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
[email protected]
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
[email protected]
Questions 1 to 10, 3 marks each
1. Which of these numbers is the smallest?
(A) 465
(B) 654
(C) 546
(D) 564
(E) 456
2. If 2 − 5 = 3 then 2 equals
(A) 10
(B) 9
(C) 8
(D) 7
(E) 6
3. What fraction of the rectangle is shaded?
(A)
1
2
(B)
1
3
(C)
1
4
(D)
1
5
(E)
1
6
.. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. ..4. What number must be added to 17 to get 23?
(A) 40
(B) 8
(C) 30
(D) 6
(E) 10
5. It takes 3 oranges to make a glass of orange juice. How many oranges
are needed to make 8 glasses of juice?
(A) 18
(B) 21
(C) 24
(D) 27
(E) 36
6. Which of the following numbers is eight thousand and seventy-nine?
(A) 80 079
(B) 8079
(C) 879
(D) 8790
(E) 80 709
MP 2
7. Here are three different
shapes:-Which of the shapes below cannot be obtained by turning around,
but not over, one of the above shapes?
(A)
(B)
(C)
(D)
(E)
8. Rhys and Helen play chess for 15 minutes and they finish playing at
11:21. Which clock shows the time they started playing?
(A)
(B)
(C)
9. Which of the following can be folded to make a square based pyramid?
(A)
...... ...... ... ... ... ... .... ... ... ... ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...... ...(B)
... ... ... ... ... ... ... ... ... ... ... ... ... ... ...... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...... ... ... ... ... ... ... ... ... ... ... ... ... ...... ...(C)
...... ... ... ... ...... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...... ... ...... ......... ...(D)
...... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...... ...... ...... ... ... ...(E)
...... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...... ...... ...... ... ... ...10. The number in each block is the sum of the numbers in the two blocks
below it.
1
3
5
7
12
What number should be in the top block?
(A) 32
(B) 16
(C) 24
(D) 48
(E) 20
Questions 11 to 20, 4 marks each
11. A bus carries 32 students. How many buses are needed to take 323
students to the school swimming carnival?
MP 4
12. The 30 students in a class are asked about the pets they have and
the results are summarised in the graph below.
0
5
10
15
Number
of pets
birds dogs
cats other
Pets
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. ..How many more cats than dogs are there?
(A) 2
(B) 5
(C) 7
(D) 10
(E) 15
13. Which of the following numbers has the tens digit twice the thousands
digit and the hundreds digit equal to the sum of the other 3 digits?
(A) 1629
(B) 1924
(C) 1962
(D) 1926
(E) 6912
14. Brett is 12 years old. Daina is half of Brett’s age. Omar is 13 years
older than Daina. How old is Omar?
(A) 39
(B) 11
(C) 25
(D) 19
(E) 16
15. A TV cost $460 and Sam has only paid $46. How much more does
he have to pay?
(A) $404
(B) $406
(C) $414
(D) $416
(E) $426
16. If each child can blow up 3 balloons in 1 minute, how many balloons
can a group of 5 children blow up in 2 minutes?
17. I roll two dice with the numbers 1 to 6 on each one and obtain a total
of 9. Which of the following numbers could not have been rolled?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
18. Henry covers his desk using 100 post-it notes. Sally’s post-it notes
are half the area of Henry’s and her desk is twice the area. How many
of Sally’s post-it notes will she need to cover her desk?
(A) 25
(B) 50
(C) 100
(D) 200
(E) 400
19. Five towns are joined by a system of roads as shown.
... ... ... ...... ... ... ...... ...... ... ...... ...... ... ... ... ...... ...... ... ... ... ... ... ...... .........
•
•
•
•
•
P
Q
R
S
T
How many different ways are there of travelling from town
P to town
T if, on any particular journey, no road is used more than once and
no town is passed more than once?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
20. In my pocket I have three coins, a 50 c coin, a $1 coin and a $2 coin.
How many different amounts of money can I make up using one or
more coins?
(A) 4
(B) 5
(C) 6
MP 6
Questions 21 to 30, 5 marks each
21. Jenny arrived at the bus stop to find she had missed the 09:27 bus
by two minutes and would have to wait for the 09:57 bus. How long
will she have to wait?
(A) 26 minutes
(B) 27 minutes
(C) 28 minutes
(D) 29 minutes
(E) 30 minutes
22. The digits 7, 5, and 9 are written on cards as shown.
7
5
9
Six different 3-digit numbers can be made using these cards. If these
numbers are arranged from the smallest to the largest, in which
po-sition is 795?
(A) second
(B) third
(C) fourth
(D) fifth
(E) sixth
23. Twelve 1 by 1 tiles, like this
, are arranged to form a rectangle.
Which of the following could be the perimeter of that rectangle?
(A) 18 cm
(B) 20 cm
(C) 22 cm
(D) 26 cm
(E) 32 cm
24. A 3 by 3 square is made up from nine 1 by 1 squares as shown.
A straight line is drawn though the large square. What is the largest
number of small squares which the line can pass through?
25. There are five blocks of different colours
stacked on top of each other.
The red
block is above the purple block, the blue
block is underneath the orange block and
the green block is below the blue and
above the red.
Which colour is the bottom block?
(A) red
(B) green
(C) blue
(D) orange
(E) purple
For questions 26 to 30, shade the answer as a whole number
from 0 to 999 in the space provided on the answer sheet.
26. Some steps are built using 36 wooden blocks as shown in the diagram.
...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ... ...... ...... ...... ... .... ... .... .... ... .... ... .... ... .... .... ... .... ... . .... .... ... .... ... .... ... .... .... ... .... ... .... ... . .... .... ... .... ... .... .... ... .... ... .... ... .... .... .. .... .... ... .... ... .... .... ... .... ... .... ... .... .... .. ...... ... ...... ... ...... ... ...... ... .... .... ... .... .... ... .... ... .... ... .... .... ... .... .. .... .... ... .... ... .... .... ... .... ... .... .... ... .... .. .... .... ... .... ... .... .... ... .... ... .... ... .... .... .. .... .... ... .... ... .... ... .... .... ... .... ... .... ... .
All the faces on the outside except the bottom ones are painted blue.
How many blocks do not get any of their faces painted?
27. In the year 5 classroom, the desks are arranged in equal rows. Phil
sits at the desk that is fourth from the front and third from the back.
There are four desks on the right of Phil’s desk but only one to the
left. How many desks are there in the room?
MP 8
28. A carpenter made 20 chairs and stools with a total number of 73 legs.
If the chairs each have 4 legs and the stools each have 3 legs, how
many chairs did she make?
29. Lisa collected 50 seashells over a period of five days. Each day she
collected three more than she had collected the day before. How
many shells did she collect on the fifth day?
30. An apartment block has a number of square apartments and a number
of square gardens. Apartments must have at least one window, either
to the outside or to a garden. In figure 1, one apartment has a window
to an internal garden G, and ten have windows to the outside.
... ... ... ... .... .... . ... ... ... ... .... . ... ... ... ... .... . ... ... ... .... ... ... ... ... ... ... ... .... ... ... ... ... ... ... ... ... ... ... ... .... ... ... ... ... ... ...
