2007 中學初級卷 英文試題(2007 Junior English Paper)

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Questions 1 to 10, 3 marks each

1. The value of 37

− 16 is

(A) 1

(B) 9

(C) 11

(D) 21

(E)

−21

2. The value of

6

× 7

3

is

(A) 7

(B) 14

(C) 21

(D) 1

(E) 39

3. In the diagram, where

P QR is a straight

line,

x equals

(A) 60 (B) 70 (C) 80 (D) 90 (E) 100

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

x

◦

25

◦

75

◦

P

Q

R

4. My mother left her car in the car park at 11 am and returned 5 hours later. The

time when she returned was

(A) 6 pm

(B) 5 pm

(C) 4 pm

(D) 3 pm

(E) 2 pm

5. The sum of the smallest and largest of the five numbers 3.1, 0.6, 3, 6 and 0.5 is

(A) 6

(B) 9

(C) 6.1

(D) 6.6

(E) 6.5

6. Tony wanted to add 97 to 298 and first added 100 to 300. What must he now

subtract from this result to obtain 97 + 298?

(A) 2

(B) 3

(C) 5

(D) 6

(E) 15

7. A tray of mangoes costs $46. Each tray has 5 rows with 6 in each row. The cost

of three mangoes is

J 2

8. Which of the following shows three-eighths of the figure shaded?

(A)

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(B)

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

(C)

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

(D)

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

(E)

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

9. If 97 +

a = 100 + b, then

(A)

a = b + 3

(B)

a = b − 3

(C)

a = 3b

(D)

b = 3a

(E)

a + 3 = b − 3

10. Of the following, which is the largest fraction?

(A)

7

15

(B)

3

7

(C)

6

11

(D)

4

9

(E)

1

2

Questions 11 to 20, 4 marks each

11. Two cats together catch 60 mice. If Tiger catches three mice for every two Shorty

catches, how many mice does Shorty catch?

(A) 20

(B) 24

(C) 30

(D) 36

(E) 40

12. A class of 30 students has a spelling quiz every day. On Monday, 17 of the students

scored 100% on the quiz. On Tuesday, 18 students scored 100% on the quiz. The

least possible number of students who scored 100% on both quizzes is

13. The game of

Four Tofu is played on a 4 × 4 grid.

When completed, each of the numbers 1, 2, 3 and

4 occurs in each row and column of the 4

× 4 grid

and also in each 2

× 2 corner of the grid.

When the grid shown is completed, the sum of the

four numbers in the corners of the 4

× 4 grid is

2

1

1

3

4

(A) 13

(B) 11

(C) 15

(D) 12

(E) 10

14. How many numbers in the range 100 to 1000 are divisible by 6?

(A) 136

(B) 150

(C) 160

(D) 165

(E) 166

15. A square with side length 2 units is placed

next to a square with side length 5 units as

shown. The shaded area, in square units, is

(A) 13.5

(B) 14.5

(C) 18.5

(D) 19.5

(E) 26

2

5

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

16. Ace, Bea, Cec, Dee, Eve, Fie and Geo are 1, 2, 3, 4, 5, 6 and 7 years old, in some

order. Dee is three times as old as Bea. Cec is four years older than Eve. Fie is

older than Ace and Ace is older than Geo, but the combined ages of Ace and Geo

is greater than the age of Fie. The age of Ace is

(A) 2

(B) 3

(C) 4

(D) 5

(E) 6

17.

P QR is an equilateral triangle, QS

and

QT divide



P QR into three equal

parts. The size of



QT S, in degrees, is

(A) 60

(B) 70

(C) 80

(D) 90

(E) 100

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

P

Q

R

S

T

18. Jim’s average score in his first six matches was 8.5. If all scores are whole numbers

and his lowest score was 5, what is the lowest value which his highest score could

have been?

J 4

19. The diagram shows a large rectangle which has been divided into six smaller

rectan-gles. Four of the smaller rectangles have

perimeters of 10, 12, 14 and 16 centimetres,

as shown by the numbers inside them.

10

12

14

16

If the sides of the rectangles are whole numbers, what is the smallest possible

perimeter, in centimetres, of the large rectangle?

(A) 30

(B) 32

(C) 34

(D) 36

(E) 40

20. Jane’s age is a prime number. Andy’s age has 8 factors and he is one year older

than Jane. Of the following numbers, which could be the sum of their ages?

(A) 27

(B) 39

(C) 75

(D) 87

(E) 107

Questions 21 to 25, 5 marks each

21. On her birthday in 2007, Rachel’s age is equal to twice the sum of the digits of the

year in which she was born. How many possible years are there in which she could

have been born?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

22.

P QR is a triangle. S lies on P R such

that

P Q = QS = SR. All the angles

in the diagram are a positive whole

number of degrees. The largest

pos-sible size, in degrees, of



_{P QR is}

(A) 171

(B) 173

(C) 175

(D) 177

(E) 179

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

P

R

Q

S

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

23. How many two-digit numbers are equal to three times the product of their digits?

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4

24. On a 3

× 5 chessboard, a counter can move one square at a time along a row or a

column, but not along any diagonal. Starting from some squares, it can visit each

of the other 14 squares exactly once, without returning to its starting square. Of

the 15 squares, how many could be the counter’s starting square?

(A) 5

(B) 6

(C) 7

(D) 8

(E) 9

25. Each of Andrew, Bill, Clair, Daniel and Eva either always lies or is always truthful,

and they know which each of them is.

Andrew says that Bill is a liar.

Bill says that Clair is a liar.

Clair says that Daniel is a liar.

Daniel says that Eva is a liar.

The largest possible number of liars among them can be

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

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

the space provided on the answer sheet.

Question 26 is 6 marks, question 27 is 7 marks, question 28 is 8 marks,

question 29 is 9 marks and question 30 is 10 marks.

26. Find the sum of all the two-digit integers,

XY , between 10 and 99, which have the

property that

X Y

× X Y

· · · X Y

27. A rectangular area measuring 3 units by 4 units on a wall is to be covered with 6

tiles each measuring 1 unit by 2 units. In how many ways can this be done?

28. There are four lifts in a building. Each makes three stops, which do not have to

be on consecutive floors or include the ground floor. For any two floors, there is

at least one lift which stops on both of them. What is the maximum number of

floors that this building can have?

J 6

29. A grid of squares measuring 9 units by 6 units has the two corners removed as

shown:

How many squares of any size are contained within this grid?

30. For any positive integer

N, consider the digits which occur either in N or in 7×N.

Let

m be the smallest digit among those digits. What is the largest possible value

of

m?