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PREFACE.

DURING several years' experience in preparing for admission to the Army, the compiler has found that a course of Examination Papers has always had a very beneficial effect upon his pupils by accustoming them to the style of paper likely to be set, and thoroughly testing their knowledge. The following collection of Papers has been published in the belief that it will be useful to the large class of Tutors and Pupils engaged in preparing for the Army. Any corrections or suggestions will be thankfully received.

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SET I.

a

a

MATHEMATICS. (1.) 1. Find by inspection a value of a such that (x + 1) (x + 2) (x + 3) = 210.

2 Express as a whole number (27)3 + (16) –

8-3 If (a) and (b) are whole numbers and unequal, show that

b 5

+- must be greater than 2. 2. Multiply

(1+2x2 – 3x + 40) by (1 – 2x2 – 3x – 4ą?).
Divide

(a + 2ab + b2 - x? + 4xy – 4yo) by (a + b - & + 2y). 3. If (m) be an odd integer, show that 2" +y" is divisible by (x + y),

and express the three last terms of the quotient.

Find the greatest common measure and the least common

multiple of (6x2 + 5x – 6) and (15x3 + 2x2 – 8x).
4. Prove
** (2 – y) + y (x – ) + 7 (y - 3)

(2 - x).
(x - y) (y – 2)
b

= a, express the equation following in terms of (a),
b
and solve it when so expressed :
a3 63

621

6 2 + 3

-4 = 0. 73 as

a? 5. State and explain the rule for clearing an equation of fractions. Solve the following equations : 2.c

Зх

4
(1.)
2x + 5 3 (ac + 4)

3

5
8
y
41

2x 1
3 2

12

4 21

+
7

10
126
1981

If +

a

+

= 0.

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(2.) x+y

2x

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7
-

.

(3.) (4.)

=

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6. A rectangular field is 60 yards long by 40 yards wide; it is sur

rounded by a road of uniform width, the whole area of which

is equal to the area of the field; find the width of the road. 7. Prove V4 +67 N 4 - 6

5 = 6.

-17-3 Form the quadratic equations whose roots are

2

5+

8. In the use of tabular logarithms, what characteristic should be

prefixed to the logarithm (1) of a whole number of 6 digits, (2)
of a decimal which has 4 ciphers between the decimal point
and the first significant digit in the decimal ? Explain briefly
why such characteristics are prefixed.

Prove log10 A.B" = m logie A+n logi, B.
Given log10 125 = 2.0969100,

Find (1) log10 16, (2) log10 (-0002)5. 9. Find the rent, at £2.58. an acre, of a rectangular park half a mile

long and a quarter of a mile wide. 10. Write down the expressions (1) for the circumference, (2) for the

area of a circle radius (r).

The hypotenuse of a right-angled triangle is 10 feet and one side is 8 feet; semicircles are described on the three sides of the triangle ; find the radius of the semicircle whose ciroumference is equal to the circumferences of the three semicircles so described ; and show that the area of the semicircle described on the hypotenuse is equal to the areas of the semicircles

described on the two sides of the triangle. 11. Each side of a rhombus is 120 yards, and two of its opposite

angles are each 60°; find the area of the rhombus in acres to

two decimal places. 12. A right cylinder open at top with a diameter of 24 inches weighs

167.5 pounds; when filled with water it weighs 2131 pounds; find the height of the cylinder, it being given that a cubic foot

of water weighs 62.5 pounds. 13. What length of canvas which is one yard wide will be required

to make a conical tent 8 feet in perpendicular height with a radius of 6 feet?

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