TIWARI TUTORIALS TIWARI TUTORIALS DATE : 04 …tiwaritutorials.in/Downloads/ICSE-X LAST MINUTE MATHS.pdfFind the amount and compound interest on Rs. 8,000 at 10% per annum for 1½

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

TIWARI TUTORIALSTIWARI TUTORIALS

Gomti Nagar : 0522-4043177Indira Nagar : 0522-4043277

Aliganj : 0522-4043477Aashiyana : 0522-4041077TIWARI TUTORIALS 1

LAST MINUTE PACKAGE :- ICSE - X

1. Amount = Principal + Interest

2. Simple Interest = 100

Principal TimeRate

3. A = P (1+r/100)n, A = Amount, P = Principalr =Rate of interest, n =Time

4. When the interest rates percent for the successive fixed periodsare r1%, r2%, r3%-------- then amount A is given by

...100

1100

1100

1 321

rrrPA

Q1. A certain sum of money amounts, at compound interest to Rs6600 in 1 years and to Rs 7986 in 3 years. Find the sum and therate percent. Ans.: 10%, Rs. 6000

Q2. On a certain sum of money. the difference between the compoundinterest for a year, payable half yearly, and the simple interest fora year is Rs. 180. Find the sum lent out, if the rate of interest inboth cases is 10%. [Ans: Rs 72000]

Q3. A man borrows Rs. 8,000 at a compound interest rate of 5% perannum. if he repays Rs. 1,600 at the end of each year. Find thesum outstanding at the end of the third year. [Ans: 5817]

Q4. Find the amount and compound interest on Rs. 8,000 at 10% perannum for 1½ years if the interest is compounded half yearly.

[Ans: Rs. 9261, Rs 1261]Q5. Rs. 4,000 becomes Rs. 4,630.50 in 3 years at certain rate of

compound interest per annum. Find the rate. [Ans: 5%]Q6. The price of car depreciates by 20% every year. By what percent

will the price of a car reduce after 3 years? [Ans: 48.8%]Q7. Compute the compound interest on Rs. 30,000 at 6% per annum

for 2½ years. Also find.(i) The new principal at the end of the second year.

[Ans: 33708](ii)The amount after 2½ years. [Ans: 34729.24]

Q8. Akhil invested Rs. 12000 in a company at compound interestcompounded semiannually.He received Rs 15972/- after 18months from the company. find the rate of interest per annum.

[Ans: 20% per annum]Q9. The S.I. in 3 years and the C.I. in 2 years on a certain sum at the

same rate are Rs. 1200 and Rs 832 respectively. Find : (i) rate ofinterest (ii) the Principal (iii) the diff. between the C.I. and S.I. for 3years. Ans.: 8% (ii) Rs. 5000 (iii) Rs. 98.56

Q10. The C.I. calculated yearly on a certain sum of money for thesecond year is Rs. 880 and for the third year it is Rs. 968. Find therate of interest and the original money. Ans.: Rs. 10% Rs. 8000

1. If the rate of sales tax is r%, then

sales tax = r% of list price = 100

r x list price

2. Selling price = list price + sales tax

3. If the selling price and list price are known, then one can obtain thesales tax and rate sales tax as follows:Sales tax = selling price - list price

Rate of sales tax = %100pricelist

taxSales

4. If the selling price and the rate of sales tax (r%) are known, the listprice (say x) is determined by solvingx + r% of x = selling price

i.e. 100

rx of x = selling price

Q1. If the rate of sales tax increases by 5% the selling price of anarticle goes up by Rs. 40. find the marked price of the article.

[Ans: 800]Q2. The price of a T.V. set inclusive of sales tax of 9% is Rs. 13,407.

Find its marked price. If the sales tax is increased to 13%, howmuch more the customers pays for the T.V. set. [Ans: Rs 12300, Rs 492]

Q3. Due to short supply in the market, a shopkeeper raises the priceof an almirah by 5% above the printed price and charges a salestax of 12% on the printed price. A customer has to pay Rs. 4,680for the almirah. Find the printed price of almirah. [Ans: Rs 4600]

Q4. A shop keeper buys an article at a rebate of 20% on the printedprice. He spends Rs. 20 on transportation of the article. Aftercharging a sales tax of 6% on the printed price, he sells the articleat Rs. 530.00 Find his profit perentage. [Ans: 19.045%]

Q5. A manufacturing company ‘P’ sells a Desert cooler to a dealer Afor Rs. 8100 including sales tax (under VAT). The dealer A sells itto a dealer B for Rs. 8500 plus sales tax and the dealer B sells itto a consumer at a pforit of Rs. 600. If the rate of sales tax (underVAt) is 8%, find(i) the cost price of the cooler for the dealer A.(ii) the amount of tax received by the Government.(iii) the amount which the consumer pays for the cooler.

[Ans: (i) Rs. 7500, (ii) Rs. 728, (iii) Rs. 9828]Q6. A shopkeeper sells an article whose listed price is Rs. 1500 and

charges sales tax on it at the prescribe rates of 12% on theconsumer. If a shopkeper pays a VAT of Rs. 36 to govt. What wasthe price inclusive of tax at which the shopkeeper bought thearticle from the wholeseller. [ Ans.: Rs. 1344]

Q7. A manufacturer listed the price of his goods at Rs. 160 per article.He allowed a discount of 25% to a wholesaler who in his turnallowed a discount of 20% on the listed price to a retailer. The rateof sales tax on the goods is 10%. If the retailer sells one article toa consumer at a discount of 5% on the listed price, then find(i) the VAT paid by the wholesaler. (ii) the VAT paid by the retailer.(iii) the VAT received by the government. Ans.: (i) Rs. 0.80 (ii) Rs. 2.40 (iii) Rs. 15.20

Q8. ‘A’ manufacturer bicycels, at a cost of Rs 1680. He sells them to‘B’, and ‘B’ sells to ‘C’ . ‘C’ sells them to ‘D’. The tax rate is 8%.Find(i) the total amount of VAT. (ii) the selling price of ‘D’, assuming thatthe profit is Rs. 150.00 at every stage of the selling chain.

[ Ans.:(i) Rs.182.40 (ii) Rs. 2462.40 ]Q9. A shopkeeper buys a drum of oil at a discount of 10% from the

wholesaler, the printed price of the drum of oil being Rs. 2400 andthe rate of sales tax is 7%. The shopkeeper sells it to the buyer atthe printed price and charged tax at the same rate. find : (i) Theprice at which the drum can be bought (ii) The VAT paid by thewholesaler. Ans: (i) Rs. 2311.20 (ii) Rs. 16.80

Q10. A shopkeeper bought a washing machine at a discount of 20%from the wholesaler, the printed price of the washing machinebeing Rs. 12000. The shopkeeper sells it to a consumer at theprinted price. If the rate of sales tax is 7.5%. Find : (i) the amountof VAT paid by the wholesaler. (ii) The amount of VAT paidby the shopkeeper (iii) The amount at which the consumerbought the machine. Ans.: (i) Rs. 720 (ii) Rs. 180 (iii) Rs. 12900

We hope your History & Civics paper would be excellent, reachyour home before 1:30 PM 1:30 - 4:00 PM - relax lunch and sleep.

4 – 6 PM , COMPOUND INTEREST

Memorise and write all formulae and basic concepts

7–9 pm SALES TAX & VAT

DATE : 04 MARCH

IF TIME IS LEFT REVISE ALL THE SOLVED EXAMPLES OF TEXTBOOK

6 to 7 pm break (free)


T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS





(i) Minimum balance from 10th day to the last day of the month quali-fies for the Interest for that month.

(ii) Time is always taken as 1 month (i.e. 1/12 year)(iii) If the account is closed in a particular month the minimum balance

for that month is taken as 0.00(iii) If the account is opened in any particular month after 10th day, the

minimum balance for that month is taken as 0.00

Q1. Mr. Roy opened a saving bank account in a branch of United Bankof India, Kolkata on 5 January 2000 by depositing Rs. 3,000 incash. On 7 January he deposited Rs. 6,750 in cash, and on 10January withdrew Rs. 820.75 through a cheque to Life InsuranceCorporation of India. On 28 January he withdrew Rs. 2,000 incash, and deposited Rs. 1,500 in cash on 8 March 2000.(a) Write the details of his transactions in the passbook for theperiod. (b) Find the interest earned by him by the end of March2000 if the simple interest rate is 5% per annum. [Ans: Rs. 92 ]

Q2. A page from the passbook of the savings bank account of Mr.Singh with entries up to the end of May is given below.

(a) If the annual simple interst rate is 4.5% then find the interestearned by Mr Singh for the period 1 January to 31 May.

[Ans: Rs. 453](b) If the interest earned by Mr. Singh for the period 1 January to

31 May is Rs. 504.25 (rounded off to Rs. 504), find the rate ofsimple interest. [Ans: 5%]

Q3. Mr. P.S. Lambh opened a saving bank account in co-operationbank. His passbook entries are shown below-

Date Particulars Debit(in Rs.)

Credit(in Rs.)

Balance(in Rs.)

Jan 1 B/F – – 6360.00

Jan 12 By Cash – 750.00 7110.00

Feb. 15 To self 5000.00 – 2110.00

June 6 To cheque 354.00 – 1756.00

July 18 By Cheque – 543.00 2299.00

He closed the account on 29th July and received Rs. 2354.20as balance. Calculate the rate of interest received by him.

Ans.: 4% p.a.

Q4. The following shows the entries in the last page of the passbookof a savings bank account holder. Some of the entries areincomplete (shown by dots).

Date Particulars Withdrawals Rs. P

Deposits Rs. P

Balance Rs. P

1 April 2002 B / F 4000.75 11 April To self 1000.00 3000.75 8 June By cheque 865.25 3866.00 10 July To cheque 1500.00 2366.00 12 Sept By cash 3000.00 5366.00 1 Oct By interest ... ... 18 Oct To cash 1800.00 ... 5 Nov. By cheque 1237.50 ...

The bank pays a simple interest of 4% p.a. compounded half-yearly at the end of March and September. The account holdercloses the account on 10 April 2003. Find the amount of moneythat the account holder will receive. [Ans: 5850]

Q5. Mr Jagwani invests Rs. 500 every month in a cumulative depositscheme for 3 years at a simple interest rate of 8% p.a. (i) Find thetotal interest she will earn at the end of the period. (ii) Find thematurity value of the deposit. [Ans: (I) Rs 2220 (ii)Rs 20220 ]

Q6. Mr. Rao has a cumulative deposit account for 3 years at 7%interest p.a. She receives Rs. 7,977 as he maturity amount afterthree years. (i) Find the monthly deposit (ii) Find the total interstreceivable after maturity. [Ans: (i) 200 (ii) 777]

Q7. Mr. Prabhakar open a recurring deposit account of Rs. 300 permonth at 8% simple interest per annum. On maturity, he gets Rs930. Find the period for which he continued with the account.

[Ans: 2.5 year]Q8. Amit depsited Rs 150 per month in bank for 8 months under the

recurring deposit scheme. What will be the maturity value of hisdeposits, if the rate of interest is 8% p.a. and interest is calculatedat the end of every month? [Ans: Rs. 1236 ]

IF TIME IS LEFT REVISE ALL THE SOLVED EXAMPLES OF TEXT BOOK9:00 - 10:00 PM Dinner

10 – 12 PM , BANKING


6:30 - 8:30 AM - QUADRATIC EQUATION

DATE : 5 MARCH (6 to 6:30 am be fresh)

IF TIME IS LEFT REVISE ALL THE SOLVED EXAMPLES OFTEXT BOOK

12:00 - 6:00 AM Sleep

Q1. Solve for x : (i) 0365 2 x (ii) 083 22 abxxa

[Ans: (i) (1, -11) (ii) (0,83

ba

) ]

Q2. Solve for x, by factorisation (i) 037103 2 xx (ii)

1021 xx [Ans: (i) (73 , 3 ) (ii) (2–1)]

Q3. Solve by using formula and give the answer to two decimal place

(i) 01052 xx (ii) 0953 2 xx[Ans: (i) 6.53, –1.53 (ii) 1.08 – 2.75]

Q4. Solve for y,

(i) 61

21

62

yy

[Ans: 1, –4]

(ii) 0;1111

ba

ybayba [Ans: y = –a, y = –b]

(ii) 233

8

y

yy

y[Ans: y = 1]


T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS





Q5. Determine value (s) of k for which the given quadratic equations

have equal roots : 01213 2 kxkxk

Ans.: 211 ,k

Q6. The sum of the squares of two consecutive natural numbers is313. Find the numbers. [Ans.: 12, 13]

Q7. The sum of two natural numbers is 8. Determine the numbers ifthe sum of their reciprocals is 8 / 15. [Ans.: 5, 3]

Q8. A two-digit number is such that the product of its digits is 12.When 36 is added to this number, the digits are interchanged. Findthe number. [Ans.: 2, 6]

Q9. The hypotenuse of a right-angled triangel is 6 metres more thantwice the shortest side. If the third side is 2 metres less than thehypotenuse, find the sides of the triangle. [Ans.: 10, 26, 24]

Q10. 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:(i) the age of the son five years ago. (ii) the present age of thewoman. [Ans.: (i) 5 yr. 30 yr.]

Q11. A plane left 30 minutes later than the scheduled time and in orderto reach its destination 1,500 km away in time it has to increaseits speed by 250 km/hr. from its usual speed. Find its usual speed.

[Ans.: 75km/hr]Q12. Swati can row her boat at a speed of 5 km / hr in still water. If it

takes her 1 hour more to row the boat 5.25km upstream than toreturn downstream. find the speed of the stream. [Ans.: 2 k/h]

LINEAR INEQUATION

Multiplication by ‘+’ ve number on both sides of inequation leadsno change in the sign of inequality e.g.

4 < 5 4 x 2 < 5 x 2Multiplication by '+'ve number on both sides changes the sign ofinequality e.g 4 < 5 4 x (-2) > 5 (-2)

Q1. Find the values of x which satisfy the inequation :

2 12

23

1 56

x, x N . Graph the solution set on the

no. line.

Ans.: {1, 2, 3} -1 0 1 2 3 4

Q2. If x z , solve 2 4 2 5 3 x x x . Also represent itsssolution on the no. line.

Ans: {-5, -4} -5 -4 -3 -2 -1 0Q3. Solve the following inequation and graph the solution set on the

no. line 2 23

13

3 13

x x R,

Ans.: -3 3Q4. The following diagram represents two inequations A and B on

real no. lines.

-2 4A ,

1 7B

(i) Write down A & B in the set builder notation.(ii) Represent A B & A B on two different no. lines.

Ans.: (i) A x x R x: , 2 4l q , B x x R x : ,1 7l q .

(ii) 1 4 -2 1 3and

Q5. If P is the solution set of 3 4 2 3x x , x N , Q is

the solution set of 4 5 12x , x w .Find

P Q Q P P Q P Q , , , .

Ans.: 2 3 4 0 1 1 0 1 2 3 4, , , , , , , , , ,l q l q l q l qQ6. Solve the following inequation and graph the solution set on the

no. line : 7 2 1 5 1 4 x x x R,

Ans.: -1 0 1 2 3 4 5


08:30 – 09:30 AM – free and breakfast


(i) Dividend is always calculated an nominal values.(ii) Dividend income is added in proceeds if shares are

sold atleast after one year.(iii) Annual income = d % x N.V. x no. of shares(iv) Return % (also known as prof it %, yield%,

interest %) = %100investedMoney

Dividend

Q1. A man invest in share for which we have the condition “7% Rs.100 shares at Rs. 120”. What is the annual income of a personholding 150 such shares. Also find his annual profit percentage.

[Ans: 5%]Q2. A man invests Rs. 8,800 on buying shares of face value Rs. 100

each at a premium of 10% in a company. If he earns Rs. 1,200 atthe end of the year as dividend, find(i) The number of shares he has in the company.(ii) The dividend percentage per share that he received, and(iii) The dividend percentage declared by the company.

[Ans: 80 shares, 13.67%, 15%]

Q3. Alok bought shares of 6% Rs. 100 shares at Rs. 120. A minbought shares of 8% Rs. 20 shares at Rs. 30. Whose investmentwas better? [Ans: 2nd investment is better]

Q4. Mrs. Tirkey buy shares of a company for Rs. 8,000 at a discountof Rs. 20 (Par value Rs. 100). The company pays a 6% dividendannually. Find(i) The number of shares bought by Mrs. Tirkey,(ii) her annualincome from the shares, and(iii) her annual profit percentage from the shares.

[Ans: (i) 100 (ii) 600 (iii) 7.5%]


10:30 - 11:00 AM Free

11:00 – 01:30 PM - PRACTICE ANY ONE MODEL TEST PAPER TIME BOUND

01:30 – 02:00 PM – SELF EVALUATE PRACTICE PAPER AND NOTEDOWN YOUR MISTAKES

02:00 – 04:00 PM - LUNCH & SLEEP

8:30 - 9:30 AM - LINEAR INEQUATION

4:00 - 6:00 PM - SHARES AND DIVIDENDS


T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS





Q5. Mr. Roy buys 500 ten - rupee shares of a company at Rs. 15each. from the stock market. The company pays 14% dividendannually. Find(i) The investment of Mr. Roy in Shares (ii) his annual income fromthe shares, and

(iii) the rate of return from the shares.

[Ans: (i) 7500 (ii) 700 (iii) 9.33%]

Q6. A man invest a sum of money in Rs. 100 shares, paying 15%dividend quoted at 20% premium. If his annual dividend is Rs. 540,calculate. (i) his total investment and (ii) the rate of return on hisinvestment. [Ans: Rs. 4320, 2.5%]

Q7. A lady holds 1,800 shares of a company of Rs. 100 par value. Thecompany pays 15% dividend annually. Calculate her annualdividend. If she had bought these shares at 40% premium whatpercentage return does she get on her investment? Give youranswer to the nearest integer. [Ans: (i) 27000 (ii) 11%]

Q8. Arun owns 560 shares of a company. The face value of eachshares is Rs. 25. The company declares a dividend of 9%calculate.

(i) The dividend Arun would received and [Ans: 1260]

(ii) The rate of interest on his investment, considering that Arunbought these shares at rate of Rs. 30 per share in the market.

[Ans: 7.5%]

Q9. Mr. Bansal has some Rs. 100 shares of a company paying 10%dividend. He sells some of the shares at a discount of 20% andinvests the proceed in Rs. 100 shares of another company paying15% dividend whose M.V. is Rs,. 80. If his income from his shareholding increases by Rs. 1,800. find the number of shares of thefirst company that he sold. [Ans: Rs 360, Rs 1500]

Q10. Mr Singh invested Rs. 8000 in 7% hundred rupee shares at Rs.80. After a year he sold these shares at Rs. 75 each and investedthe proceeds in 18% Rs. 25 shares at Rs. 41. Find :(i) his gain or loss after a year(ii) his annual income from the second investment(iii) the percentage of increase in return on his original invest-ment. Ans.: (i) Rs. 200 (ii) Rs. 900 (iii) 2.5%

Q7. Mukul invests Rs 9000 in a company paying a dividend of 6% perannum when a share of face value Rs. 100 stands at Rs 150.What is his annual income? He sells 50% of his shares when theprice rises to Rs. 200. What is his gain on this transaction?

Ans.: Rs. 360, Rs. 1500

Q8. Mr. Anuja sold a certain number of shares of Rs 20 paying 8%dividend at Rs. 18 and invested the proceeds in Rs. 10 shares,paying 12% dividend at 50% premium. If the change in her annualincome in Rs. 120, find the number of shares sold by her.

Ans.: 750 shares

Q8. A man invests Rs 6750, partly in shares of 6% at Rs 140 andpartly in shares of 5% at Rs 125. If his total income is Rs 280, howmuch has he invested in each? Ans.: Rs. 3500, Rs. 3250

Q1. (i) If (a - x) : (b - x) be the duplicate ratio of a : b, show that

x1

= a1

+ b1

. (ii) If (2a - x) : (b - 2x) be the sub-duplicate ratio

of a : b, show that x2 = ab.

Q2. (i) If 9x - 11y = 4x + 13y, find the value of 22

22

yxyx

.[Ans551601

]

(ii) If yxyx

5353

= 37

, find x : y.. [Ans x : y = 25 : 6]

Q3. If 2222 y11x8y3x212 , Find (4x + y) : (4x - y).Ans.: 3 : 2

Q4. If x, 5, 10, y are in continued proportion, then find x and y. [Ans. x = 5/2, y = 20.]

Q5. Find the fourth proportional to (a2 - 5a + 4), (a2 + a - 2) and (a2 -16). [Ans. a2 + 6a + 8]

Q6. If a = 2

cb , c =

2ba

and b is the mean proportional of a and

c, prove that a1

+c1

= b2

.

Q7. If b is the mean proportional of a and c, then show that:(i) abc (a + b+ c)3 = (ab + bc + ca)3

(ii) 222

222

cbacba

= b4.

Q8. If a, b, c are in continued proportion, then prove that

(i) 222

333

cbacba

= 3

1a + 3

1b + 3

1c .

(ii) )()(

222

2

cbacba

= cbacba

.

Q9. If (a2 + c2) (b2 + d2) = (ab + cd)2, prove that ba

= dc

.

Q10. If x = babababa

3333

,

prove that 3bx2 - 2ax + 3b = 0

Q11. If x = 32

64

, then f ind the value of

3232

2222

xx

xx

. [Ans. 2]

Q12. Using the properties of proportion, solve for x :

x163

x12xx1xx1

2

2

Ans.: x =

51

Q13. Using the properties of proportion, solve for x :

91341

1x3x3x

2

3

Ans.: x = 1


06:00 – 07:00 PM - Free

7:00 - 9:00 PM - RATIO AND PROPORTIONMemorise and write all formulae and basic concepts

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS





1. Distance formula - = 2122

12 yyxx .

2. Section formula -

21

1221

21

1221 ,mm

ymymmm

xmxm

3. Mid point formula -

2

,2

2121 yyxx.

4. Centroid Formula -

3

,3

321321 yyyxxx .

5. Slope of a line -(i) If the inclination of a line is its slope tanm .

(ii) Slope of a line 12

12

xxyym

.

6. Equation of a straight line -(i) Equation of a line parallel to x-axis is y = b(ii) Equation of a line parallel to y-axis is x = a(iii) slope form of a line y = mx + c

(iv) Equation of a line through 11 , yx and with slope m is

11 xxmyy .7. Condition of parallelism and perpendicularity

Two lines with slopes 1m and 2m are

(i) Parallel if and only if 1m = 2m

(ii) Perpendicular if and only if 121 mm .

Q1. Find the distance between the points (a, a) and 3,3 aa .

[Ans: 22a unit]Q2. What point(s) on the y-axis are at a distance of 10 units from the

point (-8, 4)? [Ans: (0, 10) & (0, -2)]Q3. If P(x, y) is equidistant from A(a+b, b - a) and B(a - b, a + b), show

that bx = ay.Q4. Find a point on the y-axis which is equidistant from (3, 2) and (-

5, -2). [Ans: (0, -2)]Q5. If (3, 2), (-3, 5) and (x, y) are collinear show that

x + 2y - 7 = 0.Q6. Find the coordinates of the centre of a circle which passes through

the points A(1, 2), B(3, -4) and C(5, -6). Also, find the radius of thecircle. [Ans: (11, 2) & 10 units]

Q7. Show that the points A(5, 6), B(1, 5) C(2, 1) and D(6, 2) are thevertices of the square.

Q8. The line joining the points A(2, -5) and B(-5, 9) is divided by thepoint P such that AP : AB = 3 : 4, find the coordinates of P.

[Ans: (-1, 1)]Q9. Find the co-ordinates of the points of trisection of the line segment

joining the points (2, 3) and (6, 5) . [Ans: (10/3, 11/3) & (14/3, 13/3)]


09:00 – 10:00 PM - Dinner

10:00 - 12:00 AM - DISTANCE & SECTION FORMULA


Q10. The centroid of a triangle whose vertices are (2, 4), (3, k) and (4,2) is (k, 3) find the value of k. [Ans: 3]

Q11. The line joining P(-4, 5) and Q(3, 2) intersects the y-axis at R. PMand QN are the perpendiculars from P and Q on the x-axis. Find :(i) the ratio PR : RQ (ii) the coordinates of R (iii) the area of quad.PMNQ.[Ans: (i)4:3(ii)(0,23/7)(iii) 24.5]

Q12. Prove that the diagonals of a rectangle bisect each other at apoint.

Q13. Find the length of the medians of a triangle whose vertices areA(-3, 3), B(-7, -7) and C(1, 1). [Ans: AD = 6units, BE = 313units & CF = 35 units]


12:00 – 06:00 AM - Sleep

6:30 - 8:30 AM - EQUATION OF ST. LINE



Q1. Prove that the lines 3x - 2y -1 =0 and 6y -9x +5 = 0 are parallel.Q2. prove that the lines 5x + 4y =9 and 4x-5y=1 are perpendicular to

each other.Q3. Find the value of a if the lines 7y = ax + 4 and 2y=3-x are (1)

parallel, (2) perpendicular. [Ans: (i) 7/2 (ii) a = 14]Q4. Find the equation of line passing through the points (0, 4) and is

parallel to the line 3x+5y+15=0. [Ans: 3x + 5y = 20]Q5. Find the equation of the line passing thgourh the points (-2,0) and

perpendicular to the line 4x-3y=2. [Ans: 3x + 4y + 6 = 0]Q6. Find the equation of a line which has the y-intercept 4 and is

parallel to the line 2x-3y =7. Find the coordinates of the pointswhere it cuts the x-axis. [Ans: (-6, 0)]

Q7. Find the equation of line passing through the intersection of thelines 3x+2y =7 and x-y+1=0 and (i) parallel to 2x+y=0 (ii)perpendicular to the x-axis. [Ans: 2x + y = 4 (ii) x = 1]

Q8. Find the equation of perpendicular bisecetor of the line segmentjoining the points (7, -3) and (1, 9). [Ans: x - 2y + 2 = 0]

Q9. Find the coordinates of the foot of the perpendicular droppedfrom the point P(3, 1) to the line AB whose equation is 2x-y =3.

[Ans: 11/5, 7/5]Q10. Find the coordinates of the image of the point A(3, - 4) When

reflected in the line x + y = 2. [Ans: 6, -1]Q11. ABCD is a rhombus. The coordinates of the point A and C are (3,

6) and (-1, 2) respectively. Write down equation of diagonal BD.[Ans: x + y = 5]

Q12. A points A(2, 3), B(3, 5) and C(-1, -1) are the vertices of triangleABC. Find the equation of the altitude of the triangle through A.

[Ans: 2x + 3y = 13]Q13. A(2, 4), B(3, 3) and C(-1, 5) are the vertices of triangle ABC. Find

the equation of(i) The median of triangle through A. (ii) The altitude of trianglethrough B. [Ans: 8x + 4 = 12]

Q14. A(1, 4), B(3, 2) and C(7, 5) are vertices of ABC,Find(i) coordinates of centroid G of triangle. (ii) equation of the throughG parallel to AB. [Ans: ( 11/3, 11/3) x + y = 22/3]

Q15. (a) Prove that the lines whose equations are2x+y=3; x-y =4; 4x + 2y =1 and x-y+2=0 form a parallelogram.(b) Prove that the lines whose equations are x + y = 3; x -y +1 =0, 2(x + y) = 5, 3(x-y) = 4 form a rectangle.

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS





Q1. Write down the coordiantes of the image of the point (3, -2),when(i) reflected in the x-axis.(ii) reflected in the y-axis.(iii) reflected in the x-axis followed by the reflection in the y-axis.(iv) reflected in the origin. [Ans.: (i) (3, 2) (ii) (-3, -2)(iii) (-3, 2) (iv) (-3, 2)]

Q2. A point P is mapped onto P’ when reflected in the y-axis and P’ ismapped onto P” when reflected in the x-axis. If the coordiantes ofP” are (-7, 4), find the coordinates of P. [Ans: (7, -4)]

Q3. The point P’ (-4, -3) is the image of a point P under reflection in theorigin. Find the cooridnates of P. Also, find the coordinates of theimages of P under reflection in the line. (i) x = 1 (ii) y = -2 (iii) x= - 4 [Ans: (i) (-2, 3) , (ii) (4, -7) (iii) (-12, 3)]

Q4. A point M(3, 2) is reflected in the line x = 5 to the point M1. Theimage M1 is then reflected in the line y = a to the point M2 (7, -4).Find the value of a. [Ans: a = -1]

Q5. Use a graph paper for this question.The points A(2, 3), B(4, 5) and C (7, 2) are vertices of ABC.(i) Write down the coordinates A’, B’ and C’ if DA’B’C’ is the image

of ABC, when reflected in the origin.[Ans: A’(-2, -3), B’ (-4, - 5) and C’ (-7, -2)].

(ii) Write down the coordinates A”, B” and C” if A”B”C” is the

image of ABC, when reflected in the x-axix.[Ans: A”(2, -3), B” (4, - 5) and C” (7, -2)].

(iii) Mention the special name of the quadrilateral BCC”B” and findits area. [Ans: Isosceles trapezium, 21 sq units].

Q6. Use a graph paper for this question (Take 10 small divisions = 1unit on both the axes).Plot the points P(3, 2) and Q (-3, -2). From P and Q drawperpendiculars PM and QN on the x-axis.(i) Name the image of P on reflection in the origin.(ii) Assign a special name to the geometrical figure PMQN and findits area.(iii) Write the coordinates of the point on which M ismapped on reflection in (a) x-axis (b) y-axis (c) origin.

[Ans: (i) Q (-3, -2), (ii) ||gm, 12sq. unit(iii) (a) 3, 0 (b) (-3, 0) (c) (-3, 0) ]

(iv) sin90cos,cos90sin

(v) tan90cot,cot90tan

(vi) sec90cos,cos90sec ececProve that :Q1. Cos4 A - sin4 A = 2 cos2A - 1.

Q2. tan

coscos2sin2sin

3

3

Q3. AA

AA

A sec2sin1

coscos

sin1

Q4.A

AAA

cos1sin

cos1cos1

Q5. tan4A + tan2A = sec4A - sec2A

Q6. tan 2 A + cot 2 A + 2 = sec 2 A . cosec 2 A

Q7. AecAAAAA

cossec1sincos

11sincos

1

Q8.

eccossec1

tan1cot

cot1tan

Q9. 1sin22

cossin2

cossincossin

cossincossin

222

Q10. 4222 sinsin1

cot11

tan11

Q11. Evaluate : (i) 02

2

0

02

0

0

45tan239sin51cos

51cos39sin

(ii)

0

0

0

0

12tan78cot

55cot35tan

[Ans: (i) 0 (ii) 2]

Q12. Evaluate : (i) 000 66cos24cos54sec.36sin ec

(ii) 0000 27sin63cos27cos.63sin [Ans: (i) 1 (ii) 1]

Q13. Prove that

190sec90cos

90cos90sin

AA

AecA

.

Q14. If 06cos3sin , find the value of . [Ans: 24]

Q15. Prove that: AecAA

AA

A cossec90cos

cos90sin

sin

.


08:30 – 09:30 AM - Free and breakfast

9:30 - 10:30 AM - REFLECTION


9:30 - 10:30 AM - REFLECTION


10:30 – 11:00 AM - Free

11:00 - 01:30 PM - PRACTICE ANY ONE MODELTEST PAPER TIME BOUND


01:30 – 02:00 PM - SELF EVALUATE PRACTICE PAPER AND NOTEDOWN YOUR MISTAKES

02:00 – 04:00 PM - LUNCH & SLEEP

4:00 - 06:30 PM - TRIGONOMETRY

(i) 122 cossin (ii) 22 sectan1 (iii) 22 cot1cos ec


06:30 – 07:00 PM - Free

7:00 - 9:00 PM - HEIGHT AND DISTANCE


Q1. The angles of depression of two ships from the top of a lighthouse are 450 and 300 towards east. If the ships are 200 metresapart, find the height of the light house. [Ans: 273.2m]

Q2. An aeroplane, when 3000 m high, passes vertically above anotheraeroplane at an instant when the angles of elevation of the twoaeroplanes from the same point on the ground are 600 and 450

respectively. Find the vertical distance between the two planes.[Ans: 1268m]

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS




LAST MINUTE PACKAGE :- ICSE - XQ3. An aeroplane flying horizontal 1 km above the ground is observed

at an elevation of 600. After 10 seconds its elevation is observedto be 300. Find the speed of the plane. [Ans: 415.66km/hr.]

Q4. From a window (60 metres high above the ground) of a house ina street the angles of elevation and depression of the top and thefoot of another house on opposite side of the street are 600 and450 respectively. Show that the height of the opposite house is

60(1+ 3 ). [Ans: 163.92m]

Q5. Two men are on the opposite sides of a tower, They measure theangles of elevation of the top of the tower as 300 and 450. If theheight of the tower is 60m, find the distance between them.

[Ans: 163.92m]Q6. The angles of elevation of the top of a tower from two points P

and Q at distances of 'a' and 'b' respectively from the base and inthe same line with it are complementary. Prove that the height of

the tower is ab .

Q7. The shadow of a vertical tower on level ground increases by 10metres when the altitude of the sun changes from 450 to 300. Findthe height of the tower. [Ans: 13.65m]

Q8. A straight highway leads to the foot of a tower. A man standing atthe top of the tower observes a car at an angle of depression of300, which is approaching the foot of the tower with a uniformspeed. Twelve second later, the angle of depression of the car isfound to be 600. From find the time taken by the car to reach thefoot of the tower from this point. [Ans.: 6 s]

Q9. The angle of elevation of a Jet plane from a point A on the groundis 600. After a flight of 15 seconds, the angle of elevation changes

to 300. If the jet Plane is flying at a constant height 1500 3 m,find the speed of the Jet Plane. [Ans: 720km/hr.]

Q10. The angle of elevation of a cloud from a point 200m above the lakeis 300 and the angle of depression of its reflection in the lake is600. Find the height of the cloud. [Ans: 400m]

Q11. An observer, 1.70 m tall, is 12.90m away from a tower 14.60 mhight. Determine the angle of elevation of the top of the towerfrom his eye. [Ans: = 450]

(b) In the figure given along-side, there are four equal quad-rants of circles each of radius3.5 cm, their centres being P,Q, R and S. [Ans: 10.5cm2]

Q5. The given figure shows arunning track surrounding a grassed enclosure PQRSTU. Theenclosure consists of a rectangle PQST with a semicircularregion at each end. PQ= 200m; PT=70m.(i) Calculatethe area of thegrassedenclosure inm2.(ii) Given thatthe track is ofa constantwidth of 7m,calculate theouter perimeter ABCDEF of the track.(Use = 22/7) [Ans: 64]

Q6. In the f igure givenalongside, AB=21 cm isthe diameter of asemicircle with C as thecentre. ABC and CEB aresemicircles withdiameters AC and CBrespectively.[Ans: 173.25cm2]

Q7. In the figure given, ABC is a right angledtriangle, B = 900,AB = 28 cm and BC = 21 cm. With AC asdiameter a semicircleis drawn and with BC as radius aquarter circle is drawn. Find the areaof the shaded region correct to two decimal places.

[Ans.: Ans.: 428.75 cm2]

Q8. The given figure showsa piece of cardboard inthe shape of a trapeziumABCD, where AB||DCand BCD=900. AAquarter circle BFEC isremoved from hecardboad. GivenAB=BC=3.5 cm and DE=2 cm. Calculate the area of the remainingpiece of he cardboad. (Take = 22/7)

[Ans: 86.625cm2]

O

A B

CD 14 cm

3.5 cm

3.5 cm

A P

B

C QR

D

S

E D

CR

B

Q

ST

P

A

F U


09:00 – 10:00 PM - Dinner

10:00 - 12:00 AM - AREA RELATED TO CIRCLEMemorise and write all formulae and basic concepts

Q1. The area of a circular ring enclosed between two concentriccircles is 286 cm2. Find the radii of the two circles, given that theirdifference is 7 cm. . [Ans: 10 cm and 3cm.]

Q2. A plot of land is in the shape of a sector of a circle of radius 28 m.If the sectorial angle (central angle) is 600, find the area and theperimeter of the plot. (Use = 22/7) [Ans: 85.33m]

Q3. Each wheel of a car is making 5 revolutions per second. If thediameter of a wheel is 84 cm, find thespeed of the car in km/h. Give youranwer correct to the nearest km[Ans:48km/hr.]

Q4. (a) In the adjoining figure, ABCD is asquare of side 14 cm and O is the centreof the circle touching all sides of thesquare. [Ans: 42cm2]

BC

D

A

E

28 c

m

21 cmB

A

C

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS





Q1. A chord of length 10 cm is at a distance of 12 cm from the centreof a circle another chord of the same circle is of length 24 cm.Findits distance from the centre. [Ans.:5 cm]

Q2. In the figure a chord PQ of a circle with centre C and radius 15 cmis bisected at M by a diameter AB. If CM=9 cm, calculate (i) PQ (ii)AP (iii) BP.

P QB

M

C

A

Q3. l is a line which interects two concentric circles (i.e. circles withthe same centre) with cmmoncentre O at A, B, C and D. Prove that AB=CD.

A DB C

O

Q7. In fig. AB and CD are equal chords of a circle with centre O.If AB and CD meet at E (outside the circle) prove that (i) BE = DE.(ii) AE = CE


12:00 – 06:00 AM - Sleep

06:30 - 09:00 AM - CIRCLEMemorise and write all formulae and basic concepts

DATE : 7 MARCH (6 to 6:30 AM be fresh)

Q9. A bucket is raised from a well by means of a rope which is woundround a wheel of diameter 77 cm. Given that the bucket ascendsin 1 minute 28 seconds with a uniform speed of 1.1 m/s, calculatethe number of complete revolutions the wheel makes in raisingthe bucket. (Take = 22/7). [Ans: 40]

Q10. In the f igure givenalongside, ACB is asemicircle whose diam-eter is 21 cm and C is apoint on the semicircleat a distance 7 cm fromB. [Ans: 104.16cm2]

Q1. In the given fig. find : (i) BCD (ii) ADC (iii) ABC

[Ans: (i) 750 (ii) 750 (iii) 1050]

Q2. In the given fig. O is the cenre of the circle. If AOB = 1400 and OAC = 500, Find(i) ACB (ii) OBC(iii) OAB (iv) CBA.

Ans.: (i) 1100 (ii) 600 (iii) 200 (iii) 400

Q3. In the given fig. O is the entre of the circle and ABC

is equilateral. Find (i) ADB (ii) AEB.

[Ans.: (i) 600 (ii) 1200 ]

Q4. In the given fig., AB is a diameter of the circle APBR. APQ andRBQ are st. lines A=350 and Q = 250

find : (i) PRB (ii) PBR (iii) BPR

[Ans.: (i) 350 (ii) 1150 (iii) 300]

O

A

C

B

D

E

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS





Q5. In the figure, O is the centre of the circle, AOE =1500, DAO=510. Calculate the size of the angles CEB and OCE.

[Ans.: (i) 510 (ii) 240]

Q6. In fig. P and Q are the centres of the two circles intersectingat B and C. Find x .

[Ans.: x = 1300]Q7. In the fig. O is the centre of the circle and PQ=QR=RS

and PTS=750, Find (i) POS (ii) QOR (iii) PQR

Ans.: (i) 1500 (ii) 500 (iii) 1300

Q8. In the given fig. length of the arc AB and are BC are inthe ratio 3:2. If angle AOB = 960, find (i) CAB (ii) ACB.

[Ans. (i) 320 (ii) 480]

Q9. In the given fig., AB is a chord of the circle with centreO, BT is a Tangent to the circle and 032OAB . Findthe values of x and y. if AB = AY find ACY .

y

Y

O

A320

B

C

T

x

[Ans. x=58º, y=58º, ACY 116 ]

Q1. ABCD is a quadrilateral such that A =900. A circle with centre O, touches thesides AB, BC, CD and DA at E,F,G,Hrespectively. If CD = 30Cm, AD = 15cmand CF = 20cm, find the radius of thecircle. [ Ans.: 5 cm ]

Q2. In the given figure, O is the centre ofthe circle . If PA = 12cm, PC = 15cm,CD = 7cm, find the length of AB.[ Ans.: 2 cm]

Q3. In the given figure, O is thecentre of the circle. Determine:(i) AMB (ii) AQB. If thetangent at A and B to thecircle meet at P and BPA =750.

[Ans.: (i) AMB = 127 ½ 0

(ii) AQB = 52½0 ]Q4. n the given figure, ABCD is a

cyclic quadrilateral. Thetangents to the circle at the pointA and C intersect at P. if ABC

= 1200, find APC[ Ans.: APC = 600 ]

Q5. In the given figure, O is the centre ofthe circle and AB is a chord of thecircle. Line QBS is a tangent to thecircle at B. If AOB = 1120, find APB and ABQ.[ Ans.: APB = 560 and ABQ =560 ]

Q6. In figure, O is the centre of a circle andB is the mid- Point of the arc ABC. IfDAE is the tangent to the circle at Aand if DAB = 650, find CAB and COA.Ans.: CAB = 650 and COA=1000

Q7. In figure, AB and AC are tangent atB and C respectively to the circlethrough B, C,D. If BAC = 700 and BCD = 900, then find the value of CBD. Ans.: CBD = 350

900AE B

F

CD G

H O

B

Q P

A

O M750

O

A

B C

650

D E


09:00 – 09:30 PM - Fre and breakfast

09:30 - 10:30 AM - FACTOR THEOREMMemorise and write all formulae and basic concepts

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS





Q1. Find the remainder (without actual division) on dividing thefollowing: 2x3 + 3x2 + 7x + 6 by (2x + 1) [Ans: 3]

Q2. What number should be added to x3 + 2x2 - 13x such that whenthe resulting polynomial is divided by (x - 3), the remainder is 4?

[Ans: -2]Q3. The polynomials p(x) = kx3 + 3x2 - 3 and g(x) = 2x3 - 5x + k when

divided by (x - 4) leaves the same remainder in each case, findthe value of k. [Ans: k = 1]

Q4. Given that ( x- 2) and (x + 1) are factors of x3 + 3x2 + ax + b, findthe values of a and b. [Ans: a = -6, b = -8]

Q5. Show that (3x + 5) is a factor of 3x 3 + 5x2 - 9x - 15. Hence,factorise 3x3 + 5x2 - 9x - 15. [Ans: (3x + 5) ( x + 3) ( x - 3)

Q6. Using factor theorem, factorise each of the followingpolynomials: 2x3 + 9x2 + 7x -6

[Ans: (x + 2) ( 2x - 1) (x + 3)]Q7. If (x + a ) is the HCF of x2 + px + q and x2 + lx + m, then show that

a = lpmq

.

Q1. A solid consists of three parts. The middle part is a right cylinderof radius 3.5 cm. On one side of it there is a hemisphere of thesame radius and on the other side there is a cone of the sameradius. The height of the cylinder is 7 cm and the total height of thesoild is 15 cm. Find the volume and the surface area of the solid.

[Ans: 293.7cm2]Q2. A solid metallic sphere of radius 9 cm is melted and the meterial is

used to make solid right cones with height 4 cm and radius of thebase 9 cm. How many cones were made? [Ans: 9]

Q3. A solid metallic right cone is melted and a number of solid rightcylinders are made with the material. Find the number of cylindersif the radius of the base of each cylinder is half the radius of thecone and the height of each cylinder is one-third the height of thecone. [Ans: 4]

Q4. A hemispherical cup of radius 4 cm is filled to the brim with coffee.The coffee is then poured into a vertical cone of radius 8 cm andheight 16 cm. What percentage of the cone remains empty?

[Ans: 87.5]Q5. The surface area of a solid metallic sphere is 1,256 cm2. It is

melted and recast into solid right circular cones of radius2.5 cm and height 8 cm. Calculate(a) the radius of the solid sphere, and (b) the number ofcones recast. (Take = 3.14) [Ans: (i) 10 (ii) 80]

Q6. A cylindrical can whose base is horizontal and internal radius 3.5cm contains sufficient water so that when a solid sphere is placedin the can, water just covers the sphere. Given that the spherejust fits in the can, calculate.(i) the total surface area of the can in contact with water whenthe sphere is in it, and [Ans: 192.5cm2]


10:30 – 11:00 AM - Free



01:30 - 02:00 PM - SELF EVALUATE PRACTICE PAPER ANDNOTE DOWN YOUR MISTAKE

02:00 – 04:00 PM - Lunch & Sleep

04:00 - 06:00 PM - MENSURATION

(ii) the depth of water in the can before the sphere was put intothe can. (Take =22/7) [Ans: 7/3cm]

Q7. A solid right cylinder is 18 cm in height and the radius of its baseis 7 cm. Two equal right cones are drilled on the plane faces of thecylinder, the height of each cone being one-third the height of thecylinder and the radius of the base of each cone being equal tothe base of the cylinder. Find (a) the volume of the remainingsolid, and(b) the total surface area of the remaining solid.

[Ans: (a) 2156cm3 (b) 1197.6cm2]Q8. An exhibition tent is in the form of a cylinder surmounted by a

cone. The height of the tent above the ground is 85m and theheight of the cylindrical part is 50m. If the diameter of the base is168m, find the quantity of canvas required to make the tent. Allow20% extra for folds and for stitching. Give your answer to thenearest m2. [Ans: 60509m2]

Q1. If ABC Construct triangle ABC, with AB = 7 cm, BC = 8 cm and

ABC = 60°. Locate by construction the point P such that : (i) Pis equidistant from B and C and (ii) P is equidistant from AB andBC (iii) Measure and record the length of PB.

Q2. AB and CD are two intersecting lines. Find the position of a pointdistant 2 cm from AB and 1.6 cm from CD.

Q3. Without using set squares or protractor construct:(i) Triangle ABC, in which AB = 5.5 cm, BC = 3.2 cm and CA = 4.8 cm.(ii) Draw the locus of a point which moves so that it is always 2.5

cm from B.(iii) Draw the locus of a point which moves so that it is equidistant

from the sides BC and CA.(iv) Mark the point of intersection of the loci with the letter P and

measure PC.Q4. Without using set squares or protractor, construct a triangle ABC

in which AB = 4 cm, BC = 5 cm and ABC = 120°.(i) Locate the point P such that BAP = 90° and BP = CP..(ii) Measure the length of BP.Q5. Construct an isosceles triangle ABC such that AB = 6 cm, BC = AC

= 4 cm. Bisect C internally and mark a point P on this bisectorsuch that CP = 5 cm. Find the points Q and R which are 5 cm fromP and also 5 cm from the line AB.

Q6. Use ruler and compasses only for this question. Draw a circle ofradius 4 cm and mark two chords AB and AC of the circle oflength 6 cm and 5 cm respectively.(i) Construct the locus of points, inside the circle, that areequidistant from A and C Prove your construction.(ii) Construct the locus of points, inside the circle, that areequidistant from AB and AC.

Q7. Ruler and compasses only may be used in this question. Allconstruction lines and arcs must be clearly shown, and be ofsufficient length and clarity to permit assessment. (i) Construct atriangle ABC, in which BC = 6 cm, AB = 9 cm, and ABC = 60°.

(ii) Construct the locus of all points, inside ABC, which areequidistant from B and C (iii) Construct the locus of the vertices ofthe triangles with BC as base, which are equal in area to ABC


06:00 – 07:00 PM - Free


07:00 - 09:00 PM - LOCUS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS





(iv) Mark the point Q, in your construction, which would make

QBC equal in area to ABC, and isosceles.(v) Measure and record the length of CQ.

Q1. If ABC and PQR QB and QRBC

PQAB

.

If 9

25

PQRarABCar

and BC = 10 cm, find QR.

Q2. In ABC, 090B , AB = 12cm and AC =15 cm. D and E arepoints on AB and ACrespectively such that AED= 900 and DE = 3 cm.

(i) find the area of ADE(ii) Find :

ABCar

ralquadrilatear

BCED

Q3. In MNPQLMN ||, such thatLP = 2 cm and PM = 6 cm. Also MN =20 cm. (i) Find PQ

(ii) Find

LPQarPQNMtrapziumar

.

Q4. In ABC, D and E are pointson AB and AC respectivelysuch that DE || BC, and DEdivides the triangle into twoparts equal in area. Find theratio into which D divides AB.

Q5. Construct a ABC so that BC = 3.5 cm, B = 600 and the areaof ABC is 7 cm2. Construct PQR which is similar to ABCand has area equal to 28 cm2.

Q6. Prove that the area of the triangle BCE described on one side BCof a square ABCD as base is one half the area of the similartriangle ACF described on the diagonal AC as base.

Q7. In a triangle DE is drawn parallel to BC. Area of the triangle ABC =25 cm2, area of the trapezium BCED=24 cm2, DE =14 cm. Calculatethe length of BC.

Q8. An iron tank has length 4 m and width 3 m, and it can contain 30m3 of water. A small model of the tank is made and its volume is240 cm3. (a) Find the dimensions of the model (b) Find the ratiobetween the total surface areas of the tank and its model.

Q9. A map of a square plot of land is drawn to a scale of 1:25,000. Ifthe area of the plot in the map is 72 cm2, find :(a) the actual area of the plot of land, and (b) the length of thediagonal in the actual plot of land.

M N

L

20 cm

QP2cm

6cm

B

A

D

C

E

A

DE

CB

12 cm3 cm 15 cm


09:00 – 10:00 PM - Dinner


10:00 - 12:00 AM - SIMILARITY


12:00 to 06:00 am - Sleep


06:30 - 8:30 AM - PROBABILITY


Q1. A die is tossed once, Find the probability of getting.(i) number 4(ii) a number greater than 4 (iii) a number less than 4(iv) an even number (v) a number greater than 6(vi) a number less than 7.

Ans.: (i) 16 (ii)

13 (iii)

12 (iv)

12 (v) 0 (vi) 1

Q2. A bag contains 5 red, 4 green and 6 white balls. If a ball is drawnat random from the bag, find the probability that it will be (i) white(ii) red (iii) green.

Ans.: (i) 25 (ii)

13 (iii) 1

Q3. Find the probability of having 53 Sunday in

(i) a non-leap year (ii) a leap year. Ans.: (i) 17 , (ii)

27

Q4. From a pack of 52 cards, a black jack, a red queen and two blackkings fell down. A card was then drawn from the pack at random.Find the probability that the card drawn is (i) a black card ( ii) aking(ii) a red queen

Ans.: (i) 2348 (ii)

124 (iii)

148

Q5. A box contains 17 cards numbered 1,2,3,.....17 and are mixedthoroughly. A card is drawn at random from the box. Find theprobability that the no. on the card is. (a) odd (b) even (c) prime(d) divisible by 3 (e) divisible by 3 or 2 both (f) divisible by 3 or 2.

Ans. (a)9/17 (b) 8/17 (c) 7/17 (d) 5/17 (e) 2/17 (f) 11/17Q6. A box has card numbered 14 to 99. Cards are mixed throughly

and a card is drawn at random from the box. Find the probabilitythat the card drawn from the box has(i) an odd number (ii) a perfect square number

Ans.: (i) 12

(ii) 3

43Q7. Cards marked with numbers 2 to 101 are are placed in a box and

mixed thorughly. One card is drawn at random from this box. Findthe probability that the number on the card is(i) an even number (ii) a number less than 14(iii) a number which is a perfect square(iv) a prime number less than 30.

Ans.: (i) 12

(ii) 3

25 (iii)

9100

(iv) 1

10Q8. A jar contains 24 marbles; some are green and others are blue. If

a marble is drawn at random from the jar, the probability that it isgreen is 2/3. Find the number of blue marbles in the jar.

Ans.: 8Q9. Two dice are rolled together, Find the probability of getting :

(a) doublet (b) a sum of 7(c) a sum of 11 (d) a sum greater than 11

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS




LAST MINUTE PACKAGE :- ICSE - X(e) a sum less than 5 (f) a sum of 13

(g) a sum less than or equal to 12

Ans.: (a) 16

, (b) 16

, (c) 1

18,

(d) 136

, (e) 16

, (f) 0 (g) 1

Q10. A bag contains 8 green balls and some red balls. If the probabil-ity of drawing a red ball is half of a green ball, then find thenumber of red balls in the bag. Ans.: 4


08:30 to 09:30 AM - free and breakfast


09:30 - 10:30 AM - MATRICES

Q1. Construct a 2 2 matrix whose elements are ai j

ij 2

2

2b g.

Ans.:

12

92

0 2

LNMM

OQPP

Q2. If A B

LNM

OQP2

5 1

3 4 and 2

5 2

4 3A B

LNM

OQP

find A & &

B. Ans.: A BL

NMOQP

LNM

OQP

3 11 2

1 02 2

,

Q3. If A LNM

OQP

1 2

3 1, B

LNM

OQP

2 1

0 4 C

LNM

OQP

3 2

0 1. Show that

A B C AB AC b g .

Q4. If A BLNM

OQP

LNM

OQP

3 02 5

1 64 0

, and C LNM

OQP

2 1

1 3 . Find the

value of (i) A - B + 3C Ans.: 8 35 14

LNM

OQP

Q5. Given 5 21 4

120

LNM

OQP

LNM

OQPX . Write down (i) the order of the

matrix X (ii) the matrix X. Ans.: (i) 2 x 1 (ii) 22LNMOQP .

Q6.

(a) Let A and find A 2LNM

OQP

LNM

OQP

1 02 1

2 31 0

2B AB B, .

(b) If 23 45 xLNM

OQP

LNM

OQP

LNM

OQP

10 1

7 010 5

y, find the value of x and y.

Q7. If f x x xb g 2 2 3 find f Ab g where A LNM

OQP

1 22 1 .

Ans.: 0 00 0LNM

OQP

Q8. Given A B

LNM

OQP

LNM

OQP

2 12 0

3 24 0

, and C

LNM

OQP

1 00 2 . find

the matrix X, such that A + X = 2B + C.

Ans.: 4 11 6LNM

OQP


10:30 – 11:00 AM - Free



01:30 - 02:00 PM - SELF EVALUATE PRACTICE PAPER ANDNOTE DOWN YOUR MISTAKE

02:00 – 04:00 PM - Lunch & Sleep

04:00 - 06:00 PM - CONSTRUCTION

Q1. Take a point O on the plane paper. With O as centre draw a circleof radius 3.0 cm. Take a point P on this circle. Draw a tangent at P.

Q2. A student drew a circle of radius 2.5 cm. But the mark of thecentre was some how missed. At a given point P on the circle,draw a tangent, without knowing the centre of the circle.

Q3. Draw a circle of radius 2.8 cm. take a point P outside the circle ata distance of 6.2 cm from the centre. Draw two tangents to thecircle from point P.

Q4. Using ruler and compasses only, construct a triangle ABC suchthat AB = 4 cm, BC = 6 cm and B = 600. Draw the circumscribedcircle of the triangle and measure its radius.

Q5. Using ruler and compasses only construct a ABC with BC =6.4 cm, CA = 5.8 cm and B = 600. Draw the in circle of thetraingle and state its radius.

Q6. Using ruler and compasses only construct a ABC with sidesBC = 2.8 cm, CA = 3.5 cm and AB = 4.5 cm. Draw the escribedcircle to the ABC so that the circle touches the side BC.Measure the radius of the circle.

Q7. Construct a circle in a regular hexagon of side 3 cm.

Q8. Construct a circle of about a regular hexagon of side 2.5 cm.

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS

T IW

ARI T

UTO

RIA

LS

T

IWAR

I TU

TOR

IALS






06:00 – 07:00 PM - Free


07:00 - 09:00 PM - STATISTICS

Q1. Find the mean, median and mode of the following arranged data :0,2,2,3,3,3,4,5,5,5,5,6, 6, 7, 8, 8. [Ans : 4.5, 5, 5]

Q2. If the numbers 25, 22, 21, x + 6, x +4, 9, 8, 6 are in order and theirmedian is 16, find the value of x. [Ans : 11]

Q3. The following data represent the number of books issued by alibrary on 12 different days :96, 180, 98, 75, 270, 80, 102, 100, 94, 75, 200, 610Find the (i) lower quartile (ii) upper quartile (iii) interquartile range(iv) semi-interquartile range, and (v) range.

[Ans : (i) 87 (ii) 190 (iii) 103 (iv) 51.5 (v) 535]Q4. The heights (in nearest cm) of 60 students of a certain school are

given in the following frequency distribution table :

Height (in cm) 151 152 153 154 155 156 157

No. of student

s

6 4 11 9 16 12 2

Find : (i) median (ii) lower quartile (iii) upper quartile (iv) interquartile-range Ans : (i) 154.5 (ii) 153 (iii) 155 (iv) 2

Q5. The following table gives the weekly wages of workers in afactory :

Weekly Wage in Rs.

50- 55

55- 60

60- 65

65- 70

70- 75

75- 80

80- 85

85- 90

No. of Workers 5 20 10 10 9 6 12 8

Calculate :(i) The mean by all three methods, (ii) The modal class; (iii)

The number of workers getting weekly wages, below Rs.80;

(iv) The number of workers getting Rs. 65 or more, but lessthan Rs. 85 as weekly wages.

Ans.: (i) 69; (ii) 55-60, (iii) 60; (iv) 37

Q6. The marks obtained by 200 students in an examination are givenbelow :

Heights (in cm)

0 - 10

10-20

20 - 30

30 - 40

40 - 50

50 - 60

60 - 70

70 - 80

80 - 90

90 - 100

No. of students 5 10 11 20 27 38 40 29 14 6

Using a graph paper, draw an ogive for the above distribution.Use your ogive to estimate :(i) the median (ii) the lower quartile (iii) the number of studentswho obtained more than 80% marks inthe examination and (iv)the number of students who did not pass, if the pass percentagewas 35. Ans : (i) 58.5 marks (ii) 42 marks (iii) 20 (iv) 33

Q7. Draw a histogram of the distribution and estimate its mode fromthe histogram :

Weight (in kg) 50-55 55-60 60-65 65-70 70-75 75-80No. of people 10 28 40 30 18 8

[Ans : 62.5 kg]

Q8. The mean of the following frequency table is 50. But thefrequencies f1 and f2 in class 20-40 and 60-80 are missing. Findthe missing frequencies :

Class : 0-20 20-40 40-60 60-80 80-100 Total

Frequency : 17 f1 32 f2 19 120Ans : f1 =28, f2 =24


09:00 – 10:00 PM - Dinner


10:00 - 12:00 PM - SYMMETRY

Q1. Plot the points A(1,4) and B(4,2) on graph paper. These twopoints are the vertices of a figure which is symmetrical about x =4 and y = 4. Complete the figure on graph paper. Write down thegeometrical name of the figure

Q2. Part of a geometrical figure is given in each of the diagram givenbelow. Complete the figure so that the line ‘m’, in each case, is theline of symmetry of completed figure. Give the geometrical nameof each of the completed figure.

R

QP

m

4cm

2cm

B

CA M

3cm3cm

A

B C

D

4cm

Y P

x

M

3cm

Q3. (i) Construct a quadrilateral ABCD in which AB=5cm, BC =7cmand ABC=1200 given the AC is its only line of symmetry. (ii)Write down the geometrical name of quadrilateral (iii) Measureand record the length of BD.

Q4. Construct a ABC in which AB=AC=3cm and BC=2cm. usingruler and compass only. draw the reflection A’BC of ABC, inBC. Draw the lines of symmetry of the figure ABA’C.

Q5. Plot the points A (8,2) and B (6,4). These two points are thevertices of a figure which is symmetrical about x = 6 and y = 2.Complete the figure on the graph paper. Write down the geometricalname of the figure.

Q6. Neatly draw a figure having (i) Only one line of symmetry (ii)Exactly two lines of symmetry (iii) Three line of symmetry (iv)More than three lines of symmetry (v) No Line of symmetry.

HAVE A SOUND SLEEP OF7 hrs. B/W 12-7AM

GOOD MORNING 9TH MARCH

Have faith in God and belive in yourself, be confident &revise all the formulae and concept once again. Don’t benervous under any circumistances, be challenging andappear in Board Examination. Success will be yours.

wish you all the best !TRAYAMBAK TIWARI

Documents

TIWARI TUTORIALS TIWARI TUTORIALS DATE : 04 …tiwaritutorials.in/Downloads/ICSE-X LAST MINUTE MATHS.pdfFind the amount and compound interest on Rs. 8,000 at 10% per annum for 1½