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[email protected] [email protected] Notice: Individual students, nonpr nonprofit ofit libraries, or schools are permitted to make fair use of the papers and its solutions. Republication, systematic copying, or or multiple reproduction 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 e-mailin g Mr. Mr. Wen-Hsien SUN
[email protected] [email protected]
Middle Primary Division Questions 1 to 10, 3 marks each 1. How How man many y dots dots are on the the plate? plate?
(A) 10
(B) 12
(C) 13
(D) 14
(E) 15
2. Jill had had 15 grapes. grapes. She ate ate 5. How man many y are lleft? eft?
(A) 7
(B) 8
(C) 9
(D) 10
3. This grid grid gives gives the position position of differen differentt shapes. For example, a ♢ is in position
1
B4. Which shape is in position D2? (A) ♢
(B) ⊕
(C) ♡
(D) ⊙
(E) △
1
(B)
2
(D)
1 5
3
4
♡ ⊙
B △
♢
⊙ ⊕ ♡
D △ ♡ ⊕ △
1
(C)
3
(E)
2
A ⊕ ♡
C ⊙
4. What fract fraction ion of this this shape is shaded shaded??
(A)
(E) 11
1 6
1 4
MP 2
5. On this spinne spinner, r, whic which shape shape ar aree you you
most likely to spin? (A)
(C) ⋆
(B)
(D) ♠
(E) •
•
⋆
♠
•
6. What time time is show shown n on this this clock? clock? 11
(A) twelve o’clock
10
(B) a quarter to nine
9
(C) a quarter past three
12
1 2 3
8
4 7
(D) a quarter past twelve
6
5
(E) three o’clock
7. The graph graph below shows shows the number number of pets owned by by the students students in
a Year 4 class. Pets in Year 4
8 6 4 2 0
Cats
Dogs Fish
Rabbits
How many pets does this class have altogether? (A) 24
(B) 22
(C) 21
(D) 14
(E) 4
MP 3
8. Which Which num number ber do you need in the box to make this number number sentenc sentencee
true? 19 + 45 = 20 + (A) 34
(B) 44
(C) 46
(D) 64
(E) 84
9. How How many 2 by 1 rect rectangl angles es will fit exactly exactly
into an 8 by 7 rectangle? (A) 14
(B) 28
(C) 36
(D) 56
(E) 63
10. Fiv Fivee swimme swimmers rs were were in a 50 m race. race. The time time each each swimmer swimmer took to
finish the race is shown in this graph. Who won the race? George Ethan Franco Henry Ivan 0 (A) George
10
20
(B) Ethan
30
40 Time in seconds
(C) Franco
(D) Henry
(E) Ivan
MP 4
Questions 11 to 20, 4 marks each 11. Ciann Ciannaa is string stringing ing beads beads for for a ne neck cklac lace, e, starti starting ng with with two roun round d
beads, then a square bead, and then repeating this pattern of three beads.
She finished her necklace with a round bead, which happens to be the 18th round bead. How many square beads are on her necklace? (A) 10
(B) 12
(C) 18
(D) 6
(E) 8
12. The triangle shown is folded in half three times without unfolding,
making another triangle each time.
Which figure shows what the triangle looks like when unfolded?
(A)
(B)
(C)
(D)
(E)
13. When complete, each row, column and diagonal in
4
this dia this diagr gram am has a sum of 15. What What is the the sum of the numbers in the shaded squares? (A) 20
(B) 25
(C) 27
(D) 30
(E) 45
5 5
MP 5
14. To which square should I add a counter so that
no two rows have the same number of counters, and no two columns have the same number of counters? (A) A
(B) B
(C) C
(D) D
A B
C D E
(E) E
15. John wrote his name on his book. Martha said he wrote with a black
pen. Aaron Aaron said it was a brown brown pencil. pencil. Frankie rankie sai said d it was a black black cray cra yon. If each each of John’ John’ss frien friends ds were were ha half lf right right,, what what did he really really use to write his name? (A) a brown pen
(B) a brown crayon
(D) a black pen
(C) a brown pencil
(E) a black pencil
16. Follow the instructions in this flow chart.
Start5 with
Subtract 2
Multiply by 3
Is this greater than 50?
Yes
Select this answer
No
(A) 57
(B) 63
(C) 75
(D) 81
(E) 84
MP 6
17. A square piece of paper is folded along the dashed lines shown and
then the top is cut off.
The paper is then unfolded. Which shape shows the unfolded piece? (A)
(B)
(C)
(D)
(E)
18. Rod had had fewer fewer than 100 bloc blocks. ks. When When he made five five equal equal rows, rows, he
had one block left over. over. With four equal equal rows, he had one block left over. With nine equal rows, there were no blocks left over. How many blocks did he have? (A) 18
(B) 49
(C) 81
19. Simo Simon some 24 24acm long long strips. strnumber ips. Each Eacof h strip nis has made from different
equal-sized tiles. Simon took 1 tile from each strip to make a new strip. How long is the new strip? (A) 18 cm cm
(B) 20 cm cm
(D) 24 cm cm
(C) 23 cm cm
(E) 33 ccm m
(D) 91
(E) 99
MP 7
20. The numbers 1 to 6 are placed in
the circles so that each side of the tria trian ngle has has a sum sum of 10. If 1 is placed in the circle shown, which number is in the shaded circle? (A) 2
(B) 3
(C) 4
(D) 5
1
(E) 6
Questions 21 to 25, 5 marks each 21. Gran Grandpa dpa had $400 in his wallet. wallet. He gave gave half the money to his wife.
From what was left, he then gave gave one-quarte one-quarterr to his son. Half of the remainde rema inderr went went to his grandson. grandson. How How much much money did his grandson grandson receive? (A) $50
(B) $125
(C) $100
(D) $200
(E) $75
22. The numbers 40 19 37 33 12 25 46 18 39 21 are matched in pairs so ,
,
,
,
,
,
,
,
,
that the sum of each each pair is the same. Which Which number number is paired paired with 39? (A) 19
(B) 33
(C) 21
(A) 35 (C) 39
(B) 37 (D) 41 (E) 43
(E) 25
6 cm
23. This shape is made from two two
overlapping rectangles. What is its area in square centimetres?
(D) 18
4 cm
3 cm 4 cm 3 cm
2 cm 5 cm
MP 8
24. Molly is thinking of a number. Twice her number take away seven is
the same as her number plus five. What is her number? (A) 19
(B) 17
(C) 15
(D) 12
(E) 10
25. Tom Tom borro b orrowe wed d some items from the stat statione ionery ry cupboard. cupboard. He found
that 5 glue sticks weigh the same as 2 staplers, and that 3 staplers weigh the same as 20 erasers.
o o o o o o o l o l o l o l l G i i G i G i G i G
How many glue sticks balance with how many erasers? (B) 3 glue sticks with 50 erasers (A) 3 glue sticks with 8 erasers (C) 1 glue stick with 6 erasers (D) 3 glue sticks with 17 erasers (E) 7 glue sticks with 23 erasers
For questions 26 to 30, shade the answer as a whole number 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. Jill Jill has has thre threee larg largee pi pile less of coins coins:: 10c, 10c, 20c 20c and and 50 50c. c. In how how man many
different ways can she make one dollar?
MP 9
27. A newspaper open on the table had page
42 opposite page 55 because someone had removed some pages from the centre. What is the number of the last page of the newspaper?
28. Alex is designing a square patio, paved by
putting bricks on edge using the basketweave pattern shown. She has 999 bricks she can use, and designs her patio to be as large a square as possible. How many bricks does she use?
29. There are many ways that you can add three different positive whole
numbers to get a total of 12. For instance, 1 + 5 + 6 = 12 is one way but 2 + 2 + 8 = 12 is not, since 2, 2 and 8 are not all different. If you mu multi ltipl ply y these these three three num numbers, bers, you you get get a num number calle called d the the product. Of all the ways to do this, what is the largest possible product?
30. A 3 × 2 flag is divided into six squares, as shown.
Each square is to be coloured green or blue, so that every square shares at least one edge with another square of the same colour. In how many different ways can this be done?
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
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重版、系統地複製或大量重製這些資料的任何部分，必 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 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] [email protected] Notice: Individual students, nonpr nonprofit ofit libraries, or schools are permitted to make fair use of the papers and its solutions. Republication, systematic copying, or or multiple reproduction 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 e-mailin g Mr. Mr. Wen-Hsien SUN
[email protected] [email protected]
學
年 級 卷
1-10 3 1.
(A) 10
(B) 12
(C) 13
(D) 14
(E) 15
5 3 5 × 3 = 15 : (E)
2.
小 15 5 (A) 7
(B) 8
(C) 9
(D) 10
(E) 11
15 − 5 = 10
3.
: (D)
♢ B4 D2 (A) ♢
(B) ⊕
(D) ⊙
(E) △
(C) ♡
1
2
A ⊕ ♡ B △ C ⊙
3
4
♡ ⊙ ♢
⊙ ⊕ ♡
D △ ♡ ⊕ △
D 2 小 ♡ : (C)
MP 2
4.
(A)
1 2
(B)
1 3
(C)
1 4
(D)
1 5
(E)
1 6
4 中 1 1 4 : (C)
5.
(A)
(D) ♠
(C) ⋆
(B)
(E) •
•
⋆
♠
•
6 中 中 • 2 • 2 1 : (E)
6.
(A) (B) (C) (D) (E)
11 12 1 10 9
2 3
8
4 7
6
5
12 : (D)
MP 3
7.
年級學 8
年級學
6 4 2 0
年級學 (A) 24
(B) 22
(C) 21
(D) 14
(E) 4
6 7 3 5 6 + 7 + 3 + 5 = 21 : (C)
8. ( 小學高年卷 4 )
19 + 45 = 20 +
(A) 34
(B) 44
(C) 46
(D) 64
(E) 84
19 1 20 45 1 44 44 : (B)
MP 4
9.
8 × 7 2 × 1 (A) 14
(B) 28
(C) 36
(D) 56
(E) 63
8 × 7 = 56 2 × 1 = 2 56 7 = 28 2 4 : (B)
10. 50 m ( ) 0 (A)
(B)
10
20
30 (C)
40
(D)
(E)
: (B)
MP 5
11-20 4 11. 小小
中 18 中 (A) 10
(B) 12
(C) 18
(D) 6
(E) 8
中 2 18 9 9 8 : (E)
MP 6
12. ( 小學高年卷 11 )
中 小
(A)
(B)
(C)
(D)
(E)
(B) : (B)
MP 7
13. 小 15
中 中 小 小 (A) 20
(B) 25
(C) 27
(D) 30
(E) 45
4 5 5
1 小 小 15 小 小 4 5 5 5 6
6 4 5 6 4 5 5 4 5 6 5 6 4 5 6 4
小 小 4 + 4 + 5 + 6 + 6 = 25 : (B) 2 15 + 15 = 30中小 5 2 小 30 − 5 = 25
: (B)
MP 8
14. ( 小學高年卷 9 )
小 小 (A) A
(B) B
(C) C
(D) D
(E) E
A B
C D E
A E 中中 中中 E A 4 1 2 3 3
2 4 1
: (A)
15. 小小小
小 小 小 小 (A) (B) (C) (D)
(E)
小小小 中 中 小 小 小 小 小 小 小小 小小 : (E)
MP 9
16. ( 小學高年卷 16 )
5
2
3
50?
(A) 57
(B) 63
(C) 75
(D) 81
(E) 84
5 − 2 = 3 3 × 3 = 9小 50 9 − 2 = 7 7 × 3 = 21小 50 21 − 2 = 19 19 × 3 = 57 50 57 : (A)
MP 10
17. ( 小學高年卷 17 )
(A)
(B)
(C)
(D)
(E)
P Q R S
T
Q R
P
P Q R S
T
中 P Q 中 中 QS 中中中 中中中 QS TQ 中 中 中 中 T Q 中 中 QR 中 (D) : (D)
MP 11
18. 小 100 5 1 4 1 9
(A) 18
(B) 49
(C) 81
(D) 91
(E) 99
小 9 小 4 5 小 4 × 5 = 20 1小 100 中 20 1 121 416181中 81 9 小 81 : (C)
19. 小
24 cm小 (A) 18 cm (B) 20 cm (C) 23 cm (D) 24 cm cm
(E) 33 cm cm
24 ÷ 6 = 4 cm24 ÷ 4 = 6 cm24 ÷ 12 = 2 cm 2 cm 24 ÷ 3 = 8 cm24 ÷ 8 = 3 cm 23cm 4 + 6 + 2 + 8 + 3 = 23cm : (C)
MP 12
20. ( 小學高年卷 15 ) 123456
10 1 中 (A) 2
(B) 3
1
(C) 4
(D) 5
(E) 6
23456 5 中 9 3 + 6 = 9 4 + 5 = 9 1 1 + 3 + 6 = 10 1 + 4 + 5 = 10 2中 5 4 1
2 6
3
: (A) 21-25 5 21. $400
(A) $50
(B) $125
(C) $100
(D) $200
(E) $75
$400 × =$200 $200 $200 × =$50 $150 $150 × =$75 : (E) 1 2
1
4
1 2
MP 13
22. 40193733122546183921 39 (A) 19
(B) 33
(C) 21
(D) 18
(E) 25
1 小 12181921253337394046 12 + 46 = 18 + 40 = 19 + 39 = 21 + 37 = 25 + 33 = 58
19 39
: (A)
2 10 5 (40 + 19 + 37 + 33 + 12 + 25 + 46 + 18 + 39 + 21) ÷ 5 = 58 39 58 − 39 = 19
: (A)
MP 14
23.
6 cm
cm
4 cm
3 cm
2
(A) 35 (A) (C) 39 (C)
4 cm 3 cm
(B) 37 (B) (D) 41 (D)
2 cm
(E) 43 (E)
5 cm
6 × 4 5 × 3 中 1 × 2 6 4 3 4
3
2 5
(6 × 4) + (5 × 3) − (1 × 2) = 24 + 15 − 2 = 37cm 37cm2
: (B) 24. 小 7 5 (A) 19
(B) 17
(C) 15
(D) 12
(E) 10
小 小 2 5 + 7 = 12 12 : (D)
MP 15
25. 小中 5 2 3 20
o o o o o o o l o l o l o l l G G i G i G i G i i
(A) 3 8 (B) 3 50 (C) 1 6 (D) 3 17 (E) 7 23 6 3 × 5 = 15 2 × 20 = 40 15 40 3 8 : (A)
MP 16
26-30 000-999 26 6 27 7 28 8 29 9 30 10
26. 小 10
20 50
50 • 2 × 50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . • 1 × 50
• 1 × 50 + 2 × 20 + 1 × 10 . . . . . . . • 1 × 50 + 1 × 20 + 3 × 10 . . . . . . . • 1 × 50 + 5 × 10 . . . . . . . . . . . . . . . • 0 × 50 50::
• 5 × 20 . . . . . . . . . . . . . . . . . . . . . . . . • 4 × 20 + 2 × 10 . . . . . . . . . . . . . . . • 3 × 20 + 4 × 10 . . . . . . . . . . . . . . . • 2 × 20 + 6 × 10 . . . . . . . . . . . . . . . • 1 × 20 + 8 × 10 . . . . . . . . . . . . . . . • 10 × 10 . . . . . . . . . . . . . . . . . . . . . . .
: (10)
MP 17
27. 中 42 55
42 55 42 41 55 41 55 + 41 = 96 : (96)
28. ( 小學高年卷 26 )
小 999
小 小 ÷ 小 999 3 = 333 18 = 324 19 = 361 18 小 3 × 324 = 972 : (972) 2
2
MP 18
29. ( 小學高年卷 27 )
12 1 + 5 + 6 = 12 中 中 2 + 2 + 8 = 12 2 28 中 中
小 abc P a × b × c a + b 小 1 + 2 = 3 c 12 − 3 = 9 c 中 中 c 12 ÷ 3 = 4 c = 98765 ab P c = 9 a + b = c = 8 a + b =
a = 1, b = 2 3 P = 18 a = 1, b = 3 4 P = 24
c = 7 a + b = c = 6 a + b = c = 5 a + b =
a , b28 = 4 a = 2= , b = 3 5 =P 1= P 42 a = 1, b = 5 a = 2, b = 4 6 P = 30 P = 42 a = 3, b = 4 7 P = 60
a = 3b = 4c = 5 P = 60 : (60)
MP 19
30. ( 小學高年卷 29 , 級卷 28 ) 3 × 2 6 小 小
小 小 小 小 小 小
中 中 中 中 023 4 0
2
3
4
11 中 中 11 22 : (22)
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
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重版、系統地複製或大量重製這些資料的任何部分，必 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 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] [email protected] Notice: Individual students, nonpr nonprofit ofit libraries, or schools are permitted to make fair use of the papers and its solutions. Republication, systematic copying, or or multiple reproduction 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 e-mailin g Mr. Mr. Wen-Hsien SUN
[email protected] [email protected]
Middle Primary Division Questions 1 to 10, 3 marks each
1. What is the value value of 20 + 16?
(A) 24
(B) 26
(C) 36
(D) 9
(E) 216
(D) 555
(E) 556
2. Which Which of these n num umbers bers is the smallest smallest??
(A) 655
(B) 566
(C) 565
3. In the num number ber 83 014, the the digit digit 3 represen represents ts
(A) three
(B) thirty
(D) three thousand
(C) three hundred (E) thirty thousand
4. My sister is 6 years years old and and I am twice twice her age. Adding our our ages gives gives
(A) 14
(B) 15
(C) 18
(D) 20
(E) 21
5. Four of these shape shapess have have one or more lines of symmetry symmetry. Which Which one
does not? (A)
(B)
(C)
(D)
(E)
6. Two pizzas pizzas are sliced sliced into into quarters quarters.. How How many slices slices
will there be? (A) 2 (D) 8
(B) 10
(C) 6 (E) 16
MP 2
7. Will has a 45-minute music music lesson every every Tuesday Tuesday afternoon afternoo n after school.
If it begins begins at 4:30 4:30 pm, at what time time does it finish? finish? (A) 4:45 pm
(B) 4:55 pm
(C) 4:75 pm
(D) 5:00 pm
(E) 5:15 pm
8. In our garage there are are 4 bicycles, bicycles, 2 tricycles
and one quad quad bi bik ke. How How many many wheels wheels are there altogether?
(A) 3
(B) 6
(C) 7
(D) 14
(E) 18
9. Ten chairs chairs are equally equally spaced spaced around around a round table. table. They are are num-
bered 1 to 10 in order. Which chair is opposite chair 9? (A) 1
(B) 2
(C) 3
(D) 4
(E) 5
10. Lee’ Lee’ss fa favo vourit uritee chocola chocolates tes are 80c each. each. He has five five
dollars to spend. How many of these chocolates can he buy? (A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Questions 11 to 20, 4 marks each 11. The four digits 2, 3, 8 and 9 are placed in the
boxes so that when both two-digit numbers are added, the sum is as large as possible. What is this sum? (A) 175 (B) 67 (C) 156 (D) 179
(E) 121
+
MP 3
12. A circula circularr piece of paper is fold folded ed in half twice and the then n a cut is made
as shown.
When the piece of paper is unfolded, what shape is the hole in the centre? (A)
(B)
(C)
(D)
(E)
13. Phoebe Phoebe put put her her hand hand in her her pock pocket and pull pulled ed out 60 cen cents. ts. How How
many different ways could this amount be made using 10c, 20c and 50c coins? (A) 2
(B) 3
(C) 4
(D) 5
14. There are 5 red, 5 green and 5 yellow jelly beans
in a jar. How many would you need to take out of the jar without looking to make sure that you have have removed at least two of the same colour? (A) 3
(B) 4 (D) 6
(C) 5 (E) 7
(E) 6
MP 4
15. A sailor coiled a rope on his ship’s deck,
and some paint was spilled across half of it. What did the rope look like when it was uncoiled? (A) (B) (C) (D) (E)
16. The students in Mr Day’s class were
asked the ask the colo colour ur of th thei eirr sun sun hat. hat. The results are shown in the graph. Mr Day chooses two colours which include the hat colours of exactly half of the class. Which two colours does he choose? (A) orange and black (B) green green and yello yellow w (C) black black and yello yellow w (D) red and orange (E) red and and yello yellow w
Sun hat colours 7 6 5 4 3 2 1 0 red
orange
black
green
yellow
17. The sum of the seven seven digits digits in Mario’s Mario’s telephon telephonee num number ber is 34. The
first five digits are 73903. How many possibilities are there for the last two digits? (A) 6
(B) 7
(C) 8
(D) 9
(E) 10
MP 5
18. If the area of the tangram shown is 64
square squa re ce cen nti time metr tres es,, what what is the the area area in square centimetres of the small square? (A) 32 (B) 24 (C) 16 (D) 8
(E) 4
19. By making just one fold on a rectangular piece of paper, which of the
following shapes is NOT possible? (A)
(B)
(C)
(D)
(E)
20. In this diagram there are four lines with three
circles each. Place the numbers from 1 to 7 into the circles, so that each each line adds up to 12. Which Which number must go into the circle at the centre of the diagram? (A) 7 (B) 6 (C) 5 (D) 4 (E) 2 Questions 21 to 25, 5 marks each 21. Fou ourr hock hockey teams play play each each of the other other three three teams once once.. A win
scores 3 points, a draw scores 1 point and a loss scores 0 points. Some figures figur es in the following following table table are missing. missing. Ho How w man many yp poin oints ts did the Hawks get? Play layed Win Draw Los osss Points Eagles 3 3 9 Hawks 3 Falcons 3 0 1 Condors 3 0 2 1 (A) 1
(B) 4
(C) 6
(D) 7
(E) 10
MP 6
22. In this grid you can only move downward, going
from point to point along the lines shown. One route from P to Q is drawn in. How many different routes are there from P to Q? (A) 2
(B) 4 (D) 8
P
(C) 6 Q
(E) 12
23. I have five coloured discs in a pile as shown.
I take the top two discs and put them on the bottom (with the red disc still on top of the blue disc). Then I again take the top two discs and put them on the bottom.
red blue green yellow orange
If I do which this until have made total of 21 moves, disc Iwill be on the abottom? (A) red
(B) blue
(C) green
(D) yellow
(E) orange
24. A zoo keeper weighed some of the animals at
Melbourne Zoo. He found that the lion weighs 90 kg more more than than th thee le leop opar ard, d, and and the the tige tigerr weigh eighss 50 kg less less than than the lion. lion. Alto Altoge geth ther er thee thre th threee anim animal alss wei eigh gh 310 kg. kg. How How muc uch h does the lion weigh? (A) 180 kg kg
(B) 150 kg kg
(C) 140 kg kg
(D) 130 kg kg
(E) 100 kg kg
MP 7
25. Jane and Tom each have $3.85 in coins, one of each Australian coin.
They each give some coins to Angus so that Tom has exactly twice as much money as Jane. What is the smallest number of coins given to Angus?
10 cents 5 cents
(A) 2
20 cents
(B) 3
50 cents
(C) 4
2 dollars 1 dollar
(D) 6
(E) 8
For questions 26 to 30, shade the answer as a whole number 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. With some 3-digit numbers, the third digit is the sum of the first two
digits. For example, digits. example, with the number number 213 we can add 1 and 2 to get 3, so the third digit is the sum of the first two digits. How many 3-digit numbers are there where the third digit is the sum of the first two digits?
MP 8
27. In a family with two sons and two daughters, the sum of the children’s
ages is 55. The two sons were born three years apart, and the two daughters were born two two year yearss apart apart.. The youn younge gerr son is twice wice the age of the the older older daughter. How old is the youngest child? 28. From this set of six stamps, how many ways
could you choose three stamps that are connected along their edges? C
A
B
D
E
F
29. A class class has 2016 2016 matchst matchstic icks. ks. Using Using blobs blobs of modelling modelling clay clay to join
the matc matches togeth together, er, they make make a lo long ng row of cubes. cubes. This This is how their row starts.
They keep adding cubes to the end of the row until they don’t have enou en ough gh matc matche hess le left ft for for anot anothe herr cube. cube. How How man many cubes cubes will will they they make?
30. Mary has four children of different ages, all under 10, and the product
of their ages is 2016. What is the sum of their ages?
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[email protected] [email protected] Notice: Individual students, nonpr nonprofit ofit libraries, or schools are permitted to make fair use of the papers and its solutions. Republication, systematic copying, or or multiple reproduction 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 e-mailin g Mr. Mr. Wen-Hsien SUN
[email protected] [email protected]
Middle primary
46
國 1-10
年 級 卷 3
1.
20 + 16 (A) 24
20 + 16 = 36
2.
(B) 26
(C) 36
(D) 9
(E) 216
: (C).
(
國小高年級卷 1 ) 中小 中小 (A) 655
(B) 566
(C) 565
(D) 555
(E) 556
小 555556565566655 : (D). 3.
83014 中 3 (A) (B) (D)
(E)
(C)
3 3000 4.
: (D).
年 6 年年年 (A) 14
(B) 15
(C) 18
(D) 20
(E) 21
年 12 年 6 + 12 = 18 5.
: (C).
中中 (A)
(B)
(C)
AMC2016 draft papers (for final mo deration)
(D)
(E)
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Middle primary
47
Z 6.
: (E).
(
國小高年級卷 2 ) (A) 2
(B) 10 (D) 8
(C) 6 (E) 16
4 2 × 4 = 8 7.
: (D).
小 45 430 (A) 445 (B) 455 (C) 475 (D) 500 (E) 515 30 500 15 515 : (E).
8.
4 2 1 (A) 3
(B) 6 (D) 14
(C) 7 (E) 18
4 × 2 + 2 × 3 + 1 × 4 = 18 9.
(
國小高年級卷 6 ) 1 10 9 (A) 1
(B) 2
(C) 3
AMC2016 draft papers (for final mo deration)
: (E).
(D) 4
(E) 5
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Middle primary
48
5 5 9 5 4
10
1
2
9
3
8
4 7
6
5
: (D). 國小高年級卷 5 ) 小 0.8 5
10. (
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
1
5 ÷ 0.8 = 6 . . . 0.2 6 0.2 : (C). 2
0.81.62.43.244.85.6 6 7 : (C). 0.8
11-20
4
2389 小 小 小 小 中 中
11.
(A) 175
(B) 67 (D) 179
+
(C) 156 (E) 121
9 8 3 2 93 + 82 = 175 92 + 83 = 175 175 : (A).
AMC2016 draft papers (for final mo deration)
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Middle primary
49
初級卷 6 )
12. (
中 (A)
(B)
(C)
(D)
(E)
: (A). 國小高年級卷 8 ) 小 60 10 20 50
13. (
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
小 50 50 10 50 + 10 = 60 50 012 3 20 10 + 10 + 10 + 10 + 10 + 10 = 60
20 + 10 + 10 + 10 + 10 = 60
20 + 20 + 10 + 10 = 60
20 + 20 + 20 = 60
5
AMC2016 draft papers (for final mo deration)
: (D).
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Middle primary
50
5 5 5
14.
(A) 3
( B) 4 ( D) 6
(C) 5 (E) 7
3 4 : (B). 國小高年級卷 11 )
15. (
中 中 (A) (B) (C) (D) (E)
(A) 中 (A) (B) (C) (D) (E)
: (A).
16.
AMC2016 draft papers (for final mo deration)
7 6 5 4 3 2 1 0
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51
3 + 6 + 2 + 1 + 4 = 16 8 : (A). 17.
34 73903 小 (A) 6
(B) 7
(C) 8
(D) 9
(E) 10
7 + 3 + 9 + 0 + 3 = 22 34 − 22 = 12 7 399348845775 66 : (B). 國小高年級卷 12 ) 64 cm 中 小 cm
18. (
2
2
(A) 32
( D) 8
(B) 24
(E) 4
(C) 16
8 cm 2 cm × 2 cm
8 cm 小 小 2 小 2 × 2 cm × 2 cm = : (D). 2
19.
(A)
(B)
(D)
AMC2016 draft papers (for final mo deration)
(C)
(E)
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Middle primary
52
中 (E)
(A)
( B)
(C)
(D)
: (E). 20.
中小 1 7 中 中小 小 小 小 12中小 (A) 7
(B) 6
(C) 5
(D) 4
(E) 2
1
中 中 5 12 7 + 4 + 1 = 12, 7 + 3 + 2 = 12, 6 + 5 + 1 = 12, 6 + 4 + 2 = 12, 5 + 4 + 3 = 12
4 中中 1 + 5 + 6 2 + 3 + 7 中 4 中 中小 小 (i)
4
(ii)
4
(iii) 4
1 + 5 + 6 2 + 3 + 7 (i) (ii) 4 中 1 5
6
3 2 7 4
4 2 3 7
1 6
5
中小 中小 4 : (D). AMC2016 draft papers (for final mo deration)
11 /5 /2 01 6
Middle primary
53
2
小 小 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 2 × 12 = 24中小 28 − 24 = 4 : (D). 21-25 21.
5
3 0 1 H E H F C (A) 1
3 3 3 3
(B) 4
3 0 0
9 1 2
(C) 6
1 (D) 7
(E) 10
3 中 中E F C E 3 3 0 0 9 H 3 F 3 0 1 2 1 C 3 0 1 2 1 E H E F C H H 2 1 6 : (C). 中 中中 中 中 P Q 中 P Q
22.
(A) 2
(B) 4
(C) 6
( D) 8
P
(E) 12 Q
AMC2016 draft papers (for final mo deration)
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Middle primary
54
P A 1 P X 1 P B A X P B 2 P Y 2 P C B Y B Y 2 P C 4 P
P A
X
B
Y
C
Z Q
4 Z Q C 4 Z 4 P Q 8 : (D).
國小高年級卷 21 ) ( ) 21 (A) (B) (C) (D)
23. (
(E)
51015 20 1 : (B). 國小高年級卷 22 ) 90kg 50kg 310 kg kg 310
24. (
(A) 180 k kgg
(B) 150 k kgg
(C) 140 k kgg
(D) 130 k kgg
(E) 100 k kgg
1
90kg 50kg 310 + 90 + 50 = 45 450 0 kg 450 ÷ 3 = 150 kg : (B). 2
100kg 10kg 50kg 160kg 150kg 150 ÷ 3 = 50 kg 150kg : (B). AMC2016 draft papers (for final mo deration)
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Middle primary
55
小小 3.85 小 小 小 小 小 小 小 小
25.
2
0.1
0.5
0.2
1
0.05
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
小 2 小 4 0.01 小 小 0.05 5 0.05 1.85 3.8 小小 小小 小 小 小 小 小 0.05 0.1 3.7 小 2 1.85 : (B).
26
000-999 26-30
6 27 7 28 29 9 30 10
8
213 中 3 1 2
26.
AMC2016 draft papers (for final mo deration)
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1 2 3 4
0 101 202 303 404
1 112 213 314 415
2 123 224 325 426
3 134 235 336 437
4 145 246 347 448
5 6 7 8 9
505 606 707 808 909
516 527 538 549 617 628 639 718 729 819
5 6 7 8 156 167 178 189 257 268 279 358 369 459
9 8 7 6 5 4 3 2 1 45
9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45
: (045).
小年 55 小 小 年 年 年 年 年小小 年小小
27.
小 小 年 年 4 小年 小 年 年 年 小年 小 年 年 年 小 年 年 年 年 年 0 1 2
2 3 4
4 6 8
7 9 11
1133 1199 25
年 6小 1 1 2 小年 小年 55 30 30 ÷ 6 = 5 小年 小 年 年 年 小 年 年 年 年 年 7
9
18
21
55
年小小 年小小 7
: (007).
中 中
28.
A B C
AMC2016 draft papers (for final mo deration)
D
E
F
11 /5 /2 01 6
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57
A B 中 D E 2 A 中 中 B 中 中 D 中 中 C E 2 B 中 A 中 E 中 D F 2 A B 中 中 CDE DEF 2 8
: (008).
國小高年級卷 28 ) 2016 初 初
29. (
12 8 2016 − 12 = 2004 2004 ÷ 8 = 250 . . . 4 1 + 250 = 251 4 : (251). 初級卷 20 ) 年小 10 小小年 2016小年
30. (
2016 2016 = 2 × 3 × 7 2016 中小 10 1234678 9 中 7 中小 中小年 年 7 中 3 3 × 6 = 2 × 3 9 = 3 小年 小 年 3 × 6 × 7 × 16 16 10 中小年 中 小年 7 × 9小年 32 4 × 8 小年 478 9 年 28 : (028). 5
2
2
AMC2016 draft papers (for final mo deration)
2
2
11 /5 /2 01 6
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
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 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 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] [email protected] Notice: Individual students, nonpr nonprofit ofit libraries, or schools are permitted to make fair use of the papers and its solutions. Republication, systematic copying, or or multiple reproduction 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 e-mailin g Mr. Mr. Wen-Hsien SUN
[email protected] [email protected]
Middle Primary Division Questions 1 to 10, 3 marks each
1.
2.
3.
4.
5.
6.
7.
28km Janesville Mary Ma ryto town wn 15 km Smi mith thto ton n
23 km
8. ff
9.
1
2
3
4
5
10.
Questions 11 to 20, 4 marks each 11.
12.
13.
3 c 4 c c 3
4 c
c 4
3 c
c 3
? c 4
4 c
3 c
4c
3 c
14.
special normal
15.
16.
2 1
17.
18.
19.
∗
20.
Questions 21 to 25, 5 marks each 21.
22.
23.
24.
ff ff
25.
11
12
1
10
2
9
3
8
4 7
6
5
For questions 26 to 30, shade the answer as a whole number 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. ff
