2014 MATH Olympiad [Grade1]

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1 2014 MATH Olympiad [Grade1] or add , , or = = = = = = = = = =504

2014 MATH Olympiad [Grade2] 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

6R3 38 1,650 48 B-A=C-B or 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 31. 22-5=17 32. 54+72=126 33.

2 2014 MATH Olympiad [Grade2] A : B : , Michael , , , and 7 2 and 6 3 and R R3 38 1, B-A=C-B or A+C=B 2 or A+C=B+B , R R = = = = = = = = = = A : B : There are 12 shaded triangles.

3 2014 MATH Olympiad [Grade3] R R R R , R4 23 7R , , R , R , R R , R or C=A+A+B or C=A 2+B or C-B=A R or The answer can be various = = =8R3 8, = = = =8R17 8, =3 39. or 0.75 or = $30 5(boxes)=$6(box) $144 $6(box)=24(boxes) 46. (1) A=1 (2) A= (No) (3) A= (Yes) (No)

4 2014 MATH Olympiad [Grade4] = =10R = =4R =20R =42+30= ( )=40-23= = Let the length of the shortest log be cm = 46 therefore, is 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 A 4 C D 48. We can find the rule as below 3 3-2=7, 5 5-4=21, 4 4-5=11, 3 3-7=2, =15 Rule : B B-A=C or A+C=B B 49. are 4 groups are 4 3=12 groups 44. Complete the table. Number of cuts Number of pieces Time (min) are 2 groups , 111,, 191 (10) 202, 212,, 292 (10) 303, 313,, 393 (10) are 2 5=10 groups Therefore, groups of 2 squares are 22.

5 50. Number of arrows that could hit each ring 1 points points points Total score The Possible scores : 3, 4, 5, 6, 7, 8, 9, 10, 12 The number of Possible scores : 9

6 2014 MATH Olympiad [Grade5] (16+10) 13 2= = (4+(4+8+4)) 12 2-(8 8)=120-64= =26R = (24 2)=15-12= (6 3) 9=2 35. (3hr 17min 30sec)+(3hr 47min 50sec) =7hr 5min 20sec = The number of squares increases by 3 when the order The number of squares order increases by = = = The 1 st Monday is 6 th = = =20 Therefore, Monday is 6 th, 13 th, 20 th, 27 th = The following shows the place of each animal in the race = Complete the table to show the ones place values. Time multiplied Ones place value Therefore, Cougar is 8cm ahead of Kangaroo. 45. Make the table as below Therefore, and

7 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 = Since the ones places is 2, 3-digit even numbers can be made as below; 352, 372, 532, 572, 732, ( -1) even odd (even) 2 ((odd+1) 2) A+B+C= = goes between 3 and 7. B D C A E 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 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] 1 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

8 2014 MATH Olympiad [Grade 6] bags of cookies 3 carton of milk 2 bags of cookies - = (2 bags of cookies) 3 carton of milk $61 $ 41 = $20 Therefore, the value of 1 bag of cookies is $ =24 2= ( ) =140-( )=140-72= (3+(40 5) 3)-10= nd stair 1 st stair = The number of pencil is Maximum number of people 2 3= exposed faces : 16 exposed faces : 24 (other sol) Top & Botton view side view Front & Back view = The total number of faces is (9 2)+(6 2)+(5 2)=40.

9 43. We can draw 4 lines of symmetry as below 50. The blocks with 2 painted faces in shown below. (1 st stair) (2 nd stair) 44. (10+8)blocks The only number that makes the ones place value 7 multiplied by 3 is 9. Therefore is 9. Therefore, the 3-digit number is We can make each cube as below Hundreds Tens Ones Number pattern Rule: A C=B+6 Therefore, missing numbers are 6 and Total number of ways : =30

10 2014 MATH Olympiad [Grade7] = Base area ; Surface area ; 42. We can draw the given set of blocks as below. Top Side Front =2 9= Therefore, the number of blocks is 6. = =2R = = ( ) 0.7= Ture statements are (2), (6) 45. Let Danny have x pieces of candy in the beginning,. 40.

11 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.

12 2014 MATH Olympiad [Grade8] From 1 Since the solutions of the two equations are 41. The perimeter of the map : cm equal, substituting 1 into Actual perimeter : m Adult Children total = = = = R Teachers : 38. cm cm cm m or m m m = Fiqure number Number of The number of squares in 10 is =36

13 45. He spent $40 on a story book 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 He saved $200 in the bank. He had $250 in the beginning. In ones place : D=8 2 B C C B The weight of 15 pieces of candy : g The weight of 40 pieces of candy : g The weight of the empty jar g ones place : 101, 111, 121,, times tens place : 110, 111, 112,, times hundreds place : 100, 101, 102,, times The numeral 1 is written 120 times. In hundreds place : B 4<10 B=1 or 2 In tens place : C 4+3=B : odd number B=1 2 1 C C Therefore, A=2, B=1, C=7, and, D=8, then A+B+C+D= The sum of the numbers in 3 arrows is. The sum of the numbers in each arrow is. (Case 1) (Case 2) 48. We can draw the symmetric line as below.

2014 MATHOlympiad [Grade

2014 MATHOlympiad [Grade 1 25 11 19 21 140 31 24 2 21 12 21 22 607 32 8 42 6 3 7 13 8 23 802 33 18 43 3 4 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