Institute of Chartered Accountants in England and.

The Accountants' manual, Volume 10 online

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Acton, A. H., Wellingborough
Whitby, E. R., Clevedon
Thistlethwaite, B., Great Ay ton
BouLD, H. S., Bristol
Spibey, J., Tottington, near Bury
Hadfield, K.. London
Marshall, C. J., London
Brown, G. R., Winchester
Carey, C. M., New Maiden
Adams, L., Bexley Heath
Lloyd, J., Famley, Leeds
OcocK, W. P., London
Hare, W., Blackburn



Where educated
King Edward's High School
Malvern College

Grammar School, Wellingborough
Mill Hill School

Leighton Park School, Reading •
Bristol Grammar School
Manchester School of Commerce
Nottingham High School
Bedford Modern School
Northgate School, Winchester
Kingston Grammar School
King's College
Kingswood School, Bath
Merchant Taylor's School



Blackburn Grammar School
(In alphabetical order)
Arnold, L. G., Saltaire, Yorks Bradford Grammar School

Barr, a. J. a. W., London Haberdashers' School. Hampstead



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November and December 1905— Successful Candidates.



46a



PRELIMINARY BXArAWATlOTi-conHnued,

(In alphabetical order)



Name
Bell, A., Newcastle-upon-Tyne

Bell, E. J., London
Bennett, D. M., London
Biggs, R. L., Birmingham
Bliss, C. C, London
Boler, J. E., Sheffield
BuRNHAM, G. N., London
Calder, M. W., London
Cavell, L. a. S., Bristol
Chew, R. L., London
Clayton, H., Sutton, Surrey
Clench, R. W. L., Wealdstone
Cooper, A. L., Hunstanton
Darbyshire, J. S., Blackpool
Davey, p. J., Gravesend
Davies, S. N., North wood
Denny, C. K., Surbiton
Denton, W., Pool, near Leeds
DoBiNsoN, S. R., Middlesbrough
Fearnley, W. H., Hampton Hill
Fielding, E. T., Cardiff
GiLLiAT, F. L., London
GiLLiAT, F. M., Manchester
GooDALE, R. R., Peterborough
GooDFELLOW, A. W., Norbitou
Gordon, E. M. B., New Maiden
Graham, H. H., Carlisle
Greaves, H. L. L., London
Green, M. H., London
Greenlees, S., London
Gribble, H., Weston-super-Mare
Groom, C, Bury St. Edmunds

Hart, K. E., London

Hesketh, J. E. B., Ashton-on-Mersey

HoLLiNS, R. J., Dudley



Where educated

Dame Allen's Endowed School,

Newcastle
United Westminster School
St. Edmund's College, Ware, Herts
King Edward VI. Grammar School
City of London School
Central Higher School, Sheffield
Cranleigh School
Westminster City School
Clifton College

Haberdashers* School, Hampstead
Dover College
Harrow School
Oundle School
Arnold House School
Skerry*s Academy, Dublin
Uppingham School
Charterhouse

St. Wilfred's Church School, Leeds
King Henry VIIL School
Huntingdon House School, Teddington
Bedford County School
H.M.S. •* Britannia"
Hulme Grammar School
Laxton Grammar School, Oundle
Charterhouse
Private Tuition
Sedburgh School

Banister Court School. Southampton
Private Tuition
Malvern College
Clarence School, Weston-super-Mare

King Edward VI. School, Bury St.
Edmunds

Highgate Grammar School

Rossall School

Tettenhall College



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464



XOVEMBKR AND DECEMBER 1905 — SrcCESSFUL CANDIDATES.



PRELIMINARY EXAMINATION— foii/i«M^.



Name
Holmes, H., London
Holmes, R. B., London
HossELL, S. H., Birmingham
Hunter, G. G. G., Leamington
Ide, p. a., London
Instox, H. ]., Birmingham
Johnston, S., Manchester
Latham, F., Manchester
Latimer, R. A., Liverpool
Lawson, H., Gosfort
Lewis, W. G., Liverpool
Lucas, A. C, London
Mack, J. J. C, Liverpool
Marbeck, W., Bolton
McKnight, R. a., Liverpool
Mercer, A, J., Blackburn

MoRBLL, A. L. , Nottingham
Neison, C. U., London
Nevill, p. B., Enfield
Newman, E. W. R., Birmingham
NiCKSON, E. H., Leicester
Oldfield, C. v., London
Orfordi H. S., Manchester
Palmer, W. G., Cardift
Parsons, R. C, Monkton
Pateman, H., Leicester
Pearce, J. C, London
Pell-Ilderton, S., Manchester



Piper, T. G., London
Plumb, N. W., Thornton Heath
Potts, B., Stockport
Powell, F. A., Birmingham
Reid, J. F., Southport
Rhodes, J. D., Morley, Leeds



(In alphabetical order)

Where educated

Cathcart College, N.

Private Tuition

King Edward's High School

Warwick School

Cowper Street School

Bourne College, Quinton

Sale Grammar School

Smart's Commercial College

Liverpool Institute

Durham Grammar School

Liverpool College

AUeyn's School, Dulwich

Waterloo High School, Blundellsands

Private Tuition

Tettenhall College

Queen Elizabeth's Grammar School,
Blackburn

Grosvenor School, Nottingham

University College School

Mill Hill School

King Edward VL High School

Wyggeston High School

Dulwich College .

Hulme Grammar School

Cardiff School of Commerce

Dean Close School, Cheltenham

Alderman Newton's School, Leicester

Kingsbridge Grammar School

Manchester Municipal Secondary-
School

Private Tuition

Haileybury College

Lucton School

King Edward VI. Grammar School

Scarisbrick College, Birkdale

Grammar School, Bridlington, Yorks



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November and December 1905 — Successful Candidates.



465



PRELIMINARY EXAMINATION— ro«/iH«^rf



Name



(In alphabetical order)



Where etlucaitd



RiDSDALE, G. E., Bloxwich
Rosenthal, M. E., Manchester
RoYLE, J., Junr., Manchester
Russell, E., Holcombe Rogus
Simpson, T. L., South Shields
Skevington, a. p., Ilkley
Smith. F. G., West Bridgford
Smith. G. J. D., Longfield, Kent
Sothers, L. W., London
Stephen, G., London
Tansley, S. a., Forest Hill
TowNEND, C. R., Goole
Turner, O. L., Nottingham
Tyldesley, B. J J., Bohon
Tyrer, N., Bedford
ViCKERS, E.. Liverpool
ViPOND, F. R., Llanfairfechan

Walker. E. H., Clevedon
Ward. H. S., Northampton
Wellesley-Colley, p., London
West, L. H., Cardiff

White, C. P., Normanton
WiDDOws, H., Lytham
Woodcock, E., Deepcar, near Sheffield
Woodcock, G., Hunmanby, E. Yorks
Young, A. F., Bedford
Young, W. H., Gt. Meols



Wolverhampton Grammar School

Manchester Grammar School

Municipal School, Manchester

County School, Wellington, Somerset

South Shields High School

Kelly College, Tavistock

Nottingham High School

The King's School, Rochester

Highgate School

Nicolson Institute, Stomoway

Alleyn's College, Dulwich

Thome Grammar School

Nottingham High School

Central Higher Grade School, Bolton

Bedford Grammar School

Liverpool College

Manchester Warehousemen and Clerks'

Orphan Schools, Cheadle Hulme
Clarence School, Weston-super-Mare
Northampton Grammar School
Stoneyhurst College, near Blackburn
Skerry *s Commercial and Civil Service

College
Grammar School, Norman top
Pembroke House School, Lytham
Sheffield Middle Class School
Pocklington School
St. George's, Llandudno
Calday Grange Grammar School,

West Kirby



55 Candidates failed to satisfy the Committee.



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466 November and December 1905 — Successful Candidates.

INTERMEDIATE EXAMINATION.

(Candidates who obtained a certain number of marks, in Order of Merit)

Peake, H. O. (Priu), (W. P: Price- Heywood), Manchester
f Anderson, A. C. (J. W. G. Hill), London
1 Hargrbaves, a. (J. Stansfield), Colne

Hayter, C. (W. Davison* Junr.), Sunderland
( Farrow. H. F. (A. H. Gibson), Birmingham
1 Harrison, E. (T. Broadhead), Dewsbury
^ Shannon, E. C. A. (A. H. Caesar), London

Owen, J. M. (C. E. Williams). Oswestry
( Berry, W. S. (A. G. Deacon), Manchester
1 Williams, H. M. (C. H. Hovey), London
( Jones, W. E. (G. Mahon), Liverpool
1 Parker, W. (G. Parker), London

Donaldson, G. J. R. (L. Blake), Great Yarmojth

LiTTLBBOY, W. E. (H. Lakin-Smith), Birmingham

Agar, F. H. (B. T. Norton), London

Glaistbr, E. W. (J. Watson), Carlisle

Gantner, S. a. (J. E. Wilson), London

Roberts, G. A. (E. E. Spicer), London

(In alphabetical order)

Adams, A. J. (C. G. Haswell), Chester
Axed. H. C. (L H. Skinner), Hali^
Allen, S. (A. E. Warburton), Leicester
Andrews, H. U. (G. Emmerson), London
Ash WORTH, C. G. (M. L. Walkden), Manchester

Baker, H. (D. Forde). London
Barnaby, E. W. (T. Walton), Manchester
Bellamy, R. C. 0- Crake), Hull
BoTTOMLBY, R. (E. B. Edwards), Manchester
Bodlton, W. W. (W. V. Manley), Blackburn
BowEN, L. P. (A. C. Boumer), London
Brewster, G. S. (H. Anstey), Bristol

Carter, O. H. (H. P. Gould). Norwich
Clare, J. \V. (S. Jude). Liverpool
Clive. E. a. (A. W. Boston). Birmingham
Comben, R. J. (W. C. Brooks). London
CowDEN, V. P. (E. D. White), Liverpool



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November anu December 1905 — Six cesskil Candidates. 467

INTERMEDIATE EXAIAWATlOf^-continuid.

(In alphabetical order)

Davibs, E. G. (T. a. Payne), Birmingham
Davies, G. J. (G. Proctor), Burnley
Dunn, F. J. (E. Bradshaw), Warrington

Fletcher, T. W. (J. W. Davidson), Liverpool
Francis, H. J. (A. P. Carryer), Leicester
Eraser, H. (W. Harris), London
Frith, P. L. (E. H. Frith), London

Gates, J. S. (J. B. Gates), London
Grundy, E. (J. Jackson), Manchester

Hargreaves, H. (F. a. Hargreaves), Burnley
Heaven, H. V. L. (J. W. Hinks), Birmingham
Hodgson, A. D. (A. Hooper). Bradford
HuGHESDON, H. C. (G. Clark), London
Humphries, H. W. (E. Hobbs), London

Jones, C. J. H. (A. T. Chew), London
Jones, H. S. (A. Whittaker), Manchester
Jones, S. H., B.A. (J. Robertson), London
Jones, W. H. (W. F. Flack), Liverpool

Kirton, H. H. (W. R. Locking). Hull

Lee, H. (F. Winter), Newcastle-upon-Tyne
Levitt, R. H. (C. E. Bradley), Scarborough
Link, C. E. (T. Wise), London
LoucH, H. T. (J. G. Andrew). London

Martin, C. N. (A. Miall), London
Matthews, G. H. (W. H. Fox), London
Mellor, L. G. (W. L. White), London
Miller, A. A. (H. J. Page), London
MiLWARD, T. E. (M. Leicester, Junr.), London
Morgan, A. B. (T. S. Jones), London

Oliver, F. O. (J. Benson), Newcastle-upon-Tyne
OvERELL, J. (W. B. Keen), London

Parks, W. B. (A. H. Caesar), London
Parle, J. A. (E. P. Chevalier), Liverpool
Peet, W. S. (B. Langley), Liverpool



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468 November axd December 1905 — Successful Candidates.

INTERMEDIATE BXANiWATlOS— cent iniud.
(In alphabetical order)

Pickering, J. G. (J. A. Sisson), Newcastle-upon-Tyne
PococK. G. C. (A. C. Roberts), London

Raine, R. C. (A, A. B. Walford), Stockton upon-Tees
Roberts, W. E. (J. Knill). Exeter
Robinson, H. A. B. (C. H. Mounsey), London
Rowell, T. E. (M. Stainton), Newcastle-upon-Tyne

Sansom, H. (A. I'Anson), Darlington
Scott, S. C. (J. Metcalf), Cardiflf
Sherlock, W. N. (W. F. Flack), Liverpool
Simpson, W. (S. A. Reynolds), Reading
Sinclair, J. R. (A. Burgess), Manchester
Skillington, S. J. (J. H. Baker), Leicester
Smith, F. E. (C. Cooper), Manchester
Stephens, C. A. S. (A. H. Downes), London

Teale, V. G. (G. E. Teale), London
Thomson, F. H. G. P. (J. H. H. Duncan), London
ToMASSON, H. H. (N. W. Burbidge), Sheffield
TuBBS, E. J. (J. E. Tubbs), London

Veale, a. E. (A. J. Hill), London

Walter, E. (E. C. Baldwin), Brighton
Warmsley. H. L. (E. J. Walker), Liverpool
Watson. J. R. (A. S. Hooper). Bradford
Widlake, C. L. (W. Holmes), Sheffield
Williamson, N. (W. H. Hughes), Huddersfield
WiLSHiRE, H. B. (L. W. Wilshire), Derby
WoMERSLEV, C. F. (F. Womersley), Manchester
Wood, C. C. (C. Keys), Birmingham
Wood, R. B. (W. S. Blackburn). Leeds

59 Candidates failed to satisfy the Committee.



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November and December 1905 — Successful Candidates.

PINAL EXAMINATION.

(First Prixe and Certificate of Merit)
Garnsby, G. F. (N. G. Harries), Walsall

(Second Prize and Certificate of Merit)
DB ZoucHB, R. C. (C. H. Mounsey), London

(Certificates in Order of Priority)

Haddon, R. C. (H. Grace), Bristol

Ash WORTH, H. (R. N. Carter), Manchester

LuNT, H. J. (J. Lunt), Manchester

Wbbstbr, W. D. (H. C. Howard). London

MuRGATROYD, G. B. (A. Shuttleworth), Manchester

DB Paula, F. R. M. (C. F. Cape), London

Boss, J. G. Junr. (T. Eyton), Newcastle-upon-Tyne

Hirst, W. H. (W. Dawson), Dewsbury
j Storrs, L. C. (H. E. Sweeting), Cardiff
I Welch, W. (C. E. Bullock). Hanley

Nixon. H. H. (W. C. Atkinson), Leeds ^

(In alphabetical order)

Albxandbr, G. (G. N. Monkhouse). West Hartlepool
Armstrong. H. J. (J. J. Gillespie). Newcastle-upon-
Tyne
Ash. G. H. (J. H. H. Duncan), London
Bailby, J. V. M. (W. Mickelwright), London
Baxter. A. J. (J. S. Cotman). London
Bbswick, J. F. (R. McN aught), Manchester
Bishop, E. E. (E. K. Bishop). London
Blbasb, H. (G. H. Ashworth), Liverpool
Blorb, F. H. (S. p. Derbyshire), Nottingham
BoARDMAfif, H. (E. Cooper), Manchester
Bolton, H. O. (A. W. Macredie), Sheffield
Bowdbn, H. H. (T. Wallace), Newcastle-upon-Tyne
Boyd, W. R. (E. H. Turner), Grimsby
Brandon, N. H. (C. D. Ross). London
Byrnb, a. J. (G. F. Toulmin). Preston
Candlbr, a. p. (L. Hardy), London
Clifton, T. E. (R. J. Ward), London
CoATBs, C. G. (H. P. Walters), London
CossART. B. (W. Chaloner), Stockport
CowLBY,*D. S. (T. G. Mellors), Nottingham



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470 November and December 1905 — Successful Candidates.

PINAL EXAMINATION— con/MM^i.

(In alphabetical order)
CowNEY, C. E. (J. W. G. Hill), Birmingham
Craven, E. (A. H. Pownall), Manchester
Croggon, J. F. S.. B.A. (S. V. Tiddy), London

Danby, S. (R. Sands), Nottingham

Davies, a. T. (W. Meacock), Newport, Mon.

Davibs, E. E. (C. E. Dovey), Cardiflf

Davis, H. McF. (A. W. Payne), London

Day, a. F. (C. C. Baker), London

Dickinson, E. (W. A. Rycroft), Newcastle-apon-Tyne

DuFFiELD, E. (T. F. Armstrong), London

Easton, C. (G. a. Gale), Hull

Edwards, V. (W. C. Grant-Smith), Wolverhampton

Evens. F. W. (R. H. Marsh), London

Flinn, T. (C. F. Finney), Liverpool
Freame-Baker. R. (W. H. Short), London
GARDNErtT A. R. (J. A. CarlUI), Hull
Gillespie, H. R. (R. Sands), Nottingham
Goodwin, G. H. (T. Wood), Manchester
Gresty, W. R. (E. N. Humphreys), Chester
'Grundy, N. D. (Sir John Craggs), London
Hamp, J. (W. B. Keen), London
Hart, S. W. (T. Ryder), Birmingham
Hedley, J. S. (J. a. Sisson), Newcastle-upon-Tyne
Henderson, I. M., B.A. (J. M. Henderson), London
Hewson, W. K. (G. Parker), Sunderland
Holland, T. W. (J. G. Fowler), London
Hooper, R. (A. S. Hooper), Bradford
Jackson. T. (G. C. Veale). Leeds
Jones, S. (R. J. Sissons), London
King, W. F. (W. A. Kirby), London
KiTsoN, T. A. (J. Gilchrist), Middlesbrough .
Lancaster, J. H. L. (J. G. Langton), London
Lane, W. S. (W. R. Lane), Birmingham
Lepine, C. H. (E. J. Palmer), London
Locking, H. W. (E. W. Shaw), Hull
LovESY, A. C. (G, Morriss), London
Lucas, G. H. (E. B. Winn), Birmingham
LuMB, L. (R, F, Miller), Barrow-in-Fumess



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November and December 1905 — Successful Candidatbs. 471
FINAL EXAMINATION - «oii/miM{.

(In alphabetical order)

Macn AUGHT, D. D. (J. Morriss). Manofaester
Matthews, J. H. S. (J. Todd), Preston
MiLLONs, T. A. L. (H. W. Tash). Middlesbrough
Moore, F. (J- W. Best), Sheffield
MoxoN, G. A. (H. G. Blackburn), Leeds
MuNDBLL, K. H. (J. M. Woodman), London

NiCHOLLS, S. H. (A. H. Downes), London
Nicholson, A. E. (E. J. Walker), Liverpool

Page, A. A. (C. W. A. Tulloch), London
Percival, J. E. (R. Nye), London
PoNKiNG, W. M. (R. Rabbidge), London
Price, E. L. (E. C. Price), London

Rbmon, J. a. (G. H. Carter), London
RiGBV, A. G. p. (W. Davies), Preston
Robinson, J. W. (E. Cooper), Bolton
RouTLBDGB, G. S.. B.L. (T. G. Bowden), Newcastle-
upon-Tyne
Rozelaar, a. (R. Nye), London

Scott, W. E. (W. Scott), Hull
Sheridan, H. H. (S. W. Tubbs), London
SiDLBv, J. C. (T. Bowden), Newcastle-upon-Tyne
Sinclair, N. (E. Sparks), Newcastle-upon-Tyne
Singlbhurst, R. B. (G. Nicholson). Liverpool
Skinner, J. (E. H. Fletcher), London
Smallbv, G. a. (H. W. Marten), London
Smith, C. E. (S. Edds), London
Smith, R. E. (W. T. Ogden), London
Snblham, J. S. (T. Bee). Preston
Southcombe, R. (S. Pears), London
Spry, J. H. S. (W. E. F. Thorp), Devizes
Stephenson, G. C. (L. E. Halsey), London
Stray, A. F., M.A. (R. Stray), London
Stretch, L. G. (J. C. Bladen), Hanley
Swayne, H. a. H. (E. G. Burnett), Southampton

Taylor, J. S. C. (S. Taylor), Swansea
Terras, H. (P. Swan wick), Manchester
Tewson, R. S. (C. Fitch Kemp). London
Theedam, C. (A. E. Mason), Dudley



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473 NOTBMB£R AMD DSCSMBEK 1905— SUCCESSFUL CANDIDATES.

PINAL BXAMiNATiON-conHnMid.

(In alphabetical order)

TiMMiNs, F. O. (T. J. Agar), Birmingham
Turner, E. J. (A. T. Littlejohn), London

Valb, F. W. (F. Brown), Stockton-upon-Tees
Vbnablbs, B. C. S. (A. W. Good), London

Webb, G. R. (W. L. EllU), London
White, J. (T. E. Y. Berrey). London
Whitley, A. de W. Q. R. WhiUey), Keighley
Williams, S. (E. Williams), Manchester
Wilson, W. (J. H. Bourne), Liverpool
WoBfBRSLEY, J. W. (F. Womersley), Manchester
Worthington, H. (W. I. Swarbrick), Preston
Worthington, J. H. (S. Pearson), Manchester
Wright, R. (F. Brown), Croydon
Wyllib, H. W. (A. G. Morrish), London

73 Candidates failed to satisfy tlie Conmittee^



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NIT n. lOL I.

Tlhie Reseiuiiiiitoiniils

Being the Answers to the
Examination Questions of the
Institute of Chartered Accoun-
tants.



Preliminary,
Intermediate, and Final.

MAY— JUNE 1906.



The Answers to the Questions set at th Preliminary Examination are by
the Rev. G. T. P. Streeter, of ike Rectory, Orcheston St, Mary,
S.O., Wilts.



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PRELIMINARY EXAMINATION. JUNE 1906.



Tfu ANSWERS to the QUESTIONS set at the Preliminary Examination are
by the Rev. G. T. P. STREETER, of the Rectory, Orcheston St. Mary, S.O,r
Wilts.



ALGEBRA.

Q. 1. — Write down algebraic expressions for the following : —

(i.) The sum of five times the cube of x, four times x,
and 5, less three times the square of x.

(ii.) Three successive even numbers of which 2n is the
middle one.

(iii.) The number of miles run by a train at s miles per
hour in m minutes.

(iv.) The present value of P pounds due y years hence at r
per cent., reckoning compound interest.



A. 1.—



(i.) 5a* + 4« + 6 - 8aJ»
(ii.) (2n + 2) 2n (2n - 2)



(iii.)
(iv.)



8tn
GO



\l00+rj



KK 2



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476 PRBUMINARY EXAMINATION.

Q. 2.^The sum of two nambers is 225 and their difference is 27.
Find, by the quiokest method you oan, the difference of their
squares.

A. 2.—

Ans. =226x27 = 226x30-226x8 = 6076

226

30

6760

676

6076

Q. 3. — Arrange the expression

2a (a* + 26*) + b (6a* + b*) + a {a + by
according to descending powers of a, and find the quotient and
remainder on dividing by a-\- 2b. Verify your answer by putting
a = b = l.

A. 3.—

Expression = 2a« + 4a6» + 6a«6 + 6» +a» + 2a«6 + a6»
= 3a* + 8a«6 + 5ad* + 6»

a+2b I 3a» + Qa^b + dab* + 6»13a» + 2a6 + 6«
I 3a» + 6a«6 I

2a«6 + 5a6*
2fl«6 + 4ay

a6« + 6»
a b^ + 2b^
- 68
Expression = 2x3 + 7 + 4 = 17 Divisor = 1 + 2 =

17 = 61=6-1
3 3 3

Quotient = 6. Remainder = - 1.

Q. 4. — Simplify the following expression : —

J a^ _ Jf .

a- 6 a»-6* a* -+06+6*'
and find the square root of

{x* ^ lx + 12) (x* - 9ic + 20) (a;* - 8a; -+ 15)
by factorisation.



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ALGEBRA. 477



A. 4.—



1 rtS



a- b df^ -l^ a* + ai» + 6«

a^ ^ db + h^ - a^ - b(a - h)

a» - 6»



V (x^ - 7a; -h 12) (x^ - 9x + 20) (3^ - 8a; + 15)
= \/ (x - 3) (a; - 4) (a; - 4) (x - 5) (x - 6) (a; - 3)
= (X - 3) (x - 4) (X - 5) Ans.

Q. 5. — Explain what is meant by the highest common factor and
the lowest common multiple. Find the highest oommon factor and
the lowest common multiple of

36a«6«, 27a*6c, 18a6»c, 64ac.

Show that the product of two expressions is equal to the product
of their H.C.F. by their L.C.M.

A. 6.—

The Highest Common Factor is the greatest expression which will
divide all of a series of expressions without remainder.

The Lowest Common Maltiple, the least expression into which all of a
series of expressions will go without remainder.
9a I 36a«& «. 27fl^ 6c, ISabfhy 5iac
2ab I 4a6^, Sabc, 2b^c, 6c

6 I 26. 8c, be, %;
2. 3c, »f
Ahs. H.C.P. = 9a

L.C.M. ^9ax2abxbx6e
= 108a«6«c

Let X and y be the two expressions.
Let X — ga
V ^gb
where g will not measure a and 6
.-. H.C.P, = g
L.C.M. = gab
their product = ^db

^ ga X gb
= xy



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478 PRELIMINARY EXAMINATION.

Q. 6. — The following observations were made on the extensions
of a spiral spring under different weights : —

Weight. Extension.

4 oz. 0'50 inches.

8 „ 103 „

12 „ 1-55 „

16 „ 210 „

20 ., 2-62 „

24 ,. 310 „

Plot a diagram on the squared paper provided, showing the
extension under different loads:

Allowing for errors of observation, find from your diagram the
law relating the extension e in inches to the weight v) in oz.

A. 6.—

Draw a vertical line down one of the lines on the squared paper, and
divide it into equal sections, each representing 4 ounces.

Draw a horizontal line at the end of each section and measure off on
each the number of inches marked against each weight corresponding.
The lines joining the ends of these horizontals will be not quite, but
nearly, one straight line. The increments of length are not equal for
equal increments of 4 ounces, but are respectively

'50 inches

•63

•62

66
52

•48

Allowing for errors of observation, we may take *52 inches as the law of
increase for each 4 oz; weight. The law regulating the extension s inches
to weight v> oz. is therefore « = 13 u;.

Q. 7. — Ilndy eiiher graphically or algebraically, to two places of
decimals, the roots of the equation

«• - 6-2a: + 61 = 0.



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ALGEBRA. 479



A, 7.—



«« - 6-2a! + 61 =

10 10

- 26^ .T5l' 169 61
6 61 25 10



= 6 76 - 610 ^ 66

100 rod

^ 13 . V~&S

*" 5 ^ *-10

_ 26 ± S/'M
^ 10

^ 26 J: 8;01
10 ^
8401 ^, 17 99
= -10-^' "TO"
= 3-401 or 1-799

Q. 8. — The product of two decimals whose sum is unity is 0*2059.
Pind them.



A. 8.—




Let X and ^ be the two deoimalB.




^ + y = 1

xy = -2059
aJ* H- 2ary + l/« = 1

^y = -8236




x« - 2icy + y» = 1764
x-y = -42
X + y = 1




2x = 1-42
2y = -58


/. X = -71
/. y = -29



Q. 9. — The weekly expenditure of three households is stated

to be: —

Members of Household. Expenditure.

£ s d

(i.) 3 men, 2 women, 1 child 1 19 6

(ii.) 1 man, 1 woman, 3 children ... 17
(ill.) 1 man, 2 women, 5 children ... 2 16

If the expenditure per man, per woman, and per child respectively

be the same in each household, find what this must be.



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480



PRELIMINARY EXAMINATION.



A. 9.—

Let X y 8 shillings be the respective weekly expenditure for a man^
woman, and child

3x + 2y + a = 39J ,

X



H- y + 32 = 27 I
+ 2y + 6« = 411 I



(i.)
(ii.)
(iii.)



By the method of determinants
13 11

2 12 X =

I 1 3 5



27
1
3



41J
2
5



/. { 3 (6-6) + 1 (2-10) + 1 (6-1) } X = 39i (-1) + 27 (-8) + 41J (6)
(- 3 - 8 + 6) X = - 39i - 216 + 207*
- 6x = - 48 /. X = 8
Subetitnte in equations (2) and (3)
then ^ + 31 = 27 -8 = 19
2y + 5iJ = 41} - 8 = 334



1 2

X

3 5



y =



19 33i



(5 - 6) y = 95 - lOOJ
- y = - 6i /.
.-. 3f = 19 - 6J = 13i
An6. 88.. 5s. 6d., 4s. 6d.



y = 5i
a = 4J



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ARITHMETIC. 481



ARITHMETIC.



Q. 1. — In the office of The Times there is a barometer in which
the fluid is glycerine instead of mercury. A chart showing the
movements of this barometer is given in The Times each morning,,
that for April 27th being reproduced below. The scale on the
left gives the readings actually taken, that on the right th&
equivalent in inches of mercury. Bead from the chart to first and
last readings, (i.) on the glycerine, (ii.) on the mercury, scale, and
state the fall in each case. Also find from the two scales th&
number of inches which the glycerine barometer will rise for a rise^
of 1 inch of the mercury barometer.

I A.M. rjc. ^



Fio. 1.



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482 PRELIMINARy EXAMINATION.

A. 1.— Taking the dots to represent the heights of the fluids : —

Glycerine. Mercury.

First Beading . . 820-1 inohen . . 29*765 inches
Last ,, .. 319-4 „ .. 297



Fall -7 „ .. -066

•7
Rise of glycerine for each inch of mercury = -^— -

'066
^700
65
= 10-76 Inches.



Q. 2. — Fig. 2 shows a sketch plan of a room, with the scale to
which it is drawn. Find the cost of flooring it with parquet at
^s, lid. per square foot. [Tick off the scale on to a spare piece of
paper.]



1 r



I I !



6

Scale op Feet.
Fig. 2.



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ARITHMETIC. 483

A. 2. — Mark ofi three outlying pieces : —

Large portion = 1 3 x 21 square feet.
Left top outlying section = 5x1 , ,
Right top „ =7x1 „

Right side „ =8x8

Area » 378 + 5 + 7 + 24 square feet.

s 809 square feet.
Price = 809 X 28. lid.

= £45 Is. 8d.

Q. 3. — The same room being 9 ft. high from skirtiDg to comioe,



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