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lAXi!: EXAMINATION PAPSaa. Paor 5 21 35 63 63 66 69 83 03 13 23 EXAMINATION PAPFRS. SUITABLE FOR THE INTERMEDIATE EXI NATION. Jlnthmcttc.--|To. I. 1. J and B begin business together ; A gives | of the capi- tal At tJie end of the first year they have made a net profit or ^2 % ; at the end of tlie second a net profit of 5 % • at the end of the third they are bankrupts and can only" pay 50 cents in the dollar. The remaining money is ^21,735 • how mucli did each contribute i ' 2. As income Irom money invested in Dominion five per cent, stock i« !^1200 ; he sells out at lOlg and invests in four per cent, stock at 80J. How will his income be afi-ected brokerage on each transaction being i 7 ? ' 3. The diameter of the fore wheel of a carriage is 3 feet 6 inches, and that of the hiaid one G feet 2 inches. If two nails on tlie outside of each wheel, touch the ground to.-other in what time wiU they do so again, allowing the circumference to be 3} times the diameter, and the rate of travelling 61 miles an hour 'i * 4. Simplify ll^tz-^f -00004502625 f81+(i.03 U INTERMEDIATE EXAMINATION PAPERS. 5. What is the weight of a cylinder of iron closed at both ends, 18 m. in diameter and 3 ft. 2 in. long, the iron being 1 inch thick, it being known that the sp. gr. of ii-on is 7.7 and a cubic foot of water weighs 1000 oz. ? 6. What per cent, payable quarterly is exactly the same as o % pivyable annually / 7. Sent my agent 5000 bu. of wheat which he sold at $1 20 per bu. on a certain comnussion. He invested the balance after deducting his 2 corns., in silks ; the second com. was at the rate of 4 %. H the two corns, amounted to |500 at what rate % was the first charged ? 8. The ready money price of a book at a bookseller's who allows mercantile discount for x^ady money is $4.50 and the credit price $4.76 ; what ought the credit price to be in order that, while charging the same ready money price he may allow twice the rate of discount ? 9. Two trains, 120 ft. and 150 ft. long respectively are moving with uniform velocities on parallel rail in opp'os't! uirections and ai. observed to pass each other in 3 s^conl bu when they are moving in the same direction their velo-' cities being the same as before, the faster is observed to pass the other m 10 seconds, find the rate in miles per hour a which each train moves. decimar?'*R'f'" 'r'""^ '"^ ^'"''"^''^^^ ^ terminating decimals ? Before reducing a fraction to a mixed repetend how can the number of places in the finite part ol the repetend be determined without dividing I Assuming the rule f^r re- ducing a pure repetend to its equivalent fraction, investLte the process for reducing a mixed repetend to a fiction ' INTERMfiDIATB EXAMINATION PAFKKrf. are ,^1-ithmetif.— No. 2. 1. Detine notation. Enumerate the points of difference between the Roman and Arabic systems of notation What IB the difference between an English billion and our billion ? 2. What two methods are employed to find the discount of a sum of money ? Which method is adopted by mercan- tile men I Why is it wrong in principle ? If the mathemati- cal discount on ^220, for a certain term and rate, is $20 what IS the mathematical discount on $220 for twice the time ? 3. Bought a quantity of wheat. Sold it all at $1.20 per bu. on half of it I gained 20 per cent., and on the rest I lost 20 per cent., find my net gain or loss per cent. 4. A divided his property among his three sons and two daughters as follows :-To the eldest son he gave i of the whole, less $12000 ; to the second i of the remainder and $0000 ; to the third f of what then remained, less $2000 • and he divided what now remained equally between his' daughters ; if a daughter's ahare was $6000 find the shares of each son. 6. A bought a rectangular field 48 rods- long for $500 ■ B bought a field similar in shape to A's for $820 ; if the land in each case was of the same value, what was the length of B'b 6. A friend lent me $3955 at 7% ; to raise the money he sold out Dominion 5% stock when it was at 99§ ; I kept the money six months, and meanwhile the Dominion fives fell to 97 How much had I to pay my friend to cover the in- terest and to replace the stuck he previously held ; brukerage upon each transaction ^ per cent. ? II 8 I-NTKKMKDIATE KXAMINATIUN PAI'K R& 7. Three months from date I promise to pay to A B or h. he sum of $7(50 witlx interest at the rite o VL ' for value received. ^^ P^"" «"num, "«r ^atn, and A B received $759. 73 f,„. ;. ^i^, , cent, per a„,>„,„ did the b,.„ker IIJ, "*"•" 8. A cistern has three aupnly tan=. 4 T> a ^ which it i. ompeied, j>.„d 'm i^nn ' ■"'' ''^ '"" ""> l"^ Jl and Z, i„ 00 hou., .„d ^ .„d ,1 f, ^ ^ \» ':;7" ^ cutting, .zi\i:"^2 " r'" ' '"' '"■^' "-M '^« noticed exact,. 18' 46' ^^ZTTSlZ^'j 'r'' port.. What i. the velocit, of ^.^J^' "'" '"'"""'"' "'" Value,, -10 ,aa.k3 to each ^luctioa. INTKUMEUIATE EXAMINATIOX PAI'ERh 9 ito. .S. 1. What Ja meant by doeiu. 1 notation 1 Write 7 00mmKll ,n words, and .xprcs seventeen, and one nidlu.n eight tliousand and nix ten-trillionths in figures. 2. Define Measure, Multiijlo, Common Measure? and Loast Common Multiple. The prime factors nf the first of three me^nbers are 2^, 3^, 5, 11, and 13 ; .,f the 2nd, 2^, 3 ?^;<«;^n;f 'l'^' ''''' ^- ^- ^ '' *^-" ^'^^-^ '-"nbers i^ I7IO808OO, what must be one of the prime factor, of the third number ? Why cannot numbers have a i^reato.i- com- mou multiple ] Z. B gold ft farm to at a loss of 15 per cent. ; C «ofd it to n at a loss of 10 per, cent ; D sold it to i?* at a jrain of 10 percent for 13780.75. What did the farm cost ii? 4. A, B, G, entered into partnership for 18 months A put m $400, B put in ?500 and (J $900 ; at the end of 10 months each drew out §200. At the end of the year, A and B each put m an amount, so that at the close of the partner- ship out of a gain of f 1710, A got 1^430 and B got |550 What sums did A and B put in? 5. Tlxo price of standard silver is Ss. 2d. per oz, tho duty on manufactured silver is Is. 6d per oz., and the cost of workmanship is 'Is. 4d. per oz. If a dozen silver forks are Bold for £12 3s. and tho silver-smith makes 12^ per cent on the transaction, how many ounces of silver are there in one of the forks ? 6. A tradesman professes to retail his goods ot 10 per cent profit, but adulterates them b^ adding i of their weight of ar inferior article, which cost him fon.r-Cfths of the price of the better. How much per cent, profit does he make ? In what proportion must he mix the two kindo so as to rrain 20 per cent ? '^ 7. Two circular gold plates each 1 inch thick, of which tlio 10 WTBKMBDIATit EXAMINATION PAPERS. diameters are respectively 6 and R m.i «I0I2 60. K?,' t "" '»"'f "r »' 1« J%. the amount i. l-ned at simple inZ™*' ""'" "^ ""■^' "" ""-^ """8 10- Find in two ways the sixtii root of 100152016000L V.lu. ^10 marks to eaol, examt,la *>.4. 1. Simplify I ?l2.'i85ri4 . , «*-«oflJ.-i)j.^(li_3^,l)J Oiva the answer in a vulgar fraction in its lowest tern,. <%»; and 10 boys B -irl, aoH T " """ ^° " '" » '»w W will it ra< ulo 3 Cn t w". °"", 1" '" ,'" ' ''»^''' 1 o men, 4) boys, and 4 girls to do it ? a4,Vnr:r °tt 1 irrr"""'"- ^'^'""^ » ^-.^ <■' 'or mS more he would Wo IS To"' """' '" "°'" '' «.e machine cost him at the ltrcW?T ""' ' """' *^ * i^ dying ,0ft ,31450 to ho diWded among 4 children INIBRMEDIATE EXAMINATION PAPERS. Jl and 5 brothers, to that after paying the legacy duty, each child shall have twice as much as a brother. The duty on a child's share is 2% and on a brother's 4%. Find the share of each. 5. Bought 2000 lbs of sugar, part at 7 cents per pound and the rest at 10 cents per pound. Had I bought the whole at 8 cents per pound it would have cost me $13 less than I paid for it ; how many pounds of each kind did I buy ? 6. Explain the following quotations from the Globe of March 26. "United States i^'s, 114|." "The posted rates of sterhng exchange are unchanged at KSO^or 60-day bills, and $4. 83 on demand. ' ' Drafts on New York firm, at ^ to 4 premium." "Commerce sold at 142 for 25 shares." 7. A note of $400, due in one year from April 12 1880 was bought July 12, 1880, for 1^390 what rate of interest does the buyer realize on his money, the note bearing inter- est at the rate of 10% ? 8. If B invests #6135 in the Dominion 5 per cents, at lOlf paying ^ per cent, brokerage, and .iter receiving a yearly dividend sells out at par, again paying ^ per cent, brokerage, does he gain or lose by the transaction, and how much, money being worth 7 per cent ? 9. If the Frer-ch 3 per cents are at 60 when the English are at 95, the exchange between the countries being 25 fr, per £1, how much French stock in francs can be bought by selling £6000 out of the English funds, brokerage on each transaction ^ per cent ? 10. A and B, starting at opposite corners of a square whose side is 100 yards loi^, walk round it in the same direction , A walks 19 yds. whilt B walks 161 yds. At what part of the square will they be fiist together, and how many times will each have passed the 3orner where he started ? Value— 10 marks each. 12 INTBKMEBUTE EXAmNATION PA.VBBS '• Simplify and — » go. 5 l?^a43+jf -0274' (:21^y + (-025)' C-075y'-(-075)C025):r(-025^r /• Define the folIomn?.._/?';,„,.,-„ .. , , how to reduce vul^^ct ::' -^' ^'^^f .^-^-n. Expl..n -n you tell before ^^^^T^'''''' ^.^'^^*^-- How 21 caslcs and /2 b2:Sl ed"ofT,r ''''''''' ^^^^ ^^^ »>^e3 separately, or ho. n.nyti.l woX l^ld^ '"^^ and the remainder'at pthf of i t ' '"f 1 ' ^^^ ^-*-' a" at a profit of 9 per cent hV ^ ''"*• ^^^^ ^« ««ld less ; What did the'wheatlt S? '''^'' '"^ '^^^ ^'^■^<^' n^i^ Sairrr':^;:: ^^i^T;^ - ^-i-. ^h. bank at 8 per cent n J« ' '"^'''^ discounted at the allowed the nZlTo Z^ZTr' ''' '''''''''• «« 3 months which discounted it 8 n'" T'" ""*^ '^^ previous noteand the costofpltltmjr TT' *^^^ face of the second note ? ^^ ' ^^^ ' "^^'^^ ^''^s the 6. Thetruediscountonan entire snm .f cent, is $50 more than the sum o th. t""""'^ '* ^ ^' half the sum at 8 per cent IZ n ^'"".'^^^^^""ts «" one- cent. Find the sum. ^ '" "^' ''^'' ^^^^ at 4 per tnst, a five per cent loan for £20000000 ; TVTBRMBDIATB EXAMINATION PAPEKS. ,o the second, a 4 i)er cent, loan for £12000000 ; the third a 3A per cent, loan fur £10000000. For the first tlie Government received £80, for tlie second £70, and for the third £60 for every £100 of stock. How much money is realized from these loans, what average rate of interest is paid on the money acuially received, and on which of the three loans does the Grovernment pay the lowest rate ? 8. Explain the principle on which we place a point over every third figure in the cube root, and show that the num- ber of tigure. in the root will be equal to the number of these points. 9. The price of gold is £3 17s lOM per oz ; a composition of gold and silrer weighing 18 lbs is worth £037 7s., but if the proportions if gold and silver were interchanged it would be worth onlr £259 Is. Find the proportion of gold and silver in the ©mposition, and the price of silver per oz. 10. The se.tion of a telegraph cable is half an inch in diameter, the jentral wire is oue-ei<,'ht of an inch in diameter, and there are > protecting wirea of one-sixteenth of an inch section embecded in the hempen cable ; what precentage of the cable couista of metal and what of hemp ? ,^0. 6. 1. Assuming he rule for reducing a pure repetend to its equivalent vulga* fraction, show how to deduce from this the rule for reducing a mixed repetend to its equivalent fraction. Simplify . \^^7^._ of 7. 714286 J (Js. 2.18 of .916 3.1 Id 2ft. — of Od 8in. 2ft. llin. fas of 6.625 (2.83 of 3.? 2. A perscn remarked that when he counted over his basket of peaches, ;wo by two, three by three, four by four, five by five, or ix by six, there was some remaining ; but when he counted hem by sevens there was no remainder. Find the least nunber he had. u INTERMKDIATE EXAMINATION rAPBRS. and ,ll n f ^'"""' ^'""' * 20 gallon cask of brand) and 1 la the cask up with water. He then draws offG ..allons and hlls he cask as before. After he has done this .rtuue:' what wvll be tlie strer.gth of the remainder ? 4. A person invests in the Tt. s. four per cents so as to ob- tain 4 per cert, dear on his investment after pay.,,, an in- come tax of 1 pel. cent. What percentage would he obtain It the tax were doubled ? 6. A manufacturer's employes consist of men, u-omen, and 7o cts. If the amount of wages paid to the wliob is the same as If eacli received $1.10 per day and there are 16 boys how many employes are there altogether ? ' G. Two women in the habit of buying botw.en them 120 oranges a day at 3d. per dozen, and selling then at 5 for 2d club together and one taking the better lialf «]ls tliem at 2 for Id. , and the other selling the remainder at i for Id How much are they better off at the end of six dajs' traffic, and what^ percentage of increased profit do thej make b; the at \n^ ''^''I'^^^^l ^'-^in- i niin. 12 sec. per dy is set right at noon on November 11th. What is the fue time wl^n this watch points to noon on the following Ohristmas-day ? Tn^;/r?."^^^'^' ^'' P'^P""'^ '"^ foursu-cesive ventures. In he first he clears 100 per cent., and in e.ch of the othen, he loses the same per cent. If there remans to him 2 4 per cent on his original outlay, what was hislos, per cent, in each of the three years ? " 9. A crovTi made of gold and silver wnghs 150 oz and displaces 13 824 cubic inches of water. H.S it.een < f pure gold It would have displaced 12.06 cubic inch, of water and Ifad It been of pure silver it would have dis.laced 23 04 cubic inches. Find the weight of gold, and of dver in the crown. , "* ^'^^ INTEUMEDIATB KXAMINATION rAl'KBa /.-; 10. A gram of gold is beaten so thin aa to cover 80 Hciuai-e mche.s ; hml the cost of the gohl ro.iuired to cover the curved surface of a cylinder 10,^ feet long, and the end of which liaa a radius of 4 inches, if an ounce of gold is wortli ^17 50 Mo. 7. NoTK-Thu, paper ia intended to embrace the wark to the end oj decimals. 1. Define the following terms, giving an example of each ■ abstract number, notation, prime number, multiple, and com- plex fraction. 2 Explain why the multiplier must always be regarded aa an abstract number. 3. Divide 780949 by the factors of 105, and show clearly how the correct remainder ia obtained. 4. Distinguish between vulgar and decimal fractions, and between sniiple and compound fractions. 5. Explain the use of the cipher in Arabic notation.and ex- press m fagures seventy quadrillions seventy thousand, and seventy million and seven ten-billionths. 6 Show that if the throe right band tigures of a number be divisible by 8 the number itself will be divisible by 8. Resolve the numbers 3384, 8272, and 7567 into their l.rime factors, and from these determine the H. 0. F. andL C. M. of these numbers. The Least Common Multiple of two numbers is 8286604200 • tJieir Greatest Common Measure ia 32.S40 and ores ot " ' •lumbers is 2522520 ; find the other. ' " ' m INTiJnfKniATR RXAMIVATroN pa, KRS. 7. A«..,m.ng the rule f.r reducing a p,.ro repotond to it i^'rml.nt vulvar fraction, «how 1.^ to deduce a rule for reducing .^ mixed repetond to its e(iuivalont fraction. Vyiiat ,nu«t 1,0 the deno,ni„at..rH of those fractions winch on being reduced to deciu.als give :,ure repetead^ <.f three figures ? Why 1 8. Co„,pare tho speed of two steamers, one of which sails 264 V} mdes in 23^ hrs., and the other SDT, rnilcs m 6-;J2 hrs If the speed of the slower be represonto.l by 12, what number will repreaoiit the speed of the faster / 0. (a). Simplify i • ()7(;<)23 of '-Vo^V(-428G7i+^) \ . f -VOOK -003^ I "^ 7/ / 1 57 7 ■ 21 / (6). Simplify 3 mi^fur. 3 hi. £88s^8d. _ 2t. 2qr. 2oz 4 mi. 4 fur. 4 in. £9 9s. !)d.~ 4tr4c wt." 4dr: * 10. (a). Find the value of 1 + -1- + J . ^ . 1-2 1-2 3 "^ 1 •'/.•? -i"*" correct to 6 decimal places. -i - J 4 (6). A lady went shopping with a certain sum .f money m her purse ; at the first store she spent ,«2.30 m... than ^ of her money ; at the next store she spent ^1.30 less than , of what money she then had ; at the next place of can she snont W5 less than ^ of what money sL now had. Sh. -Mids that she has now J of her original sum of money kit. . , inu< b had she at first I } Mo. $. ....I .!!:';::;";:::'::;:« "i «-■■■«- »-..-» »»«»*: • "'""'"•"IS your an.wor I.y ommi.Im. M::;;';;;;.ui;;;'.,;::^t^;:;!:v''",':''""'''-- "■ ■■I t..(,8, HOW, anil ijoi '( iviij, , •I- Miiltiplj. 7I18II74S liv iimifn „.i. . . "I>W.. tl.u .,.,.,-oct rc.,„U st; " °^^ ^ '"■" """'""» "> the con„ot r„.ult, "''^ ^""' P^"'" '»"»» «ive ""'."•«' f'"" >■">■'■ ■■'.■a..m in oach case. ro,)eat. ,;,, ,jj, j^_ _y^j ^j^^^ »■ W Simplify Ci^"'''^ 21 4-256 x-00«4vt sum borrowed ? ^ " "«• ^t ^vhat rate was tlie lirst 7. (a) Explain the distin.^fio,. hot^^^n T. -n- 18 INTKEMBDIATE EXAMINATION PAPERS. (6) A bought a hng'^y for .f 1 75 and gave a note for three mouths ^vhicli discounted at tlie Ontario P.ank at 7% just paid for the l)Uggy. For what amount was the note drawn ? 8. A person lias an income of £122 10a. for 3^ per cent, consols ; he sells at 92, and invests his principal in stock at 95 ; his new income is £177 18s. 5^\d. ; what rate did his new stock yield ? 0. A had a six per cent, bond of SHOO dated .Tamiary 1, 1881, and due January J, 1SH2. On July 1, 1881, A sold the bond to B in such a way as to give B 7% on his invest- ment. If B borrowed the money ncieded to pay .1 from the Dominion Bank at 8% on a note for 90 days,' what was the face of the note ? 10. (a) Explain the diffurenco between 7 ft. sq. and 7 sq. ft. (6) A rectangular park, one side of which is twice as long as the otluu-, contains 500 acres ; there is a road running rotuid its outside which contains 32900 sq. yards. How wide is the road ? I ilo. 9. 1. (a) Define the following terms : Brokerage, average, in- surance, stock. (6) A sent a sum of money to his agent in Montreal, with in.struction8 to deduct his commission at 2^ per cent., aail invest the balance in silks. The agent's conmuHsion was |!240 ; what sum was sent ? 2. Multiply 9(i879.W4852 by 144121728, using only three partial products. Show that your method must give the cor- rect result. 3. (a) What is PrP.ctico V VVliat pi'inciple in multiplication is often apparently violated by this rule ? :e for three io Bank at at amount per cent. in stock at ite did liis Fannary 1, Jl, A sold liis invest- Y A fi'om what was id 7 sq. ft. s twice as ; there is 1 contains 3ad? erage, in- Montreal, sion at 2^ Iks. The was sent ? tily three 3 the cor- iplication INTERMEDIATE EXAMINATION PAPERS. 19 (6) Find the price of 364t. 17cwt. 3qrs. lOlbs. of stec; at $40 per ton, by Practice. 4. Explain the following quotations: "Montreal Bank sold at 202 for 60. " " Dominion Government 5's were wanted at 991 without sellers. " "The posted rates of sterling exchange are unchanged at $4. 80 for 60-day bills, and 04. 84 on demand. " 5. A, B, and do a piece of work for ^159. 70 ; on the supposition that A and B do ^ of the work, A and C j%, and B and C ^, what should each receive ? 6. A merchant bought cloth If yards wide at $5.70 per yard ; the cloth getting wet shrunk 5 per cent, in length and 2| per cent, in width : at what price per square yard must he sell it so as to gain 20 per cent ? 7. A bank, by discounting a note at 8 per cent., received for Its money a discount equivalent to 8^ per cent, interest ; for Avhat length of time was the note discounted before it was due ? 8. A invests 30 per cent, of his capital in 4 per cent stock at 90, 38 per cent, of it in 4^ per cent, stock at 95, and the rest of it in 6 per cent, stock at 105 ; his total income is $1736f ; find the amount of his capital. 9. (a) What is the course of exchange ? 'ihe par of ex- change ? (6) Sold a bill of exchange on London, for £450, to a broker in Toronto, who charged me ^ per cent, brokerage. If I received $2169. 10 for it, how was sterling exchange quoted ? 10. A solid ball, 4 inches in radius, of a certain material weighs 8 lbs. ; what is the thickness of a spherical shell of the same material weighing 7^ lbs., the external diameter of which is 10 inches ? IlK qu! anc Ad 3 fra( s I INIKUMKUIATB EXAMINATION TAPKBa. 21 ^\Qthtn.-£io. I, 1. Define and apply, by examples, the following terms :— Independent equations, aymnietrical quantities, homogeneous quantities, like dimensions. Simplify ab - [{a+c)b—3ac-{ah—2c(a—b) }]. 2. Examine the principles upon which the rules of addition and subtraction of algebraical (luantities are founded. —2xv) and *^ - 7 C .r^—)/' _ Add together 4{x' - ^~~2xy) and |^ - 7 (x'~i/ _ -'^) . 3. Give a definition of multiplication which will apply to fractions. Perform the following multiplications : — (1). (x'''— 2x+3)(x^ + 2x + 3). (2). (u;'»-2j/»)(x'»-i/'0. (3). (x^VctaJ"*— &)(x"''-ax"'-f6}. (4). (a^b^riah-bh 4. Perform the following divisions ; — (J). (12x«— 192)--(3x-6). (2) , (2 -OOlar' + 9 •22x'^ + 3 •694x - 1 -2) ~ ( 51x + 2). (3). (x''+a:-«-2)--(x'^+u;-'^— 2). 22 INTERMBUIATE EXAMINATION PAl'EKS. 5. State and prove Horner's method of division, and apply it to the following ; — («" - 4(i^+ 7a'''— 5« + ()) -- (a''+ 5a— 4). 6. Define the terms " Measure " and " Greatest Common Measure." State and prove the rule for finding the greatest common measure of two compound algebraical expressions. Find the G. C, M. of the quantities : 3v'+4(u;'^ - 30)— a-(18ic+ 104), and x*—10{x^-^ 12) +x{2ix-i 36). 7. Investigate a rule for finding the square root of a com- pound algebraical quantity, and find the square root of x"P + g.*;-*'"— 4..;'^'+4(a'^^ - 3x-"')+G. 8. State the principles, or axioms, used in the solution of equations. Solve the following equations :— • /ix x-1 x^—l (2). x{bc-xy)=y(xy~ac) xy{ay + bx—xy)=abc(x + y—c). ^^^- 7'^+7T^^30' 9. Two persons A and B, can perform a piece of work iu IG days. They work together for 4 days, when A being called oft; Bis left to finish it, which he does in 30 days more; in what time would each do it separately i s. ion, and apply ,test Common g the greatest 1 expressions. oot of a corn- root of xe solution of 3 of work iu •hen A being todays more; INTEUMEDIATE EXAMINATION PAl'EJ'.S. 2a Jllgebi-a.— No. 1. 1. Define the meaning of a»»; shew that a"" . a" =a"»+». Prove that «"=!, and a» = 7 a. Is any assumption neces- sary in order that this may be true ? 2. Examine for what values of n, .r" +(-,,). is exactly divisible by x+y. The product of any three consecutive integers being formed and also the product of any other three, the ditlerence of these products will always be exactly divisible by the difference of the middle integers of the two sets. 3. Multiply x+a, x+b, x+c, x+d together, and deduce from the product the coefficient of x in the product (x+2) (*+6j (x+10) (x+14). ^ 4. If x^+y^+z^=x"-+y^+z^=x+y+z=l, then will xyz=0. 5. Divide {ax+by)^+(cx+dy)^ + (ay-bx)^+(cy-dx)^ hv 6. In the process for finding the highest common divisor of two algebraical expressions, show that the result is not affected (1) by removing any factor which is common to every term of a divisor at any stage of the operation which is not found m ev«ry term of the corresponding dividend ; (2) by mtroducmg into any dividend a factor which is not contained m every term of the corresponding divisor. Find the highest commun divisor of a^+b^+c^-3ahc and a{a+2b)+b{b+2c)+cic+2a). 24 INTKKMKDIATE EXAMINATION I'APERiL A]gehrn.~Contimi€d. r state the n^eaning of the symbol «, and show th«tit. value is unaltered by multiplying or dividing both terms by the sa,no duaut.ty. Also, exanunu how the value is ahected by increasing or diminishing both terms by the same quantity Prove that ^'^M^ + '') ^(i>±^XI>Uc) (c^+a)(c+b) (a - 6)(a - c) (b- c)\h~a) "^ (c-oj(^T^)=^- 8. Is there any fallacy in the following / if so point it out. (1) ^•'('*-a)=a''-rt*=(a-a)(a+«.). Dividing by «- a, wo have ,=a+a = 2rt; .-, 1=2. (2) If^a^=l and 6"=1, .-. a.-i^ and consequently id!nt^T " "'* "^'^'^^^^^ J^^twoen an equation and an Da 10. Solve the following equations: (2) ?^^-%-e!^Ve!^^^, 2-a x-6 x_c (3) -g-ll I _^-<^ _x+h-_2a x+a-2h_ x-a x-b x+a~2b'^ x+b-2a' b+c 'c+a' ^b~=^+^+'^ 64 56 (5)x3+"-:=7J-f''%2, a" .^ na. allow that its loth terms by ue is afl'ected ime (juautity. point it out. 2a; . •. 1=2. 3onsequontly tion and an le following -3a)+ll|1 7+x). INTEUMliDlATK BXAMiNATION I'Al'KRfl. '2b ^Igcbra.— No. 3. 1. Show that rt"» - a» ia divisible by n+l wh«i m - n ia even ; that a'-'+a'^s divisible by a+1 wlien vi-n ia odd ; and that a™ -a" is divisible by a- 1 when m-n is even or odd. 2. What ia the criterion by which it ia known that an algebraical polynomial, with integral co-efficients, and ar- ranged according to descending powers of x, is divisible (1) by x+1, and (2) by rw - 1 ? Show that xH3x< -x^-x'--2 is divisible, both by x+1 and by as- 1, and write the quotient. 3. E.\;plain how the highest common divisor of two alge- braical expressions does not always give the greatest common measure of the numbers which result, when particular num- erical values are given to the algebraical symbols. Exemplify in finding the highest common divisor of x* - x'^ -205-1, and x^+2«3-f x' - 1 ; and of 3xHax-4a'^ and Gx^ - 7ax" - 20u'x ; and their greatest common measures, when x=4: and a=:l. 4. Show that (26-c -a)3- (2c- a—hy_ 9(b - c) {c-a}^ - '(a - ly ~ " ~b + c^2a 5. Extract the square root of 7r-^+' ^ _ 9 21 ^49 6 ^14^16' , a^ 2ax . x2 ay xy I ~ ~a It A I 1 and explain why, if the terras be arranged in the reverse order, and the root be then extracted, a result will be ob- tained differing only in the sign of the whole quantity froin that obtained in the tirst instance. a ' )n and 2(i INTERMEDIATE K.VAMINATION I-APERS. Algebra.— Con6. c a a c 7. What relations must subsist between a, b, c, in order that ax'^+bx+c may be a complete square? If ax*+bx?+cx^ be subtracted from (x'^+2x+4)^ and the remainder be a perfect square ; determine the values of a, b and fl, 8. In the product of {x+a){x+b) (x+c), the co-efficient of x^ vanishes, and in the product of (x—a) (x + b) (x + c) the co- efficient of X vanishes, and the co-efflcient of x in the former is that of x'^ in the latter; find a in terms of b and c. 9. In solving the quadratic equation x"— 4a;-f-2 = ; take Qvery step in order, and describe the process leading to the 28 INTKRMrnUTB KXAAriNATION Pil'BVJ result, in plain nnd intelligible lanruago 10. Solve the equat:on8= ...J.., 1 .../J ■jyy+xy' = 2. I iXc. 5. 1. " To multiply two une.raal ii.n.l.tT.. Tnko the sum of he two numbers and .nultiply half cf it into it.d Z^ his product .subtract the sqt.are of half the dirTerence of 1^ wo nmnbers " Gi.. the Al.eb.aic fo.nuda wldre is^^ th.s rule, and state in word, at length in the si.nplc«t form X +X+1 without perfonning the oporution of division. " S. Show that x^^-na"-^.(._i),« is divisible by (.-aY w.hout performing the operation , and write tlie exact quot - ent of x<^ - 6a«a5+4a^ divided by (x-aTK aL^^'-V^'"'^^^''' ^"S^^^*'^^"''""" divisor of twocompound Algebraical quantities is the least common multiple of all the commom divisors. 5 Show that if x+c be the highest connnon factor of x»Z(at. ';"f,f+'»" + «'«^'^ir least common multiple ia 6. Show that («^±M)'_ 7. Reduce to its simplest form (^JZ^iC^Zl^) , (^:3c)_(^-a) (x-a) (x~b) (or-b) (a^c)^ (^,) (6_^^+ ^^^f^^^ 9. Solve the equations :— s-^-fi L'.-c+r "cc4-i +Tr+ij' is always a proper fraction. INTRRMRDtATE BXAMINATXON I'APEM. at.'on hftv« 16. he 8um of If. J-^iom ice of the lest form. 'isiblo b' on. icfc quoti- ampound jf all the factor of iltiple ia action. 39 (2) (x-{-2y !+- («4-li)^ ' 2 4(a:-f-2) ,i JO. If a (luadraUo eqtiatimi be satisHed by more than two didunmt values of x it will bo satislied by all values of x; find tho relation between the roots of the or| nations y^—px^q^O and x'+px+q=^0; fi„d also tho equations whose roots iwe tins i-eciprocals of ax'J -\-bx \-c=0 11. A rectanqular cotu-t, of which the sides are and ft yards rtispoctively, is surrounded by a path of initform width e((ual in area to one mth part of tho inner rectangle ; iind tho width of the patli. Ho. 6. 1. Find without division the remainder wh8n/(x) is divid- ed by x^—aK What value of j/ wiU make ax^H- 6x1/+ ci/= divisible by a: + m1 2. Define and explain clearly a negative quantity, and from your definition show that —a x —b=ab. 8. Find the continued product of (1) ix^ + a')(x*-i-a*) (x'\a'"). (2) (a-6)(a+6)(aV6^)(a*-|-?>*) to n+1 factors. 4. Tho product of two factors is (2x + 3yy-l(2y + 3zf and one of them is 2x + 5y +3z ; find the other. 5. Describe the process of finding the H.C.F. of two alge- braical expressions, and prove that the H C.F. of tnvo quanti- ties is equal to their product divided by their L.C.M. Find the H.C.F. of 2x5—11x^—9 and 4a;54-lla;«-f 81. I ;{() rNTKllMKUlATIC KXAMINATION PAl'KIUi. 6. Find thobuiu uf x*+x~l 7*—X~l and from your result i«fer Uie valun of 7. Investigate a rule f„r fincling the square root of .n a] gebraical quantity ; and lind the square root of a What value .f m will make (,v—3)''—(x~l)(x-~5)=„ »n identity ? Can any value of m make it an equation ? 9. Solve the following ecjuations :— (1) ^:^^4-?T^=__^lti^ x-j-7 a; -1-5 A-'-fl2A:+a5 / J^ _ J («=+!/ *' M.^' 2,/+r^ I (3) -i^+-L=_._L_ ^__-_ (4) a^x+h^y=.c^. \ ^, , . aacc+feai/^ca. / "^^^** ^'^^™ does the values of X and 1/ take when "a ^2 Ca and what does it indicate ? 10. Solve the equation Va^'+T^H^^ s'x'Tlx~b'= —2 and account for the circumstance, that the values of x C termined from it, apparently do not satisfy the equation.' INTERMEDIATE EXAMINATIOX I'AfElia. Ho. 7. 31 1.. Distinguish like and nniikc qiMuititiea and give exnmplos. Ex |ires8 tho aggregate of a-{h-c)-\h-~{c-n)\^-\,:-{b-n)], lir3t aa a positive quantity, and secondly as a negative quan- tity. 2. Arrange {x + y^.,:)a^^ {x + y~.)a„+(x-{-z-y)a.,^(i,-i. i-.c)at in three terms involving «, y, z respectively, witli coiimcieiits consisting of ,f ,, a^, a^, a^. ^.'«. What is inoant by tho rule of si«ns in the multi- plication of algcbniical quantities ? State whetlicr y„u re- gard tho rule as conventional or demonstrative, giviiig your reasons in the former case, or a demonstration in the latter. 4. Multiply a+x, b + },, r. + r. together, and deduce (a;+i/)» from tho result. ^ 5. By what algebraic expression must cc'+yS be multiplied 8o that the prduct maj he x^-\-x*y-^xY-\-xY + xy*i-y^l 6. Write the pth term of tho quotient of a'""— 6""' when divided by a"*— 6"*. 7. Divide a;'-t-/)x'-f^a!;4-l and x^4-px*-}-qx''+q:c'-i-px+l by x+lrespectively, employing any artifice to save the trouble of formal division. 8. Show that (a+6+c)'~(a«-f6»-fc'')=3(a+6)(Hc;(c4-a). 9. Iiay+bx=a, by-ax=b, then x" + y'' = 1. 10. Resolve the following expressions into factors : (1) x'-(a-b-c)x'-(ab - bc + ca)x + abc (3) y'~{2a + b)y'' + {2ab + a')y-a'b. I\ 32 INTEKMEDIATK EXAMINATION PAPERS. li, jS\a. 8. 1. Express in Byu.bols Uio (,u<,tiout arising from the pro- duct of two (luantities dividod l,y the product of their sum and difference. _ 2. Donne the meaning of a", (1) when m ia positive and integral ; (2) when m is negative and integral ; (3) wlien m is fractional. Explain the meaning of a™. 3. In the multiplication and division, of- algebrai.;al poly- nomials, what preliminary steps are necessary in order to avoid confusion in performing tlieso operations ? 4. (1) Divide 21x0- 2.C*- 70.--''- 23x' -{ 33,: + 27 by 7x» +4x-y, using Horner's method of division. (2) cc2+x-2-|-lbyu;+;,-i+l. 5. Show that aa;»+ 6x' +cx+ d is divisible by x' + b' if ad=ac. 6. Show that («+/,+c)*-(a I /')^- (6+c)*-(c+«y-i- a^-ft^ -fc*=12rt6c(rt-|-6-fc). 7. Investigate the rule for finding the L. C. M. of two quantities, and find the L. 0. M. of 2x»+2x^-x+l, and *» +a;^-2x+2. a If -"- = "^ b d '■ . = (n in number,) prove that — —'-Ll J bdf. . . \_aH;c "+.... 9. If a, 6, c be the three sides of a triangle, prove that a'+6^+c^>a6+i;c-fac<2(a6+6c+ac). 10. Solve the equations : (1) ^ .^2^ llx-[ 18 «-! x-2 ■ilx-18 (3) 26VaiHi = (y^-.l)V2aq-265: miKUMBKIAXii KXAmaxnON PAPEBS. 33 'om the pro- f their sunj )03itive and ) wlien m is raii;al poly- in order to 27 by 7x» vision. VI. of two -1, and «' at ace. . . bdfTT. > that ^cr. 9. 1. Why are the signs + and - used to denote operations and also signs of affection ? Can we interpret the meaning of such signs of affection independently of a knowledge of the specific nature of the magnitude represented by the^syi.bols to winch they are attaclied ? and /f w "■"' "'' "■ '"''''-"'' ^''-'''- ^'^y + V-2.V. and tod what must be subtracted from the sum to leave the remamder 2x^—3x'y + y\ X 4(. + 3) that :t may be divisible by x-G without remain- der ? (6) If the dividend be ^a^b^+2(3a*-.2b*)-.ab(5a^^nb^) and the quotient be 2(a + 6)a4-(a^_6.), wl^t is the divisor? 4. Verify the following expressions : (1) 8(« + b + cy-ia + by-.(b + c)3-(o + a") =3(2a + 6 + c)(« + 2b + cXa + b + 2c). (2) (a+b-2cr+(j, + ,^2ar^(c + a-.2hy = 3(a + b-2cXb + c~2a)(a + c~2b). ' Tr^JZT'^l T""' '"' ""'"« "'" ""^^^^ Common Factor f two algobra.c quantities, showing under what ii,„i. tat^ons factors may be introduced or suppressed at an, Z Find the H. 0. F. of ...^v+y and ..+2„^+„.,,_,; Find the L. C. M. of 2h(x' 4K-^''-10x + 24> + X--20), 3Kx»-a:-30), and '|fl 34 INTEKMEDIATE EXAMIXATION PAPERS, 6. Define a fraction, and from your definition show that the value of a fraction remains unaltered by multiplying or dividing, both numerator and denominator by the same quantity. Simplify the following : a' + b^ -c' (a + c + b){b + c~a) (1)1- 2ab 2ab (2) (3) X 1^' .3n_l X""— 1 X" + l ' a^-jb-c)' b''—(c-ay c'~(a-by .+ -o + -,l (a + cy—U' "^ (a + by—c' ■*■ (6 + cf—a'' 7. Find the square root of, (1) x^+\+2(x~^)-l. x" \ a; ^ yi x^ ^y x/ '. 8. If x+y4-.=0;then ^^'-^'"^-^ + ^-(^'-^'> +^^^^^=0. « Z Z—X X — u 5 '2" y—a x—y 9. Solve the equations, m "^+3 x + 4: X— 6 x"— 2JI-15 x+1 x + 2 X— 4" (2) xy yz -9 xz x+2y 5' 2i/ + 3r:"'l3' 3x + 42 13' 10. A person sets out from A, and travels towards B at the rate of 3^ miles an hour ; 40 minutes afterwards another sets out from B to meet him, travelling at the rate of 4:h miles an hour, and he goes half a mile beyond the middle of the distance before he meets the first traveller ; find the distance between A and B. UfTEKMEDlAIi; EXAMIxNATlO.N PAl'EKS. 35 =0. (Statics ant) i)L'i>ro0tatks.-|Jo. I. 1. Give definitions of the following :-(l) the "resultant" of two or more forces, (2) the " components ' of a force, ^3) the "tension " of a strintr 2. Enunciate the parallelogram of forces, and supposing It proved as respects the direction of the resultant, complete the proof as respects the magnitude of the resultant. Two forces, one of which is double the other, act upon a particle m directions making with each other an angle of 120° ; find their resultant. 4. Show how to find geometrically three forces, which actmg at a point in given directions, will be equivalent to one given pressure acting at the same point. 4 A force of 301bs. in a direction making an angle of 60' with a horizontal hue is the resultant of two forces which make angles of 45" and 120^ respectively, with the s.n e horizontal line ; find the magnitude of these forces. 5^ -45 and 5(7 are two uniform beams united by a hinge at B, and resting on walls at A and C, A weight of 100 lbs 100 lbs The beam aB makes with the vertical an angle of 45,. ncl the beam HP. ,r. an,lc of 30- find tlie horizontal thrust at A and C, and the pressure on the walls. •M IN'JKRMEDIATE EXAMINATION PAPERS. 6. Define the moment of a force about a point or an axis to which its direction is perpendicular. State the conditions necessary and sufficient for equilibrium wlieu forces act in one plane on a rigid body. A uniform beam AB, whose weight is JV, rests in equilibiium between a vortical wall EG and the horizontal plane AC, both smooth; CE is a string without weight, attached to a point E in tlie beam. If BAC^Ao", and ACU=30'', find the tension of the string. 7. Define the term "centre of gravity ; " and show how to find practically, the centre of gravity of an irregularly cut piece of cardboard, proving the propositions on which your method depends. The sides of a uniformly heavy tria-igle are 3a, 4a, 5a, respectively ; find the centre of gravity of the remainder after the inscribed circle is removed. 8. A uniform straight lever is sustained on a fulcrum at the middle point, and is kept at rest by two given weights ; where must they be placed in order that the distance of the one from the fulcrum may equal the distance of the other from the extremity? And where must the fulcrum be placed, if the position of the weights be reversed ? I or an axis ^uilibrium , rests in liorizontal fc weight, =45°, and >w how to ilarly cut lich your t; 4:a, 5a, eraainder Icrum at weights ; 36 of the he other ;rum be INTERMEBIATB BXAMI-NATION PAMCaS. 3? Mo. % 1- " A fluid presses equally in all directions." Explain this statement, and show how the pressure of a tiuid " at a point " is measured. A cubical box, whose edge is one foot in length, is closed by a horizontal lid ; an opening of one inch area being made in the hd, and a piston, whose weight is 1 lb., being inserted find the least weight which must be placed on the lid to keep it down. 2. State how you would find the whole pressure which a liquid exerts on a surface immersed. Find the pressure on a vertical rectangle 10 in. lon<. and 6 m. broad, immersed in water, with its longer sidcs^iori- zontal, and with the upper one two inches below the surface 3. State the conditions of equilibrum of a body floating in a fluid. A cylinder, having a weight of 1 lb. on its top, floats in water with half its axis immersed vertically ; on the weight bemg removed, it rises through one-sixth of its axis -, find the weight of the cylinder. 4. Define .^coijic gravity. To what unit are specific gravi- ties generally referred, and how can the weight in pounds of a given volume of a substance be ascertained from its specific gravity ? ^ Tke specific gravity of gold being 19.4, find the ed^e of a cube of gold which weighs one pound •^8 INTBKMEDIATK EXAMINATION PAPBES. 5. A ball of gutta percha, 2 in. in diameter, encloses abaU of cork 1 in. in diameter, and iioats in water. Specific gravity of gutta porclia is .98, of cork .24. Find what proportion of the ball will float above the surface of the water, 6. Describe the common barometer. If the tube be not exactly vertical, will the indications of the instrument be incorrect ? A water barometer has its tube inclined at 60' to the horizon, find the length of the graduations which measure variations of 1 oz. on the square inch in the atmospheric pressure, taking roughly an atmospheric pressure of 15 lbs. on the inch to be capable of sustaining a column of water 34 feet hicch. How would change of temperature affect the indications of such a barometer ? 7. Supposing the specific gravity of a man, of water, and of cork to be 1.12, 1, and .24 respectively, what ^ ,antity of cork must be attached to a man weighing 150 lbs. that he may just float in the water ? 8. A ship sailing into a river "sinks two inches, and after discharging 12000 lbs. of her cargo, rises one inch ; find the weight of the ship and cargo, given specific gravity of «ea water =1.026. INXJilliliSDlATK EXAMINATION VAPEUS. 8d loses a ball ific gravity portion of be be not ument be 0° to the measure nospheric )f 15 lbs. water 34 ations of T, and of mtity of t he may nd after find the 7 of sea 1. What is meant when a line is said to represent a forco ? Represent on paper two forces of 301bs. and 401b3. respec- tively acting along lines inclined at an angle of 00°. Assum- ing the point of intersection and the position of one line to be given, in how many ditferont ways may the forces act in conformity with the above directions i 2. State the principle of the triangle of forces. A rod A B without weight can turn freely around a fixed point or hinge at one end B ; it is held in a horizontal posi- tion by a force C of oOlbs. which acts vertically downwards through its middle point, and by a force P wliicli acts at the end A. in such a manner tliat the angle BAP eciuals 30°; determine P and the pressure on the fixed pcant. 3. Five forces act upon a particle. Their magnitudes are represented respectively by tlie figures 1, 2, 3, 4, 5, their directions make the angles 60", 120°, 180°, 240\ 300°, with a fixed line ; find the magnitude of a force wliich will just counterbalance the tendency of the particle to move. 4. State tlie Principle of Moments. Prove the Princii:)le in the case of two intersecting forces and their resultnnt. 5. A uniform rod has at one end a small heavy ball ; tho ball is pushed gently along a table wit!i the bafl foremost and falls ofi" when a quarter of the length of tlie rod is beyond the edge of the table ; show that tlie ball is as l;cavy as the rod. 0. Find the ratio of the Power to the Weight in the Third System of Pulleys. In the above system the strings are fastened to the bar wliich supports the weiglit at a distance of 2 inclios from each other, this being the radius of eacli pulley ; find from what point the weight must be suspended in order that tli^ bar may be kupt horizontal, the weights of the pulleya being neglected. 40 INTEUMEDIATR EXAMINATION PAPBRS. 7. Stfvto tho Principle of Virhml v„i u- that it is true in the syst m i thl l"" '"^ ^'"^^ SJiow that tJiis in^incinlc 1 o " ^'^^''^"'^ ^"^«*^^«"- a weight is rail bv '''f ''''' '''' ^"'^^ "'='<^ ^^'»«" i any t],o case will, maclunos in practice » Wliy ) rectangular gate whose welht' " scIL Ih" " ""' °' " ^ 'Uioies, and whose length is 8ft. height 4ft. \ ilo. 4. 1. Define a fluid, and mention any exoerimpnfa ; -n . tion of its characteristic property. '^P'"™'"*^ '" ^""'^^ra- A vortical cylinder containing water is Ho.Prl K u (•hie +,,1, 1 • . ' ^"" closed at its unoer pnd his tube being rigidly connected with the vh^oT U I^yh wiJI the water rise in the tube i ^ ^""^ 2^ Define the terms Density and Specific Gravity. m^::^'::^'''^' ^^.^ ^^^ whose density is 12, are ■1- Till, squares, whoso sides are t in,! Ji :„„i, ly, are imiiicrseii verticallv in » fl /?, ' -^'Pective. "Uelto its .urtac Th Vrsts^ l""-;"" """'^ ?"• depth of 4 inches beneath Z ZlV^:'Tf'T " which the second square must be sunk sot^aetr " '" on it may be 3 time, th.t m, the W '"'''""■'^ and prove ■ question. tJiiit when seful work 'iny power, e? Why? hormmtnl vor hinge, ust on the I case of a centre of one hinges Ft. 1 ilhjstra- * heavy- micating •per end, 1. How 12, are c-nsity is le-third. pective- ng par- ide at a spth to ressure INTEKMEDIATE EXAMINATION . a. KR.S. 4] 4 If a cubical .essel be half filled with mercury and half nth wa er, compare the pressure on the .side, wkh the p e sure on the base which is horizontal. ^ 5. When a substance is weighed in air, in what respect does Its apparent weight differ from its weight ,-. raZT whcth.z the day was bright and frosty or threatening to rain ? Show how to find the specific gravity of a solid by wei' upper extremity of the diamet " i^^^ ; 1^ l""' "' "" be pressed vertically „p,vard<. fhnrli r ' '"^^'^^'' ^" ^"^^^ A beam weiorhina 140 lbs. and ton f„ /• , two points four feet from ea ] e ,1 V f.^ ^'''"'^ ''''' "" which is unable to overture on ." '^' '''^'''' ^^^^t it is placed. *' *'" ''^'^'^^^' point of the beam INTRHMEDIATK EXAMINATION PAI'KRS, 4n 6. A rcid 11 inches long has a weight of 7 ouucom at oiio end, and a weight of 8 ounces at the other end, atul is found 10 be in eciuilibriuni when baknced on a fuh-nnii 5 inches from the heavier weight. If the weights are iiitercliangod tho fiilcirnn wuHt bo shifted jf of an inch; find the weight of the rod, and tho position of its centre of gravity. 7. 1' Wi und W^ be the apjiaront weiglita of a body when placed successively at tho two ends of a balance, what i:i its true wdght, (1) when tho arms are unequal ; (2) when one of the sca.es is loaded ? If ona of the arms of a b.tlance is twice as long as tho other and a weight of one pound is put in the scale attached to the shorter arm, will a customer gain or lose by buying two pounds, weighing one pound in each scale ? H A weight is placed upon a horii:ontal table which has thno legs A, B and G ; the portion of' the weight supported by A is 8 lbs., that by B is 5 lbs., and that by C is {) lbs. Find tho weight and its position upon the table, the distance bptweeu the legs being 2 feet, 4 feet and n feet respectively ? 9. Find the ratio of the power t- wei_,ht in the screw. Five turns of a screw working in a lixed collar have tho ellect of raising the end of the screw one inch ; what would be the effective force at tho end of the screw in the direction of its axis if a force of 10 lbs. were applied at the extremity of a lever 5 feet long working in the head of the screw ? 10. A beam is to bo placed against a vertical wall, and it is required that its inclination to tho horizontal Hoor on which its lower end rests shall not be greater than 30" • find the position of its centre of gravity, so that it may not slip at that angle when its coefficient of friction at each end is .5. And show that althouL-^h a beam may be made to stand at an inclination to the horizon when the floor is rouch and the wall smooth, it cannot be made to stand at any but a ver- tical position wlien the floor is smooth and the wall rough. 46 intbumediatb bxaminaxiok papbes. Explain the exp £io. 7. ital equa] . . - - process by which mt, euuaj transmission of lluid pressure in all directions is proved: aud define the meaning of the term "pressure atapoint." 2. State and exi-lain tho Hydrostatic Paradox. De.ccribe Bramah s Press. The diameters „f the i-iston being ore and hve and the advantage of the lever ten, what power would produce a pressure of iwo tons V 3. Give the rule for finding the whole pressure of aiuid on a surface exposed to it. Compare the pressures upon the three upper aid three lower faces of a cube suspended by one of its angles in a ho- mogeneous fluid at a deptJi equal to the side of the cabe. 4. Define specific gravity, and show how to find the specific gravity of, (1) a soHd ligliter than water; (2) of a flu^d A piece of wood weighs 7 lbs. and a piece of iron Aveighs 7-8 lbs. m air, and G -7 lbs. in water; the wood and iror to- gether weigh 6-3 lbs. in water ; what is the specilic gravity of the wood? ' 5. A watch chain which wciglis 200 grs. in air, weighs only 184-7 grs. m water ; find the ratioof the volumes of brass and gold m It, the specific gravity uf brass being 7.8, and of gold 6. Describe Nicholson's Hydrometer, and compare by means of it the specific gravities (1) of a solid and a fluid (2) of two fluids. A Nicholson's hydrometer is used as follows :-51-72 grams 18 placed on the upper cup, a Iragment of metal is placed on the cup, and It is found noc.-Hsary to take off 14-85 grams to make the instrument float at the same level ; the metal is then placed in the lower cup, and 2-03 grams added above to restore the former level j find the specific gravity of the metal. 7. Enunciate Boyle's law comieaing the volmne and t^n- Bion of a giveu weigiit of air. lyXBRMBDIATE EXA.MINATION PAPERS 47 If the height of a barometer changes from 755 mm. to 770 ram., what is the change in the weight of a litre of air at 0°C. 'i (The weight of a litre of air at 0°C and under a pres- sure of 700 ram. of naercury is l'2yi-> grams). 8. Describe the consti'uction and action of a Smeaton's single-barreled air-pump. A piece of cork is floating in a basin of water, and the basin is placed u der the receiver of an air-pump. State and explain the effect of pumping out a oortion of air in the re- ceiver. 9. Describe the construction aiid u-plain the action of the Forcing Pump. In a forcing pump the area of the piston is 3 '5 square in- ches and a power of 77 pounds is employed in forcing the piston down ; find the pressure of air within the air cham- ber. 10. A bubble of gas, whose volume is 2 cubic inches, be- gins to rise from the bottom of Lake Ontario ; what will be its volume when it bursts at the surface, the depth of the lake being 600 feet, and the pressure of the atmosphere 15 lbs. on the square inch ? £io. 8. To Triai^nle of Forces inclusive 1. Explain clearly what you understand by the weight of a body. A cubic inch of lead is sus ponded by a spiral spring, and the consequent elongation of the spring is observed. If the experiment were repeated at the E([uator, would the elonga- tion be the same or different 'i Give your reasons. 2. Define Force, and explain clearly the method of esti- mating and comparing statical forces. Show that forces may be properly repreBented by straight 48 INTEEMIDIATE .tlMJSATION FAn^ 7 lbs. acting afc an angle of 60 degrees. ^^ 5. Six vertical smoof posts aro fivo^ • xi. equal i„t,„,,,, ,„„„^ tho'o tumLtce '„" 1 e*^™""'/' sure on each post. lesultantpres- n^M a„„. .,., .„„„ ,„, ^ ^^^^,^- «". .nw ao.a „, thL!Mw :ra' r„?::''""t -' ^""-- h- » .e„t three force, ^.th'^ Ja^T™'''' " "-"> -P- »-„--._, „. ti„cl tliu racio of tlie other forces. INTERMEDIATE EXAMINATION PAPERS 49 S If tliree forces, the magnitudes of which are 3P 4P Tf ^'tn^ ''"'' P"*"* ^"'^ ^^'^ ^" equilibrium, show tlmt the forces 3P and 4P are at right angles to each other. 9. A rod 4P, without weiglit, can turn freely round a fix- ed point orjnnge B; it is ],eld in a liorizontal position by a torce Qoi oO lbs., which acts vertically doun wards throu-h Its middle point, and by a force P which acts at the end!! in such a manner that the angle BAP equals 30" ; determine ^ and tlie pressure on the fixed point. 10. A beam, capable of moving about one end, is kept in a position inclined to the horizon at an angle of 60° by a s rmg attached to the other end. The string is inclined to the horizon at an angle of G0° in an opposite direction ; comp.are the tension of th. string with the weiglit of the beam |T(T. 9. 1. Explain the meaning of tlie statement, "Three forces represented in magnitude and direction by the sides of a tri- angle taken in order, will keep a particle at rest." Show Ws P'^'P"'^*^^^'' '' '^^"^^'^ ^^«"^ <^he parallelogram of 2. A wo.glit of 8 cwt. siH^pended by a rope from the top tloor of a warehouse, on one side of a street 50 feet wide is required to be drawn across by a rope from a floor! th point in the first rope 35 feet below the point of suspen- -on, wha will be the tension of the ropes Ihen the 2Z 13 vertically over the centre of the street ? 3. Explain the meaning of the term Resolution of Forces Show how to resolve a given force into two others at right an^es to eacli other, and one of which shall be half the original force. 60 INTERMEDIATE KXAMIXATION PAPBRS U i1 4. A peg or tack A has four cords afctachod to it, at the' end of which four men pull, each with a force of 100 lbs., and in direction, which are all in the same vertical plane,' and make cqua. angles of 30^ with one another. Find the magni- tude and direction of the strain upon A when a gun weigh- ing 18 cwt. is hung upon it, and when the angles which the outer cords make with the horizon are equal. 5. (a) If the angle between the directions of two forces be increased, their resultant will be diminished. And (/i) if three forces in a plane acting upon a point be proportional to the sides of a triangle constructed upon their directions taken in order, each of them will be equal and opposite to the resultant of the other two. But (y) if an angle of this tri- angle be increased, the opposite side will be increased, and, therefore, the resultant will be increased. Demonstrate the statement ^a) and (/?), and reconcile the apparant anomaly involved in them as indicated in (r). G. What conditions must be satisfied in order that forces acting on a bar which is free to turn about a fixed axis may not produce m'.Lion about that axis. 7. A uniform lever, whose weight is 8 lbs. and length 3 feet, has a weight of 20 lbs. suspended from one end and 14 lbs. from the other. Find the position of the fulcrum when there is equilibrium. 8. A piece of timber, 25 feet long, balances upon an edge at a distance of 10 fcei from one end, and, when the edge is shifted to 12 feet, it requires 56 lbs. to be placed upon the other end to make it balance- Wliat is the weight of the piece of timber ? /NTBRALEDIATB EXAMINATION PAPERS. to it, at the 100 lbs., and plane, and 1 the magni- giin weigh- ts which tlie f two forces And {fi) if portional to ;tions taken )site to the of this tri- eased, and, nstrate the nt anomaly that forces d axis may i length 3 nd and 14 3rum when n an edge lie edge is I upon the ;ht of the 61 4flo. 10. 1. Define the terms, "force," "equilibrium," the "resul- tant" of two or more forces; the "components" of a force. 2. What force must a man exert in a horizontal direction to draw rt weight of 3 cwt. four feet out of the perpendicular, jupposing t inispended from a point twenty feet above that at which ho api)lies his strength ? 3. A parallelogram ABGD is acted upon by forces in the directions and proportional to AB, BD, and DC; find the direction and proportional magnitude of a fourth force which will produce equilibrium. 4. Show how to find the resultant of any number of forces acting at a given point and making known angles with a given straight line. Four forces of 51bs., 61bs., 81b.s., and 1 libs., make angles of 30°, 120^ 225°, and 300°, respectively, with a fixed straight line ; find the magnitude and direction of their resultant with reference to that line, 5. Three forces 5, G, and 7, all in the same plaAe and mak- ing equal angles with one atiother, act upon a point; what force, acting in the same plane, will keep the point at rest, and what angle must it make with the force ? 0. A rope runs through a ring to which is suspended a weight of 1 cwt. and two men pull at the ends of the rope ; find its tension, supposing the hands of each man to be 3 ft. above the ring, and the length of the rope to be 12 feet. 7. Define the moment of a force with respect to a given point. What is the physical notion involved in the idea of a moment? Show how a moment may be represented geometrically. Prove that if two forces meet in a point their moments with respect to any point situateaon their resultant are equal and opposite. 62 8. ii\ ITERMEDIATE EXAMINATION PAPEns, ig sum uniform rod 3 ft. hori ontau, in tl.o hand, .... «,,„orr.a t,y n.oans of a finger t c rod at the e^d ; find the pressures exerted by the finc^er and tliunib resiioctively. ^ ^^^ 9. A uniform plank 20 feet long and weighing 42 lbs is 'Xrrt= '? '*^^'^' ^^^^"""^' respectu-oly 7^ lb «nd 99 lbs. stand on the plank eacli one foot from [he end find the position of the rail for equilibriu.n * weilh!!;!; IZ ^"''' 1""°" ''''''''' ^"'^ "^^^'^ « third boy wm f Jp. T"' '^""^ '" "« *" '"'-^'"tain equilibrium without shifting the plank on the rail. cas'e'of^fo"s^ "l ^f ' ""'" •'' ^'"^^''''^^ '"■«^^" ^^ ^^ow that in case of tvvo such forces acting upon a rigid body, their " cen t e divides tiie straight line which joins their joints of Id' plication m the inverse ratio of the forces. ^' 11. Find the centre of gravity of the figure formed by describing an equilateral triangle upon one of the sides of I INTERMEmATB EXAMIVATION PAPBRS. 63 ces is helo * of a finger liiimb over the finger 42 Ib.s. i3 aly 75 lbs. 1 the end ; third buy luilibrium ow that in eir " cen- its of ap' )rmed by iides of a 1. Define the following terms, giving cxamplea :— Atom, molecule, atomic weight, molecular weight. 2. Distinguish between a chemkal compound and a mechanical mixture. Why is the atmospheric air declared to be a mixture and not a compound ? 3. What is meant by the atomicity of an element ? Give the atomicity of as many of the non-metallic elements as you can. 4. How would you demonstrate, experimentally, the com- position of water and air 'i 5. I have four vessels containing, respectively, nitrogen, hydrogen, nitrogen dioxide, and marsh gas ; give a precise account of the nature of any result observed upon mixing oxygen with each of these gases, and of the results produced on introducing a lighted taper into the several mixtures. 6. What is the cause of xiame ? Describe the construction jf the flame of a candle, or of a spirit lamp, explaining why the former is luminous and the latter not ; and state what means you would resort to for increasing the luminosity of a flame. 7. By heating coal in a retort, a mixture of the following gases is obtained : — Olefiant gas, light carburetted hydrogen, carbon monoxide, carbon dioxide, sulphuretted hydi-ogen, and ammonia ; give the composition, and a brief statement of the properties by which each of these gases is distinguished. 8. What is a crith, and how is it employed by chemists ? 9. From the percentage analysis of a compound how could you determine its formula 'i A body yields by analysis, 43-75 per cent, of nitrogen, 6-26 percent, of hydrogen, and 50 per cent, of oxyen ; what is its formula and name ? M INTERMEJMATE EXAMINATION PAPERS. Chetntetrs.— N'o.2. 1. Define 3 teniia acid, base, and salt. 2 If I allow a current of stea.n to blow throush some ir.,,. na^lB heated to redness in a crucible, what ha^^ensT If substitute copper nails for iron ou.s. in the above experiment how will this affect the result ? P^^iment , and wa or, and are reii proceed ? I each case. I a piece of 'xygen gasi ; or domestic ss " as ap- k " terapo- de of dis- ess for ob- fie process iid obtain- TOuId you Give a jctingthe measured OAv much ettve «^ compound of Oxygen and Hydro- gen. How would you prove this experimentally.? What are the characteristics of a chemical compound ? What is an Element ? How many cubic centimetres of Oxygen and Kydrogen at 0°c. and 700 mm. pressure can be obtained by the decomposi- tion of 1 gram of Avater ? 2. How would you prepare Oxygen from Manganese Diox- ide (2) from Maganese Di(..xido and Sulphuric Acid ? Express the reactions by equations. Wlieu Munganese Dioxide is added to Potassium Chlorate the Oxygen is given off at a much lower temperature. Give the most probably explanation of the action of Mangar.e3e Dioxide in this case. 3. How would you pi ove experimentally that Carbon Diox- ide is a constituent of the i.tmoaphere ? What purpose does it serve in the atmosphere ? 4. How would you prepare Nitrous Oxide ? In what re- spect does it resemble Oxygen, and in what respect does it diifer from it ? 5. How would you prepare Ammonia Gas? Explain clearly how you would find the density of Ammonia. What happens when Ammonia Gas and Hydrochloric Acid Gas are mixed together ? Illustrate the reaction by an equation. ^ 6. What is meant by the Halogens ? Explain the forma- tion of Chlorine (1) from a mixture of Manganese Dioxide and Hydrochloric Acid. (2) from Common Salt, Manganese Dioxide and Sulphuric Acid. Illustrate by equations in each case. What happens when a mixture of one volume of Chlor- ine and two volumes of Hydrogen is exposed to the sun's light. How will water act on the product of the reaction ? • 7. I want 10 litres of Clilorino. How much salt, man- - a.„i„i„ •, to show ,i densation ? '^'^"^ ^^'^ S'l^^^"^ «««- ►er on Sul- •ogeu, why lent? Sulphuric hat is the >d ? Why ich Phos. )horus act Following here you irbonate, Sulphur, Express between allowing r would ochloric obtain taining would us con- INTKRMKDIATB EXAMINATION PAl'KRS, 61" 7. When Nitric Acid is poured upon coi)por, what takes place ? Represent the reaction by an equatiim. 8. You have some Ammonium Carbonate, and Nitric Acid, and are required to make and collect lauRliin,:,' gus from tliese materials ; how would you do it ? Describe the apparatus you would employ, and give a sketch of it. What are the chief properties of laughing -as, how does it resemble Oxygen and how distinguished from it? 9. You have given you some Sulphur, Water, and Nitric Acid, describe how you would make Sulphuric Aci.l from these materials. How would you recognize the Sulphuric Acid when you had made it / 10. You have a mixture of chalk and charcoal, and wish to •eparate the charcoal £rum the chalk, how will you do it 1 11. Describe some experiments to show the dilierent " modes of chemical acti(m.' 12. 40 cc. at the nomal pressure and temperature, of a gas containing Oxygen and nitrogen, were mixed with 37cc. of Hydrogen and exploded ; 32ce. of gas remained. What was the composition of the original gas • #xr. 5. 1. State the -eneral character of acids. What is meant by the "acidreaction?" Wliat is an alkali ? What is meant by the alkaline reaction ? 2. State the physical chemical characters of Oxygen, flow does it occur in nature ? How can it be obtained pure ? In what way do planta produce free Oxygon ? 3. Explain the terms " Oxidation " and "Reduction," and give examples. 4. What is Combustion ? What function does Oxygen perform in Combustion ? What is the relation of Oxygen to the process of respiration in aii--bvsathin- and h. ,atef. breathing animals ? 58 INTERMEDIATE EXAMINATION PAPKRS. 6 State tl.e physical cJiaractors of Nitrogen ? How can Vi^^r^' -^-^-i--.onof.u..e::: 6. Ho., docs Clilorino occur in nature ? Ho» i. Chl„ri„. 8. You have given to you a piece of charcoal weiahir,cR grams, and litres of oxygen. How much Carbon Zx le .v of the Carbon in Oxygen, and how much if any, wiU be left^ 9. How does Sulphfr occur in nature? How i, it ob tamed pure? State the action of heat upon it. Gi the" formula, the character, the percentage composition and T modes of preparation .f the two mo J impor^rrcr^f a^^! 10 How much dilute Sulphuric Acid (density =1.3) must be taken to neutralise ^Oc. c. of a solution of Ln o„irof whiph the density is .9 ? ^iumonia of Elementary Principles and Oxygen. 1 Explain the terms Chemical Combination and Chemi- cal Decomposition, and give examples of each. .nuJl'V" "'' ^^^"■'^"'^ ^^*"^^" ^^^^^^ts and com- pounds? How would you endeavour to ascertain wliether a certam substance is an element or a compound ? INTEIIMEMATB EXAMINATION I'APEKS. .« 3. CJhemical combination is said to take jilace in certain deflnito proportiuua. Explain tliia and give examples. 4. NVliat hap[)ona whuu a gluaa rod, moistened with aul- phuric acid, ia brought very near to a small heap of mixture of sugar and ixjtassium chlorate, but so as not to touch the heap i What characteristic of chemical affinity is illustrat- ed by this experiment 'i 5. Enunciate ''Avogadro's Law," and st;-*- briefly the evi- dences in ita favour. Deduce from it :. /ule f- ■ finding the atomic weight of an elementary gas, a:.d also tli densFty of a compound gas. 6. Define a " molecule " and an "atom, illustrating the difference in the meaning of these terms. 7. Express by e■"=" «>« action. P'oi'an.l.o,, „f „^yg,„ , ^zplain its J; '^:f:;:ti?™: ;:i::,t7' r^ *; "■ ^ - »' -- «on, and state >£^>,r^:ZS.. """ ''° '=™'""'- 8. Of what is water comnoHcd 2 vvi,^ t position? How and when w^rtll ,n °"'™'' """<'"'■ fte ways y„„ kno. U^l^Z^'T"^ ■""<''" Give all gen from water. ""•'"""S (<0 l.ydrogen and (6) oxy- watr;^i*; ™r,^™'» "' ;"■'""'"- fo""^ iu natural Wl.at do you ™dZ: jj tt^te L'Tr-t^ f '-"™ ' -t;::;;;r;::s:;:;-x---^eair,Be. oo«nisi„, witu ^^^>^.:rj:z:::j^j:^ this state- ng weight impurities ? solution re placed by each yield the th potas- plain its c of oxy- combus- its com- ?ive all [b) oxy. natural ration j 'soft," ss of a ? De- which I those 'or re- phere, INTERMEDIATE EXAMINaTIOX PAPEE3. Ql 11. Isaira,nechanical mixture or a chemical compound? i^ive reasons in support of your answer. scale auA'^T" ^"^"-^"^ I-epared (a) on the small scale, (h) on the large scale ? AVhat impurities are generally present m the commercial acid ? gt,neraiiy ila. 8. 1. Name the elements contained in. an ordinary candle and explain fully the chemical changes which occur when i Durns in air. 2. State briefly the laws enunciated by Dalton and by Gay Lussac on the subject of chemical combination. One hundred grams of iron filings are heated with the same weight of sulphur till combination takes place Which el mucront"^"^ ^'^ ^''"'''^ "' "'"'"'' *'^*'' *^'' ''^'*^"^' ^"^ ^°^' 3. Name four oxides which when simply heated lose oxygen. Express each reaction by an equation. 4. Name any four metals which if dropped into hydro- chloric or sulphuric acids decompose these acids with evolu- tion of hydrogen. Give equations. 5. What changes are produced in air by the breathing of animals, and during the growth of plants ? A candle is burned in a closed bottle of air till it goes out, and a mouse is kept in a closed bottle of air tUl it dies Wliy does the candle go out and the mouse die ? 6. How is the reraarkilble uniformity in the composition of the air explained ? 7. What happens when hydrogen is passed over heated copper oxide ? Express the reaction by an equation. Ex- plain how the action of hydrogen on copper oxide may be used as a means of determining the composition of water. 02 INTERMEDIATE EXAMINATION PAPERS. of^any expenment which proves the existence of nitrogen in svntLl^r""' •''"" "^^ ^""^°"^^ be prepared (a) by synthesis, (6) from nitric acid, (c) from ammoniuLalts ? How af 'il ^^r '"^n " °''"' "' "^*"^'^' ^«> ^^^^' (^) ««™bined? sttofth r""*'"^"''°^™^"^«^^b'^" proved to con- Slat ot the same substance ? and 15-^0,??' "T: °' T"'*'™ *■""'*'* "■"»'"«"> "' '« »'"■ ^.W the be INMRMBDIATE EJCAMINATIOKT PAPBES 63 Book I. ; 1-16. 1. (a) Define the terras : circle, plane, superficies, postu- ate, and axiom. (•') Write out Euclid's three postulatea. 2. Show that the following are incorrect : {a) "If unequals be added to unequals the wholes are unequal. " (b) "Parallel straight lines are such as do not meet however far they may be produced." 3. Distinguish between problem and theorem, and be- tween hypotheses and data. • 4. («) The angles at the base of an isosceles triangle are equal. (b) What is a corollary ? (c) When is one proposition tlie converse of another? (d) What is the converse of the above proposition? 5. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles must be equal in all respects. 0. (a) To bisect a given rectilineal angle. (6) Why is the equilateral triangle which is employed m the construction to be described with ita vertex remote from the given angle ? 7. (a) Tu draw a straight line at right angles to a given finite straight line from a given point in the same. (6) Distinguish between drawing a line ac right angles to another and drawing it perpendicular to it. (e) If the given point is at the end of th» given line iiow do you proceed ? 64 iwTKRMEbiA'ra i;xAMi:vATiaN papers. 8. (a) If at a point in a straiglit line, two otlier straight lines, upon the opposite sides oi' it, make the ad- jacent angles together equal to t;vo right angles, then these two straight lines shall be in one and the same straight line. (6) What is meant by an indirect demonstration ? (c) Why are the words " upon the opposite sides of it " necessary ? 9. (a) If one side of a triangle be produced, the exterior angle is greater than either of the interior op- posite angles. (6) Write out the enunciations of the various proposi- tions employed in constructing and demonstrat- ing this theorem. 10. If two isosceles triangles are on the same base, the dZf ^.^;.-'"^""^? *^^^^' ^^^tices, or that straight line pro- duced, wUl bisect the base at right angle* ler straight lake the ad- ight angles, in one and ;ion? ides of it " 16 exterior iiterior op- s proposi- )nioustrat- base, the line pro- INTERMEDIATB EXAMINATION PAPEK3. gg 1. If a series of connected business transactions U clas Bified undor tho heads of Capital, Merchandise, A. B Cish Interest, C D. , Bills Payable, E. F., Rent, Bills Receivable And Expense ; from which of them do we ascertain the Finan- cial Position of tlie business at any time by a comparison of the assets and liabilities at that time ; and from which do wo ascertain the same thing from the original capital and the subse(|uent gains and losses ? 2. What item of information is that which must be con- sidered ui both of the above processes ? and explain why. 3. If we sell goods to A. B. on account, in which Lod-er accounts are entries made ! Explain the object of each entry showing that each is made for an eydirdy different purpose.' 4. Give answers to tlie following, similar to those required in the preceding cxuestion. (a) Bought goods from CD., giving in payment my cheque on Ontario Bank. (6) Sold goods toEF., receiving in payment his cheque on Imperial Ban':. (c) Got M.N's note discounted at Ontario Ban' Face of note $000. Proceeds ^00, passed .o my credit. 5. Give Day Book entry for each of the following Ledger postings in Merchandise Acct, D«. _^ MERCHANDISE. Cn issT, Jan. 1; Capital •' 15 A. Bond " 31' Cash 7' Bills Rec. 15 Bills Pay. 28 B;>nk Feb. 1200 500 100 400 300 200 1881 j Jan. 10 I Cash 8 I Bills Rec. 17 I C Dunn 20 Bills Pay. Feb It II 3001 150 I 200 i coo' fifi IfKRMEBIATE EXAMINATION PAPERS. Jan it m' f 7-^ '\'' '""^'^ °' '">' tnmsactions irom m^knf M^^ ^ "'"' c"-ny the accounts, thus sho.... Jan. 1st, 1S81. $ 280 3590 87$ From 64 952 January lat, "i IJG to March 16. 1 i t i 1 4S2» 100 729 1 40 oil 611802 OoocU hand March '^aiMtal Ca,-h A. Bond Interest Bills Beceivablo E. Ford Mdse. Bills Payable Kent 0. Dunn Espenso ! 1350 3190 473 74 65.} 94(i 4025 §63 229 (J11802 Zo. 2. 1. Explain, and illustrate by an example, the difference betv^een pure, single Entry, and Double Entry Jn'y ^^^.f/°^^ *^« ^«rd "Balance" mean as used in con- ne t.on with closing entries ? Explain with special reference tothe^entryonCr. aide of merchandise accouL of tlfe goo": 3. lu which of the following accounts will the first entry be made necessarily on the Dr. side; in which on the Cr Bide; and in which may it be on either side :-Me tha„ d.se, ntere-st. Bills Payable, Cash, Commission, Bi k Ee' ceivable, John Smith, and Expense? Give realon !n eS." 4. Give an example of four Notes, each at two months, iia, rNTERMKI.IAi* RXOriNATlOU J'ArtKa and each having a different date, but all payable «n the same daj'. 6. In what respect do the Capital and Balance accounts a;;ree, and in what respect do tliey differ ?-in other words what information is furnished alike by both, and what mfor' ination does the Capital account give wluch the Balance ac coiuit does nol give ; and vice versa ? ttie last n. I stanzaa >• SJkiw e in the ii-y witJi ;heir Sweeps through the plain, and ceaseless mines On J3()cha»tle the moulderin;,' lines, Where Rome, the Emprosa of the wurld Of yore her eagle wings unfurled ; And here hig course the Chieftain staid Threw down his target and his plaid, And to the Lowland warrior said :— Bold Saxon ! to his promise just, Vioh-Alpine has discharged his trust. Stanza xii., Canto V. fa) Point out the figures of syntax 1 of rhetoric in this passage. (<>) " Three mighty lakes, " Name them. (c) " The mouldering lines. " Explain the reference. (d) Scan line (j. 7. Brian an augury hath tried. '">f that dread kind which must not be Unloss in dread I'xlremity, Tile Taghairm called, (a) Explain ful' his augury. (6) Give the derxvation of "augur.v" and "Taehairm. " use lomaoia. 72 INTERMEDIATE EXAMINATION PAIKUH. £iO. 3. 1. Who is the hero of the Udy of the Lake ? GIv,. rei Bons for your answer. 2. Explain the follow.-, ig taken from Canto VI :- («) Rousing eacl, caitiff to his task of cure.-A7. /. ('V ivind nurse of men. — »SY. I. (c) Courf of Guard.— *SY. 2. (d) Their /tKniefs rung— .S7. ^. (e) The Italian's t^oi/z/pr/ face. -St. S, (f) Thti Fleming. ~i^t. ."l, (^) Thou now hast -lee-maiden and harp. -67. 6 (/O Like errant damo.sel of yore.— 67. 9. 0') Their guerdon took.— ^7. W. U) Antique garniture decked the sad walls. -Si /j. 3. "But Ellen boldly stepped between, And dropped at once the tartan screen ; So, from his n.orning cloud, appears The sun of May, through summer teara. The savage soldiery, amazed, As on descended angel gazed ; Even hardy Brent, abashed and tamed. Stood half admiring, luilf ashamed. "~.S7. 7. " As the tall ship, whose lufty prore Shall never stem the billows more, Deserted by her gallant band, Amid the breakers lies astrand— So, on his couch, lay Roderick Dhu !"-,Iain, and necessary was ended 3e said on and state t order- Jen, and re ; and parson, as made ers. XNTBRMEDlAXi; EXAMINATION PAPERS. 77 go. 6. GOLDSMITH. 1. Sketch briefly the following particulars regarding Gold- (iinith : (a) Give a short account of his educati(jn. (b) Give an account of his travels. (c) How did he live after his return to England ? (d) Name his most important poetical and prose works. (e) What was his object in writing the "Deserted Village " ? (/) For what are his writings most noted ? (g) Name his most famous literary contemporaries. 2. (a) Quote from the " Deserted Village " lines to show his opinions regarding the accumulation of wealth and the decay of the peasant population. (b) Do facts justify him in holding such opinions ? 3. Quote his description of : (a) The Village Preacher ; (6) The Village School- master. 4. (o) And, as a hare wliom hounds and horns pursue, Pants to the place from whence at first he flew, I still had hopes, my long vexations past, Here to return — and die at home at last. (6) As some tall cliff that lifts its awful form, Swells from the vale, and midway leaves the storm, Tho' round its breast the rolling clouds are spread, Eternal sunshine settles on its head. 1. To what does (a) refer ? to what (6) ? 2. Point out any figures. 3. Here to return — Where ? 4. Scan lines 3 and 4 of (a), and name the metre in which this poem is written. 5. My long vexations past. Expand into a clause and state its gi'ammatical connection. 78 miEESIEDIlTE EXAXmsilUi: PiPEHS, 5. Define the followin''"- '•Deserted Villngo.' by examples from the 6. •Paraplu.se this passage and parse the words in italics : iv)iii caie, tliat never nmst be mire • How West, he .^^ A 3 outh of labor with an age of ease; Id' T ?, "f ^^^'-^ «*-".? t.en,ptations try And smce tis hard to combat, learns to fly ; ^ Explore the nune, or tempt the dangerous de^p • ^< o surly porter stands in guilty statl, ^ ' To spurn imploring fan.ino from the gate ; But on he moves to meet his latter end, Angels around befriending virtue's friend ; Sinks to the grave with unperceived day, While resignation gently slopes the wajf And all his prospects brightening to the last, His heaven commences ere tlie world I. pasU Ho. 7. Disserted Villagis, &c!. 1. («) Oive a concise analysis of the Deserted ViJlaga (6 What was Goldsmith's object in writing it? itl'', '"" ?""••" ^'^S^"^'"^- '''- depopulation It deplores and the disorder it laments / 2. Quote his description of the Village Ale House. •^' r~ ^^^"^ "'^n o^ wealth and pride lakes up a space that many poor supplied • Space for his lake, has park's extended bounds ' INTERMEDIATE EXAMINATION PAPEKS. 79 Space for his horses, eaaipage, and hounds ; The robe tliat wraps hisliiubrs in silken sh)th Has robbed the neigliborin^^ fiekl« of lialf their growth • His seat, where solitary sports are seen, Indignant spurns the cottage from the green ■ Around the world each needful product flies, ' For all the luxuries the world supplies. (a) Point out any figures. (b) Scan the line beginning -Has robbed." (c) Explain the epithet silken us applied to sloth. Figure < id) To what does Goldsmith refer in the last two lines ? _ 4 Mary heard thein to the end without emotion, and cross mg herself in the name of the Father, and of the Son, an f ot f f. ' ^l'""' '''^' '""''' «^^' "--two;th7t ! oys of heaven, which repines because the body mu.st endure he stroke of the executioner ; and though I did not e^e that the Queen of England would set the first example o violating the sacred person of a sovereign prince, Tw£l submit to that which Providence has decreed to be Zy lot'' (a) Explain the use of the capital letters {b) Rewrite this passage, changing it from divert narra- tive to indirect. 6. (a) Define the following terms : couplet, rhyme, iambus, synecdoche ; and illustrate each by an examplJ from the Deserted Village. (6) Give the tests of a pefect rhyme. «. Thus fares the land, by luxury betrayed, In nature's simplest charms at first arrayed But verging to decline, its splendors rise, ' Its vistas strike, its palaces surprise Wliile, scourged by fanm,. from the smiling land, The mournful peasant loa.ls his /, nnihle band ; ™, " *"' ^^^J:^-^-"" oho arm to save. The country blooms-a garden, and a grave. 80 INTBRMKDIATK EXAMINATION PAPERS. (a) Paraplxrase. (b) Quote the lines to which " Thus " refers. (c) Analyze the words in italics. id) Parse : vergmg, wliile (line 5), and garden. 1^ ii |lo. S 1. A writer in the "Quarterly Review" characterizes the prose of Goldsmith as "the most finished model in our language, of purity, facility, and grace." Explain the terms purity, facility, and grace. 2. Campbell .ays that Goldsmitli "uses the ornaments which must alway distinguish true poetry from prose. " Distinguish between poetry and prose, and notice some of the "ornaments " referred to by Campbell. 3. Define onomatopoeia, personification, metonymy, pleon- asm, and illustrate each by examples from the "Deserted Village." 4. And thou, sweet Poetry, thou loveliest maid, Still first to fly where sensual joys invade ; Unfit, in these degenerate times of shame, To catch the heart, or strike f) ' ' Fare theo well ! " Did Goldsmith write any poetry after this ? If so, what ? (c) Explain the personal allusions. (d) Parse thee in the last line. 5. "Perhaps there is no poem in the English language more universally popular than the " Deserted Village." Its best passages arc learned in youth, and never quit the memory. — Chambers' Cyd. of Evg. Lit Point out some of these passages, quoting where you caa 6. (a) Give synomyms for shame, sensual, degenerate, charming, inclement, persuasive ; (6) And homonymes for throw, port, isle, indite, leaf, knell. 7.* In what connection do the following couplets occur :— (a) Those blazing suns that dart a downward ray, And fiercely shed intolerable day. (6) 'Tis yours to judge, how wide the limits stand Between a splendid and a happy land. (c) And still they gazed, and still their wonder grew, That one small head could carry all he knew. (d) Fools who came to scotf remained to pray, (e) And, all his prospects brightening to the last, His heaven commences ere the world be past. 8. Even now, methinks, as pondering here I stand, I see the Rur;il Virtues leave the land. (a) Analyze this sentence. (6) Give the etymology of " metliinks." (e) What is an impersonal verb ? a defective verb ? Giv« examples of these two kinds of verbs. p II IMTEliMKUI.VTB KXAMINATIO.N PAl'filUS. 83 Cnglisit C5iammnr.-|lcr. 1. 1. Show that the part of speech to which a word beloncrs depends on its use in the sentence. " What parts of speech may that, but and ivhat bo I Give sentences illustrating their use. 2 The verb " to be " is used both as a principal and an auxiliary verb. Give example of all its uses, being particular to state the purpose for which it is used. 3. General terms are of Classic, while specific terms are of Anglo-baxon origin. Illustrate the truth of this statement. 4. Correct the following where necessary, giving-reasons:- (a) I am very pleased. (b) Every one of you should try your best. (o) It lies between either you or your brother ..r your sister. (d) The crowd were umisually quiet. (e) Boys are of the masculine gender. (/) Those kind of books are better than these kind. (g) Neither of the books are authorized. 5. Explain the uses of the word self. ■ t ^J^f ^iifferent ways are employed to express the pk^-al m English ? State precisely what is peculiar in the words brethren, kine and children. 7. " Now, man to man, and steel to steel, A Chieftain's vengeance thou sJialt feel." 84 LNTEKMKl'MlK KXAMINATION PA.'ER.S. (a) What kind of a phrase is "man to ninn." {J>) Parse t]ie words in italics. (o) Distinguish between plwase and olause. 8. Distinguish between tlie following :- - (a) The king's picture. The picture of the king. (/>) The Lord's day. The day uf the Lord. (c) 1 liavu little money. I have a Mttle money. {(i) John loves James better than him. John lov«8 James better than he. (c) The lion's mane. The mane of the lion. 9. Decline the relative pronouns. Give rules for their correct use. When must Had take the place of who and which ? * n 10. " 'Now, truce, farewell ! and, ruth, begone ! Yet think not that by thee alone. Proud chief, can courtesy be shown ; Though) >iit from ccjpse, or heath, or cairn, Start :;t, t.-M- whistle clansmen stern. Of ihi,: -inisU horn one feeble blast Woviiti vV;a.i.'ful odds against thee cast. But fear iiot — doubt not — which thou wilt — We tiy this quarrel hilt to hilt. ' Then each at once hia falchion drew, Each on the ground his scabbard threw, Each looked to sun, and stream, and plain, As what they ne'er might see again ; Then foot, and point, and eye opposed, Li dubious strife they darkly closed." (a.) Give the etymology of chief, falchion, plain, ne'er, dubious. (6) Parse the words in italics. {r.) Analyze the last six lines. [d) Note any false syntax in them. i:n'KftMKi>rAT« axA-^rtxATioN papkiuj. 85 cing. ey. ohn lovMS for their who and e! m, neer, ^0. 2. 1. Name the inflections of oiich part of speech ; define gender ; di.-:tin^aiisU between gender and ^c\ ; and give ex- amjilea of the dillerent modes of distiuguialiiir,' masculine and feminine nouns. 2. Define case. If case is regarded as an inflection only, Tfliat part of speech has three cases t Why should th- "oun have onljf two cases ? t3. What adjectives cainict be compared ? Give rules for the correct use of the comparative and the superlative degree. 4. How are su))()rdinate sentences c(mnected with princi- pal ones '( Give examples illustrating your answer. 5. Classify the words ending in "nig" in the following sentences as to part of speech ;— (a) John lost his walking-stick, (6) Loving oar fellow- men is one of IMAGE EVALUATION TEST TARGET (MT-3) y; 11.25 |50 "™^S 2.2 :^ 1^ 12.0 — 6" lA. IIIIII.6 // ^ .V4^. «^>. K w Hiotographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716)872-4503 r o ; ^' % ,V4 t^ t/j /. "^^ lil! 86 IMERMKDIATB BXAMINATIOxV PAPERS. * Yes ! All 18 true my f ears could frame j A prisoner lies the noble Grseuie, And fiery Roderick soon will fee] The vengeance of the royal steel, I, only I, can ward their fate- God grant ihe ransom come not late ! The Abbess hath her promise given, My cliild shall be the bride of Heaven ; — ^Be pardoned one repining tear ! For He, who gave her, knows hmv dear, How excellent ! but that is by, And now my business h—to die.' Stanza xx. , Canto V (a) Select the clauses and explain clearly what relation they bear to the principal sentences. (6) Parse the words in italics. (c) Give the etymology of communion, prisoner, venge- ance, royal, business, ransom, excellent, sovereign, pageant, and abbess. (d) Point out any figures of syntax or of rhetoric which occur. (e) Analyze from yes to late. 8. Correct the following where necessary, giving reasons :^ (a) This word I have only found in Spenser. (b) I wrote to my brother before I received his letter. (c) Many sentences are miserably mangled, and the force of the emphasis totally lost. (d) This construction sounds rather harshly. (e) Whatever a man conceives clearly, he may put it into distinct propositions, and express it clearly to o'.hcrs. INTi;u:,J£I>i4Tj: EXA.^a^ATIO^f PAl'EJfS. ®i"aminar.— iXa. 3. 87 1. How is the absence of case-endings supplied in Eu^lhh ? Illuslrato the ellect of this absence on tho .euerul structure of Bentonces. 2. Classify in tabular form tlie various pronouns. Decline the pronouns I, she, that, and icho. 3. Explain and illustrate the restrictive ai.d continuutive torce of the relative pronouns. 4. Ex,,lain the tenns u-eak and strom, as applied to the conjugation of verbs. T. which conjugation do the following veros belong -.-buy, fight, creep, can, clothe, flee, and shoot ° 5. ^tate the various relations which words and groups of words bear to each other in a sentence. Illustrate each kind of relation by an example. 6. Defi^ . the following :~shnple sentence, complex sentence compound sentence. 7. Correct or justify the foliowin. in each case givnig your reasons. "" (g) Extravagance as well as parsimony are to be avoided. (/') " Our completest dictionaries." (c) "Newspaper usage and oral usage has made this word synonymous with .amount." (,d) "I am verily a man who am a Jew. " W " Neither precept nor discipline are so forcible as example. (/) " It is not me who ho is in love with." (?) y^ The thunder was heard roll over ov.c heads. " (h) " He lay like a warrior taking his rest. " befnZ''"''" "'f ;^*''° following .-2V,«orrot., early io oeU, go to noiv, s^ich a to-do. . 9 State the chief sources whence English words have been -.vfi red. \^ hat terms are, in generaJ, of Anglo Saxon origin 1 I ! 88 10. HrrKUMEDIATB EXAMINATION PArKES. Gravely he greets each city sire. Commends eaoh pageant'is quaint attire, Gives to the dangers thanks doud, And smiles and nods ujion the croTvd, Who rend the heavens with their acclaims, * Long live the Commons' King, King James ! * Behind the King thronged peer and knight, And noble dame and damsel brio'ht. Whose fiery steeds ill br^ 'iked the stay Of the steep street and crowded way. — But in the train you miejlit discern Dark lowering brow and visage stern ; There nobles mourned their pride restrained, And the mean burgher's joys disdained ; And chiefs who, hostage for their clan. Were each from home a banished man, There thought upon their own gray tower, Their waving woods, their feudal pow*^r. And deemed themselves a shameful part. Of pageant ivhich they cursed in heart. St. XXI. Canto v, (a) Analyze from nods to ivay. (p) Parse the words in italics. (c) Point out any figures of -. x, or of rhetoric whicli occur. (d) Give the etymology of quaint, damsel, train, might, restrained, chief, hostage, banished, and fiery. Iter. 4. 1. " Mention any English nouns which form their plurali by processes generally obsolete. Wliich of the following are genuine ])lurals, and account for the forma which are Pot Buch :-~alms, summons, hanns, costs, eaves, weeds, riches, and dice T' INTERMFnunt KXAMINATIOn PAPBHS. g() 2. Distinguish between co-ordinate and su'ix.rdinate con- junctions. Also between conjunctions and connectives. What are the various uses of the word but in Endish ? 8. How are degrees of comparison formed in English ? Give three examplos of each mode. Compare the irregu- lar forms, tvorse, fivst, ekhr, farther, further, and nexf. 4. Explain the following term& :~CoJhcthe noun, verbal noun, rejicdive verb, impersonal xerh, and defective verb. 5. Define the following and illustrate your definitions by examples -.—Phrase, clause, sentence. 6. " At what ditlerent periods has a Latin element been in- troduced into our language ? Give examples of words intro- ducedin the several periods mentioned." 7. Correct the following where necessary, giving reasons:— (a) " You will soon find such p-.ace which it is not in the power of the world to give. ' (b) " In proportion as either of these qualities (perspic- uity and sublimity) are wanting, the language is imperfect. " (c) "Many writers employ their wit in propagating of vice." (d) " As soon as they are made, they are instantly lost." (e) "The more important rules, definitions, and obser- vations, and which are therefore the most proper to be committed to memory, are printed with a la.ra»r type." " But not a glance from that proud ring Of peers who circled round the King, With Douglas held communion kind, Or called the banished man to mind ; No, not from those who, at the chase, Once held his sicle the honored place. Begirt his board, and, in the field, Found safety uudcnicath hist shield j 8. 90 INTERMEmATE EXAMINATIOX PAPRRS, il iPor he, whom royal eyes disown, When was his form to courtiers known ! Canto v., St. 24. (a) Write in prose anJ analyze. (6) What is a hybrid ? Select any in the above passage. (c) Parse the Avords in italics. 9. Parse the words in italics, in the following :— (a) '' Douglas would speak, but in his breast His struggling soul his tcards suppressed. " Canto v., St. 23. (6) "I shame me of the part I played. " Canto VI. , St. 8. (c) " Nor If ot ivc how a name— a word- Makes clansmen vassals to a lord. " Canto VI., St. 11. 10. What is the antecedent of we in (c) ? 11. Give the etymology of the following :--courtiers, lord, mllen, mitif, lorn, exile, aamge, buxom, kerchief, and purvey. State the use of the prefix be in the formation of words. Ilcr. 3. 1. '•' The meaning of the possessive case is sometimes ex- pressed by means of the preposition of, with the objective case after it." Show that the two forms do not always express the same meaning. 2. Wliat different relations of words to each other are in- cluded under the name of Objective Case in English. 3. Define Mood. Why is the Subjunctive Mood so called. Give an example of this mood occurring in an independent sentence. 4. What is meant by conjun;ating a verb ? Name the principal parts of a verb in English. Ascertam to which conjugation the following verbs belong by giving their er are in- INTBKMEDIATE EXAMINATION PAPERS. 6. " Place each of the follomng plira.es in a sentence of your cnvn construction, so as to .llustrate the way in wS may be properly used -.^Better than ke, ,etl tjj^nt^ than whom, and which, as noucl a^ T n. n ^ ! ' man, r.0H^ — Him I accuse The city gates has entered. C/') The man Moses was very ,noek, aoove all the nien which were upon the face of the earth {. (a). Define Case. (6). Distinguish between Case and Relation ; between the Nominative and Subject; between the Ob- ject and Objective. 06 III , I ■U ! Uff iNTBRMKniATE EXAMINATION PArERS (c). State the case of each of the words in italict, with your reason : (1). "Sweo* Auburn," &c. (2). I'lntu, thou rcasoneat well (3). James tore John, the baker's, coat. (4). They elected James chairman. ii>)- He seems an honest man. (t»). This said, lie sat down. «• (a). Name the different kinds of adjectives. (b). What adjectives can be compared i (cO. Compare the following: heavy, sad, barren, old, lovely, much, uninteresting. 7. "T venerate the man vhos, heart isivarm, VVhose hands are pure, whose doctrine and whose life, (omculent, exhibit lucid proof That he is honest in the sacred cause." (a) Analyze. (l>) Parse the words in italics. 8. Gijre the etymology of the following: swain, innocence, charm, decent, simply, wealth, supplied, peasantry. 9. " Works its weedy way. " (a) What peculiarity of poetry is illustrated by these V words ? (l>) Quote passages illustrating this peculiarity. 10. Correct or justify the following : (a) _" I shall not lag behind, nor err The way, thou leading "— (h "We have done many things which we ought not to have done. " (r) "No mightier tl an thyself or me." (d) ' ' Wherein doth sit the dread and fear of kings » (<') ' There was racing and chasing on Cannobie Lea." (/) Two and two are four. (if) Twice two are four. id, barren, old, and whose life, IKTfiRMEDUTB EXAMINATION PAPBRS «. £io. 8. 1. Define tho following terms: Etymolo<.y pronor rlinh thong, metre, inflection, clause. "^' ^^ ^'^^' 2. (a) Classify the Pronouns and define Relative Pronoun I>.nonstrat.ve Pronoun, and Interrogative Pro! (6) Show by examples that Relative Pronouns ,nav introduce other than adjectival sentence.. ' 8. (a) Give rules for fonning thi> plural honor; and the singular of kine, tongs, geniuses genera, and apparatus. fe^'nuses, 4 (a) Tliey strik, euck otJ.r. Parse the words each and (h) Why are these words called reciprocal pronouns ? (6) Parse the words in italics : (1) The clock struck the hour for retiring. (2) Trembling, shrinking from the spoiler's hand. Far, far away thy children leave the land (3) At Woutrol, despair and anguish fled the struyyling 6. (a) What is meant by the principal parts of a verb ? (6) Give the principal parts of the following verbs- othe, dare (to venture), reeve, lay, mow belr" (to carry), and work. ' ^^ (0 Inflect the verb "to see " in the Present Imperfect and Progres^ve Indic^Ui^e; Future. PerfeH ^nk^ md Present IndefinUe Subjunctive, ' ' 98 INTBRMEDIATE BXAaUNATION PAPERS. '■r 7. Show by examples with the word but that the part o speech which a word is depends upon its use in the sentence 8. Here, as I take my solitary rounds, Amidst thy tangling walks, and ruined grounds, And, many a year elapsed, return to view Where once the cottage stood, the hawthorn grew, Remembrance wakes with all her busy train, Swells at my breast, and turns the past to pain. (a) Write the three complex sentences in full. (6) Analyze that which has IATE KXAMINATION PAPERS. "His lovely daughter, lovelier in her tears, The fond companion of his helpless years, Silent went next, neglectful of her charms, And left a lover's for a father's arms. With louder plaints the mother spoke her woea, And blessed the cot where every pleasure rose ; Andkiased her thoughtless babes with ma?i2/a tear, And clasped them close, in sorrow doubly dear : Whilst her fond husband strove to lend relief In all the manliness of grief." (o) Illustrate from the above passage what you under- stand (1) by a simple sentence, (2) by a complex sentence, and (3) by a compound sentence. (6) Analyze the first four lines. (c) What is a clause ? Select any in the above passage. {d) Parse the words in italics. (e) Lovelier— Give rules for forming the comparative and superlative of adjectives. 9. Criticise the following : — (a) The ends of a divine and human legislator are vastly different. (&) TJie ebb and flow of the tide were explained by Newton. (c) Then there was a steel axe, or hammer, called a mace-of-arms, and which hung to the saddle-bow. (d) If I am not mistaken, a government can only be called democratic where a majority of adults are sovereign. (e) The facts, premises, and conclusions, of a subject, sometimes naturally point out the separation into paragraphs : and each of these, when of great length, will again re<]uire subdivision sA their most distinctive parts. }r woes, e rose ; lany a tear, y dear : relief t you under. by a complex itence. INTEUMEDIATE EXAMINATION PAPERS. ^jj CO A man may see a metaphor or an allegory in a pio ture, as well as read them in a description. 10. (a) Analyze the following words : intolerable, savage insidious, dependent. ' (&) Account for the difference of spelling of legal and loyal, though both are derived from the same Latin root. (c) Give the suffix and literal meaning of hamlet, bullet pumpkin, farthing, Wilkin. ' (d) Divide the following into syllables and mark the accented syllable: Precedence, premature, venison, facial, Mogul. bove passage, iparative and ior are vastly ixplained by ler, called a saddle-bow. 3an only be f adults are f a subject, aration into en of great on at their i.L i IKTEIIMEDXATE EXAMiNATION PAPiifiS. 103 1. Wliat causes the succession of the seasons ? Is the stin north or south of the equator at the present tinxe, and how 2 What are zones ? How is the position of the lines which mark their boundaries determined ! 3. Name the various oceanic currents, and state in what way they affect clin.ate. Give examples. 4 Draw an outline map of Europe, and insert tJie names of the chief seas, capes, and mountain chains ; trace the course of the Rhine, Seine, Tiber, Vistula, and Volga ; and Naples, Ulm, Augsburg, Talavera, Trieste. 5 Name the States of the American Uinon that border on each of the great lakes, those that border on the Gulf ol Mexico, and those that lie west of the Mississippi. Trace the course of (1) the Ohio, (2) the Missouri, (3) the Potomac 6. Name the counties of Ontario, (1) that border on Lake Erie (2) that border on the St. Lawrence. Trace the course of the Grand River, Red River, and the Saskatchewan. 7. Name the principal islands of Europe, and state to whom hey belong. Name the West India Islands that belong to Great Britain. 8. Name the counties of England (1) that bolder on tl,P Thames, (2) that border on the English Channel; .3 tht border on Wales. -^ 9. Several Asiatic rivers rise in Xliibet. Name them, and trace them to the sea. i ly* . \y 104 INl-EKMEDUTE EXAMINATION PAPEIW. #0. 2. 2. Places on the western sirlpq nf fi,« i- «.9 »me latitude on the eastern ,kIe,"rthB T '" berdotin, on these oeean.. Account for thii """"" '^- It has been suj'o'cstprl fli-it fi,^ * j • , i ,, '^"oo^stt-ti in.it tile trade wmrlci )iI/>,.t;», stantly Hgainst such obstructions as the indes M ?°"" would greatly retard the rotation of the elrtt t /u " "l" cause its diurnal motion to cease. Wl y cannnT .^^^ Explain fully. , ^^^^V cannot this occur ? and .o!™::" "" "" '"""- °' *^™''- '='»-" '.^'ituae 5. Define the term climatp . What countries own the following :-Goa, Jamaica Greenland Bor.^o, A ore., Falkland Islands, Bermudas, SaZ ana. Sandwich Islands, and Trinidad. 7. Where are the coal regions of Canada ? 8. Name the great soports of the Baltic and the chief er ports from them. *'^" 9. Name the countries of Europe and their capitals ; also state the form of government and prevailing religion of each (Answer in tabular form.) * 10 Where and what are the following (answer in tabular form) :-Herzegovma, Plymouth Rock, Valetta, Sandy Hook Father Pomt, Shipka, Alden^ey, Guernsey Lu Jn Ind Ho. 5. 1. Define the following .--zone, isothermal linos, isotheral hnes, isochnnenal lines, geysers, glaciers. Name the par.aUola ot latitude which bound the zones. INTERMEDIATE EXAMINATION PAPERS. 107 ex- 2. Describe the phenomena presented by the land and aea breezes, and state the causes to which they are due. 3. Why is the rainfall heavy in Brazil and along the west coast of Patagonia, and ahr.ost nothing in the Sahara ? 4. Distinguish between watershed and river-haain, and give illustrations of your answer from the maps of North America and Europe. 5. A foreign vessel reaches New York laden with rice, tea, cotton, silk, and porcelain ware ; from what country did she probably come ? Why ? 6. Assign causes for the great commercial prosperity of Great Britain. 7. Name the chief islands of the Atlantic Ocean, and state the nations to which they belong. Where is the Peak of Teneriffe ? 8. Draw a map of the Dominion of Canada from Manitoba eastward ; show on it the great lakes between Canada and the United States and their connections ; and mark the position of Collingwood, Simcoe, Peterborough, Lindsay, Stratford, St. Hyacinthe, Three Rivers, Pictou, Chatham (N. B.,) and Yarmouth. 9. If you turn to the map of Asia you will find a number of islands lying to the south of Malacca, and forming a link between Asia and Australia. Name the islands, and explain the statement in the latter part of the extract. 10. Name the colonies or possessions to which the following towns belong, and state any fact of interest in connection with each : — Adelaide, Quebec, Valetta, Galle, €ape Town, Weilingtou, Georgetown, Victoria, Ballarat, and Spanish Town. 108 INTBRMEDIATB EXAAflNATION PAPERS. 3 s #0. 6. 1. Cive proofs of the sphmioity of the earth, and also ..f Its diurnal motion. 2. Explain flio cause of the Trade Winds. Why do tliev not bl(nv in tlie ludinn Ocean ? J- ^Z-^*'^^^}^^^^'''^^oi ^^.V,ce determined by knowing the Meridian Altitude and Declination of the «un v At a place on March 20th., the meridian aUit.,de of the sun 13 47 and when it is U.Jo a.m. at Creonwich it is 10.36 • a. m. at this place ; find il.s latitu.le and loiiyitude. 4. Why does the day vary in length, and why is it longer during ^mmer than during winter ? Draw a diagr.-.m show- ing the position of the earth in her orbit to-day, marking by an arrow the direction in which she is moving. ° 5 Compare the corre.sponding latitudes T,f Europe and North America in regard to climate, and explain the cause for any existing difference. Which receives the greater 7^!T^Vu"r'" ^'''"'''^'' northern or southern hemis- pnere f VV hy ? 0. Tra 8 the course of the Ganges and of the Indus. Na^ie the most important places on them, and also the passes lead- ing from India into Afghanistan. 7. yame the most important islands to the east and south- east of Asia, and state the country to which each of thesp be- longs. 8. Describe the great river basins of South America, and name the rivers which drain each and the direction in which tney flow. 9. What are the most important exports from each of the following places: -Montreal, Charleston, New Orleans Buenos Ayres, and Liverpool. 10 Describe the position of, and state for what each of the following places is noted :-Granada, Leipsig, Leeds Saratoga, Sdamanca, Delhi, Pultowa. Cronsf.ndt Utrecht' ftfid Lyons. ' ' INTKU.MEUIATK KXAMINATION PAPKK3. 109 and also of hy do they by knowing I iide of the it is 10.30 3 it longer ;r:ini show- uarking by urope and the cause e ijreater rn heniis- 18. Na.ne isses lead- nd snuth- these be- 3rica, and in wliich ch of the Orleans, each of :, Leeds, Utrecht, Ha. 7. 1. Dtifine the following: mathematical geography, phy- sical guognipliy, axis, oblate spheroid, oclipao. 2. State a variety of facts wliicli go to prove that the earth is spherical in shape. Draw a diagram illustrating an eclipse of the sun ; explain why there are not two eclipses every r..onth, 3. The earth is said to rotate on its axis once every twenty-four hours. Is this correct ? Why ? 4. Give your reasons for supposing that the earth rotates on its axis, and revolves about the sun. 5. Supply the blanks in the passage : The of America include all that territory which stretch- es from the Gulf and northward to the ot -, and also a large - and is called — which lies to the north-west of The consist of States, Territories, and one . The capital of the L in the District on the River ■ This vast ter- ritory is divided into three great natural regions : 1st, the slope ; 2nd, the Valley ; 3rd, the slope. 6. A vessel sails from Chicago to Liverpool, in England ; state in order the waters it would traverse. What would likely form its cargo going and returning ? 7. Name the chief commercial cities of North America, and state where each is situated. 8. Name the largest islands of each of the following groups : Greater Antilles, Phillipine, Balearic, Japan ; and state to what country the following belong : Azores, Canary, Trinidad, Sandwich, Madagascar, Goa, Pondicherry. 9. Name the Continents, 1st, in the order of their size ; 2nd, in the order of their pupulatiou ; 3rd, in the oi'der of their extent of coast line. uo LJTEHMRI.MTl! BXAMmATFON PAPERII. O^wf o ,?' r'"*''" '^ ^"*"""' iBt, bordering on the the N -"'V "T^"^'^'^^^^- ^''"'- 3rd, bordering on the N agaru U.. r. State by what different routes a poLn nuiy journey from London to Peterborougli. iio. a 1. (n) Define Letitude and Longitude. {!>) Why are degrees of latitude, speaking generaliy „f the same length, and degrees of longitude of dif- feront lengths ? (c) Wh.t terms applied to the beaven« correspond to latitude and longitude ? 2. (a) Define the terms Solstice and Equinox. (b) When do the autunmal equinox and' the smnmei solstice occur to the people of Melbourne, Austmlia? 3. Name the chief islands of the Atlantic Ocean, and state the countries to which each belongs. 4. (a) Name the Gulf States of the American Union. (I>) What are their chief products ? (c) What are their most important commercial towns ? ^ive one at least in each State. 5. Describe the situation, and state the form of govern- Zrir'se"'' «1 "" '"""""^^•- ^^^-^' I^---". Mont::;,l:^^^^' ^"^^^^^^' ''"^•*^"^'^^^' ^-*-" ^^--1-; by the shortest route. State in order tarou.h wl.Vo waters she would have to pass, and what would likely form her ^'^0 7. Sketch a map of Australia, showing the vaiious colonies their capitals, and three large rivers. ^oionies, n„..iicai e^ent ^.ith which each la associated: Saratoga, INTEUMEIilx K EXAMINAIIO.M PAPEM. Ill Queenston Hoights, Yorktown, Austerlitz, Tilsit, irrlan, Dolhi, Acre, Nantos, Culloden. 9. Give a general descripti.Mi of the great phyaicui featum of A«ia. Rofer to its tablo-kndfl, inountaiua, rivers, and deserts. 10. What are the cliief articles of commerce supplied to 3reat Britain by Canada, Newfoundland, the West Indies, Austnilia, Cape Colony ? 1. (a) Define Declination and Meridian Altitude. (6) The declination of the sun on a certain day is 10' 16' south ; its meridian altitude is found to be 60' 45' ; what may be the latitude of the place where the observation is made ? 2. (a) What is a chronometer ? How is it used for deter- mining the longitude of a place ? (6) When it is 9.40 a.m. at A, what is the time at £, which is 10° 14' 15" west of A. (c) A is in east longitude 10° 14' ; £ is in west longitude 10° 16' ; when it is 6 p.m. at B, what is the time atA'i a (a) Draw a diagram illustrating the position of the earth in its orbit at the soltices and at the equi- noxes, marking with an arrow the direction in . \phich the earth moves in its orbit. 112 INTERMEDIATE EXAMINATION PAPERS. (6) TJie earth is nearer the sun during our winter than during summer. Explain fully why it is colder when we are nearest the sun. 4. (a) Explain the following terms :— Centrifugal force, centripetal force, and tangential force. (6) Why is the orbit of the earth elliptical ? 6. (a) To what circumstances doea Great Britain owe her commercial importance 'i (b) Name her great sea-porta and state where each is situated ? 6. (a) Name in order the States and Territories of the American Union which border on Canada, begin- ning with the most eastern. (6) Name the largest town in each of these States, and describe its situation. 7. Name the most important islands situated south and east of Asia, and state to what country each belongs and for wnat each is remarkable. Answer in tabular form. 8. Assign the following Provinces to their respective countries :— Silesia, Astrakhan, Armenia, Tuscany, Venetia, Moravia, Bohemia, Andalucia, Ulster, Roumelia. 9. Describe the great physical features of South America, and state the direction of the chief rivers and where they empty. 10. Sketch a map of the Continent of North America outline the Provinces of the Dommion, and mark the position of the capital of each, s. r winter than >' it is colder INTBBMEDIATi! EXAMINATION PAPEHS. 113 rifugal force, e. ? tain owe her here each ia ories of the nada, begin- Statea, and I south and igs and for 1. respective 7, Venetia, 1 America, ^here they America, e position 1. When Jid the Romans first enter Britain ? When did they finally loave it ? Mention some ot Che chief benefits derived from their occupation. 2. Describe the events which seated a Danish dynasty on the English throne at the beginning of tlie elev*ji)th century. 3. How and when did England first gain a footing in [reland ? 4. From what occasion do you date the origin of the House of Commons in its present form ? What kinds of Assembly were there in earlier times out of which it may be supposed to have grown ? 5. It has been said that the Tudors knew when to give way, and the Stuarts did not know. Is this statement borne out by facts ? 6. Account for the popularity of Charles II., and the un- popularity of William III. 7. Give the dates and results of the most important battles tought between Charles I. and hi.s Parliament, and a description of one of them. 8. Trace the descent of Queen Victoria from Henry VII. 9. State briefly the cause wh'ch led to the "War of 1812." Name the principal battle.^ fought during the war and the leaders on each side. 10. What was the cause of the Rebellion of 1837 ? Name the principal persons concerned in it, and give a short account of any one of them. 114 ^^-TERMEDIATE EXAMmATION PAl'EES. #0. 2. 1. Hnw did the contest between Rome and Carthage ong,- nate and term mat« ? What m-^of ;. ^ 2. Give a short aoco,™t of tho Second Pu„i„ War, staling «.e Pr„,c.,.a> battles f„„,M d„i„, the „, and the leader on each side. 3. Point „„t any circumstances in the condition of Italy -d the relation between its peoples and Rome, favora^ ! the prospects of Hannibal's invasion. 4. Wh^ led the Roman, to interfere (1, in the affair, of Greece, (2) in the affairs of the East / R Specify the causes and give a short account of the events ot tiie hocial or Marsi.-.n War. 6. Give an account of Sylla's return, and his capture of 7. Name the active and passive members of each triumvi- rate, and sketch the history of the second one. 8. Write brief notes on the Gracchi. Mithridates, and Cato, a Draw a map of ancient Italia, marking by an asterisk, with name wntten near it, the following places : Ostia. Tici- nus, Cann83, Metaurus, Capua, Tarentum. 10. «ive the boundaries of the Roman Empire in the tima ot Augustus. 10 affairs of INTBRMEDIATE EXAMINATION I'Al'KUS. 116 go. 3. 1. What do you understand by Cavaliers and Roundlieada ? Explain the leading principles of the two parties. 2. Write brief notes on the Wars of the Roses, Wat Tyler's Rebellion, Act of Settlement, Titus Gates, and Cabal. 3. State concisely the causes which led to the granting of Magna Charta— Give its principal provisions. 4. Name in order of their accession the kings of the early Norman period, and enumerate the chief events in the rei"n of any one of them. ° 5. What is meant by the following :-Septennial Act, The Young Pretender, Tlie Great Commoner, The Chartists The Indian Mutiny. ' 6. Relate fully the circumstances which gave rise to the dispute between England and her American Colonies, and give a brief sketch of the war whicli followed. 7. State the claim of Henry V. to the throne of France. Was this claim a just one ? 8. State the most import,-ait provisions of the following/ treaties :-Treaty of Bretigny, of Utrecht, of Versailles, of Washington. 9. Explain the nature of the reforms with whicli the names of Thomas Clarkson and Richird Cobden are respec- tivoly connocted. 10. Explain the folloTring terms :— Pill, Act, Par- liament, Cabinet, Prime Minister. Give 10 marks to each q-TCBtion. So. 4. 1. What was the nature, and what was tlie extent of the Roman occupation of Great Britain ? 2. Describe the nrofpsa l-i-r ivlil^ii +i-.o c ? 8. Explain the Feudal System. What was William's ob- ject in allotting the land in England to his nobles as he did / 9. Trace the descent of George I., and of the old Preteaid- er from James I. 10. Arrange in chronological order, and give the dates of as many as you can of the following : the battles of Poictiers, Bannockburn, Waterloo, Blenheim, Flodden, the'discovery of America, the death of General Wolfe, the accession of the House of Hanover, the peace of Utrecht, and the Declara- tion of Independence of the United States. Ilo. 8. 1. (o) Give a brief sketch of the life of Hannibal (6) Name the chief battles fought between him and the Romans, and state clearly where each battle field is situated. 2. (a) State the conditions of the treaty which brought the second Punic War to an end. (b) What were the reasons for Rome destroying Carthage ? 3. In what reign were English possessions on the Conti»ent most widely extended ? Sketch briefly how these were ac- quired. 4. Why was Edward T > popular ? Give a brief account of the condition of England during his time. 5. Explain the origin of the Wars of the Roses. Which party ultimately triumphed and where ? 6. Explain briefly the following terms ; Regicides, Pilgrim Fathers, Cavaliers, Cabal. 7. What important consequences followed the battles of Senlac (Hastings) and Waterloo ? State some of tlie chief 120 IKTERMEniATE EXAMINATION PAPERS. ill differences between the weapons used at Senlac and those in use at Waterloo. 8. State the terms of union between Great Britain and Ire- land. Who was Prime Minister of England at the time of the union ? 9. Give a brief account of the discovery and settlement of Canada by the French. 10. Arrange in chronological order and state who was king at the time of the following :— Summoning of First Parlia- ment, discovery of America, Battle of Blenheim, union of parliaments of England and Scotland, abolition of Slavery capture of Gibraltar, battle of Trafalgar, destruction of the Spanish Armada, trial of the Seven Bishops, Massacre of Cawnpore. ^0. 9. 1. (a) Sketch the life of Marius. (b) Write brief notes on the following :— Gladiators, Catiline, Proscription. 2. Give a brief history of the First Triumvirate, introduc- ing dates where you can. 3. The life of William the Conquerer has been described as "one long mastering of difficulty after difficulty." Illus- trate this statement by giving a brief sketch of the difficul- ties he overcame. 4 State clearly the claims of Edward HI. to the throne of France. What were the most important battles fought dur- ing the resulting war, and state the result of each (1) in France, (2) in England ? 5. Account for the general discontent and popular insur- rections during the reisn of Hf>nry ^T[. 6. Explain w'lat is meant by the "balance of power." INTBEMKDIATK RXAMINATION PA^BEa. 121 ^nd those in ain and Ire- the time of ittlement of lo was king irst Parlia- 1, union of of Slavery, ;ion of the [assacre of Show how England first became important in Europe by holding it. 7. What were the objects of the insurrections of Wat Tyler and Wyatt ? Sketch briefly the result of these insurrections. 8. Who first took the title of " King of Great Britain ? " State clearly his claims to the throne of England. 9. Give a short account of the exploration and settlement of America (1) by the French, (2) by the Eiv,'lish. 10. Explain the following :— School Lands, Secularization of Clergy Reserves, British North America Act, and Syn- dicate. jrladiators, introduc- described 7." IIIUS- le difficul- throne of ught dur- kch (1) in lar insur- power. tr ai V( m je ne re ta (ie sa' itii tai INTKilXliUIATJi EXAMINATION PAPERS. 123 JULY EXAMINATIONS, 1880. SECOND CLASS TEACHERS AND INTERMEDIATE. FRENCH. Tme— Three hours. JSxamimr—S. Arthur Marling, M. A.. 5 - ie Jibrts: introinution. Translate : Une aventure heureuso vint accroitre son petit tr^sor. II trouva un jour un cachet d'or armorid. II le fait annoncer au prone : un Anglais se pr 'aente, et le reclame. S'il est b. vous, dit Valentin, je vous prie de le blasonner. Tu te moques de moi, r^pond I'Anglais ^tound ; le blason n'est pas assur^- ment de ton ressort. Soit, r^pond le jeune patro ; mais, je vous de'clare qu' h moJns de blasonner votre cachet voiw ne I'aurez pas. Surpris de ce ton ferme, I'Anglais obeit, et re^ut ensuite son cachet. Voulant recompeuser celui qui le lui arait rendu, il I'invita k le venir voir. Par sa gdne(rosit^, la biblioth^ue de Valentin s'^leva k quatre cents volumes,' tandis que sa garde robe restait toujours la meme. Un sarrau de toile ou de laine, un mauvais bonnet et des sabots compo- saient tout son ajusteraent ; mais c'dtait 1^ la moindre de ses inquietudes. 1. Give the indie, pres. throughout, of " accroitre " '• ro9ut." ' 2. "Blasonner." Explain the meaning, 3. Parse surpris, ohAt. ■t ** Cents." When does cent take, and when does it not t»k«>, the form of the plural ? 124 INTEHM.OUTB KXAM.NATIO.V PAPEHS. French.— ContiimeJ. ((0 Translate : «.': " .ir:::':,;!:::;'' "° ""•"' '-' — quelle la me,„„ ai-uiUe ramin " ''"'■'''»'' •"■■ ''^ P'- .»iWe,. aucune aut:! t e I, t;™?'": *'"""""' •' -te Llus calme,. I] en est de ' ' °''"°"'» i"»iuwjd::„ ;.::„" ^"/^ -"""-^ »° ^--o-nt 1- "bohimien.." Explain thi, term. 2. Parae »,;(, gi,i„g the principal parts With Itrr-" ""°'' '°- "- P'-"' P-io.-ple .^.ee (b) Translate : vieu., n,ais tu sers toujour, ta pa" ' ''""**'■ ■"°" ./p:r:"et>;t™:v':r" '-^"'^-•— -' -„,ent ■na bonne jamb Je '1 '. "' .^'7"™" "^ M«-u,es de ea tojte. v'ingt popu- 3 caractore. i traveraent Ju ca2)rice, urs jJtablis, age sur la- les memes t^clatantee, 8 obscures ionime de eacendant ii>u laouve- pie agree •ea, mou iUe pro- irement lurea de lade ; il ii cease' INTIilRMEDIATK EXAMINATION PAI'tUii Pronch. — ro?t/inw^r/. 125 1. Kxplivia the moaniny «f the firat seutenco. '■^- Uive an acoount of the speaker. 3. Quote expressions used by him indicative of hia pro- feaaion. *^ 4. Tout. When does thi'? adverl) change its f.^rm f 6. Assainmctnent. Give the derivation. (c) Translate : J'ai d^daign.1 lea paroles qui n'avaient d'autre grace que leur sincerite; j'ai cess^ d'aimer les hommes, seulenient parce que c'#aient des ho.nmes, je les ai ain,c<8 pour leur superiority; j'ai resserre^ le monde dans les dtroitea li.uites d un pantlidon, et ma aympathio n'a pu etre dvoilWeque par 1 admiration. Cette foule vulc^aire que j'aurais dii suivre d'un c«il ami, puisqu'elle est composdo de frbrea en eap^rances ot en douleurs, je I'ai laissee passer avec indiflerence, comme un troupeau. Je m'indigno de voir celui cj^'enivre son or md- priser Ihomme pauvre des biens terrestres, et moi vain de ma science futile, je meprise le pauvre d'eaprit. J'insulte k 1 indigence de la pens(^e comme d'autres k celle de I'habit • ie m'enorgueiUis d'un don et je me fais une armo offensive d'un Donheur ! 1. Give a summary of this chapter. 2. j'ai resern- to panthJon. E.vplain the meaning. 3. enivre. What is the subject ^ 4. mJpriser. Explain the construction. 5. rinsuUe d I'indiyence. Write a list of verbs followed by