2014 MATH Olympiad [Grade1]

No. Answer No. Answer No. Answer No. Answer No. Answer

1 25 11 19 21 140 31 24 412 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 47

8 27 18 15 28 228 38 47 48 +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

【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

2014 MATH Olympiad [Grade2]

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 47

8 37 18 487 28 6R3 38 1,650 48B-A=C-Bor A+C=B×2or A+C=B+B

9 7 19 3,744 29 26R18 39 6 49

10 37 20 216 30 18R28 40 54 50 12

【Sol】31. 22-5=1732. 54+72=12633. 42-5=3734. 376-192=18435. 205-138=6736. 6×8=4837. 56×4=22438. 275×6=165039. 42÷7=640. 486÷9=54

41. A : B :

43.

47.

49.

50.

There are 12 shaded triangles.

2014 MATH Olympiad [Grade3]

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+B or C=A×2+B or C-B=A×2

9 15 19 124R7 29 10.38 39

or 0.75 49 ②

10 14 20 847R4 30 22.68 40 1.52 50 or The answer can be various.

【Sol】31. 41×4=164 32. 25×32=800 33. 43÷5=8R3 ⇒8, 334. 28÷7=435. 72÷6=12 36. 396÷9=4437. 185÷21=8R17 ⇒ 8, 17 38. 6×4÷8=3

39.

or 0.75⇒ or 0.75

40. 3.44-1.92=1.52

42. $30÷5(boxes)=$6(box) $144÷$6(box)=24(boxes)

45.

46. (1) A=1 (2) A=2

1

7 10

8 11

17

2

6 9

8 11

15 (No) (No) (3) A=3 3

5 8

8 11

13

(Yes)

47. ○ △ ○

△ △

□

△ ○ ○

○ △ □

2014 MATH Olympiad [Grade4]

No. Answer No. Answer No. Answer No. Answer No. Answer1 19 11 21 21 12 31 525 41 ④

2 27 12 37 22 8 32 8 42 13

3 23 13 32 23 12 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

Number of cuts 1 2 3

Number of pieces 2 3 4

Time (min) 8 16 24

【Sol】31. 35×15=52532. 98÷9=10R8 ⇒ 833. 126÷21=6 34. 127÷29=4R11 ⇒ 535. 1234÷60=20R34 ⇒ 3436. 6×7+5×6=42+30=7237. 40-(14÷7+3×7)=40-23=17

38.

⇒ 14

39. 7.52-7.23=0.29 ⇒ 29

40.

⇒ 31

42. Let the length of the shortest log be □ cm. □ + □ + □ + 7 = 46 therefore, □ is 13.

43. 1 1 + 2 1 + 2 + 3 ⦁⦁⦁ 1 + 2 + 3 + 4 + 5 + 6

44. Complete the table.

45. 101, 111, … , 191 (10) 202, 212, … , 292 (10) 303, 313, … , 393 (10)

46. Available numbers are 5, 6, 7, 8. Since B=8, A+D=12, C+D=11, then D=5, A=7, C=6 3

B

D

A

4 C

48. We can find the rule as below 3×3-2=7, 5×5-4=21, 4×4-5=11, 3×3-7=2, 5×5-10=15 Rule : B×B-A=C or A+C=B×B

49.

→ are 4 groups

→

are 4×3=12 groups

→ are 2 groups

→

are 2×5=10 groups Therefore, groups of 2 squares are 22.

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

50.

The Possible scores : 3, 4, 5, 6, 7, 8, 9, 10, 12The number of Possible scores : 9

2014 MATH Olympiad [Grade5]

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 6 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

The number

of squares

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

Time multiplied

1 2 3 4 5 6 7 8 9 10 11 12

Ones place value

7 9 3 1 7 9 3 1 7 9 3 1

♡ 9 10 11 12 13

◇ 1 2 3 4 5

♡×◇ 9 20 33 48 65

【Sol】29. (16+10)×13÷2=26×13÷2=169

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

36. × □

□□

37.

⇒ 5

38.

⇒

⇒24

39.

⇒ 101

40.

⇒ 41

41. Complete the table to show the ones place values.

42. The number of squares increases by 3 when the order increases by 1.

43. The 1st Monday is 6th. Therefore, Monday is 6th, 13th, 20th, 27th.

44. The following shows the place of each animal in the race.

Therefore, Cougar is 8cm ahead of Kangaroo. 45. Make the table as below.

Therefore, ♡◇ and ♡◇

3 79

B

C A E

D

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 even numbers can be made as below; 352, 372, 532, 572, 732, 752

48.

□×(□-1) △

even (even)÷2 odd ((odd+1)÷2)

∴ A+B+C=2+12+20=34

49. 9 goes between 3 and 7. B+C=16 ⇒ (B, C) = (6, 10) or (10, 6) D+E=12 ⇒ (D, E) = (4, 8) 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 6]

No. Answer No. Answer No. Answer No. Answer No. Answer1 12 11 72 21 19 31 17 41 10

2 2 12 96 22 55 32 8 42 40

3 35 13 42 23 7 33 12 43 4

4 15 14 15 24 28 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

【Sol】

28. ×

×

×

÷

÷

29. 8×3÷2=24÷2=12

30. 14×10-(6×4÷2+8×6÷2+8×6÷2+6×4÷2) =140-(12+24+24+12)=140-72=6831. (3+(40÷5)×3)-10=17

32.

⇒ 8

33. 153.9-62.78=91.12 ⇒ 12

34.

⇨ Maximum number of people

The number of pencil is 3.35.

⇨ 2×3=6

36.

⇒ 31

37.

⇒ 26

38. ×

×

39. 12.3×30=369 40.

× ××÷ ÷

41.

$61 ― $ 41 = $20 Therefore, the value of 1 bag of cookies is $10.

42. 2nd stair 1st stair

exposed faces : 16 exposed faces : 24 (other sol) Top & Botton view side view

9×2 6×2 Front & Back view

5×2 The total number of faces is (9×2)+(6×2)+(5×2)=40.

÷

4 bags of cookies 3 carton of milk

2 bags of cookies 3 carton of milk

(2 bags of cookies)- =

43. We can draw 4 lines of symmetry as below

44. The only number that makes the ones place value 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 ② ③ ④

47. Hundreds Tens Ones 6 6 7 … 667 7 6 … 676 7 … 677 7 6 6 … 766 7 … 767 7 6 … 776

48. Number pattern

Rule: A×C=B+6 Therefore, missing numbers are 6 and 4.

49.

Total number of ways : 8+6+4+2+4+3+2+1=30

50. The blocks with 2 painted faces in shown below. (1

st stair) (2

nd stair)

⇒ (10+8)blocks

2014 MATH Olympiad [Grade7]

No. Answer No. Answer No. Answer No. Answer No. Answer1 13 11 1 21 22 31 3 41 49

2 8 12 3 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 2

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 4 20 54 30 8 40 6 50 41

Top

Side

Front

【Sol】

29. ×××

×

⇒ 35.7×10=35730. Base area ; ××

Surface area ; ××× ×

×××

31. 18=2×□×□

9=□×□

□=3

32.

⇒6

33.

⇒ 43

34. ×

⇒ 3

35. ÷

⇒ 65

36. 29÷12.5=2R4 ⇒437. 4.75×2.8×10=13.3×10=13338. (5.4-0.5)÷0.7=7

39.

×

×

⇒ 8

40.

⇨

41.

42. We can draw the given set of blocks as below.

Therefore, the number of blocks is 6.

43.

44. Ture statements are (2), (6)

45. Let Danny have x pieces of candy in the beginning, .

∴ ×

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 incorrect answers then Wendy earned ××

Therefore, Wendy answered 11 correct answers.

50.

2014 MATH Olympiad [Grade8]

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 total

10 1 18×10+12=192

9 2 18×9+12×2=186

8 3 18×8+12×3=180

7 4 18×7+12×4=174

Fiqure number

1 2 3 4 5 ⋯Number of

0 0 1 3 6 ⋯

【Sol】

29. From

⋯ ①

Since the solutions of the two equations are

equal, substituting ① into

∴

31.

⇒ 101

32. ×÷

33. × ⇒ 2534. ÷ R ⇒ 435. ÷× ⇒ 536. ÷

÷× ×

⇒ 5

37. Teachers : ×

38. cm × cm cm morm ×m m

39. 27=16+8+2+1 ⇒ 440. ×× ×

× ××

41. The perimeter of the map : × cm

Actual perimeter : × m

42.

43.

1+2 1+2+3 ⋯ The number of squares in 10 is

1+2+3+ ⋯+7+8=36

45. He spent $40 on a story book

He saved $200 in the bank.

∴ He had $250 in the beginning.

46. The weight of 15 pieces of candy : g The weight of 40 pieces of candy : × ÷ g The weight of the empty jar g

47. ones place : 101, 111, 121, …,191 ⇒ 10 times tens place : 110, 111, 112, …,119 ⇒ 10 times hundreds place : 100, 101, 102, …,199 ⇒ 100 times ∴The numeral 1 is written 120 times.

48. We can draw the symmetric line as below.

49. In thousands place : A×4<10 ⇒A=1 or 2 In ones place : D×4 is even number ⇒A=2

2 B C D

× 4

D C B 2

In ones place : D=8

2 B C 8

× 4

8 C B 2

In hundreds place : B×4<10 ⇒B=1 or 2In tens place : C×4+3=B : odd number ⇒B=1

2 1 C 8

× 4

8 C 1 2⇒

2 1 7 8

× 4

8 7 1 2

Therefore, A=2, B=1, C=7, and, D=8, then A+B+C+D=18

50. The sum of the numbers in 3 arrows is ⋯ . The sum of the numbers in each arrow is ÷ . (Case 1)

∴

(Case 2)

∴