I. (a) 30,880.

1879.

ARITHMETIC.
Males.

(b) 9,986,110,000 = nine thousand nine hundred and eighty-six millions, one hundred and ten thousand.

(c) 11⁄2d.

II. (1) £2,811. (2) 84 miles. (3) 148 coins.
(a) £18 10s. (b) £1416s. (c) £7 88.

III. (1) £563 9s. 03d.

IV. (1) 248,832.

(2) 34677 feet of boarding. Or 3855 pieces 9 feet long. V. (1) 100,000 lbs. (2) 600. VI. (1) (a), (b) 175. (2) %. VII. (1) (a) 10, 900, 9900. (2) 9225.

7

VIII. (1) £5440. (2) 612.
IX. (1) (a) 12.6491106.

s. yds.

(b) 790. (c) 147·15.

(3) £255 16s. 11 274d.
(b) 2·008. (2) 932 = 8649

X. (1) 8 to 1. (2) £29 6s. 8d., £40 16s. 9d., £55.

V. (1) (a) 9a2 (b) x4

ALGEBRA.

6ab24ac + 2bc —,24b2 + 15c3. ·y4 · 2y2z2 — z1 + 4y3z + 4yz3 — 4y2x2 = x2 — y1 — z1 + 4y3z +4yz3 — 6y22. (c) (3x — 7y) (3x + 6y).

VI. (1) (a)

=

(d) (√x + √ y −√ z) (√x + √ÿ + √z).
(2x-2) (3x-12) (x3 — x2 - 4x+4)
6x5 - 36x2 + 30x3 + 120x2 - 216x + 96.
3x2 38

(b)

=

4x1y — 4y3 +8x3y2 — 8xу3
x6-x2y-x+y+yo

(3) 32x2+72xy + 162y2+

VII. (1) ∞ = 13. (2) x = (3) (a) x = 72 VIII. (1) 147 miles.

1

MENSURATION.

IX. (1) 66 sq. inches. 36 sq. inch to the sq. mile. (2) £15 158.

ARITHMETIC.

Females.

I. 55,555.

II. 35 acres 2 rds. 8 poles 26 sq. yds. 8 sq. feet.
III. £9 58. 4zd.

IV. £15 7s.

V. (1) 11664 planks. (2) 468 shares.

VI. (1) Masons, £897 15s. Labourers, £1197.
(2) 10591 oz. = 882 lbs. 74 oz. (Troy).

VII. (1) 23.

(2) 178.

VIII. (1), 215, 2175 (b) 7. (c) 44:46.

(2)

IX. (1) £997 10s. (2) £24 9s. 5·71722d.

1. (a) 57,957,638. (b) 6758. (c) £180.

II. (1) 132,480 gals. (2) 7920 miles. (3) 5,200,000.
III. (1) 153119. (2) £9 Os. 10d.

IV. (1)95·99603174.

(2) (a) ·069; ·069; ·069; ·06; ·06.

(b) 067207753+.

VI. (1) £2856 14s. 2d. (2) £4360 5s. 3 d.
VII. (1) (a) 25 hrs. (b) 70,400 gals.; 13,200 gals.

(2) £94.

VIII. (1) (a) 512 in., or 14 yds. 8 in. (b) 886·8 in., or 24 yds. 1 ft. 10'6 in.

(2) (a) £53 58. 9d. (b) 16·434 + sq. feet.

IX. (1) £473 1s. 4-6959375d.

(2) £1250 108. in the 3 per cents.; £1749 103. in the 4 per cents.

X. (1) A's share, £1581; B's, £527; C's, £421 12s. (2) (a) 2115. (b) 372-35.

Females.

SECT.

I.

(1) £26,610,016 78. 9d.

II.

(b) £6 5s. 73d.

(2) 17 tons 13 cwt. 2 qrs. 10 lb. 11 oz.
(a) £94 4s. 84d.

III. (1) £6 12s. 6d.

(2) £14 10s. 5,3d.

IV. (1) £10 2s. 7d. (2) £121 38. 2 d.
V. (1) 118. 057d. (2) £84,100.

VI. 41 yards.

VII. (1) 171 tons 9 cwt. 13 lb. 4 oz. (2) 21; 2.59375.

VIII. (1) (a) 198857142. (b) 2,300. (2) (a) £32 158.

(b) 41.92.

IX. (1) £5960. (2) 24 per cent.

(c) '000049578+. (c) 1250.

IX. (1) 3 acres 3 roods 33 0256 poles.

(2) 50 sq. yds. 3 sq. ft. 64 sq. in.

SECT.

I.

1881.

ARITHMETIC.
Males.

(a) 243,096,525 × 4936=1,199,924,447,400. Hence this is the least number from which 4936

can be subtracted the required number of
times.

(b) See any Tables of Weights and Measures.
(c) Five hundred thousand and seven millions,
fifty-nine thousands and ninety-five.

II. (1) 1s. 4d. (2) 350,000 sq. links.

III. (1) 2250, 2185

IV.

V.

VI.

2117 2325 2090. 41501 2850 2850' 2850' 2850 2850 324900'

(1) 1·44. (2) £4000.

Book work.

(2) 1.

(1) £537 10s. 9§d. (2) £3 3s. 111⁄2d. + 3s. 111⁄2d. + 78. 1d. +£1 7s. 94d. + £3 18s. 4 d. = £9 1s. 3d. £9 1s. 3d.-9s. 04d.=£8 128. 24d. VII. (1) 7 hrs. (2) £11 5s. (£4 10s. + £2 14s.) =

£4 18.

VIII. (1) 36 inches. (2) £6,600,000.
IX. (1) 21 per cent. (2) £13,333 6s. 8d.
X. (1) £100. (2) £1171%.

SECT.

Females.

I. (1) 132,000,000 ft. (2) 6 cwt. 2 qr. 5 lb.
(1) £1058 48. 3d. (2) £7 16s. 14d.

II.

III.

=

(1) 38. Od. +88. 43d. + 8s. 114d. + 78. 91d. + 168. 7 d. +£1 5s. 112d. £3 10s. 93d.; £5 - £3 10s. 93d. = £1 9s. 24d. (2) £3 17s. 4d. +£3 13s. 4d. + £1 16s. + £5 1s. 9d. + £1 3s. 3d. + £10 10s. 6d. + 6d. = £26 28. 8d.; £30 £26 2s. 8d. +

£1 11s. 6d. £5 88. 94d.

IV. (1) £244 1s. 13d. (2) £1144 2s. 4 d.

V. (1) £73 78. 8d. (2) £186 13s. 4d.

VI. (1) 27 yds. (2) 51 men.

VII. (1) The latter, by 6 cwt. 352glb. (2) £7; ·55.

VIII. (1) 158.; 21; and 1293.

2475

(2) 168 oranges.

IX. (1) 4 yrs. (2) Lost 36 per cent.

S

ALGEBRA.

·28; x2 + 3x + ; 755.

VI. (1) 4. (2) (x − y) (x + y) (x + 2y), or a3 + 2x2yxy2-2y3. (3) pr + 1o2 + q = 0.

=

VII.

(1) x = 2. (2) x = 1; y

14. (3) a =9, or 2.

VIII. (a) 18 yds., 14 yds. (b) x=;

SECT.
IX.

пр

m

MENSURATION.

(1) 35 yds., 35 yds., 42 yds. (2) 114 sq ft.

1. 12,481,875.

1882.

ARITHMETIC.

Males.

2. Eldest brother's share, 5 a. 2 r. 14 p.; each younger

SECT.

brother's share, 3 a. 2 r. 36 p.

£784 28. 918d. (4) 811d.; }

369140625; 1 ft. 1.2890625 in.

10 yds. (8) 10 days. (9) £1160.

101. (11) 3. ft. (12) 128. 11d. per yard.

250

Females.

I. (1) £9 198. Od. (2) 11 sq. yds. 8 sq. ft. 723 sq. in. to be added; 12 sq. yds. 5 sq. ft. 633 sq. in. to be subtracted; 5 sq. ft. 135 sq. in. to be added.

II. (1) £3,074 14s. 91d. (2) £1 18.

III. (1) £8 168. 3d. (2) £2 78. 42d.

IV. (1) £344 10s. 388d. (2) £172 178. 24d.
V. (1) £2,716 178. 10d. (2) Gain, £26 10s.
VI. (1) 28. 1d. (2) 7 days.

VII. (1) 90 ac. 3 r. 33 p. (2) £1,000.

VIII. (1) £16·635. (2) 4s. 91d.; 047916 of £5.
IX. (1) 4 years. (2) 44s. per quarter.