8.

IX. 6.7

6. 8 oz. I lb.

VIII. STATICS.

(x-4)*
(x-3)3°

=0, x-2a=0.

=

DYNAMICS. miles.

ARITHMETIC.

000001645, 51.

9. Sum

x2+(3+n) ax+3a2.
4. √277, a.
6. (1) 3, 6.

(ii)

IO.

I.

5.

3, 3, 2.

5: n n-.

•

2.

6. 22:

C

a2

(2) 13 and 24.

na + (n + 1) b

2n + I

71'4 yds.

II.

: c.

II. 4. LII. 11S. 3d.

7.

9.

7693, 40'5. 13. £1.9049. 35.

10. 41.
Diff. of income £253. 8s. 9d.

12 sq. ft. 81 in., £12. 8s. 6d.

14. 15. 16. 1007.67 lbs. (if packed in line 1018.3 lbs.).

17.0000790123456.

18. 60 days, 12 hrs. 16'.

19. 15'44.

9488474, 3344539, 37781513: value=6*240325; 19 and 20. 21. 10.08.

20.

(cot 0+1).

7. p2=mr.

x2

III. ALGEBRA. 1. x2+x3-a2x3 + ~ 2+ a2x−x+1,

2. x2-x+1. 3. (1)

II.

At angle cos-1 to the bank : perpendicularly.

3 oz.
Slightly over 19.

July, 1887.

I. 18. 2. £46. 55.
£100.

6. £56. 15s. 4 d.

8.

Is. 200832d., 90044890873015.
II. 1s. 708736d.

2

5. height.

3. I.

25. I1d.

12. Int. : Disc. = 5:4.

x(x-a) (x-y)"

2a2+b3±b√√b4+8a3b − 4ab3 + 4a 2 (a2 - b2)

last term (-3)2n−1 : sum – 2n, last term 1 – 42.

IO.

12.

IV.

TRIGONOMETRY.

I.

sin A, cos A=, cot A=, sec A=, cosec A=§. 7. 49° 28′32′′. 8. I93753, I-76143. II. Height=27-3307189, CD=173 ft.

9. 120o.

2.

V. PURE MAth. (1).

A circle on line, drawn from pt. perpendicular to given line, as diameter.

4. - 14.

6.

St. line.

7. y=a±ex.

1. 36 −6y4+9y2 – 2.

II. 28, 3.

1221759, 720.

35. 4d. in the £. Land: personal property=2 : 3.

6.

5. A little less than 36 years.

ea+e-a
2

sin ẞ,

e-a-ea
2

II.

4, ±√√3. 12. 2, 2, (±√3). 13. rx3- (qr-2q) x2 + ( pr2 − 4pr + 4p) x − :

8.

II.

VI. PURE MATH. (2).

A=C=1, B=-D=

VII. PURE MATH. (3).

x

a2

>

I (a2 – x2)# '

d3y

dx3+6

a√m + n

mn

n
m-n

d2y

dx2

7.

x-4 log (1+x) –

(m>n).

dy dx'

VIII. STATICS.

3. 2, 9 lbs.
7. 25, 3 inches.

cos B:

4
I+x

ny mx

4. 7P.

(2)

8.

7. 120.

ега

1 + x − (2n+1) x2 + (2n − 1 ) x2+1 (1 − x)2

sin zna 2 sin a

(sin x)* {log sin x + x cot x}.

4. x2+x3.

-=m+n.

1. 6 lbs.

2 (ea+e-a)

te

8.

2 (ea-e-a) '+2 cos 28' 2a +e-2a + 2 cos 2ẞ

-2a

2a

- p3 +6r22 − 12r+8=0.

, log (2x+1+2√√1+x+x2) or sin−1

5. 3 lbs., 3808 ft.-lbs.

5. aa (1-loga).

2x I

No5

(r log x − 1).

IX. DYNAMICS. I. 2 f. s. 2. v cot 0.

3. Accel.=4f. L=32T2 (Lft.=unit of length, 7 secs. = unit of time). 8. A parabola.

November, 1887.

IO.

II. ARITHMETIC. I. 899910. 2. £19. 15s. 6d. 3. 431. 5. 00212, 21200. 6. 27765625, 2 qrs. 7 lbs. 7.788, 8.54854470131697. 8. £1. 165. 9. £150. 10s. 51d. 14'0700007. II. 8 cub. ft. 656 in. 12. 12 yrs. 13. £3. 14. 120 days. 15. 165. 16. 34. 17. 4,5*3692159, 1*3692159, 2*3692159. 18. 0189694. 19. 367182. 20. (1) £6000. (2) £131501. 5s. 8d. I min. 52 sec. after the dog started. 22.

£819. 65. 2·669d.

21.

III. ALGEBRA.

4. (1) 2. (2)

8. (1) 6a+b, za−b.

10. 180. 11. 210.

6.

6.

TRIGONOMETRY.

IO.

I.

34xy
16x2 – y2°
(2) 3a and 3a

2

12. (−1)

IV.

2 tan A (1 - tan2 A)
(I + tan2 A)2

"

12.

5. †n (n − 1), 2n (n − 2). sin

V. PURE MATH. (1). 4.

a2

62

7.

√a2+b2' √a2+62°

I - 2x cos 0+x2°

d2+ 2ed
(e+d) cot 0 -e cot

x (a + 1) − y (b -- 1).

6.

π

4

VI. PURE MATH. (2).

3. y=1+3x2 – }x1+f3x5. ...=x+

6. 188.

II.

2

Nπ 3π

+
2 8

{b2c2+a2c2+a2b2}.

x2-y2=c2, Rect. hyperbola.

10. xx+y=0. (1) A pt. at the origin. (2) 3 st. lines-axis of y, x-y=0 and x+y=0. (3) Four points x=±a, y=±b.

π 1-No3

"

3 2√2

π

I

I

+ 2x 8x3

8.

(3) -5.

tan- tan

n

̧, z (r+ 1) (r + 2) (r+3).

3. x2+7xy-y2.

3 16x5

n

- I.

8. 20'97615.

9. 1020 yds.

2,2, -1. 9. (a+b3).

2π

(n − 1) π

n

5. A parabola.

3π tan

n

tan

I.

a

8. y = ±x+22

10. I, I,

3. 64, 11 lbs.

8. 5 in.

IO. 2a,

4. 115200 ft.
tons.

a 2

IV.

TRIGONOMETRY.

57° 16' 2111".

4.

5. 3.

cos a + cos 2a + cos 3a + cos 4a. 10. A=105° 27′ 35′′, B=15° 5′ 20′′, c=2°44844.

6.

π

3√3

16.

3.

ca-a2c+b2c-bc2 + a2b- ab2

abc (a - b) (b−c) (c − a)

7. (a) -20, (b) 5, (c) a and b.

12.

3.

22. 2 miles or 24' after.

8.

2x (x − a)

a

II.

V. PURE MATH. (1).

9. tan-110.

10.

A parabola with same vertex and 4th the parameter. 12. (i) Axis of y and a hyperbola.

(ii) 2 st. lines.

8.

14 13:31. £5. 195. 2d. 6, -6, 5.

2x2+3x-1
x2-3x-2

4. 14'56 lbs.

19. 198.5365.

149, 1317160.

απ

12

a

π

8. 538461.

12

39: 33: 25.
II.
45o.

(iii) A parabola.

4. 2

α

VII. PURE MATH. (3).

2

6. 180.

a

6. (1) 172.

16 - 3a2

2

√ax+x2+ a log

VIII. STATICS.

W2
W1+ 2 W2

4

I

6

: max.

IX. DYNAMICS.

8. 68 033 miles per hour.

x

(b-a) (b-c)

a2+b2+c2 −ab− ac - bc'

e

9. sin-1

2.

√x + √a+ x
Na

2. lb.

. BC from the hinge.

7. 1, 9 galls.

12. Slightly over 125 years.

I.

2x-I

No5

W

32

II. (i) πα?.

3.

I

√1 − x2

I

6.

I. I.

- 2x2+ 2x3- 4xa+6x3.

3.

(c-a) (c-b) a2+b2+c2 - ab - ac - bc

November, 1888.

mx ny

D-d
D

9. 80000 ft.

I

x2 - a2

cos3 x - cos x,

(ii) rab.

3. 2BC.

+ =m+n.

IO.

II.

ALGEBRA.

3. 4x2-6x+9, (2x+3)(16xa+36x2 +81) (6x2 − 5x − 6).

x

5. b24ac.

(2) a+b, and 1⁄2 (a+b). (3) 9, 6, 4 or 4, 6, 9.

2m+ I

9. 15.

V.

mm + I

a

x √√x2 - a2