2019 CAT Senior澳大利亚数学信息数学竞赛真题

A C B C D D A B l−ef→t B A C C D D A B B
C
D
,
A
: A C C D D A B B l−ef→t A C C D D A B B A C C D D A B B A l−ef→t A C C D D B B A A
3
(
2
)
B.
, ，
10 X ,
,
A
,
B
X ,
ABAB, ,
C. 543 8 4 4 7 2 1 0
5 9 7 15 16 15 22 20 18 18
5 4 8 12 11 16 18 17 19 17
17，
2，3，5，6，8
澳洲运算思维测验 2019 (11，12 年級 Solutions)
13
9.
A. A C B C D D A B
B，
B
C,
DA
,
，
19
19
18
18
14 18
18
17 11
17 MBps,
(D)
2.
1
澳洲运算思维测验 2019 (11，12 年級 Solutions)
8
12345
算 ，
1
2
3
3
4
5
4
5
1
3
5
1
3
5
3
-
→
→
→
→
→
-
2
24
241
2415
24153
53 (
2
5 BRB
RBR 3
， CAEBD
，5 2
，
3
，
，
1 2 3 4 5，
B 0 10 20 30 40 40 39 38 37 36
A = B?

C
01234
4
A 77 77 77 77 77 77 77 77 77 77 77 77 77
B < A?
B 0 10 20 30 40 50 60 70 80 80 79 78 77
6 ,7
8，
8.
，
算
，
+
，
0(
)
A. 17 5 6 8 1 0
1 8 12 12 20 15 13
1 7 6 13 14 13 14
13，
1，3，4，6
B. 57 34 954 6 0
5 12 10 12 20 22 20 26 22
5 7 8 11 17 16 21 22 20
20，
2，4，6，7
5
4，
ABCDE)
R BR-
4
3 1
2
B，
1
2
3
1
4
3
5
5
→
-
24
1
2
3
1
4
3
5
5
3
→→
-
24 2415
241 (D)
，3 5
， 4
24153 (D)
澳洲运算思维测验 2019 (11，12 年級 Solutions)
9
3.
2 1 6 1 − 2 − 6 = −7, 4 3 2 3 − 4 − 2 = −3, 4 1 2 1 − 4 − 2 = −5, 3 1 7 1 − 3 − 7 = −9.
ABCD E 5 ，
1.
2.
3.
4.
5.
3
4，
A B C D E，
(A) A
(B) B
(C) C
(D) 17 (D) D
(E) 18 (E) E
澳洲运算思维测验 2019 (11，12 年級)
2
3.
，4 5 6 8 3 2 216
(5 + 8 + 2) − (4 + 6 + 3) = 2 12 :
2019 CAT — Senior
澳洲运算思维测验 2019 (11，12 年級)
1
Part A: Questions 1–6
3
1.
， R
算 ，
20
W 21
14 15
22 19
，
W
，
MBps
12 17
18
17
13
16
20 15
19 18
19
14 18
R 11
(A) 14
(B) 15
(C) 16
2.
，
36, 77, 357 11498
A B0
B < A?
10 B
C0
A = B?
1C
B1
C
(A) 0
6. 1 4
5? (B) 1
， ，
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
27 33 34 41
1
4
(C) 2
(D) 3
(E) 4
澳洲运算思维测验 2019 (11，12 年級)
4
Part B: Questions 7–9
? AB
, ,
, .
ABBCDCAE FDFGGE
A
B
C
D
E
F
( )，
G
验
算
,
BCFG
A D E，
2+2+2 = 6
澳洲运算思维测验 2019 (11，12 年級 Solutions)
14
C.
,
.
A B B A F A B DAADA P R P RQQR R F RX F XYXYXX
432
412
317
(A) 2
4.
(B) 4
(C) 6 ，
D
C
A
A
C
→D
E
A
B
E
D
A
1. 2. 3. 4. 5.
(A) A
A， B， C， D， E，
607
(B) B
D 1 4 2
2
(C) C
(D) 8 (D) D
(E) 10 (E) E
澳洲运算思维测验 2019 (11，12 年級)
3
5.
算
,
(
)
Questions 7–9 (each with three parts) require a three-digit answer. Attempt all questions. Penalties do not apply. • You are allowed working time of one hour (60 minutes). There is no extra reading time. • Diagrams are NOT drawn to scale. They are intended only as aids. • The questions have been thoroughly checked. Each question stands as written. No further explanation of questions can be provided. • You must not leave your seat. If you have any other questions or problems, please raise your hand and wait for a supervisor. • If you wish to leave the room a supervisor must accompany you. • Record all your answers on the answer sheet provided. • Use B or 2B lead pencils only. Ball point and ink pen markings may not activate the optical scanner. • Do not make any other marks on the answer sheet as these may make the sheet unreadable. • If you make an error, use a plastic eraser to completely remove all lead marks and smudges. • Check the number of the answer you are filling in is the same as the number of the question you are answering. This is particularly important if you decide to leave a question blank. • To ensure the integrity of the CAT and to identify outstanding students, the AMT reserves the right to re-examine students before deciding whether to grant official status to their score. Reminder: You may sit this competition once, in one division only, or risk no score.
COMPUTATIONAL & ALGORITHMIC THINKING
Senior Years 11 & 12
(Australian school years)
TUESDAY 2 APRIL 2019
NAME:
INSTRUCTIONS
• Do not open the CAT paper until told to do so. • Maintain silence at all times. • Do not bring mobile phones into the room. • You may use calculators and printed language dictionaries. • You may NOT borrow equipment without a supervisor’s permission. • There are 9 questions. Questions 1–6 are multiple-choice with five possible answers given.
，2 0 – 999
7.
， ←, →, ↑, ↓

Y

*
Y
X* *
，

Y
，
， Y
A.
，
X
3
*
X
Y
3
↓→↑ Y
X
Y
← X
Y，
↑→
X
澳洲运算思维测验 2019 (11，12 年級)
5
B.
Y
X
C.
Y
X
澳洲运算思维测验 2019 (11，12 年級)
6
8.
算
，
， ，
,
，
，
?
A. 1 7 5 6 8 1
216 317
， −3 + 7 − 5 + 9 = 8，
432216412317 (D)
Fra Baidu bibliotek
4.
6
,
D
C
A
A
C
→D
E
A
E A
6, 12, 18, …, 600, 606
,
E,
B D
, (E)
607th
5.
11498
， 算
算 算
A 36 36 36 36 36 36 36 36
B < A?
Copyright © 2019 Australian Mathematics Trust AMTT Limited ACN 083 950 341
2019 CAT — Senior
2019 CAT — Senior
2019 CAT — Senior
2019 CAT — Senior
2019 CAT — Senior
B. 5 7 3 4 9 5 4 6
C. 5 4 3 8 4 4 7 2 1
9.
,
)
:
ACBADCBB
A C B A D C B B −→ B A C A D C B B B AADBBBCC
， ，
AZ (
，
B，
C
−→ C A C A D B B B C
−→ C
A. A C B C D D A B
B. A B B C D C A E F D F G G E X X X X X X X X X X
A = B?

C
0123
3
澳洲运算思维测验 2019 (11，12 年級 Solutions)
:
36 77 357 11498
40 − 36 = 4 80 − 77 = 3 360 − 357 = 3 11500 − 11498 = 2
5,
算 (E)
6. 1 4
5
134
,
，
134
10 10
20
W 21
22 19
18 17
18
17
20 19
19 R
18
17 MBps
,
17 MBps,
(D)
2
运 Djikstra s algorithm(
算)
21 MBps
22 MBps，
,
， 21 MBps
20
14
20
15
W 21
21 22
21
19
17
12
19
17
18
17
17
17
13
16 18 20
15
2 25
012345
012345
5 5,
15 ... ,
1 ( 4)
,
2
,
5
7 12 ...
4 ( 1) ,
,
5n
,
10 5n + 2
5n 5n + 2
27 = 5 × 5 + 2 33 = 5 × 6 + 3 34 = 5 × 6 + 4 41 = 5 × 8 + 1
33
5n + 1 (5n + 3, 5n + 4), ,
,
34 41
,
,
1 (1, 4)
,
(D)
澳洲运算思维测验 2019 (11，12 年級 Solutions)
11
Part B: Questions 7–9
7.
，
A.
Y
5
7
X
，
5
7，
5
B.
6Y
7
X
，
6
7，
6
澳洲运算思维测验 2019 (11，12 年級 Solutions)
12
C.
8
Y
X7
6
3
，
6
C. A B B A F A B D A A D A P R P R Q Q R R F R X F X Y X Y X X
澳洲运算思维测验 2019 (11，12 年級 Solutions)
7
Solutions Part A: Questions 1–6
1.
1 ，
,
11 12 13 14 15 16 MBps