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179英文中學會考試題預習專欄

堅道英文書院主編

數學科

(廿九)

MATHEMATICS (29)

(es).

MULTIPLE CHOICE QUESTIONS

SOLUTIONS

(Answers followed by a brief explanation)

1. The correct answer is (3),

We could solve the syston

+

and thus find the number of ordered : paira estierying the two equations. But we don't have to do this.

ransform-sach of these equation to a standard

-3219

2 (1) and

.(2)

(2), 11 y - 0, x ~

The first ellipse has fool on the x-axis while the second has foot on the y-axis. Because of this, the only ordered pairs satisfying both (1) and (2) are (1,0) and (-1,0).

The correct answer is (3).

The answer cannot be (*), since (« in)- is not

One method, which is a long and tedious one,in to solve the sinn ultaneous aquations of

-hon the values of n and n is obs the cubes of these twi values and get the anENOT.

is solved in this wayi

7. (C) is the correct answer.

Since angle AOB in 60 degrees, sector 403 = 1/6 of the area of circle.

The area of the triangle ADB is 3 (8)(43)

Area of the shaded portion in the difference of area of the sector and area of the triangle, which is

16.√3

22 π- 16√3

10

ED = 6

angle AED -

90°

By Pythagorean theorm

AB 8

Area of AED

Area of ABCD

4(6)(8),

- 24

- 2 A RED

48

Let BC 18

Since perimeter

AC 50-18

-32-

50

rap a perp. from A to BC

Let BH y

··18

Using the pythagorean relation for the two angled triangles, we geti

(32-1)

16x

1024 64% +

93 + 175

-324 36-y

Wa vant to find the smallest integer ♬ that

makan xan integer.

We rewrite the equation. 16x = 9y + 175

15+ 1716

The

What we have done here in to divide 16 into 175. It goes 10 times with a resainder of 15,- Th smallest value of y that makes x an integer is 9. For y 9, x = 14, Bo that 32 - z - 18. wider of the triangle are, therefore, 18, 18, 14, Note that winos HC - 18 – y; y must be less than 18.

(D) is correct.

3.

When the triangle is folded along the line XX,

G goinoides with B. This means that BY • TO In triangle ABC, tan C - 4/3

In triangle XTC, tanG = XT/2.5 Therefore,

3(xr)

XX

2.5 (4)

2.5 x 4/3 10/3

(B) is the correct answer.

It is obvious

Let ABGD be the square inscribed in the semicir- cle of diameter XN and centre 0. that, since ABCD is a square, 40 - OD.

+3mus

)

(3)(7)(4)

(3) is the correct answer.

1083

22 18

BC?

the

Let CD.

OD

Since 4x2-20

-5

Join OC

In the rt

OCD

25

Loc

Therefore, the radius of the circle is 5. Now,} if a square is inscribed in the entire circle with the same radius, vo have

25

is the requi

refore,

1063 27 is the AGO,

11. (C) in correcti

20.

21.

is the correct answer,

,023

2y= 100)

50

-(A) is the correct answer.

Volume of the first oylinder = Volume of the second cylinder - 8(47) Their ratio will, therefore, be 3:16;

The correct answer is (A)M.

(3)(2)

→(2)

The correct anover in (A)`

(ab)(bc)(os) - (3)(4)(6)

(abo)2

abo

(B) is the correct answer.)

The value of the estate of the youngest son, 1# $2000."

.ft.

The value of the estate of the three younger brothers is $6000 which is two-thirds of the value of the estate of his father.

value of Kr. Ho estate

Therefore, the

$9000

23. (C) is the correct answer."

The first pound is 10 cents. The rest,3(p =10

24. (A) 18-

he correct answere

(2x- → 3)(x+2)

When (2x − 3)(x + 2) is divided by (2z ➡ 3), 1ts quotient is (x + 2).

(C) is the correct

Sua of any two sides is greater than the third.]

5 + 9 is less than 15; (A) is incorrect.

6+ § is equal to 15; (B) is incorrect. 9+ 15 is equal to 24; (D) is incorrect,

15 is less than 25; (E) is incorrect,

greater than 15

is greater than 9 The only answer is (C)

[26, (E) is the answer.

Even though ñ ounces of water is evaporated, the amount of salt in the solution remains tha same which is 0.05n ounces,

(B) is the correct answer.

If the radius of a circle, R, is decreased by: 20%, it becomes 0.8R.

Ita azen decreases from TC k2 to 0.64 TC R2. Percentage decreano - (CR2 - 0.64 TR100

TC R

0.36 TCR*

100)

I 36%

(C) is the correct answer.

then":

(x = 2y)

1871 or x/

is the correct

Half the circumference of the big circle im 127

circumference is 24 TC U

AR12.

hat is,

Similarly, the radius of the smaller cirales are 8 and 4 respectively,

ren of the shaded portion is equal to area of half the big circle minus the sum of the areas.

the two smaller sexi-01

72-70 40TC

3270.

(B) the correct answer.

Since the triangle is equilateral, each angle

is 60 degrees. If we draw AH perpendicular

BO, this altitude is also

the median of the triangle.

Therefore, BH = k/c

Since area of a triangle is′′

h, where bis the basp

and his the

th

the height.

fore BH-k

In triangle AHB, tán

There-

/BA

12.

3

*16.

(A) is the correct answer,

-

(C) 18 the correct answer,|-

Both the length and the width of a rectangle).

The

is increased 100%, that means boubled. area becomes four times larger than the origin. Therefore the area is increased 300%;

(E) ie the dorrect answer=]

(A) is the correct answer. area of the square - - Ares of the rectangle = xy

45 Perimeter of the square Perimeter of the rectangle - 2x + 2y

Since the perimeters of the two figures are [@quare,

2(x + y)

The area of the rectangle is xy

The correct answer is (B)

-106% of 200 - 200 + 6% of 200

200+ 12 212

(B) is the correct answar,

There are 12 equal, edges in the cube. edge is 2 inches.

The volume of the cube is 2 x 2 x 2 ou

is the correct answer,

If the sum of two quantities is constant, their product is greatest when they are equal.

3/2

د(2)

2(1))

(E) is the correct answer.

A man has $10,000 to invest.

He invest $3,500 at 4% and $ 4,000 at 5%. and invest $2,500 at x%

-166 - 6.4%

A) is the correct answer.

thus earnя 3140.

$200

so as to earn $(500-340)

30% of 20 pinta of the solution is pure scid. that 18 2 pints of pure acid exista. The rest being water.

Let x pints of pure acid be added to strengthen the solution to 40%.

x 100 40

20+ x

* 10 pints

32, (B) is the answer.

cul yards - 18 cu.ft..

1 cu. ft. weighs 100 pounds

Therefore, 18 cu.ft, of sand weighs 1800 1b.)

(E) is the correct answer,

33.

Therefore,

tan

60

when

x -

30

∙AH

* 900

Area of AABC

of A AHBA

which is the maximum valua

(C) is the correct answer,

2(x + y){≈ » (2)(2)(x2)

2y

2(x

The answer is 4x2 (x + V}(x − 3}

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