1962-06-02 — Page 26

中學)本拙見,特於五月卅一日來

七

日一初月五年需手腳

WAH KIU YAT PO

英文中學會考數學(二)試題

MATHEMATICS IT

Time allowed Two hoursi

Attempt any TEN questions only

Ten marks are awarded for each question. Logaritmic and rigonometrical tables will be provided and may be used when- ever necessary.

Prove that in any triangle, the sum of the squares on any wo sides 19 equal to twice the aquare on half the third side Together with twice the square on the median which bisects they

third side.

Use the area formula of a triangle or otherwise prove that the triangles ABC and AXY. if XY is parallel to BC, AX AY BX CY

A A

Give the steps of a purely geometrical construction for an sosceles triangle whose area is the same as the area of the. iven quadrilateral ABCD, and whose height is one of the

agonals. Indicate how many such triangles can be constructed) *d prove your results.

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六期汽

日二月六年二六九一麼公年一十Â國民藥中

****

英文中學會考

初級數學試題

LOWER MATHEMATICS

Time allowed 24 hours

Answer any EIGHT questions from Section A and any FOUR,

questions from Section B.

Section A

Answer a questions only. from this section

C = . and a = 1.

Simplify

(1). Bc - $4a + le

(ii) x2

+ 8x + 1.

-

5x

6

(111)

(10 x 17

102)

9

5

= (19 16

34 = 24)

6

2. (a) rind the value of x(a b) when x =

1

a = 14, 0 =

cd

5

(b) factorize (1) 9a2x2

2

(11) amn хук

-ak Xymn,

(c) Expand ty

**)(2y 4x).

3. (a) Solve

(1) n +

=

6ì

>

4

(b) If N

ab

K

亞洲基金會補助下

校

港大校外課程部

「感與·院,提高學良 甲乙組排陳冠軍及 甲乙組全體員外, 國民大岛四樓脊踐中,本那座連獲全

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立案

成功機會,設有轉 、昇、變、醫

CHINS

有調音樂及大型古典

曲林姆斯基·科

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THE MARR

KY WIDOW WALT

AKBSBI

& THEN

FE FEN

ETHE LOST

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別計者,其作

Solve the following equations for angles from d° to 360.

(i)

(i) cot

(11) 2cosfe

the identities:-

1) (1.

san e

Sea

1+ csc

sing.

+ Cose = 2C9CH,

sin e

(1 + csc x + cot x)

21+ tan x + coux + sec x + csc x

Given cos2 x = 2009 X 1. Hence,

or otherwise, prove that' in the triangle whose sides are 9, 16, 20, the greatest angle, is exactly double the angle opposite the side 16.

(1); (f b = 3

the sides of the triangle ABC.

༠༠ .

X

A Z 30% find a where a,b,c are

find the value of tan x.

4. (a) Express

(11) 2x=35: 9x

+n, write x in terms of N,n,a, and b.

cwt. 1 gr. 4 lb. as a percentage of a ton7%

(b) Find the value of 27 times 23. lls, 70.

(c) If 1 litre = 61 cù. in. approximately, Ting the number

f.qu. in, of water in a vessel which contains 475 cu =

翻

Ag

2 →

5. (a) Find the simple interest on $650 for 4 years at 34% per

annum

(b). Using the Tables provided, find the value of :-

14,81 x (1.05 )2

/0.07953

6. (a) Construct a triangle whose sides are 5 in.. in. construction lines and arcs must be clearly shown.)

4 in. Bisect, the greatest angle of the triangle. (ATL

(b) The interior angle of a regular polygon is 135. How

many sides has the polygon?

(o) The sides of a rectangle are 15 ft. and 36 ft. in

Tength. Calculate the length of a diagonal.

7(a) Find the sizes of the unknown angles in the figure:

Arrows indicate parallel lines

2

$8

67

=

estion 4)

Its X, Y are taken between B and C on the side. BC of a triangle ABC such that angle BAX is equal to angle YAC. Prove that

AC BX BY ABS CX CY.

(1) A man observes the elevation of the top of a mountain to be 50, he walks 1,000 feet nearer and finds the elevation to be 60°

Find the height of the mountain.

11) Brom the top of a tower 100 ft, high the angles of depression of two objects due north of the tower are 60° and 45 Find the distance between the objects.

on the same axes and using the same scales, draw graphs snow- ing how (1) sim 29, and (ii) sine, vary with @ as increases from 0 tà. 27, From these graphs, obtain, the solutions for the

sin 20

sin e Also, find, the eval

equation:

-values_of_

by solving the equation.

(b) A field is in the shape of a quadrilateral ABCD. AB

140 yds., BAD = 74 BAC 48 ZABC

LABD

41°.

Draw a plan of the field (scale: 1 in. 50 yds.); and find the lengths of the sides AD. DO. CB by measurement.

8.(a) Express 11°15' as a decimal of one right angle.

(b) Without using Tables. find the value of :-

tan260+400s 2450+ 3sec 230°.

What 18 the size or the angle between directions SSE. and WNW?

9. (a) Given sec A 4. find cot A and sin A.

(b) If tan 03.3434, find the value of the acute angle 9,

to the nearest minute.

(c) Express cos(90° metrical ratio.

A)cosec(90 - A) as a single trigûno-

CARAS-LBTEK)

Frove that if a pair of opposite angles of a quad- rilateral are supplementary, the quadrilateral is cycli

(ii) Two circles PAB, QAB intersect at A and B; their

centres are C, and D; E is a point on the circle PAB and lies outside the circle QAB; Q is a point on the circle QAB and, lies outside the circle PAB

Prove that if (AFB + ZAQB = 90°, the points A,B,

lie on a circle..

OMS

Two circles couen internally at O; a chord PQ:

touches the smaller at

the

Prove that OP:00 PR:RQ.

for otherwise.

Use area formula.of.triangle