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I. (1) 70,707.

Females.

II. (1) 207. (2) 2,799,901.

III. (1) 7 cwt. 2 qrs. 7 lbs. 2 oz. 7 drs. (2) 753,375. IV. (1) £5,115. (2) £55.

V. (1) £55 15s. 74d. (2) £2,666 13s. 4d.

VI. (1) £5. (2) £2 48. 41d.

VII. (1) 1. (2) 1 cwt. 1 qr. 1 lb. 1 oz.

VIII. (1) 25. (2) £85. (3) 70.07.

IX. (1) £59,070 138. 83d.

(2) 1,771.

ALGEBRA AND MENSURATION.

(1) 56 — 5c.

(2) 2a5-5a1b + 10a2b3 — 10ab1 + 3b5 and a1 — x2y2 + y1.

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III. (1) 7 dwts. 12 grs.

(2) £2,171 15s. annual expenditure.

Spent daily, £5 198.

Saved

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(3) Each proprietor has 52 ac. 2 r. 10 p. IV. (1) £478,478. (2) 15s. 3d. (3) £99,711. V. (1) Length, 360 ft. 114 in. (2) £2,560. (3) 18. 3d. VI. (1) £4 58. 6d. (2) £6,704 158. 2 d. (3) 6 per cent. VII. (1) 47. (2) As 40: 41. (3) 521 days; . VIII. (1) 3571428. (2) 7,920 paces. (3) 47,620 guineas. IX. (1) 168 francs. From 2,640.75 francs to 2,808.75 francs. (2) 56,270 square yards.

(3) Difference, 15.708 metres.

Females.

I. (1) Sum, 5,315,343; Difference, 4,981,200; Quotient, 14,438.05.

II. (1) 360,555,642. (2) 45,067.

III. (1) 5 days 20 hrs. 28 min. (2) 48,592 oz.
IV. (1) and 7050 (2) 115811
V. (1) 103. 3·24975036d.

(2)

30240

338-0483870967741935.

VI. (1) (2) 6s, 333d.

VII. (1) 583 yds.; £16 3s. 11⁄2d.

and £174 18s. 1014d.

VIII. (1) £750. (2) £6.

ALGEBRA.

(2) £137 98. 111d.

III. (2) 8a5 - 4a1b — 2a312 — 4a2b3 + 2ab1 — 11⁄2b3;

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IV. (1) 1. 2x2 + 3xy — y2. 2. 5773.

(2) 1. ∞ = 2. 2. x = a/1⁄2 or

α

a2 + b2

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3. x =

a + b

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4. x = la, or - 2a.

a

(3) 27 and 36 years.

MENSURATION.

V. (1) 10 ac. 6 p. 18 sq. yds. 4 sq. ft. 72 sq. in.

(2) 34-64... (3) 26 ft.

1876.

ARITHMETIC.

Males.

I. (1) 1,223,851,035. (2) 2,007,095. (3) Each £7 128. 74d. Each woman's £15 5s. 2 d.

man's share

share =

=

(3) £7 108.

II. (1) 180 turns. (2) 1,760 packets. (3) £51 17s. 11d.
III. (1) £3 11s. 6d. (2) 28,267.
IV. (1) £80,244 68. 73d.

V.

(3) £215 1s. 44d.

(2) £102 5s. 42d.

(1) 195; 2016. (2) £28. (3) 1000 days.
(2) 30 days; or 5 weeks.

81

VI. (1) 253

VII.

IX.

(3) £49.

The first field at £1213 per rd. is the highest priced field.

(1) 005; 300,000; 5.

(2) A's = £770; B's = £8,470; D's
(3) 5.52 in quantity; £1.96 in value.

VIII. (1) £636 2s. 118d. (2) £1,200.
(1) 1s. 10 d. (2) £7 18. 8d.
(1) 24.5 in. (2) 761. (3) £1.

X.

ALGEBRA.

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(3) £50 88.

Males.

V. (1) 18, 6, 13, 0, 4. (2) No5 – 2æ1 – 22x3 – 7æ2 - 42x

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IX.

MENSURATION.

(1) 1,364 turfs, or 1363-8384. (2) £1.21. (3)

195. 45 children.

ARITHMETIC.

Females.

I. (1) Sum = 31,188,806. Difference 30,518,730,
Quotient = 350,790.

II. (1) 3,095. (2) 82,962,600.

III. (1) A £4 2s. 6d.; B £3 1s. 10d.; C £2 38. 3 d. (2) 777,777.

IV. (1) £619 168. (2) £33 38. 3 d.

V. (1) £11 28. 24d.

(2) £980 28.

VI. (1) Ratio 5: 7. (2) 2s. 6d. (3) 25 38 metres. VII. (1) 999. (2) 832.

VIII. (1) 11. (2) £1.

IX. (1) 58,070. (2) Tea costs 1s. 3d. Coffee costs 18. Sugar costs 9d. (3) For notes of lessons on Subtraction, see Livesey's "How to teach Arithmetic," price 2s. 6d.

1877.

ARITHMETIC.

Males.

=

Con

I. (1) a. 30,000,095,070,005; b. MDCCCCLXXXVIII.
c. 80 times; d. (i.) 4,548,286,386
tinued Product; (ii.) 133,722
(iii.) 34,013 Answer.

=

Difference;

II. (1) 60 threepennies. (2) £4 1s. 3d. (3) 22.

III. (1) £7,839 88. 9d.

IV. (1) £66 68. 6d. (2) £4,241 7s. 9d.

V. (1) £341. (2) £29.

20

(3) 5392 105056 miles.

VI. (2) a 27, b 137. (3) £301.

VII. (1) a. (i.) 09. (ii.) 7.8125. •21153846.

(2) £257 2s. 2ąd. (3) 2·075.

1222857

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VIII. (1) 4 per cent. at 118 is the most profitable investment. Yearly income is £176 178. 6d. (2) 66 per cent. (per annum). (3) £2,700.

IX. (1) a. 5.7196. b. 98.

(2) 58,905 florins.

X. (1) £217 16s. (2) 1d.

ALGEBRA.

V. (a) 22. (b) b. (c) (1-a) (1—b) (1—c) (1-d).

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VII. (1) 16. (2) x=23/2 or

(3) x=√a2+b2. y

=

✓ ab.

VIII. (1) (a) 5. (b) Ratio of half-sovereigns to sixpences. (The question should have been, "What is the ratio of half-sovereigns to sixpences ?" for the ratio of half-sovereigns to half-crowns is given-viz, 1 : 1.) (2) 450 miles.

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