx

yxfind x : y

7. If (3x2 – 10y2) : xy = 7 : 2, find the ratio of x : y.

8. If (x2 + y2) : xy = 5 : 2, find the ratio (x + 2y) : (2x + y).

9. Two numbers are in the ratio 3 : 5. If 8 is added to each number, the ratio becomes 2 : 3. Find the numbers.

10. A, B and C play cricket. The runs scored by A and B respectively are in the ratio 3 : 5. B's runs and C's runs are in the ratio of 4 :

7. If all the three together scored 201 runs, how many did each score?

11. The monthly pocket money of Ravi and Sanjeev are in the ratio 5 : 7. Their expenditures are in the ratio 3 : 5. If each saves Rs.

80 every month, find their monthly pocket money.

12. The ratio of the number of boys to the number of girls in a school of 560 students is 5 : 3. If 10 new boys are admitted, find how

many new girls may be admitted so that the ratio of the number of boys to the number of girls may change to 3 : 2.

13. In an examination, the ratio of passes to failures is 4 : 1. Had 15 more appeared, and 6 more passed, the ratio of passes to failures

would have been 3 : 1. Find the number of candidates who appeared for the exam.

14. A bag contains Rs. 182 in the form of 1 rupee, 50 paise and 25 paise coins in the ratio of 15 : 12 : 20. Find the total number of

coins in the bag.

15. The ratio of the pocket money saved by Joseph and his sister is 5 : 9. If Joseph saves Rs. 35 more, how much ore should his

sister save in order to keep the ratio of the savings unchanged?

16. An employer reduces the number of employees in the ratio 7 : 5 and increases their wages in the ratio 8 : 13. In what ratio is the

wages bill increased or decreased?

17.Work done by (x – 3) men in (2x +1) days and the work done by (2x + 1) men in (x + 4) days are in the ratio 3 : 10.Find the value of

x.

Test Assignment 8.2

1. If a, 5, 20 and b are in continued proportion, find a and b.

2. What number should be subtracted from each of the numbers 23, 30, 57 and 78 so that the remainders are in proportion?

3. What number must be added to each of the numbers 5, 11, 19 and 37 so that they are in proportion?

4. If 6 is the mean proportion between two numbers x and y and 48 is the third proportional to x and y, find the numbers.

5. If ba and a : b is the duplicate ratio of (a + c) and (b + c), prove that c is the mean proportional between a and b.

6. If y is the mean proportional between x and z, prove that .33 zxyzxyzyxxyz

7. If a, b, c and d are in proportion, prove that a. badcdcba 32753275

b. abcd .1111 2222

2222dcba

acbaabcd

8. If a, b, c and d are in proportion, prove that dc

dc

ba

ba

75

75

75

75

.

9. If x, y and z are in continued proportion, prove that z

x

zy

yx

2

2

10. If a : b = 2 : 3, find the value of :a.ba

ba

53

53

b.22

22

45

45

ba

ba

c.33

33

57

57

ba

ba

d.22

22

65

119

ba

ba

11. If dc

dc

ba

bathatprove

d

c

b

a

53

53

53

53,

12. If ,43

43

43

43

dc

ba

dc

ba

prove that d

c

b

a

13. If .,58

58

58

58

d

c

b

athatprove

dc

ba

dc

ba

14. If ,2

ba

mabx

find the value of

mbx

mbx

max

max

.

15. Using componendo and dividendo, find the value of x: 95343

5343

xx

xx

16. Given ,2222

2222

baba

babax

use compondendo and dividendo to prove that

1

22

22

x

xab .

17. Given that .62

63

3

323

23

bab

abaUsing componendo and dividendo, find a : b.

18. Find x from the following equations:a.xa

xa

xa

xa

3

16 b. .4142

1422

2

xx

xx

19. If ,11

11

aa

aax using properties of proportion show that x2 – 2ax + 1 = 0.

20. If ,33

33

baba

babax

prove that 2bx2 – 2ax = 3b = 0.

10. Reflection

1. The point P (a, b) is first reflected in the origin and then reflected in the x – axis to P' has co-ordinates (–3, 5), find the values of

a and b.

2. Find p and q if

a. (–2, 3) on reflection in x-axis is mapped at (p, q). b.(3, p) on reflection in y-axis is mapped at (q–1, 4)

c. (p, 3) on reflection in the origin is mapped at (–2, –q + 5)

3. Points A and B have co-ordinates (2, 5) and (0, 3). Find

a. the image A' of A under reflection in the x-axis. b.the image B' of B under reflection in the line AA'.

4. Points (3, 0) and (–1, 0) are invariant points under reflection in the line L1; points (0, –3) and (0, 1) are invariant points on

reflection in the line L2.

a. Name the lines L1 and L2.

b. Write down the images of points P(3, 4) and Q(–5, –2) on reflection in L1. Name the images as P' and Q' respectively.

c. Write down the images of P and Q on reflection in L2. Name the images as P" and Q" respectively.

d. State or describe a single transformation that maps P' onto P".

5. Attempt this question on graph paper.

a. Plot the points A (3, 2) and B(5, 4) on the graph paper.

b. Reflect A and B in the x-axis to A' and B'. Plot these on the same graph paper.

c. Write down (i) the geometrical name of the figure ABB' A'. (ii)the axis of symmetry of ABB' A'.

(iii) the measure of the angle ABB'. (iv)the image A" of A, when A is reflected in the origin.

(v) the single transformation that maps A' to A".

6. The image of the triangle OAB under reflection in the origin O is triangle OA1B1 where A1, B1 have co-ordinates (–2, –3), (1, –

4) respectively.

a.Draw a diagram to represent this information and write down the co-ordinates of A, B.

b.What kind of figure is the quadrilateral ABA1B1? State with a reason, whether the figure ABA1B1 has any line(s) of symmetry.

c.Find the co-ordinates of A2, the image of A under reflection in the x-axis followed by reflection in the origin.

d.Find the co-ordinates of B2, the image of B under reflection in the y-axis followed by reflection in the origin.

7. Use graph paper for this question.

a. The point P(2, –4) is reflected about the line x = 0 to get the image Q. Find the co-ordinates of Q.

b. Point Q is reflected about the line y = 0 to get the image R. Find the co-ordinates of R.

c. Name the figure PQR. d.Find the area of figure PQR.

8. Use graph paper for this question.

The points A (2, 3), B(4, 5) and C(7, 2) are the vertices of ABC, when reflected in the origin.

a. Write down the coordinates of A', B', C' if A'B'C' is the image of ABC, when reflected in the origin.

b. Write down the coordinates of A", B", C" if A"B"C" is the image of ABC, when reflected in the x-axis.

c. Mention the special name of the quadrilateral BCC"B" and find its area.

9. Use graph paper to answer this question.

a.Plot the points A(4, 6) and B(1, 2) b.If A' is the image of A when reflected in the x-axis, write the co-ordinates of A'.

c. If B' is the image of B when reflected in the line AA', write the co-ordinates of B'.

d. Give the geometrical name for the figure ABA'B'.

10. Use graph paper for this question. The point P(5, 3) was reflected in the origin to get the image P'.

a.Write down the co-ordinates of P'. b.If M is the foot of perpendicular from P to the x-axis, find the co-ordinates of M.

c. If N is the foot of the perpendicular from P' to the x-axis, find the co-ordinates of N.

d. Name the figure PMP'N. e.Find the area of the figure PMP'N.

11. The point P(3, 4) is reflected to P' in the x-axis; and O' is the image of O (the origin) when reflected in the line PP'. Using graph

paper, give:

a. the co-ordinates of P' and O'. b.the lengths of the segments PP' and OO'.

c. the perimeter of the quadrilateral POP' O'. d.the geometrical name of the figure POP'O'.

12. Use a graph paper for this question. (Take 10 small divisions = 1 unit on both axes). Plot the points P(3, 2) and Q(–3, –2). From

P and Q, draw perpendiculars PM and QN on the x-axis.

a. Name the mage of P on reflection in the origin.

b. Assign the special name to the geometrical figure PMQN and find its area.

c.Write the co-ordinates of the point to which M is mapped on reflection in (i) x-axis (ii) y-axis (iii) origin.

13. Use graph paper for the question.

A(1, 1), B(5, 1), C(4, 2) and D(2, 2) are the vertices of a quadrilateral. Name the quadrilateral ABCD. A, B, C and D are

reflected in the origin onto A', B', C' and D' respectively. Locate A', B', C' and D' on the graph paper and write their co-ordinates.

Are D, A, A' and D' collinear?

14. Use a graph paper for this question. (Take 10 small divisions = 1 unit on both axes). P and Q have co-ordinates (0, 5) and (–2, 4).

a.P is invariant when reflected in an axis. Name the axis. b.Find the image of Q on reflection in the axis found in (i)

c. (0, K) on reflection in the origin is invariant. Write the value of K.

d. Write the co-ordinates of the images of Q, obtained by reflecting it in the origin followed by reflection in x-axis.

15. Use graph paper for this equation.

A(0, 3), B(3, –2) and O (0, 0) are the vertices triangle ABO.

a. Plot the triangle on the graph sheet taking 2 cm = 1 unit on both axes.

b. Plot D the reflection of B in the y-axis and write its co-ordinates.

c. Give geometrical name of the figure ABOD. d. Write the equation of the line of symmetry of the figure ABOD.

11 – Distance and section Formulae

Test Assignment 11.1

1. Calculate the distance between A (7, 3) and B on the x-axis abscissa is 11.

2. KM is a straight line segment of length 13 units. If K has the co-ordinates (2, 5) and M has the co-ordinates (x, –7), find the

possible values of x.

3. Point A (2, –4) is reflected in the origin as A'. Point B (–3, 2) is reflected in x-axis at B'. Write the co-ordinates of A' and B'.

Calculate the distance A'B' correct to one decimal place.

4. a. What point (or points) on the x-axis are at a distance of 5 units from the point (5, –4)?

b. Find the points on the x-axis whose distances from the points (2, 3) and

1,

3

2are in the ratio 2 : 1.

c.Find point (or points) which are at a distance of 10 units from the point(4, 3), the ordinate of the point (or points) is twice

the abscissa.

5. Show that the points (0, –2), (3, 1) (0, 4) and (–3, 1) taken in order on the vertices of square. Also find the area of the square.

6. The points A(0, 3), B(–2, a) and C(–1, 4) are the vertices of a right angled triangle at A, find the value of a.

7. Show by distance formula that the points (–1, –1), (2, 3) and (8, 11) are collinear.

8. Show that the points (7, 3), (3, 0), (0, –4) and (4, –1) are the vertices of a rhombus. Also find the area of the rhombus.

9. If A, B and P are the points (–4, 3), (0, –2) and ( , ) respectively and P is equidistant from A and B, show that

.021108

10. The centre of a circle is 13,12 and it passes through the point (–3, –1). If a diameter of the circle is of length 20

units, find its centre.

11. Find the centre of the circle passing through the points (8, 12) (11, 3) and (0, 14). Also find its radius.

Test Assignment 11.2

1. P divides the distance between A(–2, 1) and B(1, 4) in the ratio 2 : 1. Calculate the co-ordinates of the point P.

2. The line segment joining the points (2, 1) and (5, –8) is trisected at the points P and Q. If the point P lies on the line 2 x – y + k =

0, find the value of k.

3. The mid – point of the line segment joining (2a, 4) and (–2, 2b) is (1, 2a +1). Find the values of a and b.

4. The mid – point of the line segment joining the points (3m, 6) and (–4, 3n) is (1, 2m – 1). Find the values of m and n.

5. If the points A (–2, -1), B (1, 0), C(p, 3) and D(1, q) form a parallelogram ABCD, find the values of p and q.

6. The centre of a circle is (1, –2) and one end of a diameter is (–3, 2), find the co-ordinates of the other end.

7. If the line joining the points A(4, –5) and B(4, 5) is divided by the point P such that 5

2

AB

APfind the co-ordinates of P.

8. The line segment joining

3

5,1A and B (a, 5) is divided in the ratio 1 : 3 at P, the point where the line segment AB intersects

y-axis. Find a.the value of a b.the co-ordinates of P.

9. The line segment joining A(2, 3) and B(6, –5) is intersected by x-axis at a point K. Write down the ordinate of the point K.

Hence find the ratio in which K divides AB.

10. If A = (–4, 3) and B = (8, –6),

a. find the length of AB. b.in what ratio is the line joining A and B, divided by x-axis?

11. The line joining P(–4, 5) and Q (3, 2) intersects the y-axis at R. PM and QN are perpendicular from P and Q on the x-axis. Find:

a. the ratio PR : RQ. b.the co-ordinates of R c.the area of the quadrilateral PMNQ.

12. Find the ratio in which the point (2, a) divides the join of (–4, 3) and (6, 3). Hence find a.

13. Given a line segment AB joining the points A (–4, 6) and B(8,–3). Find:

a.the ratio in which AB is divided by the y-axis. b.the coordinates of the point of the intersection. c. the length of AB.

14. Determine the ratio in which the line 2x + y – 4 = 0 divide the line segment joining the points A(2, –2) and B(3, 7). Also find the

co-ordinates of the point of division.

15. Using section formula, find the value of p for which the points (–1, 3), (2, p) and (5, –1) are collinear.

16. A(10, 5), B(6, –3) and C(2, 1) are the vertices of a triangle ABC. L is the mid – point of AB and M is the mid – point of AC.

Write down the co-ordinates of L and M. Show that LM = .2

1BC

17. Three consecutive vertices of a parallelogram ABCD are A(1, 2), B(1, 0) and C(4, 0), find the fourth vertex D.

18. Find the third vertex of a triangle if its two vertices are (–1, 4) and (5, 2) and mid-point of one side is (0, 3)

19. Find the co-ordinates of the vertices of a triangle whose mid – points.

20. In the adjoining figure, line APB meets the X-axis at A and Y – axis at B. P is the point (–4, 2) and AP : PB = 1 : 2. Write down

the coordinates of A and B.

21. Find the coordinates of the centroid of a triangle whose vertices are A(–1, 3), B(1, –1) and C(5, 1)

22. Two vertices of a triangle are (–8, 11) and (2, –5). Find the third vertex, given that the centroid of the triangle is (–1, 5).

23. ABC is a triangle and G(4, 3) is the centroid of the triangle. If A, B and C are the points (1, 3) (4, b) and (a, 1) respectively, Find

the values of a and b. Also find the length of the side BC.