1998 MATH OLYMPIAD ANSWERS (1998)

Grade 7 Answers

 Number Sense

 1. 9/16 (or .5625)
2. 1 1/2 or 1.5
3. 25 (or H = 2 and E = 5)
4. 258 / 6 = 43
5. 180 days

Measurement
1. 255 nails
2. 83 arms, 1 hand, 1 finger large
3. 13 1/2 or 13.5 sq. in. or in.2
4. 27,300 cubic cm or cm3
5. 6,944 days 10 hrs. 40 min.

Geometric Sense
1. 78 sq. in. or in2
2. (a)Angle 1 = 45o [1 point]
(b)Angle 2 = 75o [1 point]
(c)195 sq. cm or cm2 [2 points]
3. 5.25 m
4. reflect, translate, rotate (in that order) (or reflect, slide, rotate, in that order)
5. (a) 120o [(a) & (b) 2 points each]
(b) Accept any answer .56 cm through .5664 cm, inclusive.

Probability & Statistics
(a)17/60 [2 points]
(b).25 [1 point]
(c)15 [1 point]
2. .107 or 10.7%
3. 166
4.(a) 2,400 [2 points]
(b) 2,160 [2 points]
5. (a) 10 [2 points]
(b) 3/55 or 6/110 [2 points]

Algebraic Sense
1. 5/8 foot or .625 foot or 7.5 inches
2. 60
3. (a) 7 [2 points]
(b) 38 [2 points]
4. (a) 2n+2 or 2(n+1) or 2(n-2) +6 or equivalent [2 points]
(b) or -1 or equivalent [2 points]
5. d = 4 (n - 8) + 2 or d = 4n - 30 or equivalent

 

Grade 8 Answers

Number Sense
1. 49/80 or .6125
2. $450
3. .00075 cm or 75/100,000 cm or 3/4000cm1. 5/8 foot (or .625 foot) or 7.5 inches
4. C2 or 1 or "undefined"
5. 2 10/12 hours or 2 5/6 hrs. or 2 hrs. 50 min. or 2.8hrs. difference (accept 2.8 or 2.83 hrs.)

Measurement
1. 6,944 days 10 hrs. 40 min.
2. 16:1, 16 to 1, 16/1, or 16 times as large
3. 2.23 cm
4. (a) 224 mm x 224 mm [2 pts. each]
(b) 28 dominoes (7 down x 4 across)
5. 489.84 to 490.0896 cubic inches or in3 (inclusive answer range)

Geometric Sense
1. (a) Angle 1 = 21o [2 points]
(b) Angle 2 = 69o [2 points]
2. 180 m
3. 648 cubic inches or in3
4. 4.5%
5. 240o clockwise or 120ocounterclockwise

Probability & Statistics
1. (a) .3 [1 point]
(b) .27 or .278 or .28 (note: 10/36) [3 points]
2. (a) 166 [2 pts.]
(b) two scores each greater than or equal to 83 [2 pts.]
3. (a) 10 [2 points]
(b) 3/55 or 6/110 [2 points]
4. (a) 2,400 [2 points]
(b) 2,160 [2 points]
5. 14

Algebraic Sense
1. (a) 9 [2 points]
(b) or (n-1) or equivalent [2 points]
2. 5/32 foot (or .15625 ft) or 1 7/8 inches or 1.875 inches
3. [2 points each]
(a) h = 100 + 10(n-3) or h = 70 + 10n [1 point if only "70 + 10n" or equivalent]
(b) 12.5 or 12 1/2 years (12 yrs. 6 mos.)
4. 78
5. or equivalent [4 points] or 1+2+3+...+ n [2 points]