2013 MATH Olympiad [Grade1] - Eye Level Learning MATH Olympiad [Grade5] 0 Sol0 29.r%¡ ×rZr÷rqrUrb...

44.

2013 MATH Olympiad [Grade1]

45. ① 4=1+3 , ② 6=1+5 , ④ 9=1+3+5【Sol】46.31. 12+5+4=21

32. 17-9=8→ 233. 21-9=12→ 5 ⇒ 1034. 15-4-5=6→ 335. 14+12=26

36. 82+45=12737. 235+223=458

47.38. 257-124=13339. 39×2=7840. 128×5=640

41.

48.42. 1, 2, 3 - 1, 2, 2, 3 - 1, 2, 2, ②, 343. Box-shaped figures

3, 4, 2, 11 2 3 4

No. Answer No. Answer No. Answer No. Answer No. Answer1 27 11 17 21 2 31 21 41 6

2 27 12 10 22 609 32 8 42 2

3 7 13 4 23 485 33 12 43 2

4 8 14 3 24 26 34 6 44 3, 4, 2, 1

5 9 15 18 25 184 35 26 45 ③

6 3 16 20 26 2,880 36 127 46 10

7 16 17 141 27 1,872 37 458 47

8 14 18 134 28 8 38 133 48 A=13, B=16

9 18 19 385 29 9 39 78 49 ②

10 17 20 863 30 16 40 640 50 ①

4 5

13 16


45.【Sol】,31. 17+5=22

32. 438+254=69233. 657+569=122634. 75-46=29

→ 146.35. 625-348=277⇒ 7→ 336. 4×8=32

37. 28×8=224 → 338. 13×34=44239. 44÷7=6R2

48. 1 and 6, 2 and 5, 3 and 4, 1,2, and 440. 128÷21=6R2 ⇒ 6

41. 4 methods

49.17

50.42. 8

43.

15

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

1 182 11 5 21 387 31 22 41

2 112 12 4 22 485 32 692 42 A=6 , B=10

3 431 13 85 23 608 33 1,226 43 15

4 847 14 8 24 24,222 34 29 44 ④

5 1,485 15 354 25 3,864 35 277 45 2

6 7,554 16 173 26 31,780 36 32 46 7

7 33 17 197 27 8R2(8.4) 37 224 47

8 11 18 35 28 26 38 442 48 4

9 57 19 3,768 29 16R12 39 6, 2 49 17

10 8 20 76 30 15R24 40 6 50 8


【Sol】 46. 1st : 1

2nd

: 1+2=331. 56×4=2243

rd : 1+2+3=632. 274×43=11,782��33. 57÷3=19

6th

: 1+2+3+4+5+6=2134. 67÷6=11R1 ⇒ 1235. 38÷9=4R2

48. Make a table to find the answer.36. 130+1=131 or (520÷4)+1=13137. 764÷21=36R8 ⇒ 3638. kg g kg g kg g

39. �

⇒ □=7

40. × ×since 4 hours is the same as 240 minutes, the

43. left : 4 blocks , right : 6 blocksnumber of dolls is 36.

Therefore, 2 more blocks44. Thursday is 7th , 14th , 21th , 28th

49. Even number can be made when the oned placeTherefore , the fourth Thursday is on the 28th

is 2 or 6. Therefore 2-digit even numbers are45.

12, 52, 62, 16, 26, 56.

: 4 groups of 4 squares

No. Answer No. Answer No. Answer No. Answer No. Answer1 273 11 21R2 21 15R24 31 224 41 ②

2 768 12 19R2(19.5) 22 23R14 32 11,782 42 ①

3 2,144 13 10R7 23 8R3 33 19 43 2

4 3,741 14 12R3(12.6) 24 22 34 12 44 28th

5 18,639 15 11R5 25 31 35 4, 2 45 4

6 134,232 16 12R3(12.375) 26 0 36 131 46 21

7 12 17 12R6 27

37 36 47

8 14 18 182 28

38 12, 740 48 36

9 18 19 115R4 29 9.55 39 7 49 6

10 12 20 862R4 30 11.86 40 3, 3 50 ③

Time(min) 40 80 120 160 200 240

Number of dolls

6 12 18 24 30 36


【Sol】 44. Complete the table

31. 12×60=72032. 32÷2=1633. 340÷4=8534. 800÷50=1635. 435÷46=9R21 ⇒ 936. × ×× 45. One sheep has the the same weight as 337. Megan : 1hour 45minutes 50seconds rabbits. One rabbit has the same weight as

= 105minutes 50seconds = 6,350seconds 2 squirrels. So, one sheep has the sameZack : 160minutes = 9,600seconds weight as 6 squirrels.

38. ÷ 46. Use a table to find the answer.39. ⇨ × ×

41.

Therefore, = 9 , = 5AC

48. B-A=C-B, A+C=B×2, B-A=2,C-B=2,

49.(1) + + + = 18 → + = 9

∴ Rick is drinking cola. (2) + + ( + ) = 17→ + = 8 → = 4

43. Since 1×8=2×4, the number in shaded blank (3) + =9 → = 5is 3. (4) ( + ) + + =16 → = 2

Therefore, + + + = 5+2+2+2=11

No. Answer No. Answer No. Answer No. Answer No. Answer1 18,291 11 8R11 21 11 31 720 41 Rick

2 142,450 12 6R4 22 10 32 16 42 ②

3 31R1 13 31R15 23 27 33 85 43 3

4 17R4 (17.8) 14 4R42 24 6 34 16 44 60

5 11R5 15 8R3 25

35 9 45 6

6 13R4 16 76R36 (76.8) 26

36 675 46= 9

= 5

7 65 17 284R3 27 6.193 37 Zack 47

8 162 18 75R32 28 5.519 38 100 48 A+C=B×2Answers may vary

9 112 19 714R28 29

39 12 49 11

10 847R2 (847.4) 20 40 30

40 Jason, Justin, Eric, Nina 50

Number of cuts 1 2 3 4 5

Number of pieces 2 3 4 5 6

Time (min) 12 24 36 48 60

5 6 7 8 9

1 2 3 4 5

× 5 12 21 32 45

Juice Milk Cola

Devon × ○ ×Susan ○ × ×Rick × × ○


【Sol】42. Using the pattern we would complete the table.29. □ × 7 ÷ 2 = 49, □ × 7 = 98, □ = 14

30.

+3 +5 +7 +9 +11

⇒ 5 × 5 + 5 × 9 = 25 +45 =70(cm2)43.

31. 82÷7=11R5 3 bags of cookies 2 bags of cookies 1 bags of cookies- =4 cartons of milk 3 cartons of milk 1 cartons of milk32. 243÷37=6R21

33. (18÷3)-(24÷6)=6-4=2 $29 - $21 = $834. (10÷5)×3+25+7=38 44.35. 360÷(20×2)=360÷40=9 : exposed faces of 2

nd stair : 12

36.

: exposed faces of 1st stair : 2637.

38. 153.8-62.78=91.02∴ 12+26 = 38

39.

45. ×

40.

×

46. condition

41. There are 20 numbers as below.505, 515, 525, … , 595 condition

606, 616, 626, … , 696

condition


1 12R5 11 47 21

31 11, 5 41 20

2 10R8 12 11 22

32 6, 21 42 6

3 17R6 13 7 23

33 2 43 8

4 88R48 14 2 24

34 38 44 38

5 302R6 15 2km 880m 25

35 9 45 30

6 30R156 16 7kg 790g 26

36

46

7 40 17 11L 300mL 27

37 47

8 27 18 5hr 8min 20sec 28

38 91.02 48 A=1, B=2, C=120

9 50 19 1hr 34min 35sec 29 14 39

49 18

10 7 20

30 70 40 18 50 7

Figure number

Number of 4 7 12 19 28 39

47.

48. First, we find the values that belong in theblank spaces from 1st row to 4th row.Next, we find the values that belong in theblank spaces from 4th row to 7th row.

120

1

Therefore, A=1, B=2, C=120

49. ÷

50.

The Possible scores : 3, 5, 7, 9, 11, 13, 15The number of Possible scores : 7

3 1 2 52 1 3

1 23

6 203

12 10

2 5

Number of arrows that could hit each ring

1points 3 2 2 1 1 1 0 0 0 0

3points 0 1 0 2 1 0 3 2 1 0

5points 0 0 1 0 1 2 0 1 2 3

Total score 3 5 7 7 9 11 9 11 13 15

2013 MATH Olympiad [Grade 6]

38.

÷

【Sol】29. (7 + □) × 10 ÷ 2 = 110

(7 + □) × 10 = 220 39. Standard amount: 300, comparing amount: 75(7 + □) = 22, The value of the ratio

□ = 1540. width : length30.

A × ÷ m

B × ÷ m 41. ones place is 1 → 31

ones place is 2 → 62 ⇒ 31, 62, 93C × ÷ m

ones place is 3 → 93A B C m

31. ÷ × ÷×42. using the pattern, there are 36 dots in

× ×

32. ×□

□ ÷

33.

34. ⇨ Greatest common factor +5 +5 +5 +5 +5 +5 ×

43.The number of students is 6. If the value of A is 1, If the value of A is 2,

35. Sam : 16=2×2×2×2 ⇒ seat No. 2

James : 27=3×3×3 ⇒ seat No. 3

Heather : 24=2×2×2×3 ⇒ seat No. 6 36.

(No) (Yes)

37.

Therefore, the value of A, B, and C is2, 7, and 10.


1 81 11 5 21

31 51 41 31, 62, 93

2 7 12 75 22

32 6 42 36

3 29.07 13 96 23

33 3.83 43A=2, B=7,C=10

4 6.201 14 42 24 6 34 6 44 12

5 0.448 15

25

35② : Sam③ : James⑥ : Heather

45 30

6 2.173 16

26

36

46 6

7 26.838 17

27

37

47

8 0.031 18

28

38

48 11

9 12 19

29 15 39 49 300

10 2 20

30 36 40 50A=7, B=9,C=10, D=5

Number

Numberof dots

6 11 16 21 26 31 36

44.

⇒ There are 4×3=12 different ways.

45.2 cuts (It takes 6 minutes

to make 1 cut.)

: 5 cuts

Therefore, it takes 30 minutes to make 5 cuts.

46. ÷

48. There are 12 red marbles.There are 15 yellow marbles.There are 11 blue marbles

49.⇒ 300m2 of the orchard

are does not have anytrees.

50. (A+B+C)+D=31, (A+B+C)+C=36 ⇒ C=D+5(B+C)+(B+C)=38, B+C=19

⇒ B=A+2(A+C)+(B+C)=36, A+C=17

A+(B+C+D)=31, (B+C+D)+D=29 ⇒ A=D+2B=A+2 , A=D+2 ⇒ B=D+4

Since A+B+C+D = (D+2)+(D+4)+(D+5)+D= D× 4+11=31,

then D=5, A=7, B=9, C=10.


【Sol】32.

hours29. +

= (Arc length of the 12m half circle)+ (Arc length of the 8m half circle)

m 33. + (Arc length of the 4m half circle)

× ×

34.

×

× km

× ×

× × 35.

÷ × kg m

30. Base radius ; 36. m

× × × × × 37. Total number of visitors per day

∴ cm

÷ ×

Surface area ;

Total number of male students per day× × ×

× ×

× ×

cm

38. ×

31. You must frist find the greatest common factor ×

of 8 and 24 × ÷ ÷ � factor of 8 : 1, 2, 4, 8

� factor of 24 : 1, 2, 3, 4, 6, 8, 12, 24 � common factor of 8 and 24 : 1, 2, 4, 8� The greatest common factor of 8 and 24 : 8 39. ÷ × × cm


1

11

21 9 31 8 41 8

2

12

22

32

42 169

3

13 28 23 1448.4 33

43 5

4

14

24 1.0005 34 20 44 9

5

15

25 6.9 35 3 45 A+B=C×2 Answers may vary

6

16 4 26 16.05 36 111.9 46 =1, =5

7

17

27 11.4 37 500 47

8

18 30 28

38 7 48 31, 19

9

19

29 12π(=37.68)m 39 20 49 63

10 20

30

144π

(=452.16)cm40 144 50 162

)

☆

☆☆

40. 49. Pattern of the perimeters.� The width of a tile ;

1st 2nd 3rd 4th … 10th

cm cm cm cm

⇨ ×

� The number of tiles needed to fill the wall The perimeters of 10th figure : 9+6×9=63(cm)horizontally ÷

� The number of tiles needed to fill the wall50.

vertically ÷ 4th 3rd 2nd 1st original� Total number of tiles needed to fill the entire cm cm cm cm cm

wall ×

×

×

×

×

41. Numbers are below340, 342,

Therefore, original height of the ball is 162cm402, 403, 420, 423, 430, 432 (8 number)

42. 1+3+5+ … + 23+25 = 13×13 = 169

43. The number of households which have eithercows or horses is 24+18-10=32.Therefore, 5 households have neither cows norhorses.

44. From (4) , 19 × 4 = 76From (3) , 76 - 13 = 63From (2) , 63 ÷ 7 = 9Therefore, the secret number is 9.

45. A+B=C×2, A+B=C+C ,A+B-C=C, (A+B)÷2=C

1 346.

5 6 651 61 5

1

48. Complete the table.

Number of rabbits 10 20 19 18

Number of sparrows 40 30 31 32

Number of legs 120 140 138 136

Therefore, there are 31 sparrows and 19 rabbits.


30. From … ①【Sol】Since the solutions of the two equations are27. (Area of the 6m radius half circle)quual, substituting ① into - (Area of the 4m radius half circle) - (Area of the 2m radius half circle)

× × ×

∴

× × ×

× × ×

31.

⇒ 6 cm

32.

÷ ÷

L 28. Base area ;

33. × L × ÷ cm

34. ÷ R Lateral area ;

× cm

÷

× Height ; ÷ ÷ cm ×

35. 29. Base area ; ×

× × m

Volumn of cylinder ; ×

÷

÷

] × m

Mass of water ;36. (Helen) : (Susan) = 4 : 3 = 8 : 6 = 12 : 9

× kg= 16 : 12 = 20 : 15

kg t (Susan) : (Lily) = 5 : 4 = 10 : 8 = 15 : 12∴(Helen) : (Susan) : (Lily) = 20 : 15 : 12


1 18.84 11 8 21

31 6 41 6

2 1266.88 12

22 4 32

42

3 1.0005 13

23

33 0.75 43 4

4 0.15892 14

24

3414, 0.02 or

44 6, 12, 18

5 9.64 15

25 35 44 45 31, 32, 33

6 5.2 16 10 26 36 46 7

7 3.2 17

27 8π(=25.12)cm2 37John:$150,000Joan:$250,000Jill:$350,000

47

8 6.74 18 15 28 26, 7 38

48 14

9

19 12 29 18,840,00018,840 39 6, 6 49 ③

10

20 1 30 40 45 50 160

…

37. John : ×

44.

Joan : ×

⇒ The numbers belonging to A and B areJill : ×

6, 12, 18.

45. Possible combination of scores are as below.

L 38.

39.

⇨ Greatest common factor:

× cm Therefore, the Possible scores Henry can get are

31, 32, 33.The length of an edge of the cube is cm .Also, the number of cubes that fit along the 46.length of the given box is ÷

And the number of cubes that fit along thewidth of the given box is ÷

The number of cubes that make up the height The 15th

skip is the 9th

skip and the 6th

skip.of given box is ÷ . After the 15

th skip is reached numeral location 7

Therefore, the total number of cubes is× × . 48.

40. × g

× ×

41.

1 0 (10) 3 0 (30) 5 0 (50)1 (31) 1 (51)

50.3 (53)

42. The numerator : … ⇒ Total money : $72

The denominator :□=(72÷3)×2=48

Therefore, the 12th

number is□=120÷3=40

…

∴ Andy had $160 before she went shopping.43.

4 lines

9 Points 2 1 18 Points 1 2 17 Points 1 1 2

Total 33 32 31

Number of skips 1 2 3 4 5 6 7 8 9Numeral location 5 9 4 8 3 7 2 6 1

Figurenumbers

… 14

Area 1cm2 3cm2 6cm2 10cm2 15cm2 … 105cm2

Pattern +2 +3 +4 +5

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