2014 math olympiad [grade 2] - eye level learning · Î Î Î Ö Ò Ò Ð Ö Ð Î 2014 math...
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2014 MATH Olympiad [Grade 2]
【Sol】31. 19+5=2432. 15-7=833. 22-4=1834. 23-7=1635. 7+5-3=936. 47+36=8337. 75+88=16338. 75-28=4739. 29×7=20340. 9×56=504
No. Answer No. Answer No. Answer No. Answer No. Answer
1 25 11 19 21 140 31 24
2 21 12 21 22 607 32 8 42 63 7 13 8 23 802 33 18 43 34 7 14 9 24 35 34 16 44 23 28
5 8 15 16 25 667 35 9 45
6 5 16 3 26 268 36 83 46 3
7 17 17 9 27 98 37 163 48
8 27 18 15 28 228 38 47 47 +12 or add 12
9 17 19 23 29 4,963 39 203 49 ③
10 27 20 113 30 5,312 40 504 50or
2014 MATH Olympiad [Grade3]
【Sol】48.31. 22-5=17
32. 54+72=12633. 42-5=3734. 376-192=18435. 205-138=6736. 6×8=4837. 56×4=22438. 275×6=1650
49.39. 42÷7=640. 486÷9=54
50.41. A : B :
43.
There are 12 shaded triangles.
No. Answer No. Answer No. Answer No. Answer No. Answer
1 119 11 2 21 476 31 17 41 A : B :
2 130 12 5 22 460 32 126 42 11
3 643 13 27 23 432 33 37 43 6
4 599 14 18 24 2,952 34 184 44 Michael
5 901 15 323 25 4,134 35 67 45 5
6 1,040 16 316 26 29,136 36 48 461 and 72 and 63 and 5
7 74 17 469 27 4R2 37 224 48
8 37 18 487 28 6R3 38 1,650 47B-A=C-Bor A+C=B×2 or A+C=B+B
9 7 19 3,744 29 26R18 39 6 49
10 37 20 216 30 18R28 40 54 50 12
17 15
13
2014 MATH Olympiad [Grade4]
【Sol】46. (1) A=1 (2) A=231. 41×4=164
32. 25×32=800 1 233. 43÷5=8R3 ⇒8, 3
8 11 8 1134. 28÷7=435. 72÷6=12
7 10 6 936. 396÷9=44(No) (No)37. 185÷21=8R17 ⇒ 8, 17
38. 6×4÷8=3(3) A=3
39. or 0.75⇒
or 0.753
40. 3.44-1.92=1.528 11
5 842. $30÷5(boxes)=$6(box)
(Yes)$144÷$6(box)=24(boxes)
47.
45.
No. Answer No. Answer No. Answer No. Answer No. Answer1 288 11 28R1 21 35R3 31 164 41 ①
2 657 12 16R3 22 54R15 32 800 42 24
3 2,736 13 10R4 23 7R27 33 8, 3 43 ①
4 3,783 14 11R6 24 26 34 4 44 41
5 15,136 15 18R3 25 36 35 12 45
6 177,933 16 11R7 26 62 36 44 46 8
7 13 17 14R4 27
37 8, 17
8 13 18 137 28
38 3 48C=A+A+Bor C=A×2+Bor C-B=A×2
9 15 19 124R7 29 10.38 39 or 0.7549 ②
10 14 20 847R4 30 22.68 40 1.52 50 orThe answer can be various.
○ △ ○
△ △
□
△ ○ ○
○ △ □
2014 MATH Olympiad [Grade5]
No. Answer No. Answer No. Answer No. Answer No. Answer1 19 11 21 21 48 31 525 41 ④
2 27 12 37 22 80 32 8 42 13
3 23 13 32 23 48 33 6 43 21
4 19 14 12 24 11 34 5 44 24
5 18 15 13 25 5 35 34 45 30
6 14 16 92 26 11 36 72 46 7
7 83 17 255 27 489 37 17 47 ③
8 112 18 119 28 516 38 14 48 21
9 146 19 730 29 7 39 29 49 22
10 741 20 5 30 12 40 31 50 9
【Sol】46. Available numbers are 5, 6, 7, 8.31. 35×15=525
Since B=8, A+D=12, C+D=11, then D=5,32. 98÷9=10R8 ⇒ 8A=7, C=633. 126÷21=6
34. 127÷29=4R11 ⇒ 5 335. 1234÷60=20R34 ⇒ 34
B A36. 6×7+5×6=42+30=7237. 40-(14÷7+3×7)=40-23=17 D4 C
38. ⇒ 14
48. We can find the rule as below39. 7.52-7.23=0.29 ⇒ 293×3-2=7, 5×5-4=21, 4×4-5=11,
40.
⇒ 31
3×3-7=2, 5×5-10=15Rule : B×B-A=C or A+C=B×B
42. Let the length of the shortest log be □ cm.□ + □ + □ + 7 = 46 49.
therefore, □ is 13.→ are 4 groups
43. 11 + 21 + 2 + 3 →���
are 4×3=12 groups1 + 2 + 3 + 4 + 5 + 6
44. Complete the table.→ are 2 groups
Number of cuts 1 2 3
Number of pieces 2 3 4
Time (min) 8 16 24 →
are 2×5=10 groups45. 101, 111, … , 191 (10)Therefore, groups of 2 squares are 22.202, 212, … , 292 (10)
303, 313, … , 393 (10)
50.
The Possible scores : 3, 4, 5, 6, 7, 8, 9, 10, 12The number of Possible scores : 9
Number of arrows that could hit each ring
1 points 3 2 2 1 1 1 0 0 0 0
2 points 0 1 0 2 1 0 3 2 1 0
4 points 0 0 1 0 1 2 0 1 2 3
Total score 3 4 6 5 7 9 6 8 10 12
2014 MATH Olympiad [Grade6]
【Sol】42. The number of squares increases by 3 when the29. (16+10)×13÷2=26×13÷2=169
order increases by 1.30. (4+(4+8+4))×12÷2-(8×8)=120-64=5631. 80÷3=26R2
32. 1932÷21=92
33. 15-(24÷2)=15-12=3
34. 20-(6÷3)×9=2
35. (3hr 17min 30sec)+(3hr 47min 50sec)
=7hr 5min 20sec ⇒ 7+5+20=32 43. The 1st Monday is 6th.Therefore, Monday is 6th, 13th, 20th, 27th.36. ×
□
□ □ 6/24 = 1/4 44. The following shows the place of each animal
in the race.37. ⇒ 5
38. ⇒ ⇒24
39.
⇒ 101
Therefore, Cougar is 8cm ahead of Kangaroo.40.
⇒ 41
45. Make the table as below.
41. Complete the table to show the ones placevalues.
Therefore, ♡ ◇ and ♡◇
No. Answer No. Answer No. Answer No. Answer No. Answer
1 15 11 26 21 11 31 2 41 1
2 15 12 7 22 3 32 92 42 26
3 18 13 12 23 8 33 3 43 27
4 21 14 80 24 8 34 2 44 8
5 9 15 343 25 17 35 32 45 16
6 342 16 852 26 2 36 1/4 46 315
7 4 17 24 27 1 37 5 47 6
8 26 18 58 28 13 38 24 48 34
9 31 19 85 29 169 39 101 49 5
10 20 20 9 30 56 40 41 50 8
order 1 2 3 4 5 6 7 8
Thenumber
ofsquares
3×1+2=5
3×2+2=8
3×3+2=11
3×4+2=14
3×5+2=17
3×6+2=20
3×7+2=23
3×8+2=26
♡ 9 10 11 12 13
◇ 1 2 3 4 5
♡×◇ 9 20 33 48 65Time
multiplied1 2 3 4 5 6 7 8 9 10 11 12
Onesplacevalue
7 9 3 1 7 9 3 1 7 9 3 1
-1)
ven dd
46. …
The pairs having a sum of 30 are(5, 25), (6, 24), … , (14, 16).
There are 10 pairs and 15 alone.Therefore, the sum is 30×10+15=315.
47. Since the ones places is 2, 3-digit evennumbers can be made as below;352, 372, 532, 572, 732, 752
48.
□×(□ △
e (even)÷2o ((odd+1)÷2)
∴ A+B+C=2+12+20=34
49. 3 9 7 9 goes between 3 and 7.B+C=16 ⇒ (B, C) = (6, 10)
D or (10, 6)BD+E=12 ⇒ (D, E) = (4, 8)
C A E or (8, 4)Then, available number A is 5.
50. We can calculate step by step as below.
Since A=4, B=4, the value of A+B is 4×4=16
2014 MATH Olympiad [Grade 7]
【Sol】
× 28. 41.
4 bags of cookies 2 bags of cookies(2 bags of cookies) -×
= 3 carton of milk 3 carton of milk
$61 ― $ 41 = $20×
÷ ÷
Therefore, the value of 1 bag of cookies is $10.
42.29. 8×3÷2=24÷2=12
2nd stair 1st stair30. 14×10-(6×4÷2+8×6÷2+8×6÷2+6×4÷2)=140-(12+24+24+12)=140-72=68
31. (3+40)-10=33
32.
⇒ 8
exposed faces : 16 exposed faces : 2433. 153.9-62.78=91.12 ⇒ 12
34. ⇨ Maximum number of people (other sol) Top & Botton view side view ÷
The number of pencil is 3.35. ⇨ 2×3=6
9×2 6×2
36.
⇒ 31 Front & Back view
37.
⇒ 26
38. ×
×
5×239. 12.3×30=369 The total number of faces is40. (9×2)+(6×2)+(5×2)=40.× ×
× ÷ ÷
No. Answer No. Answer No. Answer No. Answer No. Answer1 48 11 72 21 19 31 33 41 10
2 2 12 96 22 55 32 8 42 40
3 35 13 42 23 28 33 12 43 4
4 15 14 15 24 7 34 3 44 933
5 53 15 12 25 30 35 6 45 ③
6 5 16 11 26 83 36 31 46 ④
7 988 17 7 27 12 37 26 47 6
8 3 18 6 28 9 38 7 48 10
9 14 19 11 29 12 39 369 49 30
10 4 20 9 30 68 40 45 50 18
② ③ ④
43. We can draw 4 lines of symmetry as below 50. The blocks with 2 painted faces in shownbelow.
(1st stair) (2
nd stair)
44.⇒ (10+8)blocks
The only number that makes the ones placevalue 7 multiplied by 3 is 9. Therefore □ is 9.Therefore, the 3-digit number □△○ is 933.
46. We can make each cube as below
①
47. Hundreds Tens Ones6 6 7 … 667
7 6 … 6767 … 677
7 6 6 … 7667 … 767
7 6 … 776
48. Number pattern
Rule: A×C=B+6Therefore, missing numbers are 6 and 4.
49.
Total number of ways : 8+6+4+2+4+3+2+1=30
2014 MATH Olympiad [Grade8]
【Sol】× × × × 29. 41.
⇒ 35.7×10=357 42. We can draw the given set of blocks as below.30. Base area ;
Top
× ×
Surface area ;× × × ×
× × × Side
Front
31. 18=2×□×□ Therefore, the number of blocks is 6.9=□×□□=3 43.32.
⇒6
33.
⇒ 43
34. × ⇒ 3
35. ÷
⇒ 6544. True statement is (4)
36. 29÷12.5=2R4 ⇒437. 4.75×2.8×10=13.3×10=13338. (5.4-0.5)÷0.7=7
45. Let Danny have x pieces of candy in the39.
×
×
⇒ 8 beginning, .
40. ∴ ⇨ ×
No. Answer No. Answer No. Answer No. Answer No. Answer1 13 11 1 21 22 31 3 41 49
2 8 12 9 22 192 32 6 42 6
3 1 13 7 23 386 33 43 43 ③
4 17 14 7 24 472 34 3 44 4
5 19 15 2 25 3 35 65 45 32
6 1 16 3 26 3 36 4 46 4
7 7 17 9 27 213 37 133 47 5
8 20 18 1 28 27 38 7 48 12
9 19 19 56 29 357 39 8 49 11
10 8 20 54 30 8 40 6 50 41
∴
47. Hundreds Tens Ones 3-digit number
∴ 3-digit even number :102, 110, 112, 120, 210 (5 numbers)
48. AB × , and AB ×C ≥ ⇒ C
Therefore, AB ≤ and AB ≥
AB
49.· Guess 10 correct answers and 5 incorrect
answers then Wendy earned × ×
· Guess 11 correct answers and 4 incorrectanswers then Wendy earned × ×
Therefore, Wendy answered 11 correct answers.
50.
10
2014 MATH Olympiad [Grade9]
【Sol】41. The perimeter of the map :29. From
… ①
× cm
Since the solutions of the two equations are
equal, substituting ① into
Actual perimeter : × m
42.
∴
31.
⇒ 101
32. × ÷
33. × ⇒ 2543.
34. ÷ R ⇒ 435. ÷ × ⇒ 536. ÷
÷ × ×
⇒ 51+2 1+2+3 …37. Teachers : ×
The number of squares in is
38. cm × cm cm m 1+2+3+ … +7+8=36orm × m m
39. 27=16+8+2+1 ⇒ 440. × × ×
× ××
No. Answer No. Answer No. Answer No. Answer No. Answer1 1 11 14 21 13 31 101 41 260
2 23 12 692 22 27 32 7 42 7
3 6 13 25 23 18 33 25 43 36
4 2 14 96 24 8 34 4 44 ②
5 9 15 608 25 9 35 5 45 250
6 1 16 266 26 29 36 5 46 120
7 5 17 178 27 17 37 180 47 120
8 29 18 124 28 156 38 420 48 4
9 38 19 16 29 5 39 4 49 18
10 32 20 12 30 351 40 16 50 15
Adult Children total10 1 18×10+12=1929 2 18×9+12×2=1868 3 18×8+12×3=1807 4 18×7+12×4=174
Fiqurenumber
1 2 3 4 5 …
Number of0 0 1 3 6 …
48. We can draw the symmetric line as below.
45. He spent $40 on a story book 49. In thousands place : A×4<10 ⇒A=1 or 2In ones place : D×4 is even number ⇒A=2
2 B C D
× 4
D C B 2
In ones place : D=8He saved $200 in the bank.
2 B C 8
× 4
8 C B 2∴ He had $250 in the beginning.
In hundreds place : B×4<10 ⇒B=1 or 2In tens place : C×4+3=B : odd number ⇒B=1
2 1 C 8 2 1 7 846.× 4 × 4The weight of 15 pieces of candy : ⇒
8 C 1 2 8 7 1 2 g
The weight of 40 pieces of candy :Therefore, A=2, B=1, C=7, and, D=8, then
× ÷ gA+B+C+D=18
The weight of the empty jar g
50.The sum of the numbers in 3 arrows is… .The sum of the numbers in each arrow is
47.÷ .
ones place : 101, 111, 121, …,191(Case 1)
⇒ 10 timestens place : 110, 111, 112, …,119⇒ 10 timeshundreds place : 100, 101, 102, …,199⇒ 100 times ∴
∴The numeral 1 is written 120 times.(Case 2)
∴