2006 中學中級卷 英文試題(2006 Intermediate English Paper)

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Questions 1 to 10, 3 marks each

1.

92.2

_{− 85.3 equals}

(A) 6.1

(B) 6.9

(C) 7.1

(D) 7.5

(E) 7.9

2.

In the diagram, the value of x is

(A) 35

(B) 40

(C) 45

(D) 50

(E) 55

... ... ... ... ... ... ... ... ..._... ..._... ..._... ..._... ..._... ..._... ...

95

◦

x

◦

₁₃₅

◦

3.

If a = 2b

_{− 5, then b equals}

(A)

a

2

(B)

a

2

+ 5

(C)

a

_{− 5}

2

(D)

a + 5

2

(E) 2a + 5

4.

Which of the spinners below would give a one-in-four chance of the arrow landing

in the shaded region?

(A)

... ..._... ..._... ..._...... ... ... ... ... ... ... ... .... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .. .. .. .. .. .. ... ... ... ... ... .... ..._... ..._... ..._... ..._... ... ... ... ... ... ... ... ... .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. . .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. . .. .._... ... ... . .. .. . .. .. .. .. .. .. . .. .. .. .. .. .. .. .. . .. .. .. .. . .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . ... ... ... ... ... ... ... ..._......_......._......_......._...... .... .... .... .... .. .... .... . .... .... . .... ...

(B)

... ..._... ..._... ..._...... ... ... ... ... ... ... ... ... ... ... .. ... .. .. .. .. .. .. .. .. .. .. .. . .. . .. . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .. .. .. .. .. .. ... ... ... ... ... ... ..._... ..._... ..._... ..._... ... ... ... ... ... ... ... ... ... . .. .. . .. .. .. .. .. .. . .. .. .. .. .. .. .. .. . .. .. .. .. . .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. . .. .. .. . .. .. . .. . ... ... ... ... ... ... ... ..._......... .. ... .. .... .... . .... .... . .... ...

(C)

... ..._... ..._... ..._...... ... ... ... ... ... .... ... ... .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . .. .. .. . .. .. ... ... ... ... ... ... .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. . .. .. .. . .. .. . .. . ... . .. .. . .. .. .. .. .. .. . .. .. .. . .. .. .. .. . .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . ... ... ... ... ... ... ... ..._......_......._...._......._...... .... .... .... .... .. .... .... . .... .... . .... ...

(D)

..._... ..._... ..._... ... ... ... ... ... ... .... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .. .. . .. .. .. ... ... ... ... ... ... ... ... ... ... ... ... ... ... . .. .. . .. .. .. .. .. .. . .. .. .. .. .. .. .. .. . .. .. .. .. . .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . ... ... ... ... ... ... ... ..._...._....... ... . .... ...

(E)

... ..._... ..._... ..._...... ... ... ... ... ... .... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .. .. .. .. ... .. .... ... ... ... ... ..._... ..._... ..._... .. .... ... .... ... ... .... ... ... .... ... .... ... ... .... ... .... ... ... .... ... ... .. .. .. .. . .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. . .. .. .. . .. .. .._..... ... ... ... ... ... ... ... ..._....... .. ... . .... ...

5.

The area, in square centimetres, of one face of a cube whose volume is 64 cm

3

_is

(A) 8

(B) 16

(C) 24

(D) 32

(E) 64

6.

The average of five numbers is 4. Four of them are 1, 2, 3 and 4. What is the

other?

I 2

7.

1

4

%

expressed as a decimal is

(A) 0.235

(B) 0.14

(C) 0.025

(D) 0.014

(E) 0.0025

8.

In the diagram, P OR = 120

◦

and QOS = 145

◦

.

The size of T OV is

(A) 45

◦

_{(B) 60}

◦

_{(C) 85}

◦

(D) 90

◦

_{(E) 95}

◦

... ..._... ..._... ..._... ..._... ..._... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

T

V

P

Q

R

S

O

9.

The page numbers of a book are consecutive whole numbers. If you begin reading

at the top of page x and stop reading at the bottom of page y, the number of pages

you have read is

(A) x

_{− y}

(B) y

_{− x}

(C) x + y

(D) y

_{− x + 1}

(E) y

_{− x − 1}

10.

Jim notices the odometer of his car reads 062319 km where all the digits are

different. The shortest distance, in kilometres, he will travel before the digits are

all different again is

(A) less than 10

(B) between 10 and 20

(C) between 20 and 30

(D) between 30 and 40

(E) greater than 40

Questions 11 to 20, 4 marks each

11.

The middle date of the year in 2006 is

(A) 29th June

(B) 30th June

(C) 1st July

(D) 2nd July

(E) 3rd July

12.

Each of the vertices of a square P QRS is given a number. For each of the sides of

the square the sum of the numbers at its endpoints is calculated. If for P Q this

sum is 3, for QR it is 7 and for RS it is 12, what is the sum for P S?

13.

In the sequence of numbers . . ., q, r, s, t, 0, 1, 1, 2, 3, 5, 8, . . . , each number is

the sum of its two preceeding numbers. What is the value of q?

(A)

₋₃

(B)

₋₁

(C) 0

(D) 1

(E) 3

14.

What fraction of the rectangle P QRS

in the diagram is shaded?

(A)

1

16

(B)

3

5

(C)

1

8

(D)

1

10

(E)

10

77

... ... ... ... ... ... ... ... ..._... ..._... ..._... ..._... ..._... ... ... ... ... ... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

4

3

8

P

Q

R

S

15.

A train travelling at constant speed takes a quarter of a minute to pass a signpost

and takes three-quarters of a minute to pass completely through a tunnel which is

600 m in length. The speed of the train, in kilometres per hour, is

(A) 50

(B) 56

(C) 64

(D) 72

(E) 80

16.

In the multiplication

P

7

_{∗ ∗}

6

_×

∗

2

_{∗ 8 4}

P and

_{∗ stand for digits. P could be}

(A) 7

(B) 6

(C) 5

(D) 9

(E) 8

17.

How many different pairs of 2-digit numbers multiply to give a 3-digit number with

all digits the same?

(A) 5

(B) 6

(C) 7

(D) 8

(E) 9

18.

In

the

quadrilateral

KLM N ,

KM = KL = KN .

If

N KL = 110

◦

_{, then the size of}

LM N is

(A) 70

◦

(B) 115

◦

(C) 125

◦

(D) 140

◦

_{(E) 145}

◦

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... ... ... ... ... ... ... ... ..._... ..._... ..._... ..._... ..._... ..._... ..._... ..._... ..._... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

K

L

M

N

110

◦

I 4

19.

Define the operation

_{⊕ as a ⊕ b =}

b

a

− 1. The value of (3 ⊕ 4) ⊕ (1 ⊕ 2) is

(A) 0

(B) 2

(C)

1

2

(D)

3

4

(E) 5

20.

I have 450 grams of salt and flour mix. How many grams of flour should I add to

reduce the percentage of salt in the mixture to 90% of what it was?

(A) 50

(B) 10

(C) 30

(D) 45

(E) 60

Questions 21 to 30, 5 marks each

21.

How many positive integers less than 72 have the property that the highest common

factor of the number and 72 is equal to 1?

(A) 12

(B) 30

(C) 36

(D) 18

(E) 24

22.

The nine squares of a 3

_{× 3 grid painted on a wall}

are to be coloured red, white and blue so that no

row or column contains squares of the same colour.

One such pattern is shown in the diagram. How

many different patterns can be made?

(A) 15

(B) 6

(C) 9

(D) 12

(E) 24

W

B

R

B

R

W

R

W

B

23.

Five bales of hay are weighed two at a time in all possible combinations. The

weights, in kilograms,

are:-110, 112, 113, 114, 115, 116, 117, 118, 120 and 121.

What is the weight, in kilograms, of the heaviest bale?

24.

The squares P QRS and LM N O have equal sides of 1 m

and are initially placed so that the side SR touches LM

as shown. The square P QRS is rotated about R until

Q coincides with N . The square is then rotated about

Q until P coincides with O.

It is then rotated about P until S coincides with L and

then finally rotated about S until R coincides with M

and the square is now back to its original position.

P

S

Q

R

L

M

O

N

The length, in metres, of the path traced out by the point P in these rotations is

(A) π(2 +

√

2)

(B) 4π

(C) 2π(2 +

√

2)

(D) 2π

(E) π(3 +

√

2)

25.

The vertices of a cube are each labelled with one of the integers 1, 2, 3, . . ., 8.

A face-sum is the sum of the labels of the four vertices on a face of the cube. What

is the maximum number of equal face-sums in any of these labellings?

(A) 2

(B) 3

(C) 4

(D) 5

(E) 6

For questions 26 to 30, shade the answer as an integer from 0 to 999 in

the space provided on the answer sheet.

26.

If (1 + 3 + 5 +

_{· · · + p) + (1 + 3 + 5 + · · · + q) = (1 + 3 + 5 + · · · + 25),}

what is the value of p + q?

27.

Each of the students in a class writes a different 2-digit number on the whiteboard.

The teacher claims that no matter what the students write, there will be at least

three numbers on the whiteboard whose digits have the same sum. What is the

smallest number of students in the class for the teacher to be correct?

28.

In a quadrilateral P QRS, X is a point on QR and Y is point on P S. One circle

touches all four sides of the quadrilateral P QXY , and another circle touches all

four sides of XRSY . If P Q = 10 cm, QR = 20 cm, RS = 14 cm and P S = 26 cm,

what is the length, in centimetres, of XY ?

29.

In a regular polygon there are two diagonals such that the angle between them is

50

◦

. What is the smallest number of sides of the polygon for which this is possible?

30.

The sum of n positive integers is 19. What is the maximum possible product of

these n numbers?