2005 中學初級卷 英文試題(2005 Junior English Paper)

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Questions 1 to 10, 3 marks each

1.

The value of 25 + 32 is

(A) 89

(B) 57

(C) 35

(D) 43

(E) 34

2.

Which of these shapes has the largest area?

(A)

(B)

(C)

(D)

(E)

3.

Holly turned 8 years old in 2005. In what year was she born?

(A) 1996

(B) 2013

(C) 2000

(D) 1998

(E) 1997

4.

The size of P RQ, in degrees, is

(A) 20

(B) 30

(C) 40

(D) 50

(E) 60

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

50

◦

100

◦

P

Q

R

5.

A rockmelon weighs 740 g and a mango weighs 170 g. The total weight of the two

fruits, in grams, is

(A) 910

(B) 800

(C) 810

(D) 570

(E) 760

6.

The value of 456 + 567

_{− 455 − 566 is}

J 2

7.

If I buy three chocolate bars worth $2.50 each and five milkshakes worth $1.50

each, how much change do I get from a $20 note?

(A) $3.00

(B) $3.50

(C) $4.00

(D) $4.50

(E) $5.00

8.

The figure is composed of two squares

with areas shown. The length of P Q is

(A) 2 (B) 15 (C) 32 (D) 16 (E) 130

P

Q

49

81

9.

A lesson finished at 10:10 am. If the duration of the lesson was 55 minutes, it

started at

(A) 9:15 am

(B) 9:45 am

(C) 9:00 am

(D) 8:45 am

(E) 8:30 am

10.

During the Tai Chi move called Jade Lady, you rotate 180

◦

_{clockwise, then 90}

◦

anticlockwise then 270

◦

_{clockwise and finally 90}

◦

_{anticlockwise again. The single}

move which would get you to this position is

(A) 0

◦

_{(B) 90}

◦

_{anticlockwise}

_{(C) 90}

◦

_clockwise

(D) 180

◦

_clockwise

_{(E) 135}

◦

_clockwise

Questions 11 to 20, 4 marks each

11.

If ‘Anne

-

Jane’ means ‘Anne is taller than Jane’, who is the tallest?

Alan

Ed

Mike

Anne

Jane

½

½

½

½

½=

P P P

_{P Pq}

@

@

@R

¢

¢

¢

¢

¢¢¸

½

½=

@

@I

12.

The average of 6 numbers is 4.5. A further 2 numbers are added and the average

is still 4.5. What is the sum of these two numbers?

(A) 27

(B) 9

(C) 36

(D) 4.5

(E) 8

13.

Seven consecutive integers are listed. The sum of the smallest three is 33. What

is the sum of the largest three?

(A) 39

(B) 37

(C) 42

(D) 48

(E) 45

14.

The diagonals of the square P QRS intersect

at O. The shaded region has area 16. What

is the perimeter of the square?

(A) 4

(B) 8

(C) 16

(D) 32

(E) 64

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

P

Q

R

S

O

15.

How many numbers are there from 10 to 99 in which the digits differ by 3?

(A) 10

(B) 11

(C) 12

(D) 13

(E) 14

16.

When 707 is divided by a secret number the remainder is 5. The secret number

could be

(A) 7

(B) 8

(C) 9

(D) 10

(E) 11

17.

A bag contains six sticks of the following lengths: 1 cm, 3 cm, 5 cm, 7 cm, 11 cm

and 13 cm. How many different triangles can be made using any three of these

sticks?

(A) 20

(B) 11

(C) 8

(D) 1

(E) 5

18.

Hamilton High School starts at 8:30 am and finishes at 3:30 pm each day. The

number of times the hour and minute hand form a right angle on the school clock

during the school day is

J 4

19.

A large cube is constructed from 125 smaller equal cubes. The number of smaller

cubes whose faces touch the faces of exactly four other cubes is

(A) 24

(B) 36

(C) 48

(D) 64

(E) 81

20.

Hexagonal paving stones are laid to form

a continuous path across a lawn.

This

path is bordered by lengths of wood, one

for each side of a paving stone not

touch-ing another pavtouch-ing stone.

If 98 pieces

of wood are used, how many hexagonal

paving stones are used?

(A) 24

(B) 25

(C) 16

(D) 17

(E) 49

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

•

•

•

•

Questions 21 to 30, 5 marks each

21.

A 64 page magazine is made up of 16 sheets which have been folded over and

stapled down the middle. Pages 1, 2, 63, 64 are on the same sheet. Pages 31, 32,

33, 34 are on the same sheet. The sheet with page 15 also has on it page number

(A) 14

(B) 47

(C) 48

(D) 50

(E) 52

22.

The number 119 has exactly 4 factors, 1, 7, 17 and 119. Another integer which has

exactly four factors is

(A) 120

(B) 125

(C) 127

(D) 121

(E) 126

23.

P , Q, R and S are four different points on a straight line such that Q and R lie

between P and S. P S = 10 m and QR = 3 m. If, for every two of these four points,

the distance between them is measured, the sum of all six such distances is

(A) 33 m

(B) 52 m

(C) 58 m

(D) 60 m

(E) 65 m

24.

In the multiplication

P

Q

R

3

_×

Q

Q

Q

each of P , Q and R represents a different digit. The sum of P , Q and R is

25.

A 3

_{× 3 square is divided into nine 1 × 1 unit squares. Different integers from 1}

to 9 are written into these nine unit squares. Consider the pairs of numbers in the

squares sharing a common edge. What is the largest number of pairs where one

number is a factor of the other number?

(A) 7

(B) 8

(C) 9

(D) 10

(E) 12

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

the space provided on the answer sheet.

26.

In the year 2004, there were 5 Sundays in February. What are the last two digits

of the next year in which this will occur?

27.

I had some 2 cm by 1 cm by 1 cm bricks

and decided to build a large block.

When I had built this much, I ran out

of bricks. How many bricks did I have

to start with?

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . .. ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. . . .. . . .. . . .. . . .. . . .. . . .. . . ... ... ... ... ... ... ... ... ... ... . . . .. . .. . . .. . . .. . . .. . . .. . . .. . . .. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28.

The decagon shown has a reflex angle at P .

What is the largest possible number of reflex

angles in a decagon?

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

P

29.

Given a cube, how many acute angled triangles are there whose vertices are vertices

of that cube?

30.

A positive integer is equal to the sum of the squares of its four smallest positive

divisors. What is the largest prime that divides this positive integer?