What is the difference between the sum of the first2003 even counting numbers and the sum of the first2003 odd counting numbers?
(A)0(B)1(C)2(D)2003(E)4006
2003 AMC 10 A, Problem #1—2003 AMC 12 A, Problem #1—“Each even counting number is one more than thepreceding odd counting number.”
Difficulty:
Medium
NCTM Standard:
Number and Operations Standard for Grades 9–12: Understand numbers, ways
of representing numbers, relationships among numbers, and number systems.
Mathworld.com Classification:
Number Theory
>
Integers
Members of the Rockham Soccer League buy socksand T–shirts.Socks cost4 per pair and each T–shirt costs5 more than a pair of socks. Each memberneeds one pair of socks and a shirt for home gamesand another pair of socks and a shirt for away games.If the total cost is2366, how many members are inthe League?
2003 AMC 10 A, Problem #2—2003 AMC 12 A, Problem #2—“Each member will have two pairs of socks, and twoshirts.”
Difficulty:
Easy
NCTM Standard:
Algebra Standard for Grades 9–12: Use mathematical models to represent and
understand quantitative relationships.
Mathworld.com Classification:
Number Theory
>
Arithmetic
>
General Arithmetic
A solid box is 15 cm by 10 cm by 8 cm. A new solidis formed by removing a cube 3 cm on a side fromeach corner of this box. What percent of the originalvolume is removed?
(A)4.5(B)9(C)12(D)18(E)24
2003 AMC 10 A, Problem #3—2003 AMC 12 A, Problem #3—“The total volume of the eight removed cubes is8×33=216cubic centimeters.”
Difficulty:
Medium-hard
NCTM
Standard:
Geometry Standard for Grades 9–12:
Analyze properties and determine
attributes of two- and three-dimensional objects.
Mathworld.com Classification:
Geometry
>
Solid Geometry
>
Polyhedra
>
Cubes
It takes Mary 30 minutes to walk uphill 1 km fromher home to school, but it takes her only 10 minutesto walk from school to home along the same route.What is her average speed, in km/hr, for the roundtrip?
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- Winter '13
- Kramer
- Prime number, triangle, Numeral system
