2011 中學初級卷 英文試題(2011 Junior English Paper)

注意：

允許學生個人、非營利性的圖書館或公立學校合理使用

本基金會網站所提供之各項試題及其解答。可直接下載

而不須申請。

重版、系統地複製或大量重製這些資料的任何部分，必

須獲得財團法人臺北市九章數學教育基金會的授權許

可。

申請此項授權請電郵

ccmp@seed.net.tw

Notice:

Individual students, nonprofit libraries, or schools are

permitted to make fair use of the papers and its

solutions. Republication, systematic copying, or

multiple reproduction of any part of this material is

permitted only under license from the Chiuchang

Mathematics Foundation.

Requests for such permission should be made by

e-mailing Mr. Wen-Hsien SUN

ccmp@seed.net.tw

Questions 1 to 10, 3 marks each

1.

_{The value of 2011 − 1102 is}

(A) 1111

(B) 1191

(C) 1001

(D) 989

(E) 909

2.

In the diagram, the value of x is

... ..

50

◦

₄₅

◦

x

◦

(A) 75

(B) 80

(C) 85

(D) 90

(E) 95

3.

I left for a walk at 2:15 pm and returned at 3:20 pm. How long was I out walking?

(A) 50 minutes (B) 55 minutes (C) 60 minutes (D) 65 minutes (E) 70 minutes

4.

On this number line,

✛

..._...

✲

.. ... ...

Q

7

8

the point 15 units to the left of Q is

(A) −10

(B) −9

(C) 0

(D) 5

(E) 10

5.

_{The value of 888 − (88 − 8) is}

(A) 808

(B) 880

(C) 800

(D) 792

(E) 2011

6.

_{We know that 5 × 7 × 11 = 385. What is the value of 0.5 × 0.7 × 0.11?}

J 2

7.

In the diagram, lines P T , QU, RV and SW intersect at O.

6

QOR = 20

◦

_,

₆

_{SOT = 50}

◦

_and

₆

_{V OW = 70}

◦

_{. The size of}

₆

_{P OQ is}

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

_U

W

P

Q

S

T

R

V

O

(A) 30

◦

_{(B) 40}

◦

_{(C) 50}

◦

_{(D) 60}

◦

_{(E) 80}

◦

8.

The value of 2

4

_{+ 4}

2

_is

(A) 16

(B) 32

(C) 34

(D) 36

(E) 64

9.

Warren reads 20 pages in 30 minutes. At this rate how long will it take him to

read 66 pages?

(A) 1 hr 34 min

(B) 1 hr 36 min

(C) 1 hr 37 min

(D) 1 hr 38 min

(E) 1 hr 39 min

10.

Each of the following 2-digit numbers has one digit covered. Which of the five

numbers is the only possible multiple of 12?

(A) 3

(B)

9

(C)

5

(D)

3

(E) 5

Questions 11 to 20, 4 marks each

11.

In the diagram, ABCD is a square. What

is the value of x?

(A) 142

(B) 128

(C) 48

(D) 104

(E) 52

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

52

◦

x

◦

A

B

C

D

12.

Billy counts backwards by 7, starting at 5907. When he reaches a single-digit

number, he stops counting. The number he stops at is

(A) 4

(B) 6

(C) 7

(D) 8

(E) 9

13.

The following tile is made from three unit squares.

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

What is the area, in square units, of the smallest square which can be made from

tiles of this shape?

(A) 16

(B) 25

(C) 36

(D) 64

(E) 81

14.

Which of the following is closest to

0.333

0.222 × 0.111

?

(A) 0.01

(B) 0.1

(C) 1

(D) 10

(E) 100

15.

In the diagram, P T divides

6

_{RP Q in half and}

SQ divides

6

P QR in half.

6

P RQ = 60

◦

_.

What is the size of

6

SU P ?

(A) 75

◦

_{(B) 60}

◦

_{(C) 45}

◦

(D) 40

◦

_{(E) 30}

◦

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

P

Q

R

S

T

U

60

◦

... ...

16.

The numbers on the six faces of this cube are consecutive even numbers.

If the sums of the numbers on each of the three pairs of opposite faces are equal,

find the sum of all six numbers on this cube.

J 4

17.

If m and n are positive whole numbers and mn = 100, then m + n cannot be equal

to

(A) 25

(B) 29

(C) 50

(D) 52

(E) 101

18.

In the following addition, some of the digits are missing.

9

+

8

7

0

2

The sum of the missing digits is

(A) 23

(B) 21

(C) 20

(D) 18

(E) 15

19.

If Peter lost 20 kg in weight he would then weigh 4 times as much as his pet wombat.

Together they weigh 200 kg. How much does the wombat weigh?

(A) 30 kg

(B) 36 kg

(C) 40 kg

(D) 164 kg

(E) 170 kg

20.

Two tourists are walking 12 km apart along a flat track at a constant speed of

4 km/h. When each tourist reaches the slope of a mountain, she begins to climb

with a constant speed of 3 km/h.

✲

✛

_{12 km}

✡

✡

✡

✣

✑

✑

✸

✑

✑

✰

? km

What is the distance, in kilometres, between the two tourists during the climb?

Questions 21 to 25, 5 marks each

21.

Each of thirty-four students wrote a story. All thirty-four stories were of different

lengths ranging from 1 to 34 pages. These were put into a single book where the

book starts at page 1, each new story begins on a new page and there are no blank

pages. What is the largest possible number of stories that start at an odd page

number of such a book?

(A) 8

(B) 9

(C) 17

(D) 26

(E) 33

22.

_{The six faces of a dice are numbered −3, −2, −1, 0, 1, 2. If the dice is rolled twice}

and the two numbers are multiplied together, what is the probability that the

result is negative?

(A)

1

2

(B)

1

4

(C)

11

36

(D)

13

36

(E)

1

3

23.

A grocer packed 52 boxes of oranges each with the same number of oranges in it

and had 8 oranges left over. If he had packed 2 less oranges in each box, he would

have filled 60 boxes. How many oranges did he have?

(A) 540

(B) 480

(C) 840

(D) 720

(E) 900

24.

A square-based pyramid is built using cubical blocks, 1 on top, 4 on the next layer,

9 on the next, 16 on the next, and so on.

What is the minimum number of blocks needed if the pyramid is to be dismantled

and rebuilt into 2 separate cubes with no blocks left over?

(A) 55

(B) 91

(C) 140

(D) 204

(E) 285

25.

_{In 4P QR, U is the midpoint of RQ, P U = RU, P T bisects}

6

_{RP Q and}

6

RT P = 60

◦

_.

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

R

Q

P

T

U

What is the size of

6

_{RU P ?}

J 6

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.

The diagram shows the net of a cube. On each face there is an integer: 1, 2011,

1207, x, y and z.

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

x

y

2011

z

1207

1

If each of the numbers 1207, x, y and z equals the average of the numbers written

on the four faces of the cube adjacent to it, find the value of x.

27.

An arrangement of numbers has different differences when the differences between

neighbours are all different. For example, the numbers

1 4 2 3

have differences 3, 2 and 1 − all different.

If the numbers from 1 to 6 are arranged with different differences, and with 3 in

the third position,

3

what are the last three digits?

28.

Which two-digit number is equal to the sum of its first digit plus the square of its

second digit?

29.

The first digit of a six-digit number is 1. This digit 1 is now moved from the first

digit position to the end, so it becomes the last digit. The new six-digit number is

now 3 times larger than the original number. What are the last three digits of the

original number?

30.

Joe the handyman was employed to fix house numbers onto the doors of 80 new

houses in a row. He screwed digits on their front doors, numbering them from 1

to 80. Then he noticed that there were houses already numbered 1 to 64 in the

street, so he had to replace all the numbers with new ones, 65 to 144. If he re-used

as many digits as possible (where he could use an upside down 6 as a 9 and vice

versa), how many new digits must he have supplied?